First LIGO review

Review
Add comments by Mohit and Christophe
2021-09-14 13:46:28 +02:00 · 2021-09-08 10:56:25 +02:00 · 2021-09-02 10:04:30 +02:00 · 2021-09-02 10:04:16 +02:00 · 2021-09-02 10:02:12 +02:00 · 2021-09-01 17:05:20 +02:00
130 changed files with 12191 additions and 21677 deletions
--- a/LICENSE.txt
+++ b/LICENSE.txt
@@ -1,6 +1,6 @@
 MIT License

-Copyright (c) 2020 Dehaeze Thomas
+Copyright (c) 2021 Dehaeze Thomas

 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
--- a/dehaeze21_desig_compl_filte.bib
+++ b/dehaeze21_desig_compl_filte.bib
@@ -0,0 +1,8 @@
+@article{dehaeze21_new_method_desig_compl_filter,
+  author          = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
+  title           = {A New Method of Designing Complementary Filters for Sensor
+                  Fusion Using the $\mathcal{H}_\infty$ Synthesis},
+  journal         = {Mechanical Systems and Signal Processing},
+  year            = 2021,
+  month           = {Nov},
+}
--- a/index.html
+++ b/index.html
@@ -3,9 +3,9 @@
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2021-06-21 lun. 11:42 -->
+<!-- 2021-09-02 jeu. 10:02 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
-<title>Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis</title>
+<title>A new method of designing complementary filters for sensor fusion using the $\mathcal{H}_\infty$ synthesis</title>
 <meta name="author" content="Thomas Dehaeze" />
 <meta name="generator" content="Org Mode" />
 <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
@@ -33,8 +33,8 @@
 <a accesskey="h" href="../index.html"> UP </a>
 |
 <a accesskey="H" href="../index.html"> HOME </a>
-</div><div id="content">
-<h1 class="title">Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis
+</div><div id="content" class="content">
+<h1 class="title">A new method of designing complementary filters for sensor fusion using the \(\mathcal{H}_\infty\) synthesis
 <br />
 <span class="subtitle">Dehaeze Thomas, Verma Mohit and Collette Christophe</span>
 </h1>
@@ -44,33 +44,88 @@
 </p>

 <p>
-For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using complementary filters.
-This paper presents a method for designing these complementary filters using \(\mathcal{H}_\infty\) synthesis that allows to shape the filter norms.
-This method is shown to be easily applicable for the synthesis of complex complementary filters.
+In order to obtain a better estimate of a quantity being measured, several sensors having different characteristics can be merged with a technique called &ldquo;sensor fusion&rdquo;.
+The obtained &ldquo;super sensor&rdquo; can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
+Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
+Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
+In this study, we address this issue and propose a new method for designing complementary filters.
+This method uses weighting functions to specify the wanted shape of the complementary filter that are then easily obtained using the standard \(\mathcal{H}_\infty\) synthesis.
+The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
+Such synthesis method is further extended for the shaping of more than two complementary filters.
 </p>
 </blockquote>

-<div id="outline-container-org16737c1" class="outline-2">
-<h2 id="org16737c1">Paper (<a href="journal/journal.pdf">link</a>)</h2>
-<div class="outline-text-2" id="text-org16737c1">
+<div id="outline-container-org8d13d5d" class="outline-2">
+<h2 id="org8d13d5d">Journal Article (<a href="journal/dehaeze21_desig_compl_filte.pdf">link</a>)</h2>
+<div class="outline-text-2" id="text-org8d13d5d">
 <p>
 The paper has been created <a href="https://orgmode.org/">Org Mode</a> (generating <a href="https://www.latex-project.org/">LaTeX</a> code) under <a href="https://www.gnu.org/software/emacs/">Emacs</a>.
 </p>
+
+<p>
+To cite this paper use the following BibTeX code.
+</p>
+<div class="org-src-container">
+<pre class="src src-bibtex"><span class="org-function-name">@article</span>{<span class="org-constant">dehaeze21_new_method_desig_compl_filter</span>,
+  <span class="org-variable-name">author</span>          = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
+  <span class="org-variable-name">title</span>           = {A New Method of Designing Complementary Filters for Sensor
+                  Fusion Using the <span class="org-string">$\mathcal{H}_\infty$</span> Synthesis},
+  <span class="org-variable-name">journal</span>         = {Mechanical Systems and Signal Processing},
+  <span class="org-variable-name">year</span>            = 2021,
+  <span class="org-variable-name">month</span>           = {Nov},
+}
+</pre>
+</div>
+
+<p>
+You can also use the formatted citation below.
+</p>
+<blockquote>
+<p>
+Dehaeze, T., Vermat, M., &amp; Collette, C., A new method of designing complementary filters for sensor fusion using the \(H_\infty\) synthesis, Mechanical Systems and Signal Processing, (2021).
+</p>
+</blockquote>
 </div>
 </div>

-<div id="outline-container-orgb50a720" class="outline-2">
-<h2 id="orgb50a720">Matlab Scripts (<a href="matlab/index.html">link</a>)</h2>
-<div class="outline-text-2" id="text-orgb50a720">
+<div id="outline-container-org71c1b40" class="outline-2">
+<h2 id="org71c1b40">Matlab Scripts (<a href="matlab/dehaeze21_desig_compl_filte_matlab.html">link</a>)</h2>
+<div class="outline-text-2" id="text-org71c1b40">
 <p>
 All the <a href="https://fr.mathworks.com/">Matlab</a> code that was used for the paper are accessible so that all the results are reproducible.
+The source code is hosted on <a href="https://zenodo.org/record/5361920">Zenodo</a>.
 </p>
+
+<p>
+If you use this code and want to refer to it in a publication, you can use the following BibTeX reference:
+</p>
+<div class="org-src-container">
+<pre class="src src-bibtex"><span class="org-function-name">@misc</span>{<span class="org-constant">dehaeze21_new_method_desig_compl_filter_code</span>,
+  <span class="org-variable-name">author</span>          = {Dehaeze, Thomas},
+  <span class="org-variable-name">doi</span>             = {<span class="org-button">10.5281/zenodo.5361943</span>},
+  <span class="org-variable-name">howpublished</span>    = {Source code on Zenodo},
+  <span class="org-variable-name">month</span>           = sep,
+  <span class="org-variable-name">title</span>           = {{A New Method of Designing Complementary Filters for Sensor
+                  Fusion Using the <span class="org-string">$\mathcal{H}_\infty$</span> Synthesis}},
+  <span class="org-variable-name">year</span>            = 2021,
+}
+</pre>
+</div>
+
+<p>
+You can also use the formatted citation below.
+</p>
+<blockquote>
+<p>
+Dehaeze Thomas. (2021). A New Method of Designing Complementary Filters for Sensor Fusion Using the H-Infinity Synthesis. Source code on Zenodo. 10.5281/zenodo.5361943
+</p>
+</blockquote>
 </div>
 </div>

-<div id="outline-container-org06a9b71" class="outline-2">
-<h2 id="org06a9b71">Tikz Figures (<a href="tikz/index.html">link</a>)</h2>
-<div class="outline-text-2" id="text-org06a9b71">
+<div id="outline-container-org1b73cc9" class="outline-2">
+<h2 id="org1b73cc9">Tikz Figures (<a href="tikz/dehaeze21_desig_compl_filte_tikz.html">link</a>)</h2>
+<div class="outline-text-2" id="text-org1b73cc9">
 <p>
 All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>.
 </p>
--- a/index.org
+++ b/index.org
@@ -1,4 +1,4 @@
-#+TITLE: Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis
+#+TITLE: A new method of designing complementary filters for sensor fusion using the $\mathcal{H}_\infty$ synthesis
 :DRAWER:
 #+SUBTITLE: Dehaeze Thomas, Verma Mohit and Collette Christophe

@@ -13,39 +13,71 @@
 :END:

 #+begin_quote
-  *Abstract*:
+*Abstract*:

-  For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using complementary filters.
-  This paper presents a method for designing these complementary filters using $\mathcal{H}_\infty$ synthesis that allows to shape the filter norms.
-  This method is shown to be easily applicable for the synthesis of complex complementary filters.
+In order to obtain a better estimate of a quantity being measured, several sensors having different characteristics can be merged with a technique called "sensor fusion".
+The obtained "super sensor" can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
+Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
+Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
+In this study, we address this issue and propose a new method for designing complementary filters.
+This method uses weighting functions to specify the wanted shape of the complementary filter that are then easily obtained using the standard $\mathcal{H}_\infty$ synthesis.
+The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
+Such synthesis method is further extended for the shaping of more than two complementary filters.
 #+end_quote

-* Paper ([[file:journal/journal.pdf][link]])
+* Journal Article ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]])
 :PROPERTIES:
 :UNNUMBERED: t
 :END:
+
 The paper has been created [[https://orgmode.org/][Org Mode]] (generating [[https://www.latex-project.org/][LaTeX]] code) under [[https://www.gnu.org/software/emacs/][Emacs]].

-* Matlab Scripts ([[file:matlab/index.org][link]])
+To cite this paper use the following BibTeX code.
+#+begin_src bibtex
+@article{dehaeze21_new_method_desig_compl_filter,
+  author          = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
+  title           = {A New Method of Designing Complementary Filters for Sensor
+                  Fusion Using the $\mathcal{H}_\infty$ Synthesis},
+  journal         = {Mechanical Systems and Signal Processing},
+  year            = 2021,
+  month           = {Nov},
+}
+#+end_src
+
+You can also use the formatted citation below.
+#+begin_quote
+Dehaeze, T., Vermat, M., & Collette, C., A new method of designing complementary filters for sensor fusion using the $H_\infty$ synthesis, Mechanical Systems and Signal Processing, (2021).
+#+end_quote
+
+* Matlab Scripts ([[file:matlab/dehaeze21_desig_compl_filte_matlab.org][link]])
 :PROPERTIES:
 :UNNUMBERED: t
 :END:
-All the [[https://fr.mathworks.com/][Matlab]] code that was used for the paper are accessible so that all the results are reproducible.

-* Tikz Figures ([[file:tikz/index.org][link]])
+All the [[https://fr.mathworks.com/][Matlab]] code that was used for the paper are accessible so that all the results are reproducible.
+The source code is hosted on [[https://zenodo.org/record/5361920][Zenodo]].
+
+If you use this code and want to refer to it in a publication, you can use the following BibTeX reference:
+#+begin_src bibtex
+@misc{dehaeze21_new_method_desig_compl_filter_code,
+  author          = {Dehaeze, Thomas},
+  doi             = {10.5281/zenodo.5361943},
+  howpublished    = {Source code on Zenodo},
+  month           = sep,
+  title           = {{A New Method of Designing Complementary Filters for Sensor
+                  Fusion Using the $\mathcal{H}_\infty$ Synthesis}},
+  year            = 2021,
+}
+#+end_src
+
+You can also use the formatted citation below.
+#+begin_quote
+Dehaeze Thomas. (2021). A New Method of Designing Complementary Filters for Sensor Fusion Using the H-Infinity Synthesis. Source code on Zenodo. 10.5281/zenodo.5361943
+#+end_quote
+
+* Tikz Figures ([[file:tikz/dehaeze21_desig_compl_filte_tikz.org][link]])
 :PROPERTIES:
 :UNNUMBERED: t
 :END:
 All the figures for the paper have been generated using [[https://sourceforge.net/projects/pgf/][TikZ]].

-* Cite this paper                                                   :noexport:
-:PROPERTIES:
-:UNNUMBERED: t
-:END:
-To cite this paper use the following bibtex code.
-#+begin_src bibtex
-#+end_src
-
-You can also use the formatted citation below.
-#+begin_quote
-#+end_quote
--- a/journal/.latexmkrc
+++ b/journal/.latexmkrc
@@ -0,0 +1,98 @@
+#!/bin/env perl
+
+# Shebang is only to get syntax highlighting right across GitLab, GitHub and IDEs.
+# This file is not meant to be run, but read by `latexmk`.
+
+# ======================================================================================
+# Perl `latexmk` configuration file
+# ======================================================================================
+
+# ======================================================================================
+# PDF Generation/Building/Compilation
+# ======================================================================================
+
+@default_files=('dehaeze21_desig_compl_filte.tex');
+
+# PDF-generating modes are:
+# 1: pdflatex, as specified by $pdflatex variable (still largely in use)
+# 2: postscript conversion, as specified by the $ps2pdf variable (useless)
+# 3: dvi conversion, as specified by the $dvipdf variable (useless)
+# 4: lualatex, as specified by the $lualatex variable (best)
+# 5: xelatex, as specified by the $xelatex variable (second best)
+$pdf_mode = 1;
+
+# Treat undefined references and citations as well as multiply defined references as
+# ERRORS instead of WARNINGS.
+# This is only checked in the *last* run, since naturally, there are undefined references
+# in initial runs.
+# This setting is potentially annoying when debugging/editing, but highly desirable
+# in the CI pipeline, where such a warning should result in a failed pipeline, since the
+# final document is incomplete/corrupted.
+#
+# However, I could not eradicate all warnings, so that `latexmk` currently fails with
+# this option enabled.
+# Specifically, `microtype` fails together with `fontawesome`/`fontawesome5`, see:
+# https://tex.stackexchange.com/a/547514/120853
+# The fix in that answer did not help.
+# Setting `verbose=silent` to mute `microtype` warnings did not work.
+# Switching between `fontawesome` and `fontawesome5` did not help.
+$warnings_as_errors = 0;
+
+# Show used CPU time. Looks like: https://tex.stackexchange.com/a/312224/120853
+$show_time = 1;
+
+# Default is 5; we seem to need more owed to the complexity of the document.
+# Actual documents probably don't need this many since they won't use all features,
+# plus won't be compiling from cold each time.
+$max_repeat=7;
+
+# --shell-escape option (execution of code outside of latex) is required for the
+#'svg' package.
+# It converts raw SVG files to the PDF+PDF_TEX combo using InkScape.
+#
+# SyncTeX allows to jump between source (code) and output (PDF) in IDEs with support
+# (many have it). A value of `1` is enabled (gzipped), `-1` is enabled but uncompressed,
+# `0` is off.
+# Testing in VSCode w/ LaTeX Workshop only worked for the compressed version.
+# Adjust this as needed. Of course, only relevant for local use, no effect on a remote
+# CI pipeline (except for slower compilation, probably).
+#
+# %O and %S will forward Options and the Source file, respectively, given to latexmk.
+#
+# `set_tex_cmds` applies to all *latex commands (latex, xelatex, lualatex, ...), so
+# no need to specify these each. This allows to simply change `$pdf_mode` to get a
+# different engine. Check if this works with `latexmk --commands`.
+set_tex_cmds("--shell-escape -interaction=nonstopmode --synctex=1 %O %S");
+
+# Use default pdf viewer
+$pdf_previewer = 'zathura';
+
+# option 2 is same as 1 (run biber when necessary), but also deletes the
+# regeneratable bbl-file in a clenaup (`latexmk -c`). Do not use if original
+# bib file is not available!
+$bibtex_use = 2;  # default: 1
+
+# Change default `biber` call, help catch errors faster/clearer. See
+# https://web.archive.org/web/20200526101657/https://www.semipol.de/2018/06/12/latex-best-practices.html#database-entries
+$biber = "biber --validate-datamodel %O %S";
+
+# ======================================================================================
+# Auxiliary Files
+# ======================================================================================
+
+# Let latexmk know about generated files, so they can be used to detect if a
+# rerun is required, or be deleted in a cleanup.
+# loe: List of Examples (KOMAScript)
+# lol: List of Listings (`listings` and `minted` packages)
+# run.xml: biber runs
+# glg: glossaries log
+# glstex: generated from glossaries-extra
+push @generated_exts, 'loe', 'lol', 'run.xml', 'glg', 'glstex';
+
+# Also delete the *.glstex files from package glossaries-extra. Problem is,
+# that that package generates files of the form "basename-digit.glstex" if
+# multiple glossaries are present. Latexmk looks for "basename.glstex" and so
+# does not find those. For that purpose, use wildcard.
+# Also delete files generated by gnuplot/pgfplots contour plots
+# (.dat, .script, .table).
+$clean_ext = "%R-*.glstex %R_contourtmp*.*";
--- a/journal/dehaeze21_desig_compl_filte.org
+++ b/journal/dehaeze21_desig_compl_filte.org
@@ -0,0 +1,849 @@
+#+TITLE: Designing complementary filters for sensor fusion using $\mathcal{H}_\infty$ synthesis
+:DRAWER:
+#+LATEX_CLASS: elsarticle
+#+LATEX_CLASS_OPTIONS: [preprint, sort&compress]
+#+OPTIONS: toc:nil todo:nil title:nil author:nil date:nil
+#+STARTUP: overview
+
+#+LATEX_HEADER_EXTRA: \journal{Mechanical Systems and Signal Processing}
+
+#+LATEX_HEADER_EXTRA: \author[a1,a2]{Thomas Dehaeze\corref{cor1}}
+#+LATEX_HEADER_EXTRA: \author[a3,a4]{Mohit Verma}
+#+LATEX_HEADER_EXTRA: \author[a2,a4]{Christophe Collette}
+#+LATEX_HEADER_EXTRA: \cortext[cor1]{Corresponding author. Email Address: thomas.dehaeze@esrf.fr}
+
+#+LATEX_HEADER_EXTRA: \address[a1]{European Synchrotron Radiation Facility, 38000 Grenoble, France}
+#+LATEX_HEADER_EXTRA: \address[a2]{University of Li\`{e}ge, PML, Department of Aerospace and Mechanical Engineering, 4000 Li\`{e}ge, Belgium.}
+#+LATEX_HEADER_EXTRA: \address[a3]{CSIR --- Structural Engineering Research Centre, Taramani, Chennai --- 600113, India.}
+#+LATEX_HEADER_EXTRA: \address[a4]{Universit\'{e} Libre de Bruxelles, Precision Mechatronics Laboratory, BEAMS Department, 1050 Brussels, Belgium.}
+
+#+LATEX_HEADER: \usepackage{caption,subcaption}
+#+LATEX_HEADER: \usepackage{amsfonts}
+#+LATEX_HEADER: \usepackage{siunitx}
+#+LATEX_HEADER_EXTRA: \usepackage{tabularx}
+#+LATEX_HEADER_EXTRA: \usepackage{booktabs}
+#+LATEX_HEADER_EXTRA: \usepackage{array}
+#+LATEX_HEADER_EXTRA: \usepackage[hyperref]{xcolor}
+#+LATEX_HEADER_EXTRA: \usepackage[top=2cm, bottom=2cm, left=2cm, right=2cm]{geometry}
+#+LATEX_HEADER_EXTRA: \hypersetup{colorlinks=true}
+#+LATEX_HEADER_EXTRA: \setlength{\parskip}{1em}
+:END:
+
+* Build                                                             :noexport:
+#+NAME: startblock
+#+BEGIN_SRC emacs-lisp :results none
+(add-to-list 'org-latex-classes
+             '("elsarticle"
+               "\\documentclass{elsarticle}"
+               ("\\section{%s}" . "\\section*{%s}")
+               ("\\subsection{%s}" . "\\subsection*{%s}")
+               ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
+               ("\\paragraph{%s}" . "\\paragraph*{%s}")
+               ("\\subparagraph{%s}" . "\\subparagraph*{%s}"))
+             )
+;; Remove automatic org headings
+(defun my-latex-filter-removeOrgAutoLabels (text backend info)
+  "Org-mode automatically generates labels for headings despite explicit use of `#+LABEL`. This filter forcibly removes all automatically generated org-labels in headings."
+  (when (org-export-derived-backend-p backend 'latex)
+    (replace-regexp-in-string "\\\\label{sec:org[a-f0-9]+}\n" "" text)))
+
+(add-to-list 'org-export-filter-headline-functions
+             'my-latex-filter-removeOrgAutoLabels)
+
+;; Automatic delete org org-comments
+(defun delete-org-comments (backend)
+  (loop for comment in (reverse (org-element-map (org-element-parse-buffer)
+                                    'comment 'identity))
+        do
+        (setf (buffer-substring (org-element-property :begin comment)
+                                (org-element-property :end comment))
+              "")))
+
+;; add to export hook
+(add-hook 'org-export-before-processing-hook 'delete-org-comments)
+
+;; Remove hypersetup
+(setq org-latex-with-hyperref nil)
+#+END_SRC
+
+* =hypersetup=                                                        :ignore:
+
+\hypersetup{allcolors=teal}
+
+* Abstract and Keywords                                               :ignore:
+#+begin_frontmatter
+#+begin_abstract
+In order to obtain a better estimate of a quantity being measured, several sensors having different characteristics can be merged with a technique called "sensor fusion".
+The obtained "super sensor" combines the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
+Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
+Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
+In this study, this issue is addressed and a new method for designing complementary filters is proposed.
+This method uses weighting functions to specify the wanted shape of the complementary filters that are then obtained using the standard $\mathcal{H}_\infty$ synthesis.
+The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
+Such synthesis method is further extended for the shaping of a set of more than two complementary filters.
+#+end_abstract
+
+#+begin_keyword
+Sensor fusion \sep{} Complementary filters \sep{} $\mathcal{H}_\infty$ synthesis \sep{} Vibration isolation \sep{} Motion control
+#+end_keyword
+#+end_frontmatter
+
+* Introduction
+<<sec:introduction>>
+** Introduction to Sensor Fusion                                     :ignore:
+
+Measuring a physical quantity using sensors is always subject to several limitations.
+First, the accuracy of the measurement is affected by several noise sources, such as electrical noise of the conditioning electronics being used.
+Second, the frequency range in which the measurement is relevant is bounded by the bandwidth of the sensor.
+One way to overcome these limitations is to combine several sensors using a technique called "sensor fusion"\nbsp{}cite:bendat57_optim_filter_indep_measur_two.
+Fortunately, a wide variety of sensors exists, each with different characteristics.
+By carefully choosing the fused sensors, a so called "super sensor" is obtained that can combines benefits of the individual sensors. \par
+
+** Advantages of Sensor Fusion                                       :ignore:
+
+In some situations, sensor fusion is used to increase the bandwidth of the measurement\nbsp{}cite:shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,min15_compl_filter_desig_angle_estim.
+For instance, in\nbsp{}cite:shaw90_bandw_enhan_posit_measur_using_measur_accel the bandwidth of a position sensor is increased by fusing it with an accelerometer providing the high frequency motion information.
+For other applications, sensor fusion is used to obtain an estimate of the measured quantity with lower noise\nbsp{}cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system,plummer06_optim_compl_filter_their_applic_motion_measur,robert12_introd_random_signal_applied_kalman.
+More recently, the fusion of sensors measuring different physical quantities has been proposed to obtain interesting properties for control\nbsp{}cite:collette15_sensor_fusion_method_high_perfor,yong16_high_speed_vertic_posit_stage.
+In\nbsp{}cite:collette15_sensor_fusion_method_high_perfor, an inertial sensor used for active vibration isolation is fused with a sensor collocated with the actuator for improving the stability margins of the feedback controller. \par
+
+** Applications                                                      :ignore:
+
+Practical applications of sensor fusion are numerous.
+It is widely used for the attitude estimation of several autonomous vehicles such as unmanned aerial vehicle\nbsp{}cite:baerveldt97_low_cost_low_weigh_attit,corke04_inert_visual_sensin_system_small_auton_helic,jensen13_basic_uas and underwater vehicles\nbsp{}cite:pascoal99_navig_system_desig_using_time,batista10_optim_posit_veloc_navig_filter_auton_vehic.
+Naturally, it is of great benefits for high performance positioning control as shown in\nbsp{}cite:shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,min15_compl_filter_desig_angle_estim,yong16_high_speed_vertic_posit_stage.
+Sensor fusion was also shown to be a key technology to improve the performance of active vibration isolation systems\nbsp{}cite:tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip.
+Emblematic examples are the isolation stages of gravitational wave detectors\nbsp{}cite:collette15_sensor_fusion_method_high_perfor,heijningen18_low such as the ones used at the LIGO\nbsp{}cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system and at the Virgo\nbsp{}cite:lucia18_low_frequen_optim_perfor_advan. \par
+
+** Kalman Filtering / Complementary filters                          :ignore:
+
+There are mainly two ways to perform sensor fusion: either using a set of complementary filters\nbsp{}cite:anderson53_instr_approac_system_steer_comput or using Kalman filtering\nbsp{}cite:brown72_integ_navig_system_kalman_filter,odry18_kalman_filter_mobil_robot_attit_estim.
+For sensor fusion applications, both methods are sharing many relationships\nbsp{}cite:brown72_integ_navig_system_kalman_filter,higgins75_compar_compl_kalman_filter,robert12_introd_random_signal_applied_kalman,becker15_compl_filter_desig_three_frequen_bands.
+However, for Kalman filtering, assumptions must be made about the probabilistic character of the sensor noises\nbsp{}cite:robert12_introd_random_signal_applied_kalman whereas it is not the case with complementary filters.
+Furthermore, the advantages of complementary filters over Kalman filtering for sensor fusion are their general applicability, their low computational cost\nbsp{}cite:higgins75_compar_compl_kalman_filter, and the fact that they are intuitive as their effects can be easily interpreted in the frequency domain. \par
+
+** Design Methods of Complementary filters                           :ignore:
+
+A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies.
+In the early days of complementary filtering, analog circuits were employed to physically realize the filters\nbsp{}cite:anderson53_instr_approac_system_steer_comput.
+Analog complementary filters are still used today\nbsp{}cite:yong16_high_speed_vertic_posit_stage,moore19_capac_instr_sensor_fusion_high_bandw_nanop, but most of the time they are now implemented digitally as it allows for much more flexibility. \par
+
+Several design methods have been developed over the years to optimize complementary filters.
+The easiest way to design complementary filters is to use analytical formulas.
+Depending on the application, the formulas used are of first order\nbsp{}cite:corke04_inert_visual_sensin_system_small_auton_helic,yeh05_model_contr_hydraul_actuat_two,yong16_high_speed_vertic_posit_stage, second order\nbsp{}cite:baerveldt97_low_cost_low_weigh_attit,stoten01_fusion_kinet_data_using_compos_filter,jensen13_basic_uas or even higher orders\nbsp{}cite:shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,stoten01_fusion_kinet_data_using_compos_filter,collette15_sensor_fusion_method_high_perfor,matichard15_seism_isolat_advan_ligo. \par
+
+As the characteristics of the super sensor depends on the proper design of the complementary filters\nbsp{}cite:dehaeze19_compl_filter_shapin_using_synth, several optimization techniques have been developed.
+Some are based on the finding of optimal parameters of analytical formulas\nbsp{}cite:jensen13_basic_uas,min15_compl_filter_desig_angle_estim,becker15_compl_filter_desig_three_frequen_bands, while other are using convex optimization tools\nbsp{}cite:hua04_polyp_fir_compl_filter_contr_system,hua05_low_ligo such as linear matrix inequalities\nbsp{}cite:pascoal99_navig_system_desig_using_time.
+As shown in\nbsp{}cite:plummer06_optim_compl_filter_their_applic_motion_measur, the design of complementary filters can also be linked to the standard mixed-sensitivity control problem.
+Therefore, all the powerful tools developed for the classical control theory can also be used for the design of complementary filters.
+For instance, in\nbsp{}cite:jensen13_basic_uas the two gains of a Proportional Integral (PI) controller are optimized to minimize the noise of the super sensor. \par
+
+** Problematic / gap in the research                                 :ignore:
+
+The common objective of all these complementary filters design methods is to obtain a super sensor that has desired characteristics, usually in terms of noise and dynamics.
+Moreover, as reported in\nbsp{}cite:zimmermann92_high_bandw_orien_measur_contr,plummer06_optim_compl_filter_their_applic_motion_measur, phase shifts and magnitude bumps of the super sensors dynamics can be observed if either the complementary filters are poorly designed or if the sensors are not well calibrated.
+Hence, the robustness of the fusion is also of concern when designing the complementary filters.
+Although many design methods of complementary filters have been proposed in the literature, no simple method that allows to specify the desired super sensor characteristic while ensuring good fusion robustness has been proposed. \par
+
+** Describe the paper itself / the problem which is addressed        :ignore:
+
+Fortunately, both the robustness of the fusion and the super sensor characteristics can be linked to the magnitude of the complementary filters\nbsp{}cite:dehaeze19_compl_filter_shapin_using_synth.
+Based on that, this paper introduces a new way to design complementary filters using the $\mathcal{H}_\infty$ synthesis which allows to shape the complementary filters' magnitude in an easy and intuitive way. \par
+
+** Introduce Each part of the paper                                  :ignore:
+
+Section\nbsp{}ref:sec:requirements introduces the sensor fusion architecture and demonstrates how typical requirements can be linked to the complementary filters' magnitude.
+In Section\nbsp{}ref:sec:hinf_method, the shaping of complementary filters is formulated as an $\mathcal{H}_\infty$ optimization problem using weighting functions, and the simplicity of the proposed method is illustrated with an example.
+The synthesis method is further validated in Section\nbsp{}ref:sec:application_ligo by designing complex complementary filters.
+Section\nbsp{}ref:sec:discussion compares the proposed synthesis method with the classical mixed-sensitivity synthesis, and extends it for the shaping of more than two complementary filters.
+
+* Sensor Fusion and Complementary Filters Requirements
+<<sec:requirements>>
+** Introduction                                                      :ignore:
+
+Complementary filtering provides a framework for fusing signals from different sensors.
+As the effectiveness of the fusion depends on the proper design of the complementary filters, they are expected to fulfill certain requirements.
+These requirements are discussed in this section.
+
+** Sensor Fusion Architecture
+<<sec:sensor_fusion>>
+
+A general sensor fusion architecture using complementary filters is shown in Fig.\nbsp{}ref:fig:sensor_fusion_overview where several sensors (here two) are measuring the same physical quantity $x$.
+The two sensors output signals $\hat{x}_1$ and $\hat{x}_2$ are estimates of $x$.
+These estimates are then filtered out by complementary filters and combined to form a new estimate $\hat{x}$.
+
+The resulting sensor, termed as super sensor, can have larger bandwidth and better noise characteristics in comparison to the individual sensors.
+This means that the super sensor provides an estimate $\hat{x}$ of $x$ which can be more accurate over a larger frequency band than the outputs of the individual sensors.
+
+#+name: fig:sensor_fusion_overview
+#+caption: Schematic of a sensor fusion architecture using complementary filters.
+[[file:figs/sensor_fusion_overview.pdf]]
+
+The complementary property of filters $H_1(s)$ and $H_2(s)$ implies that the sum of their transfer functions is equal to one.
+That is, unity magnitude and zero phase at all frequencies.
+Therefore, a pair of complementary filter needs to satisfy the following condition:
+#+name: eq:comp_filter
+\begin{equation}
+  H_1(s) + H_2(s) = 1
+\end{equation}
+
+It will soon become clear why the complementary property is important for the sensor fusion architecture.
+
+** Sensor Models and Sensor Normalization
+<<sec:sensor_models>>
+
+In order to study such sensor fusion architecture, a model for the sensors is required.
+Such model is shown in Fig.\nbsp{}ref:fig:sensor_model and consists of a linear time invariant (LTI) system $G_i(s)$ representing the sensor dynamics and an input $n_i$ representing the sensor noise.
+The model input $x$ is the measured physical quantity and its output $\tilde{x}_i$ is the "raw" output of the sensor.
+
+Before filtering the sensor outputs $\tilde{x}_i$ by the complementary filters, the sensors are usually normalized to simplify the fusion.
+This normalization consists of using an estimate $\hat{G}_i(s)$ of the sensor dynamics $G_i(s)$, and filtering the sensor output by the inverse of this estimate $\hat{G}_i^{-1}(s)$ as shown in Fig.\nbsp{}ref:fig:sensor_model_calibrated.
+It is here supposed that the sensor inverse $\hat{G}_i^{-1}(s)$ is proper and stable.
+This way, the units of the estimates $\hat{x}_i$ are equal to the units of the physical quantity $x$.
+The sensor dynamics estimate $\hat{G}_i(s)$ can be a simple gain or a more complex transfer function.
+
+#+begin_export latex
+\begin{figure}[htbp]
+\begin{subfigure}[b]{0.49\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model.pdf}
+\caption{\label{fig:sensor_model} Basic sensor model consisting of a noise input $n_i$ and a linear time invariant transfer function $G_i(s)$.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.49\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model_calibrated.pdf}
+\caption{\label{fig:sensor_model_calibrated} Normalized sensors using the inverse of an estimate $\hat{G}_i(s)$ of the sensor dynamics.}
+\end{subfigure}
+\caption{\label{fig:sensor_models}Sensor models with and without normalization.}
+\centering
+\end{figure}
+#+end_export
+
+Two normalized sensors are then combined to form a super sensor as shown in Fig.\nbsp{}ref:fig:fusion_super_sensor.
+The two sensors are measuring the same physical quantity $x$ with dynamics $G_1(s)$ and $G_2(s)$, and with /uncorrelated/ noises $n_1$ and $n_2$.
+The signals from both normalized sensors are fed into two complementary filters $H_1(s)$ and $H_2(s)$ and then combined to yield an estimate $\hat{x}$ of $x$.
+
+The super sensor output is therefore equal to:
+#+name: eq:comp_filter_estimate
+\begin{equation}
+  \hat{x} = \Big( H_1(s) \hat{G}_1^{-1}(s) G_1(s) + H_2(s) \hat{G}_2^{-1}(s) G_2(s) \Big) x + H_1(s) \hat{G}_1^{-1}(s) G_1(s) n_1 + H_2(s) \hat{G}_2^{-1}(s) G_2(s) n_2
+\end{equation}
+
+#+name: fig:fusion_super_sensor
+#+caption: Sensor fusion architecture with two normalized sensors.
+[[file:figs/fusion_super_sensor.pdf]]
+
+** Noise Sensor Filtering
+<<sec:noise_filtering>>
+
+In this section, it is supposed that all the sensors are perfectly normalized, such that:
+#+name: eq:perfect_dynamics
+\begin{equation}
+  \frac{\hat{x}_i}{x} = \hat{G}_i(s) G_i(s) = 1
+\end{equation}
+
+The effect of a non-perfect normalization will be discussed in the next section.
+
+Provided\nbsp{}eqref:eq:perfect_dynamics is verified, the super sensor output $\hat{x}$ is then equal to:
+#+name: eq:estimate_perfect_dyn
+\begin{equation}
+  \hat{x} = x + H_1(s) n_1 + H_2(s) n_2
+\end{equation}
+
+From\nbsp{}eqref:eq:estimate_perfect_dyn, the complementary filters $H_1(s)$ and $H_2(s)$ are shown to only operate on the noise of the sensors.
+Thus, this sensor fusion architecture permits to filter the noise of both sensors without introducing any distortion in the physical quantity to be measured.
+This is why the two filters must be complementary.
+
+The estimation error $\delta x$, defined as the difference between the sensor output $\hat{x}$ and the measured quantity $x$, is computed for the super sensor\nbsp{}eqref:eq:estimate_error.
+#+name: eq:estimate_error
+\begin{equation}
+  \delta x \triangleq \hat{x} - x = H_1(s) n_1 + H_2(s) n_2
+\end{equation}
+
+As shown in\nbsp{}eqref:eq:noise_filtering_psd, the Power Spectral Density (PSD) of the estimation error $\Phi_{\delta x}$ depends both on the norm of the two complementary filters and on the PSD of the noise sources $\Phi_{n_1}$ and $\Phi_{n_2}$.
+#+name: eq:noise_filtering_psd
+\begin{equation}
+  \Phi_{\delta x}(\omega) = \left|H_1(j\omega)\right|^2 \Phi_{n_1}(\omega) + \left|H_2(j\omega)\right|^2 \Phi_{n_2}(\omega)
+\end{equation}
+
+If the two sensors have identical noise characteristics, $\Phi_{n_1}(\omega) = \Phi_{n_2}(\omega)$, a simple averaging ($H_1(s) = H_2(s) = 0.5$) is what would minimize the super sensor noise.
+This is the simplest form of sensor fusion with complementary filters.
+
+However, the two sensors have usually high noise levels over distinct frequency regions.
+In such case, to lower the noise of the super sensor, the norm $|H_1(j\omega)|$ has to be small when $\Phi_{n_1}(\omega)$ is larger than $\Phi_{n_2}(\omega)$ and the norm $|H_2(j\omega)|$ has to be small when $\Phi_{n_2}(\omega)$ is larger than $\Phi_{n_1}(\omega)$.
+Hence, by properly shaping the norm of the complementary filters, it is possible to reduce the noise of the super sensor.
+
+** Sensor Fusion Robustness
+<<sec:fusion_robustness>>
+
+In practical systems the sensor normalization is not perfect and condition\nbsp{}eqref:eq:perfect_dynamics is not verified.
+
+In order to study such imperfection, a multiplicative input uncertainty is added to the sensor dynamics (Fig.\nbsp{}ref:fig:sensor_model_uncertainty).
+The nominal model is the estimated model used for the normalization $\hat{G}_i(s)$, $\Delta_i(s)$ is any stable transfer function satisfying $|\Delta_i(j\omega)| \le 1,\ \forall\omega$, and $w_i(s)$ is a weighting transfer function representing the magnitude of the uncertainty.
+
+The weight $w_i(s)$ is chosen such that the real sensor dynamics $G_i(j\omega)$ is contained in the uncertain region represented by a circle in the complex plane, centered on $1$ and with a radius equal to $|w_i(j\omega)|$.
+
+As the nominal sensor dynamics is taken as the normalized filter, the normalized sensor can be further simplified as shown in Fig.\nbsp{}ref:fig:sensor_model_uncertainty_simplified.
+
+#+begin_export latex
+\begin{figure}[htbp]
+\begin{subfigure}[b]{0.59\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model_uncertainty.pdf}
+\caption{\label{fig:sensor_model_uncertainty} Sensor with multiplicative input uncertainty.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.39\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model_uncertainty_simplified.pdf}
+\caption{\label{fig:sensor_model_uncertainty_simplified} Simplified sensor model.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:sensor_models_uncertainty}Sensor models with dynamical uncertainty.}
+\centering
+\end{figure}
+#+end_export
+
+The sensor fusion architecture with the sensor models including dynamical uncertainty is shown in Fig.\nbsp{}ref:fig:sensor_fusion_dynamic_uncertainty.
+
+#+name: fig:sensor_fusion_dynamic_uncertainty
+#+caption: Sensor fusion architecture with sensor dynamics uncertainty.
+[[file:figs/sensor_fusion_dynamic_uncertainty.pdf]]
+
+The super sensor dynamics\nbsp{}eqref:eq:super_sensor_dyn_uncertainty is no longer equal to $1$ and now depends on the sensor dynamical uncertainty weights $w_i(s)$ as well as on the complementary filters $H_i(s)$.
+#+name: eq:super_sensor_dyn_uncertainty
+\begin{equation}
+  \frac{\hat{x}}{x} = 1 + w_1(s) H_1(s) \Delta_1(s) + w_2(s) H_2(s) \Delta_2(s)
+\end{equation}
+
+The dynamical uncertainty of the super sensor can be graphically represented in the complex plane by a circle centered on $1$ with a radius equal to $|w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)|$ (Fig.\nbsp{}ref:fig:uncertainty_set_super_sensor).
+
+#+name: fig:uncertainty_set_super_sensor
+#+caption: Uncertainty region of the super sensor dynamics in the complex plane (grey circle). The contribution of both sensors 1 and 2 to the total uncertainty are represented respectively by a blue circle and a red circle. The frequency dependency $\omega$ is here omitted.
+[[file:figs/uncertainty_set_super_sensor.pdf]]
+
+The super sensor dynamical uncertainty, and hence the robustness of the fusion, clearly depends on the complementary filters' norm.
+For instance, the phase $\Delta\phi(\omega)$ added by the super sensor dynamics at frequency $\omega$ is bounded by $\Delta\phi_{\text{max}}(\omega)$ which can be found by drawing a tangent from the origin to the uncertainty circle of the super sensor (Fig.\nbsp{}ref:fig:uncertainty_set_super_sensor) and that is mathematically described by\nbsp{}eqref:eq:max_phase_uncertainty.
+
+#+name: eq:max_phase_uncertainty
+\begin{equation}
+    \Delta\phi_\text{max}(\omega) = \arcsin\big( |w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)| \big)
+\end{equation}
+
+As it is generally desired to limit the maximum phase added by the super sensor, $H_1(s)$ and $H_2(s)$ should be designed such that $\Delta \phi$ is bounded to acceptable values.
+Typically, the norm of the complementary filter $|H_i(j\omega)|$ should be made small when $|w_i(j\omega)|$ is large, i.e., at frequencies where the sensor dynamics is uncertain.
+
+* Complementary Filters Shaping
+<<sec:hinf_method>>
+** Introduction                                                     :ignore:
+
+As shown in Section\nbsp{}ref:sec:requirements, the noise and robustness of the super sensor are a function of the complementary filters' norm.
+Therefore, a synthesis method of complementary filters that allows to shape their norm would be of great use.
+In this section, such synthesis is proposed by writing the synthesis objective as a standard $\mathcal{H}_\infty$ optimization problem.
+As weighting functions are used to represent the wanted complementary filters' shape during the synthesis, their proper design is discussed.
+Finally, the synthesis method is validated on an simple example.
+
+** Synthesis Objective
+<<sec:synthesis_objective>>
+
+The synthesis objective is to shape the norm of two filters $H_1(s)$ and $H_2(s)$ while ensuring their complementary property\nbsp{}eqref:eq:comp_filter.
+This is equivalent as to finding proper and stable transfer functions $H_1(s)$ and $H_2(s)$ such that conditions\nbsp{}eqref:eq:hinf_cond_complementarity, eqref:eq:hinf_cond_h1 and\nbsp{}eqref:eq:hinf_cond_h2 are satisfied.
+
+#+name: eq:comp_filter_problem_form
+\begin{subequations}
+  \begin{align}
+  & H_1(s) + H_2(s) = 1 \label{eq:hinf_cond_complementarity} \\
+  & |H_1(j\omega)| \le \frac{1}{|W_1(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h1} \\
+  & |H_2(j\omega)| \le \frac{1}{|W_2(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h2}
+  \end{align}
+\end{subequations}
+$W_1(s)$ and $W_2(s)$ are two weighting transfer functions that are carefully chosen to specify the maximum wanted norm of the complementary filters during the synthesis.
+
+** Shaping of Complementary Filters using $\mathcal{H}_\infty$ synthesis
+<<sec:hinf_synthesis>>
+
+In this section, it is shown that the synthesis objective can be easily expressed as a standard $\mathcal{H}_\infty$ optimization problem and therefore solved using convenient tools readily available.
+
+Consider the generalized plant $P(s)$ shown in Fig.\nbsp{}ref:fig:h_infinity_robust_fusion_plant and mathematically described by\nbsp{}eqref:eq:generalized_plant.
+
+#+name: eq:generalized_plant
+\begin{equation}
+  \begin{bmatrix} z_1 \\ z_2 \\ v \end{bmatrix} = P(s) \begin{bmatrix} w\\u \end{bmatrix}; \quad P(s) = \begin{bmatrix}W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) \\  1 & 0 \end{bmatrix}
+\end{equation}
+
+#+begin_export latex
+\begin{figure}[htbp]
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/h_infinity_robust_fusion_plant.pdf}
+\caption{\label{fig:h_infinity_robust_fusion_plant} Generalized plant.}
+\vfill
+\end{subfigure}
+\hfill
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/h_infinity_robust_fusion_fb.pdf}
+\caption{\label{fig:h_infinity_robust_fusion_fb} Generalized plant with the synthesized filter.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:h_infinity_robust_fusion} Architecture for the $\mathcal{H}_\infty$ synthesis of complementary filters.}
+\centering
+\end{figure}
+#+end_export
+
+Applying the standard $\mathcal{H}_\infty$ synthesis to the generalized plant $P(s)$ is then equivalent as finding a stable filter $H_2(s)$ which based on $v$, generates a signal $u$ such that the $\mathcal{H}_\infty$ norm of the system in Fig.\nbsp{}ref:fig:h_infinity_robust_fusion_fb from $w$ to $[z_1, \ z_2]$ is less than one\nbsp{}eqref:eq:hinf_syn_obj.
+#+name: eq:hinf_syn_obj
+\begin{equation}
+  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
+\end{equation}
+
+By then defining $H_1(s)$ to be the complementary of $H_2(s)$ eqref:eq:definition_H1, the $\mathcal{H}_\infty$ synthesis objective becomes equivalent to\nbsp{}eqref:eq:hinf_problem which ensures that\nbsp{}eqref:eq:hinf_cond_h1 and\nbsp{}eqref:eq:hinf_cond_h2 are satisfied.
+
+#+name: eq:definition_H1
+\begin{equation}
+  H_1(s) \triangleq 1 - H_2(s)
+\end{equation}
+
+#+name: eq:hinf_problem
+\begin{equation}
+  \left\|\begin{matrix} H_1(s) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
+\end{equation}
+
+Therefore, applying the $\mathcal{H}_\infty$ synthesis to the standard plant $P(s)$ eqref:eq:generalized_plant will generate two filters $H_2(s)$ and $H_1(s) \triangleq 1 - H_2(s)$ that are complementary\nbsp{}eqref:eq:comp_filter_problem_form and such that there norms are bellow specified bounds [[eqref:eq:hinf_cond_h1]],\nbsp{}eqref:eq:hinf_cond_h2.
+
+Note that there is only an implication between the $\mathcal{H}_\infty$ norm condition\nbsp{}eqref:eq:hinf_problem and the initial synthesis objectives\nbsp{}eqref:eq:hinf_cond_h1 and\nbsp{}eqref:eq:hinf_cond_h2 and not an equivalence.
+Hence, the optimization may be a little bit conservative with respect to the set of filters on which it is performed, see\nbsp{}[[cite:skogestad07_multiv_feedb_contr][Chap. 2.8.3]].
+In practice, this is however not an found to be an issue.
+
+** Weighting Functions Design
+<<sec:hinf_weighting_func>>
+
+Weighting functions are used during the synthesis to specify the maximum allowed complementary filters' norm.
+The proper design of these weighting functions is of primary importance for the success of the presented $\mathcal{H}_\infty$ synthesis of complementary filters.
+
+First, only proper and stable transfer functions should be used.
+Second, the order of the weighting functions should stay reasonably small in order to reduce the computational costs associated with the solving of the optimization problem and for the physical implementation of the filters (the synthesized filters' order being equal to the sum of the weighting functions' order).
+Third, one should not forget the fundamental limitations imposed by the complementary property\nbsp{}eqref:eq:comp_filter.
+This implies for instance that $|H_1(j\omega)|$ and $|H_2(j\omega)|$ cannot be made small at the same frequency.
+
+When designing complementary filters, it is usually desired to specify their slopes, their "blending" frequency and their maximum gains at low and high frequency.
+To easily express these specifications, formula\nbsp{}eqref:eq:weight_formula is proposed to help with the design of weighting functions.
+
+#+name: eq:weight_formula
+\begin{equation}
+  W(s) = \left( \frac{
+           \hfill{} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{G_0}{G_c}\right)^{\frac{1}{n}}
+         }{
+           \left(\frac{1}{G_\infty}\right)^{\frac{1}{n}} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{1}{G_c}\right)^{\frac{1}{n}}
+         }\right)^n
+\end{equation}
+
+The parameters in formula\nbsp{}eqref:eq:weight_formula are:
+- $G_0 = \lim_{\omega \to 0} |W(j\omega)|$: the low frequency gain
+- $G_\infty = \lim_{\omega \to \infty} |W(j\omega)|$: the high frequency gain
+- $G_c = |W(j\omega_c)|$: the gain at a specific frequency $\omega_c$ in $\si{rad/s}$.
+- $n$: the slope between high and low frequency. It also corresponds to the order of the weighting function.
+
+The parameters $G_0$, $G_c$ and $G_\infty$ should either satisfy\nbsp{}eqref:eq:cond_formula_1 or\nbsp{}eqref:eq:cond_formula_2.
+#+name: eq:condition_params_formula
+\begin{subequations}
+  \begin{align}
+    G_0 < 1 < G_\infty \text{ and } G_0 < G_c < G_\infty \label{eq:cond_formula_1}\\
+    G_\infty < 1 < G_0 \text{ and } G_\infty < G_c < G_0 \label{eq:cond_formula_2}
+  \end{align}
+\end{subequations}
+
+The typical magnitude of a weighting function generated using\nbsp{}eqref:eq:weight_formula is shown in Fig.\nbsp{}ref:fig:weight_formula.
+
+#+name: fig:weight_formula
+#+caption: Magnitude of a weighting function generated using formula\nbsp{}eqref:eq:weight_formula, $G_0 = 1e^{-3}$, $G_\infty = 10$, $\omega_c = \SI{10}{Hz}$, $G_c = 2$, $n = 3$.
+[[file:figs/weight_formula.pdf]]
+
+** Validation of the proposed synthesis method
+<<sec:hinf_example>>
+
+The proposed methodology for the design of complementary filters is now applied on a simple example.
+Let's suppose two complementary filters $H_1(s)$ and $H_2(s)$ have to be designed such that:
+- the blending frequency is around $\SI{10}{Hz}$.
+- the slope of $|H_1(j\omega)|$ is $+2$ below $\SI{10}{Hz}$.
+  Its low frequency gain is $10^{-3}$.
+- the slope of $|H_2(j\omega)|$ is $-3$ above $\SI{10}{Hz}$.
+  Its high frequency gain is $10^{-3}$.
+
+The first step is to translate the above requirements by properly designing the weighting functions.
+The proposed formula\nbsp{}eqref:eq:weight_formula is here used for such purpose.
+Parameters used are summarized in Table\nbsp{}ref:tab:weights_params.
+The inverse magnitudes of the designed weighting functions, which are representing the maximum allowed norms of the complementary filters, are shown by the dashed lines in Fig.\nbsp{}ref:fig:weights_W1_W2.
+
+#+begin_export latex
+\begin{figure}
+\begin{minipage}[b]{0.49\linewidth}
+\centering
+\begin{tabularx}{0.60\linewidth}{ccc}
+\toprule
+Parameters   & \(W_1(s)\)      & \(W_2(s)\)\\
+\midrule
+\(G_0\)      & \(0.1\)         & \(1000\)\\
+\(G_\infty\) & \(1000\)        & \(0.1\)\\
+\(\omega_c\) & \(2\pi\cdot10\) & \(2\pi\cdot10\)\\
+\(G_c\)      & \(0.45\)        & \(0.45\)\\
+\(n\)        & \(2\)           & \(3\)\\
+\bottomrule
+\end{tabularx}
+\captionof{table}{\label{tab:weights_params}Parameters used for \(W_1(s)\) and \(W_2(s)\) using~\eqref{eq:weight_formula}.}
+\end{minipage}
+\hfill
+\begin{minipage}[b]{0.49\linewidth}
+\centering
+\includegraphics[scale=1]{figs/weights_W1_W2.pdf}
+\caption{\label{fig:weights_W1_W2}Inverse magnitude of the weighting functions.}
+\end{minipage}
+\end{figure}
+#+end_export
+
+The standard $\mathcal{H}_\infty$ synthesis is then applied to the generalized plant of Fig.\nbsp{}ref:fig:h_infinity_robust_fusion_plant and efficiently solved using Matlab\nbsp{}cite:matlab20.
+The filter $H_2(s)$ that minimizes the $\mathcal{H}_\infty$ norm between $w$ and $[z_1,\ z_2]^T$ is obtained.
+The $\mathcal{H}_\infty$ norm is here found to be close to one\nbsp{}eqref:eq:hinf_synthesis_result which indicates that the synthesis is successful: the complementary filters norms are below the maximum specified upper bounds.
+This is confirmed by the bode plots of the obtained complementary filters in Fig.\nbsp{}ref:fig:hinf_filters_results.
+
+#+name: eq:hinf_synthesis_result
+\begin{equation}
+  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \approx 1
+\end{equation}
+
+The transfer functions in the Laplace domain of the complementary filters are given in\nbsp{}eqref:eq:hinf_synthesis_result_tf.
+As expected, the obtained filters are of order $5$, that is the sum of the weighting functions' order.
+
+#+name: eq:hinf_synthesis_result_tf
+\begin{subequations}
+  \begin{align}
+    H_2(s) &= \frac{(s+6.6e^4) (s+160) (s+4)^3}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)} \\
+    H_1(s) &\triangleq H_2(s) - 1 = \frac{10^{-8} (s+6.6e^9) (s+3450)^2 (s^2 + 49s + 895)}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)}
+  \end{align}
+\end{subequations}
+
+
+#+name: fig:hinf_filters_results
+#+caption: Bode plot of the obtained complementary filters.
+[[file:figs/hinf_filters_results.pdf]]
+
+This simple example illustrates the fact that the proposed methodology for complementary filters shaping is easy to use and effective.
+A more complex real life example is taken up in the next section.
+
+* Application: Design of Complementary Filters used in the Active Vibration Isolation System at the LIGO
+<<sec:application_ligo>>
+** Introduction                                                     :ignore:
+
+Sensor fusion using complementary filters are widely used in the active vibration isolation systems at gravitational wave detectors, such as at the LIGO\nbsp{}cite:matichard15_seism_isolat_advan_ligo,hua05_low_ligo, the Virgo\nbsp{}cite:lucia18_low_frequen_optim_perfor_advan,heijningen18_low and the KAGRA [[cite:sekiguchi16_study_low_frequen_vibrat_isolat_system][Chap. 5]].
+
+In the first isolation stage at the LIGO, two sets of complementary filters are used to form a super sensor that is incorporated in a feedback loop\nbsp{}cite:hua04_low_ligo.
+A set of complementary filters ($L_2,H_2$) is first used to fuse a seismometer and a geophone.
+Then, another set of complementary filters ($L_1,H_1$) is used to merge the output of the first "inertial super sensor" with a position sensor.
+A simplified block diagram of the sensor fusion architecture is shown in Fig.\nbsp{}ref:fig:ligo_super_sensor_architecture.
+
+#+name: fig:ligo_super_sensor_architecture
+#+caption: Simplified block diagram of the sensor blending strategy for the first stage at the LIGO\nbsp{}cite:hua04_low_ligo.
+[[file:figs/ligo_super_sensor_architecture.pdf]]
+
+The fusion of the position sensor at low frequency with the "inertial super sensor" at high frequency using the complementary filters ($L_1,H_1$) is done for several reasons, first of which is to give the super sensor a DC sensibility that allows the feedback loop to have authority at zero frequency.
+The requirements on those filters are stringent and thus their design is complex and should be expressed as an optimization problem.
+
+The approach used in\nbsp{}cite:hua05_low_ligo is to use FIR complementary filters and to write the synthesis as a convex optimization problem.
+After synthesis, the obtained FIR filters were found to be compliant with the requirements.
+However they are of high order so their implementation is quite complex.
+In this section, the effectiveness of the proposed complementary filter synthesis strategy is demonstrated by using the same set of requirements.
+
+** Complementary Filters Specifications
+<<sec:ligo_specifications>>
+
+The specifications for the set of complementary filters ($L_1,H_1$) used at the LIGO are summarized below (for further details, refer to\nbsp{}cite:hua04_polyp_fir_compl_filter_contr_system):
+- Below $\SI{0.008}{Hz}$, the magnitude $|L_1(j\omega)|$ should be less than $8 \times 10^{-4}$.
+- From $\SI{0.008}{Hz}$ to $\SI{0.04}{Hz}$, the filter $L_1(s)$ should attenuate the input signal proportional to frequency cubed.
+- From $\SI{0.04}{Hz}$ to $\SI{0.1}{Hz}$, the magnitude $|L_1(j\omega)|$ should be less than $3$.
+- Above $\SI{0.1}{Hz}$, the magnitude $|H_1(j\omega)|$ should be less than $0.045$.
+
+These specifications are therefore upper bounds on the complementary filters' magnitude.
+They are physically represented in Fig.\nbsp{}ref:fig:fir_filter_ligo as well as the obtained magnitude of the FIR filters in\nbsp{}cite:hua05_low_ligo.
+
+#+name: fig:fir_filter_ligo
+#+caption: Specifications and Bode plot of the obtained FIR complementary filters in\nbsp{}cite:hua05_low_ligo. The filters are here obtained using the SeDuMi Matlab toolbox\nbsp{}cite:sturm99_using_sedum.
+[[file:figs/fir_filter_ligo.pdf]]
+
+** Weighting Functions Design
+<<sec:ligo_weights>>
+
+The weighting functions should be designed such that their inverse magnitude is as close as possible to the specifications in order to not over-constrain the synthesis problem.
+However, the order of each weight should stay reasonably small in order to reduce the computational costs of the optimization problem as well as for the physical implementation of the filters.
+
+A Type I Chebyshev filter of order $20$ is used for the weighting transfer function $W_L(s)$ corresponding to the low pass filter.
+For the one corresponding to the high pass filter $W_H(s)$, a $7^{\text{th}}$ order transfer function is manually designed.
+The inverse magnitudes of the weighting functions are shown in Fig.\nbsp{}ref:fig:ligo_weights.
+
+#+name: fig:ligo_weights
+#+caption: Specifications and weighting functions' inverse magnitude.
+[[file:figs/ligo_weights.pdf]]
+
+** $\mathcal{H}_\infty$ Synthesis of the complementary filters
+<<sec:ligo_results>>
+
+The proposed $\mathcal{H}_\infty$ synthesis is performed on the generalized plant shown in Fig.\nbsp{}ref:fig:h_infinity_robust_fusion_plant.
+After optimization, the $\mathcal{H}_\infty$ norm from $w$ to $[z_1,\ z_2]^T$ is found close to one indication successful synthesis.
+In Fig.\nbsp{}ref:fig:comp_fir_ligo_hinf, the bode plot of the obtained complementary filters are compared with the FIR filters of order 512 obtained in\nbsp{}cite:hua05_low_ligo.
+Even though the complementary filters using the $\mathcal{H}_\infty$ synthesis are of much lower order (order 27), they are found to be close to the FIR filters.
+This confirms the effectiveness of the proposed synthesis method even when the complementary filters are subject to complex requirements.
+
+#+name: fig:comp_fir_ligo_hinf
+#+caption: Comparison of the FIR filters (dashed) designed in\nbsp{}cite:hua05_low_ligo with the filters obtained with $\mathcal{H}_\infty$ synthesis (solid).
+[[file:figs/comp_fir_ligo_hinf.pdf]]
+
+* Discussion
+<<sec:discussion>>
+** "Closed-Loop" complementary filters
+<<sec:closed_loop_complementary_filters>>
+
+An alternative way to implement complementary filters is by using a fundamental property of the classical feedback architecture shown in Fig.\nbsp{}ref:fig:feedback_sensor_fusion.
+This idea is discussed in\nbsp{}cite:mahony05_compl_filter_desig_special_orthog,plummer06_optim_compl_filter_their_applic_motion_measur,jensen13_basic_uas.
+
+#+name: fig:feedback_sensor_fusion
+#+caption: "Closed-Loop" complementary filters.
+[[file:figs/feedback_sensor_fusion.pdf]]
+
+Consider the feedback architecture of Fig.\nbsp{}ref:fig:feedback_sensor_fusion, with two inputs $\hat{x}_1$ and $\hat{x}_2$, and one output $\hat{x}$.
+The output $\hat{x}$ is linked to the inputs by\nbsp{}eqref:eq:closed_loop_complementary_filters.
+
+#+name: eq:closed_loop_complementary_filters
+\begin{equation}
+\hat{x} = \underbrace{\frac{1}{1 + L(s)}}_{S(s)} \hat{x}_1 + \underbrace{\frac{L(s)}{1 + L(s)}}_{T(s)} \hat{x}_2
+\end{equation}
+
+As for any classical feedback architecture, we have that the sum of the sensitivity transfer function $S(s)$ and complementary sensitivity transfer function $T_(s)$ is equal to one\nbsp{}eqref:eq:sensitivity_sum.
+
+#+name: eq:sensitivity_sum
+\begin{equation}
+S(s) + T(s) = 1
+\end{equation}
+
+Therefore, provided that the the closed-loop system in Fig.\nbsp{}ref:fig:feedback_sensor_fusion is stable, it can be used as a set of two complementary filters.
+Two sensors can then be merged as shown in Fig.\nbsp{}ref:fig:feedback_sensor_fusion_arch.
+
+#+name: fig:feedback_sensor_fusion_arch
+#+caption: Classical feedback architecture used for sensor fusion.
+[[file:figs/feedback_sensor_fusion_arch.pdf]]
+
+One of the main advantage of implementing and designing complementary filters using the feedback architecture of Fig.\nbsp{}ref:fig:feedback_sensor_fusion is that all the tools of the linear control theory can be applied for the design of the filters.
+If one want to shape both $\frac{\hat{x}}{\hat{x}_1}(s) = S(s)$ and $\frac{\hat{x}}{\hat{x}_2}(s) = T(s)$, the $\mathcal{H}_\infty$ mixed-sensitivity synthesis can be easily applied.
+
+To do so, weighting functions $W_1(s)$ and $W_2(s)$ are added to respectively shape $S(s)$ and $T(s)$ (Fig.\nbsp{}ref:fig:feedback_synthesis_architecture).
+Then the system is rearranged to form the generalized plant $P_L(s)$ shown in Fig.\nbsp{}ref:fig:feedback_synthesis_architecture_generalized_plant.
+The $\mathcal{H}_\infty$ mixed-sensitivity synthesis can finally be performed by applying the standard $\mathcal{H}_\infty$ synthesis to the generalized plant $P_L(s)$ which is described by\nbsp{}eqref:eq:generalized_plant_mixed_sensitivity.
+
+#+name: eq:generalized_plant_mixed_sensitivity
+\begin{equation}
+  \begin{bmatrix} z \\ v \end{bmatrix} = P_L(s) \begin{bmatrix} w_1 \\ w_2 \\ u \end{bmatrix}; \quad P_L(s) = \begin{bmatrix}
+    \phantom{+}W_1(s) & 0      & \phantom{+}1 \\
+              -W_1(s) & W_2(s) &           -1
+  \end{bmatrix}
+\end{equation}
+
+The output of the synthesis is a filter $L(s)$ such that the "closed-loop" $\mathcal{H}_\infty$ norm from $[w_1,\ w_2]$ to $z$ of the system in Fig.\nbsp{}ref:fig:feedback_sensor_fusion is less than one\nbsp{}eqref:eq:comp_filters_feedback_obj.
+
+#+name: eq:comp_filters_feedback_obj
+\begin{equation}
+  \left\| \begin{matrix} \frac{z}{w_1} \\ \frac{z}{w_2} \end{matrix} \right\|_\infty = \left\| \begin{matrix} \frac{1}{1 + L(s)} W_1(s) \\ \frac{L(s)}{1 + L(s)} W_2(s) \end{matrix} \right\|_\infty \le 1
+\end{equation}
+
+If the synthesis is successful, the transfer functions from $\hat{x}_1$ to $\hat{x}$ and from $\hat{x}_2$ to $\hat{x}$ have their magnitude bounded by the inverse magnitude of the corresponding weighting functions.
+The sensor fusion can then be implemented using the feedback architecture in Fig.\nbsp{}ref:fig:feedback_sensor_fusion_arch or more classically as shown in Fig.\nbsp{}ref:fig:sensor_fusion_overview by defining the two complementary filters using\nbsp{}eqref:eq:comp_filters_feedback.
+The two architectures are equivalent regarding their inputs/outputs relationships.
+
+#+name: eq:comp_filters_feedback
+\begin{equation}
+H_1(s) = \frac{1}{1 + L(s)}; \quad H_2(s) = \frac{L(s)}{1 + L(s)}
+\end{equation}
+
+#+begin_export latex
+\begin{figure}[htbp]
+\begin{subfigure}[t]{0.6\linewidth}
+\centering
+\includegraphics[scale=1]{figs/feedback_synthesis_architecture.pdf}
+\caption{\label{fig:feedback_synthesis_architecture} Feedback architecture with included weights.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[t]{0.4\linewidth}
+\centering
+\includegraphics[scale=1]{figs/feedback_synthesis_architecture_generalized_plant.pdf}
+\caption{\label{fig:feedback_synthesis_architecture_generalized_plant} Generalized plant.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:h_inf_mixed_sensitivity_synthesis} $\mathcal{H}_\infty$ mixed-sensitivity synthesis.}
+\centering
+\end{figure}
+#+end_export
+
+As an example, two "closed-loop" complementary filters are designed using the $\mathcal{H}_\infty$ mixed-sensitivity synthesis.
+The weighting functions are designed using formula\nbsp{}eqref:eq:weight_formula with parameters shown in Table\nbsp{}ref:tab:weights_params.
+After synthesis, a filter $L(s)$ is obtained whose magnitude is shown in Fig.\nbsp{}ref:fig:hinf_filters_results_mixed_sensitivity by the black dashed line.
+The "closed-loop" complementary filters are compared with the inverse magnitude of the weighting functions in Fig.\nbsp{}ref:fig:hinf_filters_results_mixed_sensitivity confirming that the synthesis is successful.
+The obtained "closed-loop" complementary filters are indeed equal to the ones obtained in Section\nbsp{}ref:sec:hinf_example.
+
+#+name: fig:hinf_filters_results_mixed_sensitivity
+#+caption: Bode plot of the obtained complementary filters after $\mathcal{H}_\infty$ mixed-sensitivity synthesis.
+[[file:figs/hinf_filters_results_mixed_sensitivity.pdf]]
+
+** Synthesis of a set of three complementary filters
+<<sec:hinf_three_comp_filters>>
+
+Some applications may require to merge more than two sensors\nbsp{}cite:stoten01_fusion_kinet_data_using_compos_filter,becker15_compl_filter_desig_three_frequen_bands.
+For instance at the LIGO, three sensors (an LVDT, a seismometer and a geophone) are merged to form a super sensor\nbsp{}cite:matichard15_seism_isolat_advan_ligo (Fig.\nbsp{}ref:fig:ligo_super_sensor_architecture).\par
+
+When merging $n>2$ sensors using complementary filters, two architectures can be used as shown in Fig.\nbsp{}ref:fig:sensor_fusion_three.
+The fusion can either be done in a "sequential" way where $n-1$ sets of two complementary filters are used (Fig.\nbsp{}ref:fig:sensor_fusion_three_sequential), or in a "parallel" way where one set of $n$ complementary filters is used (Fig.\nbsp{}ref:fig:sensor_fusion_three_parallel).
+
+In the first case, typical sensor fusion synthesis techniques can be used.
+However, when a parallel architecture is used, a new synthesis method for a set of more than two complementary filters is required as only simple analytical formulas have been proposed in the literature\nbsp{}cite:stoten01_fusion_kinet_data_using_compos_filter,becker15_compl_filter_desig_three_frequen_bands.
+A generalization of the proposed synthesis method of complementary filters is presented in this section. \par
+
+#+begin_export latex
+\begin{figure}[htbp]
+\begin{subfigure}[b]{0.59\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_fusion_three_sequential.pdf}
+\caption{\label{fig:sensor_fusion_three_sequential}Sequential fusion.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.39\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_fusion_three_parallel.pdf}
+\caption{\label{fig:sensor_fusion_three_parallel}Parallel fusion.}
+\end{subfigure}
+\caption{\label{fig:sensor_fusion_three}Possible sensor fusion architecture when more than two sensors are to be merged.}
+\centering
+\end{figure}
+#+end_export
+
+The synthesis objective is to compute a set of $n$ stable transfer functions $[H_1(s),\ H_2(s),\ \dots,\ H_n(s)]$ such that conditions\nbsp{}eqref:eq:hinf_cond_compl_gen and\nbsp{}eqref:eq:hinf_cond_perf_gen are satisfied.
+#+name: eq:hinf_problem_gen
+\begin{subequations}
+  \begin{align}
+  & \sum_{i=1}^n H_i(s) = 1 \label{eq:hinf_cond_compl_gen} \\
+  & \left| H_i(j\omega) \right| < \frac{1}{\left| W_i(j\omega) \right|}, \quad \forall \omega,\ i = 1 \dots n \label{eq:hinf_cond_perf_gen}
+  \end{align}
+\end{subequations}
+
+$[W_1(s),\ W_2(s),\ \dots,\ W_n(s)]$ are weighting transfer functions that are chosen to specify the maximum complementary filters' norm during the synthesis.
+
+Such synthesis objective is closely related to the one described in Section\nbsp{}ref:sec:synthesis_objective, and indeed the proposed synthesis method is a generalization of the one presented in Section\nbsp{}ref:sec:hinf_synthesis. \par
+
+A set of $n$ complementary filters can be shaped by applying the standard $\mathcal{H}_\infty$ synthesis to the generalized plant $P_n(s)$ described by\nbsp{}eqref:eq:generalized_plant_n_filters.
+
+#+name: eq:generalized_plant_n_filters
+\begin{equation}
+  \begin{bmatrix} z_1 \\ \vdots \\ z_n \\ v \end{bmatrix} = P_n(s) \begin{bmatrix} w \\ u_1 \\ \vdots \\ u_{n-1} \end{bmatrix}; \quad
+  P_n(s) = \begin{bmatrix}
+    W_1    & -W_1   & \dots  & \dots  & -W_1 \\
+    0      &  W_2   & 0      & \dots  & 0 \\
+    \vdots & \ddots & \ddots & \ddots & \vdots \\
+    \vdots &        & \ddots & \ddots & 0 \\
+    0      & \dots  & \dots  & 0      & W_n \\
+    1      & 0      & \dots  & \dots  & 0
+    \end{bmatrix}
+\end{equation}
+
+If the synthesis if successful, a set of $n-1$ filters $[H_2(s),\ H_3(s),\ \dots,\ H_n(s)]$ are obtained such that\nbsp{}eqref:eq:hinf_syn_obj_gen is verified.
+
+#+name: eq:hinf_syn_obj_gen
+\begin{equation}
+  \left\|\begin{matrix} \left(1 - \left[ H_2(s) + H_3(s) + \dots + H_n(s) \right]\right) W_1(s) \\ H_2(s) W_2(s) \\ \vdots \\ H_n(s) W_n(s) \end{matrix}\right\|_\infty \le 1
+\end{equation}
+
+$H_1(s)$ is then defined using\nbsp{}eqref:eq:h1_comp_h2_hn which is ensuring the complementary property for the set of $n$ filters\nbsp{}eqref:eq:hinf_cond_compl_gen.
+Condition\nbsp{}eqref:eq:hinf_cond_perf_gen is satisfied thanks to\nbsp{}eqref:eq:hinf_syn_obj_gen.
+
+#+name: eq:h1_comp_h2_hn
+\begin{equation}
+H_1(s) \triangleq 1 - \big[ H_2(s) + H_3(s) + \dots + H_n(s) \big]
+\end{equation}
+
+An example is given to validate the proposed method for the synthesis of a set of three complementary filters.
+The sensors to be merged are a displacement sensor from DC up to $\SI{1}{Hz}$, a geophone from $1$ to $\SI{10}{Hz}$ and an accelerometer above $\SI{10}{Hz}$.
+Three weighting functions are designed using formula\nbsp{}eqref:eq:weight_formula and their inverse magnitude are shown in Fig.\nbsp{}ref:fig:three_complementary_filters_results (dashed curves).
+
+Consider the generalized plant $P_3(s)$ shown in Fig.\nbsp{}ref:fig:comp_filter_three_hinf_gen_plant which is also described by\nbsp{}eqref:eq:generalized_plant_three_filters.
+
+#+name: eq:generalized_plant_three_filters
+\begin{equation}
+  \begin{bmatrix} z_1 \\ z_2 \\ z_3 \\ v \end{bmatrix} = P_3(s) \begin{bmatrix} w \\ u_1 \\ u_2 \end{bmatrix}; \quad P_3(s) = \begin{bmatrix}W_1(s) & -W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) & 0 \\ 0 & 0 & \phantom{+}W_3(s) \\ 1 & 0 & 0 \end{bmatrix}
+\end{equation}
+
+#+begin_export latex
+\begin{figure}[htbp]
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/comp_filter_three_hinf_gen_plant.pdf}
+\caption{\label{fig:comp_filter_three_hinf_gen_plant} Generalized plant.}
+\vfill
+\end{subfigure}
+\hfill
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/comp_filter_three_hinf_fb.pdf}
+\caption{\label{fig:comp_filter_three_hinf_fb} Generalized plant with the synthesized filter.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:comp_filter_three_hinf} Architecture for the $\mathcal{H}_\infty$ synthesis of three complementary filters.}
+\centering
+\end{figure}
+#+end_export
+
+The standard $\mathcal{H}_\infty$ synthesis is performed on the generalized plant $P_3(s)$.
+Two filters $H_2(s)$ and $H_3(s)$ are obtained such that the $\mathcal{H}_\infty$ norm of the closed-loop transfer from $w$ to $[z_1,\ z_2,\ z_3]$ of the system in Fig.\nbsp{}ref:fig:comp_filter_three_hinf_fb is less than one.
+Filter $H_1(s)$ is defined using\nbsp{}eqref:eq:h1_compl_h2_h3 thus ensuring the complementary property of the obtained set of filters.
+
+#+name: eq:h1_compl_h2_h3
+\begin{equation}
+H_1(s) \triangleq 1 - \big[ H_2(s) + H_3(s) \big]
+\end{equation}
+
+Figure\nbsp{}ref:fig:three_complementary_filters_results displays the three synthesized complementary filters (solid lines) which confirms that the synthesis is successful.\par
+
+#+name: fig:three_complementary_filters_results
+#+caption: Bode plot of the inverse weighting functions and of the three complementary filters obtained using the $\mathcal{H}_\infty$ synthesis.
+[[file:figs/three_complementary_filters_results.pdf]]
+
+* Conclusion
+<<sec:conclusion>>
+
+A new method for designing complementary filters using the $\mathcal{H}_\infty$ synthesis has been proposed.
+It allows to shape the magnitude of the filters by the use of weighting functions during the synthesis.
+This is very valuable in practice as the characteristics of the super sensor are linked to the complementary filters' magnitude.
+Therefore typical sensor fusion objectives can be translated into requirements on the magnitudes of the filters.
+Several examples were used to emphasize the simplicity and the effectiveness of the proposed method.
+
+However, the shaping of the complementary filters' magnitude does not allow to directly optimize the super sensor noise and dynamical characteristics.
+Future work will aim at developing a complementary filter synthesis method that minimizes the super sensor noise while ensuring the robustness of the fusion.
+
+* Acknowledgment
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+This research benefited from a FRIA grant from the French Community of Belgium.
+This paper has been assigned the LIGO document number LIGO-P2100328.
+
+* Data Availability
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+Matlab\nbsp{}cite:matlab20 was used for this study.
+The source code is available under a MIT License and archived in Zenodo\nbsp{}cite:dehaeze21_new_method_desig_compl_filter_code.
+
+* Bibliography                                                       :ignore:
+\bibliographystyle{elsarticle-num}
+\bibliography{ref}
+
+* Local Variables                                                   :noexport:
+# Local Variables:
+# org-latex-packages-alist: nil
+# End:
--- a/journal/dehaeze21_desig_compl_filte.pdf
+++ b/journal/dehaeze21_desig_compl_filte.pdf
--- a/journal/dehaeze21_desig_compl_filte.tex
+++ b/journal/dehaeze21_desig_compl_filte.tex
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+% Created 2021-09-14 mar. 13:38
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+\documentclass[preprint, sort&compress]{elsarticle}
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+\usepackage{graphicx}
+\usepackage{grffile}
+\usepackage{longtable}
+\usepackage{wrapfig}
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+\usepackage{hyperref}
+\usepackage{caption,subcaption}
+\usepackage{amsfonts}
+\usepackage{siunitx}
+\journal{Mechanical Systems and Signal Processing}
+\author[a1,a2]{Thomas Dehaeze\corref{cor1}}
+\author[a3,a4]{Mohit Verma}
+\author[a2,a4]{Christophe Collette}
+\cortext[cor1]{Corresponding author. Email Address: thomas.dehaeze@esrf.fr}
+\address[a1]{European Synchrotron Radiation Facility, 38000 Grenoble, France}
+\address[a2]{University of Li\`{e}ge, PML, Department of Aerospace and Mechanical Engineering, 4000 Li\`{e}ge, Belgium.}
+\address[a3]{CSIR --- Structural Engineering Research Centre, Taramani, Chennai --- 600113, India.}
+\address[a4]{Universit\'{e} Libre de Bruxelles, Precision Mechatronics Laboratory, BEAMS Department, 1050 Brussels, Belgium.}
+\usepackage{tabularx}
+\usepackage{booktabs}
+\usepackage{array}
+\usepackage[hyperref]{xcolor}
+\usepackage[top=2cm, bottom=2cm, left=2cm, right=2cm]{geometry}
+\hypersetup{colorlinks=true}
+\setlength{\parskip}{1em}
+\date{}
+\title{Designing complementary filters for sensor fusion using \(\mathcal{H}_\infty\) synthesis}
+\begin{document}
+
+
+\hypersetup{allcolors=teal}
+
+\begin{frontmatter}
+\begin{abstract}
+In order to obtain a better estimate of a quantity being measured, several sensors having different characteristics can be merged with a technique called ``sensor fusion''.
+The obtained ``super sensor'' combines the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
+Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
+Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
+In this study, this issue is addressed and a new method for designing complementary filters is proposed.
+This method uses weighting functions to specify the wanted shape of the complementary filters that are then obtained using the standard \(\mathcal{H}_\infty\) synthesis.
+The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
+Such synthesis method is further extended for the shaping of a set of more than two complementary filters.
+\end{abstract}
+
+\begin{keyword}
+Sensor fusion \sep{} Complementary filters \sep{} \(\mathcal{H}_\infty\) synthesis \sep{} Vibration isolation \sep{} Motion control
+\end{keyword}
+\end{frontmatter}
+
+\section{Introduction}
+\label{sec:introduction}
+Measuring a physical quantity using sensors is always subject to several limitations.
+First, the accuracy of the measurement is affected by several noise sources, such as electrical noise of the conditioning electronics being used.
+Second, the frequency range in which the measurement is relevant is bounded by the bandwidth of the sensor.
+One way to overcome these limitations is to combine several sensors using a technique called ``sensor fusion''~\cite{bendat57_optim_filter_indep_measur_two}.
+Fortunately, a wide variety of sensors exists, each with different characteristics.
+By carefully choosing the fused sensors, a so called ``super sensor'' is obtained that can combines benefits of the individual sensors. \par
+In some situations, sensor fusion is used to increase the bandwidth of the measurement~\cite{shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,min15_compl_filter_desig_angle_estim}.
+For instance, in~\cite{shaw90_bandw_enhan_posit_measur_using_measur_accel} the bandwidth of a position sensor is increased by fusing it with an accelerometer providing the high frequency motion information.
+For other applications, sensor fusion is used to obtain an estimate of the measured quantity with lower noise~\cite{hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system,plummer06_optim_compl_filter_their_applic_motion_measur,robert12_introd_random_signal_applied_kalman}.
+More recently, the fusion of sensors measuring different physical quantities has been proposed to obtain interesting properties for control~\cite{collette15_sensor_fusion_method_high_perfor,yong16_high_speed_vertic_posit_stage}.
+In~\cite{collette15_sensor_fusion_method_high_perfor}, an inertial sensor used for active vibration isolation is fused with a sensor collocated with the actuator for improving the stability margins of the feedback controller. \par
+Practical applications of sensor fusion are numerous.
+It is widely used for the attitude estimation of several autonomous vehicles such as unmanned aerial vehicle~\cite{baerveldt97_low_cost_low_weigh_attit,corke04_inert_visual_sensin_system_small_auton_helic,jensen13_basic_uas} and underwater vehicles~\cite{pascoal99_navig_system_desig_using_time,batista10_optim_posit_veloc_navig_filter_auton_vehic}.
+Naturally, it is of great benefits for high performance positioning control as shown in~\cite{shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,min15_compl_filter_desig_angle_estim,yong16_high_speed_vertic_posit_stage}.
+Sensor fusion was also shown to be a key technology to improve the performance of active vibration isolation systems~\cite{tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip}.
+Emblematic examples are the isolation stages of gravitational wave detectors~\cite{collette15_sensor_fusion_method_high_perfor,heijningen18_low} such as the ones used at the LIGO~\cite{hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system} and at the Virgo~\cite{lucia18_low_frequen_optim_perfor_advan}. \par
+There are mainly two ways to perform sensor fusion: either using a set of complementary filters~\cite{anderson53_instr_approac_system_steer_comput} or using Kalman filtering~\cite{brown72_integ_navig_system_kalman_filter,odry18_kalman_filter_mobil_robot_attit_estim}.
+For sensor fusion applications, both methods are sharing many relationships~\cite{brown72_integ_navig_system_kalman_filter,higgins75_compar_compl_kalman_filter,robert12_introd_random_signal_applied_kalman,becker15_compl_filter_desig_three_frequen_bands}.
+However, for Kalman filtering, assumptions must be made about the probabilistic character of the sensor noises~\cite{robert12_introd_random_signal_applied_kalman} whereas it is not the case with complementary filters.
+Furthermore, the advantages of complementary filters over Kalman filtering for sensor fusion are their general applicability, their low computational cost~\cite{higgins75_compar_compl_kalman_filter}, and the fact that they are intuitive as their effects can be easily interpreted in the frequency domain. \par
+A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies.
+In the early days of complementary filtering, analog circuits were employed to physically realize the filters~\cite{anderson53_instr_approac_system_steer_comput}.
+Analog complementary filters are still used today~\cite{yong16_high_speed_vertic_posit_stage,moore19_capac_instr_sensor_fusion_high_bandw_nanop}, but most of the time they are now implemented digitally as it allows for much more flexibility. \par
+
+Several design methods have been developed over the years to optimize complementary filters.
+The easiest way to design complementary filters is to use analytical formulas.
+Depending on the application, the formulas used are of first order~\cite{corke04_inert_visual_sensin_system_small_auton_helic,yeh05_model_contr_hydraul_actuat_two,yong16_high_speed_vertic_posit_stage}, second order~\cite{baerveldt97_low_cost_low_weigh_attit,stoten01_fusion_kinet_data_using_compos_filter,jensen13_basic_uas} or even higher orders~\cite{shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,stoten01_fusion_kinet_data_using_compos_filter,collette15_sensor_fusion_method_high_perfor,matichard15_seism_isolat_advan_ligo}. \par
+
+As the characteristics of the super sensor depends on the proper design of the complementary filters~\cite{dehaeze19_compl_filter_shapin_using_synth}, several optimization techniques have been developed.
+Some are based on the finding of optimal parameters of analytical formulas~\cite{jensen13_basic_uas,min15_compl_filter_desig_angle_estim,becker15_compl_filter_desig_three_frequen_bands}, while other are using convex optimization tools~\cite{hua04_polyp_fir_compl_filter_contr_system,hua05_low_ligo} such as linear matrix inequalities~\cite{pascoal99_navig_system_desig_using_time}.
+As shown in~\cite{plummer06_optim_compl_filter_their_applic_motion_measur}, the design of complementary filters can also be linked to the standard mixed-sensitivity control problem.
+Therefore, all the powerful tools developed for the classical control theory can also be used for the design of complementary filters.
+For instance, in~\cite{jensen13_basic_uas} the two gains of a Proportional Integral (PI) controller are optimized to minimize the noise of the super sensor. \par
+The common objective of all these complementary filters design methods is to obtain a super sensor that has desired characteristics, usually in terms of noise and dynamics.
+Moreover, as reported in~\cite{zimmermann92_high_bandw_orien_measur_contr,plummer06_optim_compl_filter_their_applic_motion_measur}, phase shifts and magnitude bumps of the super sensors dynamics can be observed if either the complementary filters are poorly designed or if the sensors are not well calibrated.
+Hence, the robustness of the fusion is also of concern when designing the complementary filters.
+Although many design methods of complementary filters have been proposed in the literature, no simple method that allows to specify the desired super sensor characteristic while ensuring good fusion robustness has been proposed. \par
+Fortunately, both the robustness of the fusion and the super sensor characteristics can be linked to the magnitude of the complementary filters~\cite{dehaeze19_compl_filter_shapin_using_synth}.
+Based on that, this paper introduces a new way to design complementary filters using the \(\mathcal{H}_\infty\) synthesis which allows to shape the complementary filters' magnitude in an easy and intuitive way. \par
+Section~\ref{sec:requirements} introduces the sensor fusion architecture and demonstrates how typical requirements can be linked to the complementary filters' magnitude.
+In Section~\ref{sec:hinf_method}, the shaping of complementary filters is formulated as an \(\mathcal{H}_\infty\) optimization problem using weighting functions, and the simplicity of the proposed method is illustrated with an example.
+The synthesis method is further validated in Section~\ref{sec:application_ligo} by designing complex complementary filters.
+Section~\ref{sec:discussion} compares the proposed synthesis method with the classical mixed-sensitivity synthesis, and extends it for the shaping of more than two complementary filters.
+
+\section{Sensor Fusion and Complementary Filters Requirements}
+\label{sec:requirements}
+Complementary filtering provides a framework for fusing signals from different sensors.
+As the effectiveness of the fusion depends on the proper design of the complementary filters, they are expected to fulfill certain requirements.
+These requirements are discussed in this section.
+\subsection{Sensor Fusion Architecture}
+\label{sec:sensor_fusion}
+
+A general sensor fusion architecture using complementary filters is shown in Fig.~\ref{fig:sensor_fusion_overview} where several sensors (here two) are measuring the same physical quantity \(x\).
+The two sensors output signals \(\hat{x}_1\) and \(\hat{x}_2\) are estimates of \(x\).
+These estimates are then filtered out by complementary filters and combined to form a new estimate \(\hat{x}\).
+
+The resulting sensor, termed as super sensor, can have larger bandwidth and better noise characteristics in comparison to the individual sensors.
+This means that the super sensor provides an estimate \(\hat{x}\) of \(x\) which can be more accurate over a larger frequency band than the outputs of the individual sensors.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/sensor_fusion_overview.pdf}
+\caption{\label{fig:sensor_fusion_overview}Schematic of a sensor fusion architecture using complementary filters.}
+\end{figure}
+
+The complementary property of filters \(H_1(s)\) and \(H_2(s)\) implies that the sum of their transfer functions is equal to one.
+That is, unity magnitude and zero phase at all frequencies.
+Therefore, a pair of complementary filter needs to satisfy the following condition:
+\begin{equation}
+\label{eq:comp_filter}
+  H_1(s) + H_2(s) = 1
+\end{equation}
+
+It will soon become clear why the complementary property is important for the sensor fusion architecture.
+
+\subsection{Sensor Models and Sensor Normalization}
+\label{sec:sensor_models}
+
+In order to study such sensor fusion architecture, a model for the sensors is required.
+Such model is shown in Fig.~\ref{fig:sensor_model} and consists of a linear time invariant (LTI) system \(G_i(s)\) representing the sensor dynamics and an input \(n_i\) representing the sensor noise.
+The model input \(x\) is the measured physical quantity and its output \(\tilde{x}_i\) is the ``raw'' output of the sensor.
+
+Before filtering the sensor outputs \(\tilde{x}_i\) by the complementary filters, the sensors are usually normalized to simplify the fusion.
+This normalization consists of using an estimate \(\hat{G}_i(s)\) of the sensor dynamics \(G_i(s)\), and filtering the sensor output by the inverse of this estimate \(\hat{G}_i^{-1}(s)\) as shown in Fig.~\ref{fig:sensor_model_calibrated}.
+It is here supposed that the sensor inverse \(\hat{G}_i^{-1}(s)\) is proper and stable.
+This way, the units of the estimates \(\hat{x}_i\) are equal to the units of the physical quantity \(x\).
+The sensor dynamics estimate \(\hat{G}_i(s)\) can be a simple gain or a more complex transfer function.
+
+\begin{figure}[htbp]
+\begin{subfigure}[b]{0.49\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model.pdf}
+\caption{\label{fig:sensor_model} Basic sensor model consisting of a noise input $n_i$ and a linear time invariant transfer function $G_i(s)$.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.49\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model_calibrated.pdf}
+\caption{\label{fig:sensor_model_calibrated} Normalized sensors using the inverse of an estimate $\hat{G}_i(s)$ of the sensor dynamics.}
+\end{subfigure}
+\caption{\label{fig:sensor_models}Sensor models with and without normalization.}
+\centering
+\end{figure}
+
+Two normalized sensors are then combined to form a super sensor as shown in Fig.~\ref{fig:fusion_super_sensor}.
+The two sensors are measuring the same physical quantity \(x\) with dynamics \(G_1(s)\) and \(G_2(s)\), and with \emph{uncorrelated} noises \(n_1\) and \(n_2\).
+The signals from both normalized sensors are fed into two complementary filters \(H_1(s)\) and \(H_2(s)\) and then combined to yield an estimate \(\hat{x}\) of \(x\).
+
+The super sensor output is therefore equal to:
+\begin{equation}
+\label{eq:comp_filter_estimate}
+  \hat{x} = \Big( H_1(s) \hat{G}_1^{-1}(s) G_1(s) + H_2(s) \hat{G}_2^{-1}(s) G_2(s) \Big) x + H_1(s) \hat{G}_1^{-1}(s) G_1(s) n_1 + H_2(s) \hat{G}_2^{-1}(s) G_2(s) n_2
+\end{equation}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/fusion_super_sensor.pdf}
+\caption{\label{fig:fusion_super_sensor}Sensor fusion architecture with two normalized sensors.}
+\end{figure}
+
+\subsection{Noise Sensor Filtering}
+\label{sec:noise_filtering}
+
+In this section, it is supposed that all the sensors are perfectly normalized, such that:
+\begin{equation}
+\label{eq:perfect_dynamics}
+  \frac{\hat{x}_i}{x} = \hat{G}_i(s) G_i(s) = 1
+\end{equation}
+
+The effect of a non-perfect normalization will be discussed in the next section.
+
+Provided~\eqref{eq:perfect_dynamics} is verified, the super sensor output \(\hat{x}\) is then equal to:
+\begin{equation}
+\label{eq:estimate_perfect_dyn}
+  \hat{x} = x + H_1(s) n_1 + H_2(s) n_2
+\end{equation}
+
+From~\eqref{eq:estimate_perfect_dyn}, the complementary filters \(H_1(s)\) and \(H_2(s)\) are shown to only operate on the noise of the sensors.
+Thus, this sensor fusion architecture permits to filter the noise of both sensors without introducing any distortion in the physical quantity to be measured.
+This is why the two filters must be complementary.
+
+The estimation error \(\delta x\), defined as the difference between the sensor output \(\hat{x}\) and the measured quantity \(x\), is computed for the super sensor~\eqref{eq:estimate_error}.
+\begin{equation}
+\label{eq:estimate_error}
+  \delta x \triangleq \hat{x} - x = H_1(s) n_1 + H_2(s) n_2
+\end{equation}
+
+As shown in~\eqref{eq:noise_filtering_psd}, the Power Spectral Density (PSD) of the estimation error \(\Phi_{\delta x}\) depends both on the norm of the two complementary filters and on the PSD of the noise sources \(\Phi_{n_1}\) and \(\Phi_{n_2}\).
+\begin{equation}
+\label{eq:noise_filtering_psd}
+  \Phi_{\delta x}(\omega) = \left|H_1(j\omega)\right|^2 \Phi_{n_1}(\omega) + \left|H_2(j\omega)\right|^2 \Phi_{n_2}(\omega)
+\end{equation}
+
+If the two sensors have identical noise characteristics, \(\Phi_{n_1}(\omega) = \Phi_{n_2}(\omega)\), a simple averaging (\(H_1(s) = H_2(s) = 0.5\)) is what would minimize the super sensor noise.
+This is the simplest form of sensor fusion with complementary filters.
+
+However, the two sensors have usually high noise levels over distinct frequency regions.
+In such case, to lower the noise of the super sensor, the norm \(|H_1(j\omega)|\) has to be small when \(\Phi_{n_1}(\omega)\) is larger than \(\Phi_{n_2}(\omega)\) and the norm \(|H_2(j\omega)|\) has to be small when \(\Phi_{n_2}(\omega)\) is larger than \(\Phi_{n_1}(\omega)\).
+Hence, by properly shaping the norm of the complementary filters, it is possible to reduce the noise of the super sensor.
+
+\subsection{Sensor Fusion Robustness}
+\label{sec:fusion_robustness}
+
+In practical systems the sensor normalization is not perfect and condition~\eqref{eq:perfect_dynamics} is not verified.
+
+In order to study such imperfection, a multiplicative input uncertainty is added to the sensor dynamics (Fig.~\ref{fig:sensor_model_uncertainty}).
+The nominal model is the estimated model used for the normalization \(\hat{G}_i(s)\), \(\Delta_i(s)\) is any stable transfer function satisfying \(|\Delta_i(j\omega)| \le 1,\ \forall\omega\), and \(w_i(s)\) is a weighting transfer function representing the magnitude of the uncertainty.
+
+The weight \(w_i(s)\) is chosen such that the real sensor dynamics \(G_i(j\omega)\) is contained in the uncertain region represented by a circle in the complex plane, centered on \(1\) and with a radius equal to \(|w_i(j\omega)|\).
+
+As the nominal sensor dynamics is taken as the normalized filter, the normalized sensor can be further simplified as shown in Fig.~\ref{fig:sensor_model_uncertainty_simplified}.
+
+\begin{figure}[htbp]
+\begin{subfigure}[b]{0.59\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model_uncertainty.pdf}
+\caption{\label{fig:sensor_model_uncertainty} Sensor with multiplicative input uncertainty.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.39\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_model_uncertainty_simplified.pdf}
+\caption{\label{fig:sensor_model_uncertainty_simplified} Simplified sensor model.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:sensor_models_uncertainty}Sensor models with dynamical uncertainty.}
+\centering
+\end{figure}
+
+The sensor fusion architecture with the sensor models including dynamical uncertainty is shown in Fig.~\ref{fig:sensor_fusion_dynamic_uncertainty}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/sensor_fusion_dynamic_uncertainty.pdf}
+\caption{\label{fig:sensor_fusion_dynamic_uncertainty}Sensor fusion architecture with sensor dynamics uncertainty.}
+\end{figure}
+
+The super sensor dynamics~\eqref{eq:super_sensor_dyn_uncertainty} is no longer equal to \(1\) and now depends on the sensor dynamical uncertainty weights \(w_i(s)\) as well as on the complementary filters \(H_i(s)\).
+\begin{equation}
+\label{eq:super_sensor_dyn_uncertainty}
+  \frac{\hat{x}}{x} = 1 + w_1(s) H_1(s) \Delta_1(s) + w_2(s) H_2(s) \Delta_2(s)
+\end{equation}
+
+The dynamical uncertainty of the super sensor can be graphically represented in the complex plane by a circle centered on \(1\) with a radius equal to \(|w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)|\) (Fig.~\ref{fig:uncertainty_set_super_sensor}).
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/uncertainty_set_super_sensor.pdf}
+\caption{\label{fig:uncertainty_set_super_sensor}Uncertainty region of the super sensor dynamics in the complex plane (grey circle). The contribution of both sensors 1 and 2 to the total uncertainty are represented respectively by a blue circle and a red circle. The frequency dependency \(\omega\) is here omitted.}
+\end{figure}
+
+The super sensor dynamical uncertainty, and hence the robustness of the fusion, clearly depends on the complementary filters' norm.
+For instance, the phase \(\Delta\phi(\omega)\) added by the super sensor dynamics at frequency \(\omega\) is bounded by \(\Delta\phi_{\text{max}}(\omega)\) which can be found by drawing a tangent from the origin to the uncertainty circle of the super sensor (Fig.~\ref{fig:uncertainty_set_super_sensor}) and that is mathematically described by~\eqref{eq:max_phase_uncertainty}.
+
+\begin{equation}
+\label{eq:max_phase_uncertainty}
+    \Delta\phi_\text{max}(\omega) = \arcsin\big( |w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)| \big)
+\end{equation}
+
+As it is generally desired to limit the maximum phase added by the super sensor, \(H_1(s)\) and \(H_2(s)\) should be designed such that \(\Delta \phi\) is bounded to acceptable values.
+Typically, the norm of the complementary filter \(|H_i(j\omega)|\) should be made small when \(|w_i(j\omega)|\) is large, i.e., at frequencies where the sensor dynamics is uncertain.
+
+\section{Complementary Filters Shaping}
+\label{sec:hinf_method}
+As shown in Section~\ref{sec:requirements}, the noise and robustness of the super sensor are a function of the complementary filters' norm.
+Therefore, a synthesis method of complementary filters that allows to shape their norm would be of great use.
+In this section, such synthesis is proposed by writing the synthesis objective as a standard \(\mathcal{H}_\infty\) optimization problem.
+As weighting functions are used to represent the wanted complementary filters' shape during the synthesis, their proper design is discussed.
+Finally, the synthesis method is validated on an simple example.
+\subsection{Synthesis Objective}
+\label{sec:synthesis_objective}
+
+The synthesis objective is to shape the norm of two filters \(H_1(s)\) and \(H_2(s)\) while ensuring their complementary property~\eqref{eq:comp_filter}.
+This is equivalent as to finding proper and stable transfer functions \(H_1(s)\) and \(H_2(s)\) such that conditions~\eqref{eq:hinf_cond_complementarity}, \eqref{eq:hinf_cond_h1} and~\eqref{eq:hinf_cond_h2} are satisfied.
+
+\begin{subequations}
+\label{eq:comp_filter_problem_form}
+  \begin{align}
+  & H_1(s) + H_2(s) = 1 \label{eq:hinf_cond_complementarity} \\
+  & |H_1(j\omega)| \le \frac{1}{|W_1(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h1} \\
+  & |H_2(j\omega)| \le \frac{1}{|W_2(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h2}
+  \end{align}
+\end{subequations}
+\(W_1(s)\) and \(W_2(s)\) are two weighting transfer functions that are carefully chosen to specify the maximum wanted norm of the complementary filters during the synthesis.
+
+\subsection{Shaping of Complementary Filters using \(\mathcal{H}_\infty\) synthesis}
+\label{sec:hinf_synthesis}
+
+In this section, it is shown that the synthesis objective can be easily expressed as a standard \(\mathcal{H}_\infty\) optimization problem and therefore solved using convenient tools readily available.
+
+Consider the generalized plant \(P(s)\) shown in Fig.~\ref{fig:h_infinity_robust_fusion_plant} and mathematically described by~\eqref{eq:generalized_plant}.
+
+\begin{equation}
+\label{eq:generalized_plant}
+  \begin{bmatrix} z_1 \\ z_2 \\ v \end{bmatrix} = P(s) \begin{bmatrix} w\\u \end{bmatrix}; \quad P(s) = \begin{bmatrix}W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) \\  1 & 0 \end{bmatrix}
+\end{equation}
+
+\begin{figure}[htbp]
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/h_infinity_robust_fusion_plant.pdf}
+\caption{\label{fig:h_infinity_robust_fusion_plant} Generalized plant.}
+\vfill
+\end{subfigure}
+\hfill
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/h_infinity_robust_fusion_fb.pdf}
+\caption{\label{fig:h_infinity_robust_fusion_fb} Generalized plant with the synthesized filter.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:h_infinity_robust_fusion} Architecture for the $\mathcal{H}_\infty$ synthesis of complementary filters.}
+\centering
+\end{figure}
+
+Applying the standard \(\mathcal{H}_\infty\) synthesis to the generalized plant \(P(s)\) is then equivalent as finding a stable filter \(H_2(s)\) which based on \(v\), generates a signal \(u\) such that the \(\mathcal{H}_\infty\) norm of the system in Fig.~\ref{fig:h_infinity_robust_fusion_fb} from \(w\) to \([z_1, \ z_2]\) is less than one~\eqref{eq:hinf_syn_obj}.
+\begin{equation}
+\label{eq:hinf_syn_obj}
+  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
+\end{equation}
+
+By then defining \(H_1(s)\) to be the complementary of \(H_2(s)\) \eqref{eq:definition_H1}, the \(\mathcal{H}_\infty\) synthesis objective becomes equivalent to~\eqref{eq:hinf_problem} which ensures that~\eqref{eq:hinf_cond_h1} and~\eqref{eq:hinf_cond_h2} are satisfied.
+
+\begin{equation}
+\label{eq:definition_H1}
+  H_1(s) \triangleq 1 - H_2(s)
+\end{equation}
+
+\begin{equation}
+\label{eq:hinf_problem}
+  \left\|\begin{matrix} H_1(s) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
+\end{equation}
+
+Therefore, applying the \(\mathcal{H}_\infty\) synthesis to the standard plant \(P(s)\) \eqref{eq:generalized_plant} will generate two filters \(H_2(s)\) and \(H_1(s) \triangleq 1 - H_2(s)\) that are complementary~\eqref{eq:comp_filter_problem_form} and such that there norms are bellow specified bounds \eqref{eq:hinf_cond_h1},~\eqref{eq:hinf_cond_h2}.
+
+Note that there is only an implication between the \(\mathcal{H}_\infty\) norm condition~\eqref{eq:hinf_problem} and the initial synthesis objectives~\eqref{eq:hinf_cond_h1} and~\eqref{eq:hinf_cond_h2} and not an equivalence.
+Hence, the optimization may be a little bit conservative with respect to the set of filters on which it is performed, see~\cite[Chap. 2.8.3]{skogestad07_multiv_feedb_contr}.
+In practice, this is however not an found to be an issue.
+
+\subsection{Weighting Functions Design}
+\label{sec:hinf_weighting_func}
+
+Weighting functions are used during the synthesis to specify the maximum allowed complementary filters' norm.
+The proper design of these weighting functions is of primary importance for the success of the presented \(\mathcal{H}_\infty\) synthesis of complementary filters.
+
+First, only proper and stable transfer functions should be used.
+Second, the order of the weighting functions should stay reasonably small in order to reduce the computational costs associated with the solving of the optimization problem and for the physical implementation of the filters (the synthesized filters' order being equal to the sum of the weighting functions' order).
+Third, one should not forget the fundamental limitations imposed by the complementary property~\eqref{eq:comp_filter}.
+This implies for instance that \(|H_1(j\omega)|\) and \(|H_2(j\omega)|\) cannot be made small at the same frequency.
+
+When designing complementary filters, it is usually desired to specify their slopes, their ``blending'' frequency and their maximum gains at low and high frequency.
+To easily express these specifications, formula~\eqref{eq:weight_formula} is proposed to help with the design of weighting functions.
+
+\begin{equation}
+\label{eq:weight_formula}
+  W(s) = \left( \frac{
+           \hfill{} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{G_0}{G_c}\right)^{\frac{1}{n}}
+         }{
+           \left(\frac{1}{G_\infty}\right)^{\frac{1}{n}} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{1}{G_c}\right)^{\frac{1}{n}}
+         }\right)^n
+\end{equation}
+
+The parameters in formula~\eqref{eq:weight_formula} are:
+\begin{itemize}
+\item \(G_0 = \lim_{\omega \to 0} |W(j\omega)|\): the low frequency gain
+\item \(G_\infty = \lim_{\omega \to \infty} |W(j\omega)|\): the high frequency gain
+\item \(G_c = |W(j\omega_c)|\): the gain at a specific frequency \(\omega_c\) in \(\si{rad/s}\).
+\item \(n\): the slope between high and low frequency. It also corresponds to the order of the weighting function.
+\end{itemize}
+
+The parameters \(G_0\), \(G_c\) and \(G_\infty\) should either satisfy~\eqref{eq:cond_formula_1} or~\eqref{eq:cond_formula_2}.
+\begin{subequations}
+\label{eq:condition_params_formula}
+  \begin{align}
+    G_0 < 1 < G_\infty \text{ and } G_0 < G_c < G_\infty \label{eq:cond_formula_1}\\
+    G_\infty < 1 < G_0 \text{ and } G_\infty < G_c < G_0 \label{eq:cond_formula_2}
+  \end{align}
+\end{subequations}
+
+The typical magnitude of a weighting function generated using~\eqref{eq:weight_formula} is shown in Fig.~\ref{fig:weight_formula}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/weight_formula.pdf}
+\caption{\label{fig:weight_formula}Magnitude of a weighting function generated using formula~\eqref{eq:weight_formula}, \(G_0 = 1e^{-3}\), \(G_\infty = 10\), \(\omega_c = \SI{10}{Hz}\), \(G_c = 2\), \(n = 3\).}
+\end{figure}
+
+\subsection{Validation of the proposed synthesis method}
+\label{sec:hinf_example}
+
+The proposed methodology for the design of complementary filters is now applied on a simple example.
+Let's suppose two complementary filters \(H_1(s)\) and \(H_2(s)\) have to be designed such that:
+\begin{itemize}
+\item the blending frequency is around \(\SI{10}{Hz}\).
+\item the slope of \(|H_1(j\omega)|\) is \(+2\) below \(\SI{10}{Hz}\).
+Its low frequency gain is \(10^{-3}\).
+\item the slope of \(|H_2(j\omega)|\) is \(-3\) above \(\SI{10}{Hz}\).
+Its high frequency gain is \(10^{-3}\).
+\end{itemize}
+
+The first step is to translate the above requirements by properly designing the weighting functions.
+The proposed formula~\eqref{eq:weight_formula} is here used for such purpose.
+Parameters used are summarized in Table~\ref{tab:weights_params}.
+The inverse magnitudes of the designed weighting functions, which are representing the maximum allowed norms of the complementary filters, are shown by the dashed lines in Fig.~\ref{fig:weights_W1_W2}.
+
+\begin{figure}
+\begin{minipage}[b]{0.49\linewidth}
+\centering
+\begin{tabularx}{0.60\linewidth}{ccc}
+\toprule
+Parameters   & \(W_1(s)\)      & \(W_2(s)\)\\
+\midrule
+\(G_0\)      & \(0.1\)         & \(1000\)\\
+\(G_\infty\) & \(1000\)        & \(0.1\)\\
+\(\omega_c\) & \(2\pi\cdot10\) & \(2\pi\cdot10\)\\
+\(G_c\)      & \(0.45\)        & \(0.45\)\\
+\(n\)        & \(2\)           & \(3\)\\
+\bottomrule
+\end{tabularx}
+\captionof{table}{\label{tab:weights_params}Parameters used for \(W_1(s)\) and \(W_2(s)\) using~\eqref{eq:weight_formula}.}
+\end{minipage}
+\hfill
+\begin{minipage}[b]{0.49\linewidth}
+\centering
+\includegraphics[scale=1]{figs/weights_W1_W2.pdf}
+\caption{\label{fig:weights_W1_W2}Inverse magnitude of the weighting functions.}
+\end{minipage}
+\end{figure}
+
+The standard \(\mathcal{H}_\infty\) synthesis is then applied to the generalized plant of Fig.~\ref{fig:h_infinity_robust_fusion_plant} and efficiently solved using Matlab~\cite{matlab20}.
+The filter \(H_2(s)\) that minimizes the \(\mathcal{H}_\infty\) norm between \(w\) and \([z_1,\ z_2]^T\) is obtained.
+The \(\mathcal{H}_\infty\) norm is here found to be close to one~\eqref{eq:hinf_synthesis_result} which indicates that the synthesis is successful: the complementary filters norms are below the maximum specified upper bounds.
+This is confirmed by the bode plots of the obtained complementary filters in Fig.~\ref{fig:hinf_filters_results}.
+
+\begin{equation}
+\label{eq:hinf_synthesis_result}
+  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \approx 1
+\end{equation}
+
+The transfer functions in the Laplace domain of the complementary filters are given in~\eqref{eq:hinf_synthesis_result_tf}.
+As expected, the obtained filters are of order \(5\), that is the sum of the weighting functions' order.
+
+\begin{subequations}
+\label{eq:hinf_synthesis_result_tf}
+  \begin{align}
+    H_2(s) &= \frac{(s+6.6e^4) (s+160) (s+4)^3}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)} \\
+    H_1(s) &\triangleq H_2(s) - 1 = \frac{10^{-8} (s+6.6e^9) (s+3450)^2 (s^2 + 49s + 895)}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)}
+  \end{align}
+\end{subequations}
+
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/hinf_filters_results.pdf}
+\caption{\label{fig:hinf_filters_results}Bode plot of the obtained complementary filters.}
+\end{figure}
+
+This simple example illustrates the fact that the proposed methodology for complementary filters shaping is easy to use and effective.
+A more complex real life example is taken up in the next section.
+
+\section{Application: Design of Complementary Filters used in the Active Vibration Isolation System at the LIGO}
+\label{sec:application_ligo}
+Sensor fusion using complementary filters are widely used in the active vibration isolation systems at gravitational wave detectors, such as at the LIGO~\cite{matichard15_seism_isolat_advan_ligo,hua05_low_ligo}, the Virgo~\cite{lucia18_low_frequen_optim_perfor_advan,heijningen18_low} and the KAGRA \cite[Chap. 5]{sekiguchi16_study_low_frequen_vibrat_isolat_system}.
+
+In the first isolation stage at the LIGO, two sets of complementary filters are used to form a super sensor that is incorporated in a feedback loop~\cite{hua04_low_ligo}.
+A set of complementary filters (\(L_2,H_2\)) is first used to fuse a seismometer and a geophone.
+Then, another set of complementary filters (\(L_1,H_1\)) is used to merge the output of the first ``inertial super sensor'' with a position sensor.
+A simplified block diagram of the sensor fusion architecture is shown in Fig.~\ref{fig:ligo_super_sensor_architecture}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/ligo_super_sensor_architecture.pdf}
+\caption{\label{fig:ligo_super_sensor_architecture}Simplified block diagram of the sensor blending strategy for the first stage at the LIGO~\cite{hua04_low_ligo}.}
+\end{figure}
+
+The fusion of the position sensor at low frequency with the ``inertial super sensor'' at high frequency using the complementary filters (\(L_1,H_1\)) is done for several reasons, first of which is to give the super sensor a DC sensibility that allows the feedback loop to have authority at zero frequency.
+The requirements on those filters are stringent and thus their design is complex and should be expressed as an optimization problem.
+
+The approach used in~\cite{hua05_low_ligo} is to use FIR complementary filters and to write the synthesis as a convex optimization problem.
+After synthesis, the obtained FIR filters were found to be compliant with the requirements.
+However they are of high order so their implementation is quite complex.
+In this section, the effectiveness of the proposed complementary filter synthesis strategy is demonstrated by using the same set of requirements.
+\subsection{Complementary Filters Specifications}
+\label{sec:ligo_specifications}
+
+The specifications for the set of complementary filters (\(L_1,H_1\)) used at the LIGO are summarized below (for further details, refer to~\cite{hua04_polyp_fir_compl_filter_contr_system}):
+\begin{itemize}
+\item Below \(\SI{0.008}{Hz}\), the magnitude \(|L_1(j\omega)|\) should be less than \(8 \times 10^{-4}\).
+\item From \(\SI{0.008}{Hz}\) to \(\SI{0.04}{Hz}\), the filter \(L_1(s)\) should attenuate the input signal proportional to frequency cubed.
+\item From \(\SI{0.04}{Hz}\) to \(\SI{0.1}{Hz}\), the magnitude \(|L_1(j\omega)|\) should be less than \(3\).
+\item Above \(\SI{0.1}{Hz}\), the magnitude \(|H_1(j\omega)|\) should be less than \(0.045\).
+\end{itemize}
+
+These specifications are therefore upper bounds on the complementary filters' magnitude.
+They are physically represented in Fig.~\ref{fig:fir_filter_ligo} as well as the obtained magnitude of the FIR filters in~\cite{hua05_low_ligo}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/fir_filter_ligo.pdf}
+\caption{\label{fig:fir_filter_ligo}Specifications and Bode plot of the obtained FIR complementary filters in~\cite{hua05_low_ligo}. The filters are here obtained using the SeDuMi Matlab toolbox~\cite{sturm99_using_sedum}.}
+\end{figure}
+
+\subsection{Weighting Functions Design}
+\label{sec:ligo_weights}
+
+The weighting functions should be designed such that their inverse magnitude is as close as possible to the specifications in order to not over-constrain the synthesis problem.
+However, the order of each weight should stay reasonably small in order to reduce the computational costs of the optimization problem as well as for the physical implementation of the filters.
+
+A Type I Chebyshev filter of order \(20\) is used for the weighting transfer function \(W_L(s)\) corresponding to the low pass filter.
+For the one corresponding to the high pass filter \(W_H(s)\), a \(7^{\text{th}}\) order transfer function is manually designed.
+The inverse magnitudes of the weighting functions are shown in Fig.~\ref{fig:ligo_weights}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/ligo_weights.pdf}
+\caption{\label{fig:ligo_weights}Specifications and weighting functions' inverse magnitude.}
+\end{figure}
+
+\subsection{\(\mathcal{H}_\infty\) Synthesis of the complementary filters}
+\label{sec:ligo_results}
+
+The proposed \(\mathcal{H}_\infty\) synthesis is performed on the generalized plant shown in Fig.~\ref{fig:h_infinity_robust_fusion_plant}.
+After optimization, the \(\mathcal{H}_\infty\) norm from \(w\) to \([z_1,\ z_2]^T\) is found close to one indication successful synthesis.
+In Fig.~\ref{fig:comp_fir_ligo_hinf}, the bode plot of the obtained complementary filters are compared with the FIR filters of order 512 obtained in~\cite{hua05_low_ligo}.
+Even though the complementary filters using the \(\mathcal{H}_\infty\) synthesis are of much lower order (order 27), they are found to be close to the FIR filters.
+This confirms the effectiveness of the proposed synthesis method even when the complementary filters are subject to complex requirements.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/comp_fir_ligo_hinf.pdf}
+\caption{\label{fig:comp_fir_ligo_hinf}Comparison of the FIR filters (dashed) designed in~\cite{hua05_low_ligo} with the filters obtained with \(\mathcal{H}_\infty\) synthesis (solid).}
+\end{figure}
+
+\section{Discussion}
+\label{sec:discussion}
+\subsection{``Closed-Loop'' complementary filters}
+\label{sec:closed_loop_complementary_filters}
+
+An alternative way to implement complementary filters is by using a fundamental property of the classical feedback architecture shown in Fig.~\ref{fig:feedback_sensor_fusion}.
+This idea is discussed in~\cite{mahony05_compl_filter_desig_special_orthog,plummer06_optim_compl_filter_their_applic_motion_measur,jensen13_basic_uas}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/feedback_sensor_fusion.pdf}
+\caption{\label{fig:feedback_sensor_fusion}``Closed-Loop'' complementary filters.}
+\end{figure}
+
+Consider the feedback architecture of Fig.~\ref{fig:feedback_sensor_fusion}, with two inputs \(\hat{x}_1\) and \(\hat{x}_2\), and one output \(\hat{x}\).
+The output \(\hat{x}\) is linked to the inputs by~\eqref{eq:closed_loop_complementary_filters}.
+
+\begin{equation}
+\label{eq:closed_loop_complementary_filters}
+\hat{x} = \underbrace{\frac{1}{1 + L(s)}}_{S(s)} \hat{x}_1 + \underbrace{\frac{L(s)}{1 + L(s)}}_{T(s)} \hat{x}_2
+\end{equation}
+
+As for any classical feedback architecture, we have that the sum of the sensitivity transfer function \(S(s)\) and complementary sensitivity transfer function \(T_(s)\) is equal to one~\eqref{eq:sensitivity_sum}.
+
+\begin{equation}
+\label{eq:sensitivity_sum}
+S(s) + T(s) = 1
+\end{equation}
+
+Therefore, provided that the the closed-loop system in Fig.~\ref{fig:feedback_sensor_fusion} is stable, it can be used as a set of two complementary filters.
+Two sensors can then be merged as shown in Fig.~\ref{fig:feedback_sensor_fusion_arch}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/feedback_sensor_fusion_arch.pdf}
+\caption{\label{fig:feedback_sensor_fusion_arch}Classical feedback architecture used for sensor fusion.}
+\end{figure}
+
+One of the main advantage of implementing and designing complementary filters using the feedback architecture of Fig.~\ref{fig:feedback_sensor_fusion} is that all the tools of the linear control theory can be applied for the design of the filters.
+If one want to shape both \(\frac{\hat{x}}{\hat{x}_1}(s) = S(s)\) and \(\frac{\hat{x}}{\hat{x}_2}(s) = T(s)\), the \(\mathcal{H}_\infty\) mixed-sensitivity synthesis can be easily applied.
+
+To do so, weighting functions \(W_1(s)\) and \(W_2(s)\) are added to respectively shape \(S(s)\) and \(T(s)\) (Fig.~\ref{fig:feedback_synthesis_architecture}).
+Then the system is rearranged to form the generalized plant \(P_L(s)\) shown in Fig.~\ref{fig:feedback_synthesis_architecture_generalized_plant}.
+The \(\mathcal{H}_\infty\) mixed-sensitivity synthesis can finally be performed by applying the standard \(\mathcal{H}_\infty\) synthesis to the generalized plant \(P_L(s)\) which is described by~\eqref{eq:generalized_plant_mixed_sensitivity}.
+
+\begin{equation}
+\label{eq:generalized_plant_mixed_sensitivity}
+  \begin{bmatrix} z \\ v \end{bmatrix} = P_L(s) \begin{bmatrix} w_1 \\ w_2 \\ u \end{bmatrix}; \quad P_L(s) = \begin{bmatrix}
+    \phantom{+}W_1(s) & 0      & \phantom{+}1 \\
+              -W_1(s) & W_2(s) &           -1
+  \end{bmatrix}
+\end{equation}
+
+The output of the synthesis is a filter \(L(s)\) such that the ``closed-loop'' \(\mathcal{H}_\infty\) norm from \([w_1,\ w_2]\) to \(z\) of the system in Fig.~\ref{fig:feedback_sensor_fusion} is less than one~\eqref{eq:comp_filters_feedback_obj}.
+
+\begin{equation}
+\label{eq:comp_filters_feedback_obj}
+  \left\| \begin{matrix} \frac{z}{w_1} \\ \frac{z}{w_2} \end{matrix} \right\|_\infty = \left\| \begin{matrix} \frac{1}{1 + L(s)} W_1(s) \\ \frac{L(s)}{1 + L(s)} W_2(s) \end{matrix} \right\|_\infty \le 1
+\end{equation}
+
+If the synthesis is successful, the transfer functions from \(\hat{x}_1\) to \(\hat{x}\) and from \(\hat{x}_2\) to \(\hat{x}\) have their magnitude bounded by the inverse magnitude of the corresponding weighting functions.
+The sensor fusion can then be implemented using the feedback architecture in Fig.~\ref{fig:feedback_sensor_fusion_arch} or more classically as shown in Fig.~\ref{fig:sensor_fusion_overview} by defining the two complementary filters using~\eqref{eq:comp_filters_feedback}.
+The two architectures are equivalent regarding their inputs/outputs relationships.
+
+\begin{equation}
+\label{eq:comp_filters_feedback}
+H_1(s) = \frac{1}{1 + L(s)}; \quad H_2(s) = \frac{L(s)}{1 + L(s)}
+\end{equation}
+
+\begin{figure}[htbp]
+\begin{subfigure}[t]{0.6\linewidth}
+\centering
+\includegraphics[scale=1]{figs/feedback_synthesis_architecture.pdf}
+\caption{\label{fig:feedback_synthesis_architecture} Feedback architecture with included weights.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[t]{0.4\linewidth}
+\centering
+\includegraphics[scale=1]{figs/feedback_synthesis_architecture_generalized_plant.pdf}
+\caption{\label{fig:feedback_synthesis_architecture_generalized_plant} Generalized plant.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:h_inf_mixed_sensitivity_synthesis} $\mathcal{H}_\infty$ mixed-sensitivity synthesis.}
+\centering
+\end{figure}
+
+As an example, two ``closed-loop'' complementary filters are designed using the \(\mathcal{H}_\infty\) mixed-sensitivity synthesis.
+The weighting functions are designed using formula~\eqref{eq:weight_formula} with parameters shown in Table~\ref{tab:weights_params}.
+After synthesis, a filter \(L(s)\) is obtained whose magnitude is shown in Fig.~\ref{fig:hinf_filters_results_mixed_sensitivity} by the black dashed line.
+The ``closed-loop'' complementary filters are compared with the inverse magnitude of the weighting functions in Fig.~\ref{fig:hinf_filters_results_mixed_sensitivity} confirming that the synthesis is successful.
+The obtained ``closed-loop'' complementary filters are indeed equal to the ones obtained in Section~\ref{sec:hinf_example}.
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/hinf_filters_results_mixed_sensitivity.pdf}
+\caption{\label{fig:hinf_filters_results_mixed_sensitivity}Bode plot of the obtained complementary filters after \(\mathcal{H}_\infty\) mixed-sensitivity synthesis.}
+\end{figure}
+
+\subsection{Synthesis of a set of three complementary filters}
+\label{sec:hinf_three_comp_filters}
+
+Some applications may require to merge more than two sensors~\cite{stoten01_fusion_kinet_data_using_compos_filter,becker15_compl_filter_desig_three_frequen_bands}.
+For instance at the LIGO, three sensors (an LVDT, a seismometer and a geophone) are merged to form a super sensor~\cite{matichard15_seism_isolat_advan_ligo} (Fig.~\ref{fig:ligo_super_sensor_architecture}).\par
+
+When merging \(n>2\) sensors using complementary filters, two architectures can be used as shown in Fig.~\ref{fig:sensor_fusion_three}.
+The fusion can either be done in a ``sequential'' way where \(n-1\) sets of two complementary filters are used (Fig.~\ref{fig:sensor_fusion_three_sequential}), or in a ``parallel'' way where one set of \(n\) complementary filters is used (Fig.~\ref{fig:sensor_fusion_three_parallel}).
+
+In the first case, typical sensor fusion synthesis techniques can be used.
+However, when a parallel architecture is used, a new synthesis method for a set of more than two complementary filters is required as only simple analytical formulas have been proposed in the literature~\cite{stoten01_fusion_kinet_data_using_compos_filter,becker15_compl_filter_desig_three_frequen_bands}.
+A generalization of the proposed synthesis method of complementary filters is presented in this section. \par
+
+\begin{figure}[htbp]
+\begin{subfigure}[b]{0.59\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_fusion_three_sequential.pdf}
+\caption{\label{fig:sensor_fusion_three_sequential}Sequential fusion.}
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.39\linewidth}
+\centering
+\includegraphics[scale=1]{figs/sensor_fusion_three_parallel.pdf}
+\caption{\label{fig:sensor_fusion_three_parallel}Parallel fusion.}
+\end{subfigure}
+\caption{\label{fig:sensor_fusion_three}Possible sensor fusion architecture when more than two sensors are to be merged.}
+\centering
+\end{figure}
+
+The synthesis objective is to compute a set of \(n\) stable transfer functions \([H_1(s),\ H_2(s),\ \dots,\ H_n(s)]\) such that conditions~\eqref{eq:hinf_cond_compl_gen} and~\eqref{eq:hinf_cond_perf_gen} are satisfied.
+\begin{subequations}
+\label{eq:hinf_problem_gen}
+  \begin{align}
+  & \sum_{i=1}^n H_i(s) = 1 \label{eq:hinf_cond_compl_gen} \\
+  & \left| H_i(j\omega) \right| < \frac{1}{\left| W_i(j\omega) \right|}, \quad \forall \omega,\ i = 1 \dots n \label{eq:hinf_cond_perf_gen}
+  \end{align}
+\end{subequations}
+
+\([W_1(s),\ W_2(s),\ \dots,\ W_n(s)]\) are weighting transfer functions that are chosen to specify the maximum complementary filters' norm during the synthesis.
+
+Such synthesis objective is closely related to the one described in Section~\ref{sec:synthesis_objective}, and indeed the proposed synthesis method is a generalization of the one presented in Section~\ref{sec:hinf_synthesis}. \par
+
+A set of \(n\) complementary filters can be shaped by applying the standard \(\mathcal{H}_\infty\) synthesis to the generalized plant \(P_n(s)\) described by~\eqref{eq:generalized_plant_n_filters}.
+
+\begin{equation}
+\label{eq:generalized_plant_n_filters}
+  \begin{bmatrix} z_1 \\ \vdots \\ z_n \\ v \end{bmatrix} = P_n(s) \begin{bmatrix} w \\ u_1 \\ \vdots \\ u_{n-1} \end{bmatrix}; \quad
+  P_n(s) = \begin{bmatrix}
+    W_1    & -W_1   & \dots  & \dots  & -W_1 \\
+    0      &  W_2   & 0      & \dots  & 0 \\
+    \vdots & \ddots & \ddots & \ddots & \vdots \\
+    \vdots &        & \ddots & \ddots & 0 \\
+    0      & \dots  & \dots  & 0      & W_n \\
+    1      & 0      & \dots  & \dots  & 0
+    \end{bmatrix}
+\end{equation}
+
+If the synthesis if successful, a set of \(n-1\) filters \([H_2(s),\ H_3(s),\ \dots,\ H_n(s)]\) are obtained such that~\eqref{eq:hinf_syn_obj_gen} is verified.
+
+\begin{equation}
+\label{eq:hinf_syn_obj_gen}
+  \left\|\begin{matrix} \left(1 - \left[ H_2(s) + H_3(s) + \dots + H_n(s) \right]\right) W_1(s) \\ H_2(s) W_2(s) \\ \vdots \\ H_n(s) W_n(s) \end{matrix}\right\|_\infty \le 1
+\end{equation}
+
+\(H_1(s)\) is then defined using~\eqref{eq:h1_comp_h2_hn} which is ensuring the complementary property for the set of \(n\) filters~\eqref{eq:hinf_cond_compl_gen}.
+Condition~\eqref{eq:hinf_cond_perf_gen} is satisfied thanks to~\eqref{eq:hinf_syn_obj_gen}.
+
+\begin{equation}
+\label{eq:h1_comp_h2_hn}
+H_1(s) \triangleq 1 - \big[ H_2(s) + H_3(s) + \dots + H_n(s) \big]
+\end{equation}
+
+An example is given to validate the proposed method for the synthesis of a set of three complementary filters.
+The sensors to be merged are a displacement sensor from DC up to \(\SI{1}{Hz}\), a geophone from \(1\) to \(\SI{10}{Hz}\) and an accelerometer above \(\SI{10}{Hz}\).
+Three weighting functions are designed using formula~\eqref{eq:weight_formula} and their inverse magnitude are shown in Fig.~\ref{fig:three_complementary_filters_results} (dashed curves).
+
+Consider the generalized plant \(P_3(s)\) shown in Fig.~\ref{fig:comp_filter_three_hinf_gen_plant} which is also described by~\eqref{eq:generalized_plant_three_filters}.
+
+\begin{equation}
+\label{eq:generalized_plant_three_filters}
+  \begin{bmatrix} z_1 \\ z_2 \\ z_3 \\ v \end{bmatrix} = P_3(s) \begin{bmatrix} w \\ u_1 \\ u_2 \end{bmatrix}; \quad P_3(s) = \begin{bmatrix}W_1(s) & -W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) & 0 \\ 0 & 0 & \phantom{+}W_3(s) \\ 1 & 0 & 0 \end{bmatrix}
+\end{equation}
+
+\begin{figure}[htbp]
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/comp_filter_three_hinf_gen_plant.pdf}
+\caption{\label{fig:comp_filter_three_hinf_gen_plant} Generalized plant.}
+\vfill
+\end{subfigure}
+\hfill
+\begin{subfigure}[t]{0.5\linewidth}
+\centering
+\includegraphics[scale=1]{figs/comp_filter_three_hinf_fb.pdf}
+\caption{\label{fig:comp_filter_three_hinf_fb} Generalized plant with the synthesized filter.}
+\end{subfigure}
+\hfill
+\caption{\label{fig:comp_filter_three_hinf} Architecture for the $\mathcal{H}_\infty$ synthesis of three complementary filters.}
+\centering
+\end{figure}
+
+The standard \(\mathcal{H}_\infty\) synthesis is performed on the generalized plant \(P_3(s)\).
+Two filters \(H_2(s)\) and \(H_3(s)\) are obtained such that the \(\mathcal{H}_\infty\) norm of the closed-loop transfer from \(w\) to \([z_1,\ z_2,\ z_3]\) of the system in Fig.~\ref{fig:comp_filter_three_hinf_fb} is less than one.
+Filter \(H_1(s)\) is defined using~\eqref{eq:h1_compl_h2_h3} thus ensuring the complementary property of the obtained set of filters.
+
+\begin{equation}
+\label{eq:h1_compl_h2_h3}
+H_1(s) \triangleq 1 - \big[ H_2(s) + H_3(s) \big]
+\end{equation}
+
+Figure~\ref{fig:three_complementary_filters_results} displays the three synthesized complementary filters (solid lines) which confirms that the synthesis is successful.\par
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{figs/three_complementary_filters_results.pdf}
+\caption{\label{fig:three_complementary_filters_results}Bode plot of the inverse weighting functions and of the three complementary filters obtained using the \(\mathcal{H}_\infty\) synthesis.}
+\end{figure}
+
+\section{Conclusion}
+\label{sec:conclusion}
+
+A new method for designing complementary filters using the \(\mathcal{H}_\infty\) synthesis has been proposed.
+It allows to shape the magnitude of the filters by the use of weighting functions during the synthesis.
+This is very valuable in practice as the characteristics of the super sensor are linked to the complementary filters' magnitude.
+Therefore typical sensor fusion objectives can be translated into requirements on the magnitudes of the filters.
+Several examples were used to emphasize the simplicity and the effectiveness of the proposed method.
+
+However, the shaping of the complementary filters' magnitude does not allow to directly optimize the super sensor noise and dynamical characteristics.
+Future work will aim at developing a complementary filter synthesis method that minimizes the super sensor noise while ensuring the robustness of the fusion.
+
+\section*{Acknowledgment}
+This research benefited from a FRIA grant from the French Community of Belgium.
+This paper has been assigned the LIGO document number LIGO-P2100328.
+
+\section*{Data Availability}
+Matlab~\cite{matlab20} was used for this study.
+The source code is available under a MIT License and archived in Zenodo~\cite{dehaeze21_new_method_desig_compl_filter_code}.
+
+\bibliographystyle{elsarticle-num}
+\bibliography{ref}
+\end{document}
--- a/journal/figs/comp_filter_three_hinf.tex
+++ b/journal/figs/comp_filter_three_hinf.tex
@@ -1,36 +0,0 @@
-\begin{tikzpicture}
-   \node[block={5.0cm}{3.5cm}, fill=black!20!white, dashed] (P) {};
-   \node[above] at (P.north) {$P(s)$};
-
-   \coordinate[] (inputw)  at ($(P.south west)!0.8!(P.north west) + (-0.7, 0)$);
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--- a/journal/figs/comp_filter_three_hinf_fb.pdf
+++ b/journal/figs/comp_filter_three_hinf_fb.pdf
--- a/journal/figs/comp_filter_three_hinf_fb.png
+++ b/journal/figs/comp_filter_three_hinf_fb.png
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--- a/journal/figs/comp_filter_three_hinf_gen_plant.pdf
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--- a/journal/figs/comp_filters_H2_feature.pdf
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--- a/journal/figs/hinf_comp_H1_H2_syn.pdf
+++ b/journal/figs/hinf_comp_H1_H2_syn.pdf
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--- a/journal/figs/weight_formula.pdf
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--- a/journal/journal.org
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@@ -1,881 +0,0 @@
-#+TITLE: A new method of designing complementary filters for sensor fusion using $\mathcal{H}_\infty$ synthesis
-:DRAWER:
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-
-#+LATEX_HEADER_EXTRA: \journal{Mechanical Systems and Signal Processing}
-
-#+LATEX_HEADER_EXTRA: \author[a1,a2]{Thomas Dehaeze\corref{cor1}}
-#+LATEX_HEADER_EXTRA: \author[a3,a4]{Mohit Verma}
-#+LATEX_HEADER_EXTRA: \author[a2,a4]{Christophe Collette}
-#+LATEX_HEADER_EXTRA: \cortext[cor1]{Corresponding author. Email Address: dehaeze.thomas@gmail.com}
-
-#+LATEX_HEADER_EXTRA: \address[a1]{European Synchrotron Radiation Facility, Grenoble, France}
-#+LATEX_HEADER_EXTRA: \address[a2]{University of Li\`{e}ge, Department of Aerospace and Mechanical Engineering, 4000 Li\`{e}ge, Belgium.}
-#+LATEX_HEADER_EXTRA: \address[a3]{CSIR --- Structural Engineering Research Centre, Taramani, Chennai --- 600113, India.}
-#+LATEX_HEADER_EXTRA: \address[a4]{Universit\'{e} Libre de Bruxelles, Precision Mechatronics Laboratory, BEAMS Department, 1050 Brussels, Belgium.}
-
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-* Build                                                             :noexport:
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-#+BEGIN_SRC emacs-lisp :results none
-(add-to-list 'org-latex-classes
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-               "\\documentclass{elsarticle}"
-               ("\\section{%s}" . "\\section*{%s}")
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-               ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
-               ("\\paragraph{%s}" . "\\paragraph*{%s}")
-               ("\\subparagraph{%s}" . "\\subparagraph*{%s}"))
-             )
-
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-  (loop for comment in (reverse (org-element-map (org-element-parse-buffer)
-                                    'comment 'identity))
-        do
-        (setf (buffer-substring (org-element-property :begin comment)
-                                (org-element-property :end comment))
-              "")))
-
-;; add to export hook
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-
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-* =hypersetup=                                                        :ignore:
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-
-* Abstract and Keywords                                               :ignore:
-#+begin_frontmatter
-#+begin_abstract
-Sensor have limited bandwidth and are accurate only in a certain frequency band.
-In many applications, the signals of different sensor are fused together in order to either enhance the stability or improve the operational bandwidth of the system.
-The sensor signals can be fused using complementary filters.
-The tuning of complementary filters is a complex task and is the subject of this paper.
-The filters needs to meet design specifications while satisfying the complementary property.
-This paper presents a framework to shape the norm of complementary filters using the $\mathcal{H}_\infty$ norm minimization.
-The design specifications are imposed as constraints in the optimization problem by appropriate selection of weighting functions.
-The proposed method is quite general and easily extendable to cases where more than two sensors are fused.
-Finally, the proposed method is applied to the design of complementary filter design for active vibration isolation of the Laser Interferometer Gravitation-wave Observatory (LIGO).
-#+end_abstract
-
-#+begin_keyword
-Sensor fusion \sep{} Optimal filters \sep{} $\mathcal{H}_\infty$ synthesis \sep{} Vibration isolation \sep{} Precision
-#+end_keyword
-#+end_frontmatter
-
-* Introduction
-<<sec:introduction>>
-** New introduction                                                  :ignore:
-*** Introduction to Sensor Fusion                                   :ignore:
-
-# Basic explanations of sensor fusion
-
- cite:bendat57_optim_filter_indep_measur_two roots of sensor fusion
-
-*** Advantages of Sensor Fusion                                     :ignore:
-
-# Sensor Fusion can have many advantages / can be applied for various purposes
-
- Increase the bandwidth: cite:zimmermann92_high_bandw_orien_measur_contr
- Increased robustness: cite:collette15_sensor_fusion_method_high_perfor
- Decrease the noise:
-
-*** Applications                                                    :ignore:
-
-# The applications of sensor fusion are numerous
-
- UAV: cite:pascoal99_navig_system_desig_using_time, cite:jensen13_basic_uas
- Gravitational wave observer: cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system,lucia18_low_frequen_optim_perfor_advan,heijningen18_low,akutsu21_vibrat_isolat_system_beam_split
-
-*** Kalman Filtering or Complementary filters                       :ignore:
-
-# There are mainly two ways to perform sensor fusion: using complementary filters or using Kalman filtering
-
- cite:brown72_integ_navig_system_kalman_filter alternate form of complementary filters => Kalman filtering
- cite:higgins75_compar_compl_kalman_filter Compare Kalman Filtering with sensor fusion using complementary filters
- cite:robert12_introd_random_signal_applied_kalman advantage of complementary filters over Kalman filtering
-
-*** Design Methods of Complementary filters                         :ignore:
-
-# In some cases, complementary filters are implemented in an analog way such as in [...], but most of the time it is implemented numerically which allows much more complex
-
- Analog complementary filters: cite:yong16_high_speed_vertic_posit_stage, cite:moore19_capac_instr_sensor_fusion_high_bandw_nanop
-
-# Multiple design methods have been used for complementary filters
-
- Analytical methods:
-  - first order: cite:corke04_inert_visual_sensin_system_small_auton_helic
-  - second order: cite:baerveldt97_low_cost_low_weigh_attit, cite:stoten01_fusion_kinet_data_using_compos_filter, cite:jensen13_basic_uas
-  - higher order: cite:shaw90_bandw_enhan_posit_measur_using_measur_accel, cite:zimmermann92_high_bandw_orien_measur_contr, cite:collette15_sensor_fusion_method_high_perfor, cite:matichard15_seism_isolat_advan_ligo
- cite:pascoal99_navig_system_desig_using_time use LMI to generate complementary filters (convex optimization techniques), specific for navigation systems
- cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system: FIR + convex optimization
- Similar to feedback system:
-  - cite:plummer06_optim_compl_filter_their_applic_motion_measur use H-Infinity to optimize complementary filters (flatten the super sensor noise spectral density)
-  - cite:jensen13_basic_uas design of complementary filters with classical control theory, PID
-
- 3 complementary filters: cite:becker15_compl_filter_desig_three_frequen_bands
-
-*** Problematics / gap in the research                              :ignore:
-
- Robustness problems: cite:zimmermann92_high_bandw_orien_measur_contr change of phase near the merging frequency
- Trial and error
- Although many design methods of complementary filters have been proposed in the literature, no simple method that allows to shape the norm of the complementary filters is available.
-
-*** Describe the paper itself / the problem which is addressed      :ignore:
-
-Most of the requirements => shape of the complementary filters
-=> propose a way to shape complementary filters.
-
-*** Introduce Each part of the paper                                :ignore:
-
-** Old Introduction                                         :ignore:noexport:
-*** Establish the importance of the research topic                 :ignore:
-# What are Complementary Filters
-A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies.
-These filters are used when two or more sensors are measuring the same physical quantity with different noise characteristics.
-Unreliable frequencies of each sensor are filtered out by the complementary filters and then combined to form a super sensor giving a better estimate of the physical quantity over a wider bandwidth.
-This technique is called sensor fusion and is used in many applications.\par
-
-*** Applications of complementary filtering                        :ignore:
-# Improve bandwidth for UAV
-In cite:zimmermann92_high_bandw_orien_measur_contr,corke04_inert_visual_sensin_system_small_auton_helic, various sensors (accelerometers, gyroscopes, vision sensors, etc.) are merged using complementary filters for the attitude estimation of Unmanned Aerial Vehicles (UAV).
-# Improving the control robustness
-In cite:collette15_sensor_fusion_method_high_perfor, several sensor fusion configurations using different types of sensors are discussed in order to increase the control bandwidth of active vibration isolation systems.
-# Merging of different sensor types
-Furthermore, sensor fusion is used in the isolation systems of the Laser Interferometer Gravitational-Wave Observator (LIGO) to merge inertial sensors with relative sensors
-cite:matichard15_seism_isolat_advan_ligo,hua04_polyp_fir_compl_filter_contr_system. \par
-
-*** Current design methods for complementary filters               :ignore:
-# Why Design of Complementary Filter is important
-As the super sensor noise characteristics largely depend on the complementary filter norms, their proper design is of primary importance for sensor fusion.
-# Discuss the different approach to complementary filter design
-In cite:corke04_inert_visual_sensin_system_small_auton_helic,jensen13_basic_uas, first and second order analytical formulas of complementary filters have been presented.
-# Third Order and Higher orders
-Higher order complementary filters have been used in
-cite:shaw90_bandw_enhan_posit_measur_using_measur_accel,zimmermann92_high_bandw_orien_measur_contr,collette15_sensor_fusion_method_high_perfor.
-# Alternate Formulation
-In cite:jensen13_basic_uas, the sensitivity and complementary sensitivity transfer functions of a feedback architecture have been proposed to be used as complementary filters. The design of such filters can then benefit from the classical control theory developments.
-# LMI / convex Optimization
-Linear Matrix Inequalities (LMIs) are used in cite:pascoal99_navig_system_desig_using_time for the synthesis of complementary filters satisfying some frequency-like performance.
-# FIR Filters
-Finally, a synthesis method of high order Finite Impulse Response (FIR) complementary filters using convex optimization has been developed in cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system. \par
-
-*** Describe a gap in the research                                 :ignore:
-# There is a need for easy synthesis methods for complementary filters
-Although many design methods of complementary filters have been proposed in the literature, no simple method that allows to shape the norm of the complementary filters is available.
-
-*** Describe the paper itself / the problem which is addressed     :ignore:
-# In this paper, we propose a synthesis method for the shaping of complementary filters using the $\mathcal{H}_\infty$ norm.\par
-This paper presents a new design method of complementary filters based on $\mathcal{H}_\infty$ synthesis.
-This design method permits to easily shape the norms of the generated filters.\par
-
-*** Introduce Each part of the paper                               :ignore:
-The section ref:sec:requirements gives a brief overview of sensor fusion using complementary filters and explains how the typical requirements for such fusion can be expressed as upper bounds on the filters norms.
-In section ref:sec:hinf_method, a new design method for the shaping of complementary filters using $\mathcal{H}_\infty$ synthesis is proposed.
-In section ref:sec:application_ligo, the method is used to design complex complementary filters that are used for sensor fusion at the LIGO.
-Our conclusions are drawn in the final section.
-
-** Mohit's Introduction                                            :noexport:
-The sensors used for measuring physical quantity often works well within a limited frequency range called as the bandwidth of the sensor.
-The signals recorded by the sensor beyond its bandwidth are often corrupt with noise and are not reliable.
-Many dynamical systems require measurements over a wide frequency range.
-Very often a variety of sensors are utilized to sense the same quantity.
-These sensors have different operational bandwidth and are reliable only in a particular frequency range.
-The signals from the different sensors are fused together in order to get the reliable measurement of the physical quantity over wider frequency band.
-The combining of signals from various sensor is called sensor fusion cite:hua04_polyp_fir_compl_filter_contr_system.
-The resulting sensor is referred as "super sensor" since it can have better noise characteristics and can operate over a wider frequency band as compared to the individual sensor used for merging cite:shaw90_bandw_enhan_posit_measur_using_measur_accel.
-
-Sensor fusion is most commonly employed in the navigation systems to accurately measure the position of a vehicle.
-The GPS sensors, which are accurate in low frequency band, are merged with the high-frequency accelerometers.
-Zimmermann and Sulzer cite:zimmermann92_high_bandw_orien_measur_contr used sensor fusion to measure the orientation of a robot.
-They merged inclinometer and accelerometers for accurate angular measurements over large frequency band.
-Corke cite:corke04_inert_visual_sensin_system_small_auton_helic merged inertial measurement unit with the stereo vision system for measurement of attitude, height and velocity of an unmanned helicopter.
-Baerveldt and Klang cite:baerveldt97 used an inclinometer and a gyroscope to measure the orientation of the autonomous helicopter.
-The measurement of the 3D orientation using a gyroscope and an accelerometer was demonstrated by Roberts et al. cite:roberts03_low.
-Cao et al. cite:cao20_adapt_compl_filter_based_post used sensor fusion to obtain the lateral and longitudinal velocities of the autonomous vehicle.
-
-Sensor fusion is also used for enhancing the working range of the active isolation system.
-For example, the active vibration isolation system at the Laser Interferometer Gravitational-Wave Observatory (LIGO) cite:matichard15_seism_isolat_advan_ligo utilizes sensor fusion.
-The position sensors, seismometer and geophones are used for measuring the motion of the LIGO platform in different frequency bands cite:hua05_low_ligo.
-Tjepkema et al. cite:tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip used sensor fusion to isolate precision equipment from the ground motion.
-The feedback from the accelerometer was used for active isolation at low frequency while force sensor was used at high frequency.
-Various configurations of sensor fusion for active vibration isolation systems are discussed by Collette and Matichard cite:collette15_sensor_fusion_method_high_perfor.
-Ma and Ghasemi-Nejhad cite:ma04_frequen_weigh_adapt_contr_simul used laser sensor and piezoelectric patches for simultaneous tracking and vibration control in smart structures.
-Recently, Verma et al. cite:verma21_virtual_sensor_fusion_high_precis_contr presented virtual sensor fusion for high precision control where the signals from a physical sensor are fused with a sensor simulated virtually.
-
-Fusing signals from different sensors can typically be done using Kalman filtering cite:odry18_kalman_filter_mobil_robot_attit_estim, ren19_integ_gnss_hub_motion_estim, faria19_sensor_fusion_rotat_motion_recon, liu18_innov_infor_fusion_method_with, abdel15_const_low_cost_gps_filter, biondi17_attit_recov_from_featur_track or complementary filters cite:brown72_integ_navig_system_kalman_filter.
-A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies.
-When two filters are complementary, usually one is a low pass filter while the other is an high pass filter.
-The complementary filters are designed in such a way that their magnitude is close to one in the bandwidth of the sensor they are combined with.
-This enables to measure the physical quantity over larger bandwidth.
-There are two different categories of complementary filters --- frequency domain complementary filters and state space complementary filters.
-Earliest application of the frequency domain complementary filters was seen in Anderson and Fritze cite:anderson53_instr_approac_system_steer_comput.
-A simple RC circuit was used to physically realize the complementary filters.
-Frequency domain complementary filters were also used in cite:shaw90_bandw_enhan_posit_measur_using_measur_accel, zimmermann92_high_bandw_orien_measur_contr, baerveldt97, roberts03_low.
-State space complementary filter finds application in tracking orientation of the flexible links in a robot cite:bachmann03_desig_marg_dof,salcudean91_global_conver_angul_veloc_obser,mahony08_nonlin_compl_filter_special_orthog_group and are particularly useful for multi-input multi-output systems.
-Pascoal et al. cite:pascoal00_navig_system_desig_using_time presented complementary filters which can adapt with time for navigation system capable of estimating position and velocity using GPS and SONAR sensors.
-
-The noise characteristics of the super sensor are governed by the norms of the complementary filters.
-Therefore, the proper design of the complementary filters for sensor fusion is of immense importance.
-The design of complementary filters is a complex task as they need to tuned as per the specification of the sensor.
-In many applications, analytical formulas of first and second order complementary filters are used cite:corke04_inert_visual_sensin_system_small_auton_helic,jensen13_basic_uas.
-However, these low order complementary filters are not optimal, and high order complementary filters can lead to better fusion cite:jensen13_basic_uas,shaw90_bandw_enhan_posit_measur_using_measur_accel.
-
-Several design techniques have been proposed to design higher order complementary filters.
-Pascoal cite:pascoal00_navig_system_desig_using_time used linear matrix inequalities (LMIs) cite:boyd94_linear for the design of time varying complementary filters.
-LMIs were also used by Hua et al. cite:hua04_polyp_fir_compl_filter_contr_system to design finite impulse response (FIR) filters for the active vibration isolation system at LIGO.
-Plummer cite:plummer06_optim_compl_filter_their_applic_motion_measur proposed an optimal design method using the $\mathcal{H}_{\infty}$ synthesis and weighting functions representing the measurement noise of the sensors.
-
-Although various methods have been presented in the literature for the design of complementary filters, there is a lack of general and simple framework that allows to shape the norm of complementary filters.
-Such a method would prove to be very useful as the noise of the "supper sensor" and its dynamical characteristics depend on the norm of the filters.
-This paper presents such a framework based on the $\mathcal{H}_\infty$ norm minimization.
-The proposed method is quite general and can be easily extended to a case where more than two complementary filters needs to be designed.
-The organization of this paper is as follows.
-Section 2 presents the design requirements of ideal complementary filters.
-It also demonstrates how the noise and robustness characteristics of the "super sensor" can be transformed into upper bounds on the norm of the complementary filters.
-The framework for the design of complementary filters is detailed in Section 3.
-This is followed by the application of the design method to complementary filter design for the active vibration isolation at LIGO in Section 4.
-Finally, concluding remarks are presented in Section 5.
-
-* Sensor Fusion and Complementary Filters Requirements
-<<sec:requirements>>
-** Introduction                                                      :ignore:
-
-Complementary filters provides a framework for fusing signals from different sensors.
-As the effectiveness of the fusion depends on the proper design of the complementary filters, they are expected to fulfill certain requirements.
-These requirements are discussed in this section.
-
-** Sensor Fusion Architecture
-<<sec:sensor_fusion>>
-
-A general sensor fusion architecture using complementary filters is shown in Figure ref:fig:sensor_fusion_overview where several sensors (here two) are measuring the same physical quantity $x$.
-The two sensors output signals are estimates $\hat{x}_1$ and $\hat{x}_2$ of $x$.
-Each of these estimates are then filtered out by complementary filters and combined to form a new estimate $\hat{x}$.
-
-The resulting sensor, termed as "super sensor", can have larger bandwidth and better noise characteristics in comparison to the individual sensor.
-This means that the super sensor provides an estimate $\hat{x}$ of $x$ which can be more accurate over a larger frequency band than the outputs of the individual sensors.
-
-#+name: fig:sensor_fusion_overview
-#+caption: Schematic of a sensor fusion architecture
-[[file:figs/sensor_fusion_overview.pdf]]
-
-The complementary property of filters $H_1(s)$ and $H_2(s)$ implies that the summation of their transfer functions is equal to unity.
-That is, unity magnitude and zero phase at all frequencies.
-Therefore, a pair of strict complementary filter needs to satisfy the following condition:
-#+name: eq:comp_filter
-\begin{equation}
-  H_1(s) + H_2(s) = 1
-\end{equation}
-
-It will soon become clear why the complementary property is important.
-
-** Sensor Models and Sensor Normalization
-<<sec:sensor_models>>
-
-In order to study such sensor fusion architecture, a model of the sensors is required.
-
-Such model is shown in Figure ref:fig:sensor_model and consists of a linear time invariant (LTI) system $G_i(s)$ representing the dynamics of the sensor and an additive noise input $n_i$ representing its noise.
-The model input $x$ is the measured physical quantity and its output $\tilde{x}_i$ is the "raw" output of the sensor.
-
-Before filtering the sensor outputs $\tilde{x}_i$ by the complementary filters, the sensors are usually normalized to simplify the fusion.
-This normalization consists of first obtaining an estimate $\hat{G}_i(s)$ of the sensor dynamics $G_i(s)$.
-It is supposed that the estimate of the sensor dynamics $\hat{G}_i(s)$ can be inverted and that its inverse $\hat{G}_i^{-1}(s)$ is proper and stable.
-The raw output of the sensor $\tilde{x}_i$ is then passed through $\hat{G}_i^{-1}(s)$ as shown in Figure ref:fig:sensor_model_calibrated.
-This way, the units of the estimates $\hat{x}_i$ are equal to the units of the physical quantity $x$.
-The sensor dynamics estimate $\hat{G}_1(s)$ can be a simple gain or more complex transfer functions.
-
-#+begin_export latex
-\begin{figure}[htbp]
-\begin{subfigure}[b]{0.49\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model.pdf}
-\caption{\label{fig:sensor_model} Basic sensor model consisting of a noise input $n_i$ and a dynamics $G_i(s)$}
-\end{subfigure}
-\hfill
-\begin{subfigure}[b]{0.49\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model_calibrated.pdf}
-\caption{\label{fig:sensor_model_calibrated} Calibrated sensors using the inverse of an estimate $\hat{G}_1(s)$ of the sensor dynamics}
-\end{subfigure}
-\caption{\label{fig:sensor_models}Sensor models with an without normalization}
-\centering
-\end{figure}
-#+end_export
-
-Two calibrated sensors and then combined to form a super sensor as shown in Figure ref:fig:fusion_super_sensor.
-
-The two sensors are measuring the same physical quantity $x$ with dynamics $G_1(s)$ and $G_2(s)$, and with /uncorrelated/ noises $n_1$ and $n_2$.
-The normalized signals from both calibrated sensors are fed into two complementary filters $H_1(s)$ and $H_2(s)$ and then combined to yield an estimate $\hat{x}$ of $x$ as shown in Fig. ref:fig:fusion_super_sensor.
-
-The super sensor output is therefore equal to:
-#+name: eq:comp_filter_estimate
-\begin{equation}
-  \hat{x} = \Big( H_1(s) \hat{G}_1^{-1}(s) G_1(s) + H_2(s) \hat{G}_2^{-1}(s) G_2(s) \Big) x + H_1(s) \hat{G}_1^{-1}(s) G_1(s) n_1 + H_2(s) \hat{G}_2^{-1}(s) G_2(s) n_2
-\end{equation}
-
-#+name: fig:fusion_super_sensor
-#+caption: Sensor fusion architecture
-#+attr_latex: :scale 1
-[[file:figs/fusion_super_sensor.pdf]]
-
-** Noise Sensor Filtering
-<<sec:noise_filtering>>
-
-In this section, it is supposed that all the sensors are perfectly calibrated, such that:
-#+name: eq:perfect_dynamics
-\begin{equation}
-  \frac{\hat{x}_i}{x} = \hat{G}_i(s) G_i(s) = 1
-\end{equation}
-
-The effect of a non-perfect normalization will be discussed in the next section.
-
-The super sensor output $\hat{x}$ is then:
-#+name: eq:estimate_perfect_dyn
-\begin{equation}
-  \hat{x} = x + H_1(s) n_1 + H_2(s) n_2
-\end{equation}
-
-From eqref:eq:estimate_perfect_dyn, the complementary filters $H_1(s)$ and $H_2(s)$ are shown to only operate on the sensor's noises.
-Thus, this sensor fusion architecture permits to filter the noise of both sensors without introducing any distortion in the physical quantity to be measured.
-
-The estimation error $\delta x$, defined as the difference between the sensor output $\hat{x}$ and the measured quantity $x$, is computed for the super sensor eqref:eq:estimate_error.
-#+name: eq:estimate_error
-\begin{equation}
-  \delta x \triangleq \hat{x} - x = H_1(s) n_1 + H_2(s) n_2
-\end{equation}
-
-As shown in eqref:eq:noise_filtering_psd, the Power Spectral Density (PSD) of the estimation error $\Phi_{\delta x}$ depends both on the norm of the two complementary filters and on the PSD of the noise sources $\Phi_{n_1}$ and $\Phi_{n_2}$.
-#+name: eq:noise_filtering_psd
-\begin{equation}
-  \Phi_{\delta x}(\omega) = \left|H_1(j\omega)\right|^2 \Phi_{n_1}(\omega) + \left|H_2(j\omega)\right|^2 \Phi_{n_2}(\omega)
-\end{equation}
-
-If the two sensors have identical noise characteristics ($\Phi_{n_1}(\omega) = \Phi_{n_2}(\omega)$), a simple averaging ($H_1(s) = H_2(s) = 0.5$) is what would minimize the super sensor noise.
-This the simplest form of sensor fusion with complementary filters.
-
-However, the two sensors have usually high noise levels over distinct frequency regions.
-In such case, to lower the noise of the super sensor, the value of the norm $|H_1|$ has to be lowered when $\Phi_{n_1}$ is larger than $\Phi_{n_2}$ and that of $|H_2|$ lowered when $\Phi_{n_2}$ is larger than $\Phi_{n_1}$.
-Therefore, by properly shaping the norm of the complementary filters, it is possible to minimize the noise of the super sensor noise.
-
-** Sensor Fusion Robustness
-<<sec:fusion_robustness>>
-
-In practical systems the sensor normalization is not perfect and condition eqref:eq:perfect_dynamics is not verified.
-
-In order to study such imperfection, a multiplicative input uncertainty is added to the sensor dynamics (Figure ref:fig:sensor_model_uncertainty), where the nominal model is taken as the estimated model for the normalization $\hat{G}_i(s)$, $\Delta_i$ is any stable transfer function satisfying $|\Delta_i(j\omega)| \le 1,\ \forall\omega$, and $w_i(s)$ is a weight representing the magnitude of the uncertainty.
-
-The weight $w_i(s)$ is chosen such that the real sensor dynamics is always contained in the uncertain region represented by a circle centered on $1$ and with a radius equal to $|w_i(j\omega)|$.
-
-As the nominal sensor dynamics is taken as the normalized filter, the normalized sensor can be further simplified as shown in Figure ref:fig:sensor_model_uncertainty_simplified.
-
-#+begin_export latex
-\begin{figure}[htbp]
-\begin{subfigure}[b]{0.59\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model_uncertainty.pdf}
-\caption{\label{fig:sensor_model_uncertainty} Sensor with multiplicative input uncertainty}
-\end{subfigure}
-\hfill
-\begin{subfigure}[b]{0.39\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model_uncertainty_simplified.pdf}
-\caption{\label{fig:sensor_model_uncertainty_simplified} Simplified sensor model}
-\end{subfigure}
-\hfill
-\caption{\label{fig:sensor_models_uncertainty}Sensor models with dynamical uncertainty}
-\centering
-\end{figure}
-#+end_export
-
-A sensor fusion architecture with two sensors with dynamical uncertainty is shown in Figure ref:fig:sensor_fusion_dynamic_uncertainty.
-
-#+name: fig:sensor_fusion_dynamic_uncertainty
-#+caption: Sensor fusion architecture with sensor dynamics uncertainty
-[[file:figs/sensor_fusion_dynamic_uncertainty.pdf]]
-
-The super sensor dynamics eqref:eq:super_sensor_dyn_uncertainty is no longer equal to $1$ and now depends on the sensor dynamics uncertainty weights $w_i(s)$ as well as on the complementary filters $H_i(s)$.
-#+name: eq:super_sensor_dyn_uncertainty
-\begin{equation}
-  \frac{\hat{x}}{x} = 1 + w_1(s) H_1(s) \Delta_1(s) + w_2(s) H_2(s) \Delta_2(s)
-\end{equation}
-
-The dynamical uncertainty of the super sensor can be graphically represented in the complex plane by a circle centered on $1$ with a radius equal to $|w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)|$ as shown in Figure ref:fig:uncertainty_set_super_sensor.
-
-#+name: fig:uncertainty_set_super_sensor
-#+caption: Uncertainty region of the super sensor dynamics in the complex plane (solid circle). The contribution of both sensors 1 and 2 to the uncertainty are represented respectively by a blue circle and a red circle. The frequency dependency $\omega$ is here omitted.
-[[file:figs/uncertainty_set_super_sensor.pdf]]
-
-The super sensor dynamical uncertainty (i.e. the robustness of the fusion) clearly depends on the complementary filters norms.
-For instance, the phase uncertainty $\Delta\phi(\omega)$ added by the super sensor dynamics at frequency $\omega$ can be found by drawing a tangent from the origin to the uncertainty circle of super sensor (Figure ref:fig:uncertainty_set_super_sensor) and is bounded by eqref:eq:max_phase_uncertainty.
-
-#+name: eq:max_phase_uncertainty
-\begin{equation}
-    \Delta\phi(\omega) < \arcsin\big( |w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)| \big)
-\end{equation}
-
-As it is generally desired to limit the maximum phase added by the super sensor, $H_1(s)$ and $H_2(s)$ should be designed such that $\Delta \phi$ is bounded to acceptable values.
-Typically, the norm of the complementary filter $|H_i(j\omega)|$ should be made small when $|w_i(j\omega)|$ is large, i.e., at frequencies where the sensor dynamics is uncertain.
-
-* Complementary Filters Shaping
-<<sec:hinf_method>>
-** Introduction                                                     :ignore:
-As shown in Section ref:sec:requirements, the noise and robustness of the "super sensor" are determined by the complementary filters norms.
-Therefore, a complementary filters synthesis method that allows to shape their norms would be of great use.
-
-In this section, such synthesis is proposed by expressing this problem as a $\mathcal{H}_\infty$ norm optimization.
-
-** Synthesis Objective
-<<sec:synthesis_objective>>
-
-The synthesis objective is to shape the norm of two filters $H_1(s)$ and $H_2(s)$ while ensuring their complementary property eqref:eq:comp_filter.
-This is equivalent as to finding proper and stable transfer functions $H_1(s)$ and $H_2(s)$ such that conditions eqref:eq:comp_filter_problem_form are satisfied.
-
-#+name: eq:comp_filter_problem_form
-\begin{subequations}
-  \begin{align}
-  & H_1(s) + H_2(s) = 1 \label{eq:hinf_cond_complementarity} \\
-  & |H_1(j\omega)| \le \frac{1}{|W_1(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h1} \\
-  & |H_2(j\omega)| \le \frac{1}{|W_2(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h2}
-  \end{align}
-\end{subequations}
-where $W_1(s)$ and $W_2(s)$ are two weighting transfer functions that are chosen to specify the maximum wanted norms of the complementary filters during the synthesis.
-
-** Shaping of Complementary Filters using $\mathcal{H}_\infty$ synthesis
-<<sec:hinf_synthesis>>
-
-In this section, it is shown that the synthesis objective can be easily expressed as a standard $\mathcal{H}_\infty$ optimal control problem and therefore solved using convenient tools readily available.
-
-Consider the generalized plant $P(s)$ shown in Figure ref:fig:h_infinity_robust_fusion and mathematically described by eqref:eq:generalized_plant.
-
-#+name: eq:generalized_plant
-\begin{equation}
-  \begin{bmatrix} z_1 \\ z_2 \\ v \end{bmatrix} = P(s) \begin{bmatrix} w\\u \end{bmatrix}; \quad P(s) = \begin{bmatrix}W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) \\  1 & 0 \end{bmatrix}
-\end{equation}
-
-#+name: fig:h_infinity_robust_fusion
-#+caption: Generalized plant used for $\mathcal{H}_\infty$ synthesis of complementary filters
-#+attr_latex: :scale 1
-[[file:figs/h_infinity_robust_fusion.pdf]]
-
-Applying the standard $\mathcal{H}_\infty$ synthesis on the generalized plant $P(s)$ is then equivalent as finding a stable filter $H_2(s)$ which based on $v$, generates a signal $u$ such that the $\mathcal{H}_\infty$ norm from $w$ to $[z_1, \ z_2]$ is less than one eqref:eq:hinf_syn_obj.
-#+name: eq:hinf_syn_obj
-\begin{equation}
-  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
-\end{equation}
-
-By then defining $H_1(s)$ to be the complementary of $H_2(s)$ eqref:eq:definition_H1, the $\mathcal{H}_\infty$ synthesis objective becomes equivalent to eqref:eq:hinf_problem which ensure that eqref:eq:hinf_cond_h1 and eqref:eq:hinf_cond_h2 are satisfied.
-
-#+name: eq:definition_H1
-\begin{equation}
-  H_1(s) \triangleq 1 - H_2(s)
-\end{equation}
-
-#+name: eq:hinf_problem
-\begin{equation}
-  \left\|\begin{matrix} H_1(s) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
-\end{equation}
-
-Therefore, applying the $\mathcal{H}_\infty$ synthesis on the standard plant $P(s)$ eqref:eq:generalized_plant will generate two filters $H_2(s)$ and $H_1(s) \triangleq 1 - H_2(s)$ that are complementary eqref:eq:comp_filter_problem_form and such that there norms are bellow specified bounds [[eqref:eq:hinf_cond_h1]],eqref:eq:hinf_cond_h2.
-
-The above optimization problem can be efficiently solved in Matlab cite:matlab20 using the Robust Control Toolbox.
-
-** Weighting Functions Design
-<<sec:hinf_weighting_func>>
-
-Weighting functions are used during the synthesis to specify what is the maximum allowed norms of the complementary filters.
-The proper design of these weighting functions is of primary importance for the success of the presented complementary filters $\mathcal{H}_\infty$ synthesis.
-
-First, only proper and stable transfer functions should be used.
-Second, the order of the weighting functions should stay reasonably small in order to reduce the computational costs associated with the solving of the optimization problem and for the physical implementation of the filters (the order of the synthesized filters being equal to the sum of the weighting functions order).
-Third, one should not forget the fundamental limitations imposed by the complementary property eqref:eq:comp_filter.
-This implies for instance that $|H_1(j\omega)|$ and $|H_2(j\omega)|$ cannot be made small at the same frequency.
-
-
-When designing complementary filters, it is usually desired to specify its slope, its crossover frequency and its maximum gain at low and high frequency.
-To help with the design of the weighting functions such that the above specification can be easily expressed, the formula eqref:eq:weight_formula is proposed.
-
-#+name: eq:weight_formula
-\begin{equation}
-  W(s) = \left( \frac{
-           \hfill{} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{G_0}{G_c}\right)^{\frac{1}{n}}
-         }{
-           \left(\frac{1}{G_\infty}\right)^{\frac{1}{n}} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{1}{G_c}\right)^{\frac{1}{n}}
-         }\right)^n
-\end{equation}
-
-The parameters in formula eqref:eq:weight_formula are:
- $G_0 = lim_{\omega \to 0} |W(j\omega)|$: the low frequency gain
- $G_\infty = lim_{\omega \to \infty} |W(j\omega)|$: the high frequency gain
- $G_c = |W(j\omega_c)|$: the gain at $\omega_c$
- $n$: the slope between high and low frequency. It is also the order of the weighting function.
-
-The parameters $G_0$, $G_c$ and $G_\infty$ should either satisfy condition eqref:eq:cond_formula_1 or eqref:eq:cond_formula_2.
-#+name: eq:condition_params_formula
-\begin{subequations}
-  \begin{align}
-    G_0 < 1 < G_\infty \text{ and } G_0 < G_c < G_\infty \label{eq:cond_formula_1}\\
-    G_\infty < 1 < G_0 \text{ and } G_\infty < G_c < G_0 \label{eq:cond_formula_2}
-  \end{align}
-\end{subequations}
-
-The typical shape of a weighting function generated using eqref:eq:weight_formula is shown in Figure ref:fig:weight_formula.
-
-#+name: fig:weight_formula
-#+caption: Magnitude of a weighting function generated using the proposed formula eqref:eq:weight_formula, $G_0 = 1e^{-3}$, $G_\infty = 10$, $\omega_c = \SI{10}{Hz}$, $G_c = 2$, $n = 3$
-#+attr_latex: :scale 1
-[[file:figs/weight_formula.pdf]]
-
-** Validation of the proposed synthesis method
-<<sec:hinf_example>>
-
-The proposed methodology for the design of complementary filters is now applied on a simple example where two complementary filters $H_1(s)$ and $H_2(s)$ have to be designed such that:
- the merging frequency is around $\SI{10}{Hz}$
- the slope of $|H_1(j\omega)|$ is $-2$ above $\SI{10}{Hz}$
- the slope of $|H_2(j\omega)|$ is $+3$ below $\SI{10}{Hz}$
- the maximum gain of both filters is $10^{-3}$ away from the merging frequency
-
-The first step is to design weighting functions that translate the above requirements.
-They are here designed using eqref:eq:weight_formula with parameters summarized in table ref:tab:weights_params.
-The magnitudes of the weighting functions are shown by dashed lines in Figure ref:fig:hinf_filters_results.
-
-#+name: tab:weights_params
-#+caption: Parameters used for weighting functions $W_1(s)$ and $W_2(s)$ using eqref:eq:weight_formula
-#+ATTR_LATEX: :environment tabularx :width 0.29\linewidth :align ccc
-#+ATTR_LATEX: :center t :booktabs t :float t
-| Parameters | $W_1(s)$      | $W_2(s)$      |
-|------------+---------------+---------------|
-| $G_0$      | $0.1$         | $1000$        |
-| $G_\infty$ | $1000$        | $0.1$         |
-| $\omega_c$ | $2\pi\cdot10$ | $2\pi\cdot10$ |
-| $G_c$      | $0.45$        | $0.45$        |
-| $n$        | $2$           | $3$           |
-
-The $\mathcal{H}_\infty$ synthesis is applied on the generalized plant of Figure ref:fig:h_infinity_robust_fusion using the Matlab =hinfsyn= command.
-The synthesized filter $H_2(s)$ is such that $\mathcal{H}_\infty$ norm between $w$ and $[z_1,\ z_2]^T$ is minimized and here found close to one eqref:eq:hinf_synthesis_result.
-
-#+name: eq:hinf_synthesis_result
-\begin{equation}
-  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \approx 1
-\end{equation}
-
-The bode plots of the obtained complementary filters are shown by solid lines in Figure ref:fig:hinf_filters_results and their transfer functions in the Laplace domain are given in eqref:eq:hinf_synthesis_result_tf.
-
-#+name: eq:hinf_synthesis_result_tf
-\begin{subequations}
-  \begin{align}
-    H_2(s) &= \frac{(s+6.6e^4) (s+160) (s+4)^3}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)} \\
-    H_1(s) &\triangleq H_2(s) - 1 = \frac{10^{-8} (s+6.6e^9) (s+3450)^2 (s^2 + 49s + 895)}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)}
-  \end{align}
-\end{subequations}
-
-The obtained transfer functions are of order $5$ as expected (sum of the weighting functions orders), and their magnitudes are bellow the maximum specified ones as ensured by eqref:eq:hinf_synthesis_result.
-
-#+name: fig:hinf_filters_results
-#+caption: Frequency response of the weighting functions and complementary filters obtained using $\mathcal{H}_\infty$ synthesis
-[[file:figs/hinf_filters_results.pdf]]
-
-This simple example illustrates the fact that the proposed methodology for complementary filters shaping is quite easy to use and effective.
-A more complex real life example is taken up in the next section.
-
-* Application: Design of Complementary Filters used in the Active Vibration Isolation System at the LIGO
-<<sec:application_ligo>>
-** Introduction                                                     :ignore:
-
-Sensor fusion using complementary filters are widely used in active vibration isolation systems in gravitational wave detectors such at the LIGO cite:matichard15_seism_isolat_advan_ligo,hua05_low_ligo, the VIRGO cite:lucia18_low_frequen_optim_perfor_advan,heijningen18_low and the KAGRA cite:akutsu21_vibrat_isolat_system_beam_split.
-
-In the first isolation stage at the LIGO, two sets of complementary filters are used and included in a feedback loop cite:hua04_low_ligo.
-A set of complementary filters ($L_2,H_2$) is first used to fuse a seismometer and a geophone.
-Then, another set of complementary filters ($L_1,H_1$) is used to merge the output of the first "inertial super sensor" with a position sensor.
-A simplified block diagram of the sensor fusion architecture is shown in Figure ref:fig:ligo_super_sensor_architecture.
-
-#+name: fig:ligo_super_sensor_architecture
-#+caption: Simplified block diagram of the sensor blending strategy for the first stage at the LIGO cite:hua04_low_ligo
-#+attr_latex: :scale 1
-[[file:figs/ligo_super_sensor_architecture.pdf]]
-
-The fusion of the position sensor at low frequency with the "inertial super sensor" at high frequency using the complementary filters ($L_1,H_1$) is done for several reasons, first of which is to give the super sensor a DC sensibility and therefore allow the feedback loop to have authority at zero frequency.
-The requirements on those filters are very tight and thus their design is complex and should be expressed as an optimization problem.
-
-The approach used in cite:hua05_low_ligo is to use FIR complementary filters and to write the synthesis as a convex optimization problem.
-After synthesis, the obtained FIR filters were found to be compliant with the requirements.
-However they are of very high order so their implementation is quite complex.
-In this section, the effectiveness of the proposed complementary filter synthesis strategy is demonstrated on the same set of requirements.
-
-# Example where clearly manual tuning of the complementary filters is not an option
-
-** Complementary Filters Specifications
-<<sec:ligo_specifications>>
-The specifications for the set of complementary filters ($L_1,H_1$) used at the LIGO are summarized below (for further details, refer to cite:hua04_polyp_fir_compl_filter_contr_system):
- From $0$ to $\SI{0.008}{Hz}$, the magnitude $|L_1(j\omega)|$ should be less or equal to $8 \times 10^{-4}$
- Between $\SI{0.008}{Hz}$ to $\SI{0.04}{Hz}$, the filter $L_1(s)$ should attenuate the input signal proportional to frequency cubed
- Between $\SI{0.04}{Hz}$ to $\SI{0.1}{Hz}$, the magnitude $|L_1(j\omega)|$ should be less than $3$
- Above $\SI{0.1}{Hz}$, the magnitude $|H_1(j\omega)|$ should be less than $0.045$
-
-These specifications are therefore upper bounds on the complementary filters' magnitudes.
-They are physically represented in Figure ref:fig:fir_filter_ligo as well as the obtained magnitude of the FIR filters in cite:hua05_low_ligo.
-
-#+name: fig:fir_filter_ligo
-#+caption: Specifications and Bode plot of the obtained FIR filters in cite:hua05_low_ligo
-#+attr_latex: :scale 1
-[[file:figs/fir_filter_ligo.pdf]]
-
-** Weighting Functions Design
-<<sec:ligo_weights>>
-The weighting functions should be designed such that their inverse magnitude is as close as possible to the specifications in order to not over-constrain the synthesis problem.
-However, the order of each weight should stay reasonably small in order to reduce the computational costs of the optimization problem as well as for the physical implementation of the filters.
-
-A Type I Chebyshev filter of order $20$ is used as the weighting transfer function $w_L(s)$ corresponding to the low pass filter.
-For the one corresponding to the high pass filter $w_H(s)$, a $7^{\text{th}}$ order transfer function is designed.
-The magnitudes of the weighting functions are shown in Fig. ref:fig:ligo_weights.
-
-#+name: fig:ligo_weights
-#+caption: Specifications and weighting functions magnitudes
-#+attr_latex: :scale 1
-[[file:figs/ligo_weights.pdf]]
-
-** $\mathcal{H}_\infty$ Synthesis
-<<sec:ligo_results>>
-$\mathcal{H}_\infty$ synthesis is performed using the architecture shown in Fig. ref:eq:generalized_plant.
-The complementary filters obtained are of order $27$.
-In Fig. ref:fig:comp_fir_ligo_hinf, their bode plot is compared with the FIR filters of order 512 obtained in cite:hua05_low_ligo.
-They are found to be very close to each other and this shows the effectiveness of the proposed synthesis method.
-
-#+name: fig:comp_fir_ligo_hinf
-#+caption: Comparison of the FIR filters (solid) designed in cite:hua05_low_ligo with the filters obtained with $\mathcal{H}_\infty$ synthesis (dashed)
-#+attr_latex: :scale 1
-[[file:figs/comp_fir_ligo_hinf.pdf]]
-
-* Discussion
-<<sec:discussion>>
-** Introduction                                                      :ignore:
-
-** "Closed-Loop" complementary filters
-<<sec:closed_loop_complementary_filters>>
-*** Introduction to using feedback architecture for CF              :ignore:
-It is possible to use the fundamental properties of a feedback architecture to generate complementary filters.
-
-It has been proposed by:
- cite:plummer06_optim_compl_filter_their_applic_motion_measur use H-Infinity to optimize complementary filters (flatten the super sensor noise spectral density)
- cite:jensen13_basic_uas design of complementary filters with classical control theory, PID
- Maybe also cite cite:mahony05_compl_filter_desig_special_orthog
-
-Consider the feedback architecture of Figure ref:fig:feedback_sensor_fusion, with two inputs $\hat{x}_1$ and $\hat{x}_2$, and one output $\hat{x}$.
-
-#+name: fig:feedback_sensor_fusion
-#+caption: "Closed-Loop" complementary filters
-#+attr_latex: :scale 1
-[[file:figs/feedback_sensor_fusion.pdf]]
-
-The output $\hat{x}$ is described by eqref:eq:closed_loop_complementary_filters.
-
-#+name: eq:closed_loop_complementary_filters
-\begin{equation}
-\hat{x} = \underbrace{\frac{1}{1 + L(s)}}_{S(s)} \hat{x}_1 + \underbrace{\frac{L(s)}{1 + L(s)}}_{T(s)} \hat{x}_2
-\end{equation}
-
-with the famous relationship
-\begin{equation}
-T(s) + S(s) = 1
-\end{equation}
-
-Provided that the closed-loop system is stable, this indeed forms two complementary filters.
-
-*** Sensor Fusion with "closed-loop" complementary filters          :ignore:
-Therefore, two filters can be merged as shown in Figure ref:fig:feedback_sensor_fusion_arch.
-
-#+name: fig:feedback_sensor_fusion_arch
-#+caption: Classical feedback architecture for sensor fusion
-#+attr_latex: :scale 1
-[[file:figs/feedback_sensor_fusion_arch.pdf]]
-
-One of the main advantage of this configuration is that standard tools of the linear control theory can be applied.
-
-*** Mixed Sensitivity Synthesis                                     :ignore:
-If one want to shape both the transfer functions $\frac{\hat{x}}{\hat{x}_1}(s) = S(s)$ and $\frac{\hat{x}}{\hat{x}_2}(s) = T(s)$, this corresponds to the $\mathcal{H}_\infty$ mixed-sensitivity synthesis.
-
-The $\mathcal{H}_\infty$ mixed-sensitivity synthesis can be perform by applying the $\mathcal{H}_\infty$ synthesis to the generalized plant $P_L(s)$ shown in Figure ref:fig:feedback_synthesis_architecture_generalized_plant and described by eqref:eq:generalized_plant_mixed_sensitivity where $W_1(s)$ and $W_2(s)$ are weighting functions used to respectively shape $S(s)$ and $T(s)$.
-
-#+name: eq:generalized_plant_mixed_sensitivity
-\begin{equation}
-  \begin{bmatrix} z \\ v \end{bmatrix} = P_L(s) \begin{bmatrix} w_1 \\ w_2 \\ u \end{bmatrix}; \quad P_L(s) = \begin{bmatrix}
-    \phantom{+}W_1(s) & 0      & \phantom{+}1 \\
-              -W_1(s) & W_2(s) &           -1
-  \end{bmatrix}
-\end{equation}
-
-This is equivalent as to find a filter $L(s)$ such that eqref:eq:comp_filters_feedback_obj is verified.
-
-#+name: eq:comp_filters_feedback_obj
-\begin{equation}
-  \left\|\begin{matrix} \frac{1}{1 + L(s)} W_1(s) \\ \frac{L(s)}{1 + L(s)} W_2(s) \end{matrix}\right\|_\infty \le 1
-\end{equation}
-
-The sensor fusion can be implemented as shown in Figure ref:fig:feedback_sensor_fusion_arch using the feedback architecture or more classically as shown in Figure ref:fig:sensor_fusion_overview using eqref:eq:comp_filters_feedback.
-
-#+name: eq:comp_filters_feedback
-\begin{equation}
-H_1(s) = \frac{1}{1 + L(s)}; \quad H_2(s) = \frac{L(s)}{1 + L(s)}
-\end{equation}
-
-The two being equivalent considering only the inputs/outputs relationships.
-
-#+name: fig:feedback_synthesis_architecture_generalized_plant
-#+caption: Generalized plant for the $\mathcal{H}_\infty$ mixed-sensitivity synthesis
-#+attr_latex: :scale 1
-[[file:figs/feedback_synthesis_architecture_generalized_plant.pdf]]
-
-*** Example and equivalence with our synthesis method               :ignore:
-
-Example: same weights as in ref:tab:weights_params.
-
-Therefore, complementary filter design is very similar to mixed-sensitivity synthesis.
-
-They are actually equivalent by taking
-\begin{equation}
-L = H_H^{-1} - 1
-\end{equation}
-(provided $H_H$ is invertible, therefore bi-proper)
-
-** Imposing zero at origin / roll-off
-<<sec:add_features_in_filters>>
-
-3 methods:
-
-Link to literature about doing that with mixed sensitivity
-
-** Synthesis of Three Complementary Filters
-<<sec:hinf_three_comp_filters>>
-
-*** Why it is used sometimes                                        :ignore:
-Some applications may require to merge more than two sensors.
-For instance at the LIGO, three sensors (an LVDT, a seismometer and a geophone) are merged to form a super sensor (Figure ref:fig:ligo_super_sensor_architecture). \par
-
-*** Sequential vs Parallel                                          :ignore:
-When merging $n>2$ sensors using complementary filters, two architectures can be used as shown in Figure ref:fig:sensor_fusion_three.
-
-The fusion can either be done in a "sequential" way where $n-1$ sets of two complementary filters are used (Figure ref:fig:sensor_fusion_three_sequential), or in a "parallel" way where one set of $n$ complementary filters is used (Figure ref:fig:sensor_fusion_three_parallel).
-
-In the first case, typical sensor fusion synthesis techniques can be used.
-However, when a parallel architecture is used, a new synthesis method for a set of more than two complementary filters is required.
-Such synthesis method is presented in this section. \par
-
-*************** TODO Say possible advantages of parallel architecture
-*************** END
-
-#+begin_export latex
-\begin{figure}[htbp]
-\begin{subfigure}[b]{0.59\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_fusion_three_sequential.pdf}
-\caption{\label{fig:sensor_fusion_three_sequential}Sequential fusion}
-\end{subfigure}
-\hfill
-\begin{subfigure}[b]{0.39\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_fusion_three_parallel.pdf}
-\caption{\label{fig:sensor_fusion_three_parallel}Parallel fusion}
-\end{subfigure}
-\caption{\label{fig:sensor_fusion_three}Sensor fusion architecture with more than two sensors}
-\centering
-\end{figure}
-#+end_export
-
-*** Mathematical Problem                                            :ignore:
-The synthesis objective is to compute a set of $n$ stable transfer functions $[H_1(s),\ H_2(s),\ \dots,\ H_n(s)]$ such that eqref:eq:hinf_problem_gen is satisfied.
-#+name: eq:hinf_problem_gen
-\begin{subequations}
-  \begin{align}
-  & \sum_{i=0}^n H_i(s) = 1 \label{eq:hinf_cond_compl_gen} \\
-  & \left| H_i(j\omega) \right| < \frac{1}{\left| W_i(j\omega) \right|}, \quad \forall \omega,\ i = 1 \dots n \label{eq:hinf_cond_perf_gen}
-  \end{align}
-\end{subequations}
-where $[W_1(s),\ W_2(s),\ \dots,\ W_n(s)]$ are weighting transfer functions that are chosen to specify the maximum wanted norms of the complementary filters during the synthesis.
-
-Such synthesis objective is very close to the one described in Section ref:sec:synthesis_objective, and indeed the proposed synthesis architecture is also very similar. \par
-
-*** H-Infinity Architecture                                         :ignore:
-Consider the generalized plant $P_3(s)$ shown in Figure ref:fig:comp_filter_three_hinf which is also described by eqref:eq:generalized_plant_three_filters.
-
-#+name: eq:generalized_plant_three_filters
-\begin{equation}
-  \begin{bmatrix} z_1 \\ z_2 \\ z_3 \\ v \end{bmatrix} = P_3(s) \begin{bmatrix} w \\ u_1 \\ u_2 \end{bmatrix}; \quad P_3(s) = \begin{bmatrix}W_1(s) & -W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) & 0 \\ 0 & 0 & \phantom{+}W_3(s) \\ 1 & 0 & 0 \end{bmatrix}
-\end{equation}
-
-#+name: fig:comp_filter_three_hinf
-#+caption: Architecture for $\mathcal{H}_\infty$ synthesis of three complementary filters
-#+attr_latex: :scale 1
-[[file:figs/comp_filter_three_hinf.pdf]]
-
-Applying the $\mathcal{H}_\infty$ synthesis on the generalized plant $P_3(s)$ is equivalent as to find two stable filters $[H_2(s),\ H_3(s)]$ (shown in Figure ref:fig:comp_filter_three_hinf) such that the $\mathcal{H}_\infty$ norm of the transfer function from $w$ to $[z_1,\ z_2, \ z_3]$ is less than one eqref:eq:hinf_syn_obj_three.
-
-#+name: eq:hinf_syn_obj_three
-\begin{equation}
-  \left\| \begin{matrix} \left[1 - H_2(s) - H_3(s)\right] W_1(s) \\ H_2(s) W_2(s) \\ H_3(s) W_3(s) \end{matrix} \right\|_\infty \le 1
-\end{equation}
-
-By defining $H_1(s) \triangleq 1 - H_2(s) - H_3(s)$, the proposed $\mathcal{H}_\infty$ synthesis solves the design problem eqref:eq:hinf_problem_gen with $n=3$. \par
-
-*** Example of generated complementary filters                      :ignore:
-An example is given to validate the method where three sensors are used in different frequency bands (up to $\SI{1}{Hz}$, from $1$ to $\SI{10}{Hz}$ and above $\SI{10}{Hz}$ respectively).
-Three weighting functions are designed using eqref:eq:weight_formula and shown by dashed curves in Fig. ref:fig:three_complementary_filters_results.
-The bode plots of the obtained complementary filters are shown in Fig. ref:fig:three_complementary_filters_results. \par
-
-#+name: fig:three_complementary_filters_results
-#+caption: Frequency response of the weighting functions and three complementary filters obtained using $\mathcal{H}_\infty$ synthesis
-#+attr_latex: :scale 1
-[[file:figs/three_complementary_filters_results.pdf]]
-
-*** Generalization                                                  :ignore:
-Such synthesis method can be generalized to a set of $n$ complementary filters, even though there might not be any practical application for $n>3$.
-
-#+name: eq:generalized_plant_n_filters
-\begin{equation}
-  \begin{bmatrix} z_1 \\ \vdots \\ z_n \\ v \end{bmatrix} = P_n(s) \begin{bmatrix} w \\ u_1 \\ \vdots \\ u_{n-1} \end{bmatrix}; \quad
-  P_n(s) = \begin{bmatrix}
-    W_1    & -W_1   & \dots  & \dots  & -W_1 \\
-    0      &  W_2   & 0      & \dots  & 0 \\
-    \vdots & \ddots & \ddots & \ddots & \vdots \\
-    \vdots &        & \ddots & \ddots & 0 \\
-    0      & \dots  & \dots  & 0      & W_n \\
-    1      & 0      & \dots  & \dots  & 0
-    \end{bmatrix}
-\end{equation}
-
-* Conclusion
-<<sec:conclusion>>
-This paper has shown how complementary filters can be used to combine multiple sensors in order to obtain a super sensor.
-Typical specification on the super sensor noise and on the robustness of the sensor fusion has been shown to be linked to the norm of the complementary filters.
-Therefore, a synthesis method that permits the shaping of the complementary filters norms has been proposed and has been successfully applied for the design of complex filters.
-Future work will aim at further developing this synthesis method for the robust and optimal synthesis of complementary filters used in sensor fusion.
-
-* Acknowledgment
-:PROPERTIES:
-:UNNUMBERED: t
-:END:
-This research benefited from a FRIA grant from the French Community of Belgium.
-
-* Bibliography                                                       :ignore:
-\bibliographystyle{elsarticle-num}
-\bibliography{ref}
-
-
-* Local Variables                                                   :noexport:
-# Local Variables:
-# org-latex-packages-alist: nil
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-\journal{Mechanical Systems and Signal Processing}
-\author[a1,a2]{Thomas Dehaeze\corref{cor1}}
-\author[a3,a4]{Mohit Verma}
-\author[a2,a4]{Christophe Collette}
-\cortext[cor1]{Corresponding author. Email Address: dehaeze.thomas@gmail.com}
-\address[a1]{European Synchrotron Radiation Facility, Grenoble, France}
-\address[a2]{University of Li\`{e}ge, Department of Aerospace and Mechanical Engineering, 4000 Li\`{e}ge, Belgium.}
-\address[a3]{CSIR --- Structural Engineering Research Centre, Taramani, Chennai --- 600113, India.}
-\address[a4]{Universit\'{e} Libre de Bruxelles, Precision Mechatronics Laboratory, BEAMS Department, 1050 Brussels, Belgium.}
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-\date{}
-\title{A new method of designing complementary filters for sensor fusion using \(\mathcal{H}_\infty\) synthesis}
-\begin{document}
-
-
-\hypersetup{allcolors=teal}
-
-\begin{frontmatter}
-\begin{abstract}
-Sensor have limited bandwidth and are accurate only in a certain frequency band.
-In many applications, the signals of different sensor are fused together in order to either enhance the stability or improve the operational bandwidth of the system.
-The sensor signals can be fused using complementary filters.
-The tuning of complementary filters is a complex task and is the subject of this paper.
-The filters needs to meet design specifications while satisfying the complementary property.
-This paper presents a framework to shape the norm of complementary filters using the \(\mathcal{H}_\infty\) norm minimization.
-The design specifications are imposed as constraints in the optimization problem by appropriate selection of weighting functions.
-The proposed method is quite general and easily extendable to cases where more than two sensors are fused.
-Finally, the proposed method is applied to the design of complementary filter design for active vibration isolation of the Laser Interferometer Gravitation-wave Observatory (LIGO).
-\end{abstract}
-
-\begin{keyword}
-Sensor fusion \sep{} Optimal filters \sep{} \(\mathcal{H}_\infty\) synthesis \sep{} Vibration isolation \sep{} Precision
-\end{keyword}
-\end{frontmatter}
-
-\section{Introduction}
-\label{sec:org3356a46}
-\label{sec:introduction}
-\begin{itemize}
-\item \cite{bendat57_optim_filter_indep_measur_two} roots of sensor fusion
-\end{itemize}
-\begin{itemize}
-\item Increase the bandwidth: \cite{zimmermann92_high_bandw_orien_measur_contr}
-\item Increased robustness: \cite{collette15_sensor_fusion_method_high_perfor}
-\item Decrease the noise:
-\end{itemize}
-\begin{itemize}
-\item UAV: \cite{pascoal99_navig_system_desig_using_time}, \cite{jensen13_basic_uas}
-\item Gravitational wave observer: \cite{hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system,lucia18_low_frequen_optim_perfor_advan,heijningen18_low,akutsu21_vibrat_isolat_system_beam_split}
-\end{itemize}
-\begin{itemize}
-\item \cite{brown72_integ_navig_system_kalman_filter} alternate form of complementary filters => Kalman filtering
-\item \cite{higgins75_compar_compl_kalman_filter} Compare Kalman Filtering with sensor fusion using complementary filters
-\item \cite{robert12_introd_random_signal_applied_kalman} advantage of complementary filters over Kalman filtering
-\end{itemize}
-\begin{itemize}
-\item Analog complementary filters: \cite{yong16_high_speed_vertic_posit_stage}, \cite{moore19_capac_instr_sensor_fusion_high_bandw_nanop}
-
-\item Analytical methods:
-\begin{itemize}
-\item first order: \cite{corke04_inert_visual_sensin_system_small_auton_helic}
-\item second order: \cite{baerveldt97_low_cost_low_weigh_attit}, \cite{stoten01_fusion_kinet_data_using_compos_filter}, \cite{jensen13_basic_uas}
-\item higher order: \cite{shaw90_bandw_enhan_posit_measur_using_measur_accel}, \cite{zimmermann92_high_bandw_orien_measur_contr}, \cite{collette15_sensor_fusion_method_high_perfor}, \cite{matichard15_seism_isolat_advan_ligo}
-\end{itemize}
-\item \cite{pascoal99_navig_system_desig_using_time} use LMI to generate complementary filters (convex optimization techniques), specific for navigation systems
-\item \cite{hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system}: FIR + convex optimization
-\item Similar to feedback system:
-\begin{itemize}
-\item \cite{plummer06_optim_compl_filter_their_applic_motion_measur} use H-Infinity to optimize complementary filters (flatten the super sensor noise spectral density)
-\item \cite{jensen13_basic_uas} design of complementary filters with classical control theory, PID
-\end{itemize}
-
-\item 3 complementary filters: \cite{becker15_compl_filter_desig_three_frequen_bands}
-\end{itemize}
-\begin{itemize}
-\item Robustness problems: \cite{zimmermann92_high_bandw_orien_measur_contr} change of phase near the merging frequency
-\item Trial and error
-\item Although many design methods of complementary filters have been proposed in the literature, no simple method that allows to shape the norm of the complementary filters is available.
-\end{itemize}
-Most of the requirements => shape of the complementary filters
-=> propose a way to shape complementary filters.
-
-\section{Sensor Fusion and Complementary Filters Requirements}
-\label{sec:org32c05cb}
-\label{sec:requirements}
-Complementary filters provides a framework for fusing signals from different sensors.
-As the effectiveness of the fusion depends on the proper design of the complementary filters, they are expected to fulfill certain requirements.
-These requirements are discussed in this section.
-\subsection{Sensor Fusion Architecture}
-\label{sec:orgcfc6167}
-\label{sec:sensor_fusion}
-
-A general sensor fusion architecture using complementary filters is shown in Figure \ref{fig:sensor_fusion_overview} where several sensors (here two) are measuring the same physical quantity \(x\).
-The two sensors output signals are estimates \(\hat{x}_1\) and \(\hat{x}_2\) of \(x\).
-Each of these estimates are then filtered out by complementary filters and combined to form a new estimate \(\hat{x}\).
-
-The resulting sensor, termed as ``super sensor'', can have larger bandwidth and better noise characteristics in comparison to the individual sensor.
-This means that the super sensor provides an estimate \(\hat{x}\) of \(x\) which can be more accurate over a larger frequency band than the outputs of the individual sensors.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1]{figs/sensor_fusion_overview.pdf}
-\caption{\label{fig:sensor_fusion_overview}Schematic of a sensor fusion architecture}
-\end{figure}
-
-The complementary property of filters \(H_1(s)\) and \(H_2(s)\) implies that the summation of their transfer functions is equal to unity.
-That is, unity magnitude and zero phase at all frequencies.
-Therefore, a pair of strict complementary filter needs to satisfy the following condition:
-\begin{equation}
-\label{eq:comp_filter}
-  H_1(s) + H_2(s) = 1
-\end{equation}
-
-It will soon become clear why the complementary property is important.
-
-\subsection{Sensor Models and Sensor Normalization}
-\label{sec:orga2c7e39}
-\label{sec:sensor_models}
-
-In order to study such sensor fusion architecture, a model of the sensors is required.
-
-Such model is shown in Figure \ref{fig:sensor_model} and consists of a linear time invariant (LTI) system \(G_i(s)\) representing the dynamics of the sensor and an additive noise input \(n_i\) representing its noise.
-The model input \(x\) is the measured physical quantity and its output \(\tilde{x}_i\) is the ``raw'' output of the sensor.
-
-Before filtering the sensor outputs \(\tilde{x}_i\) by the complementary filters, the sensors are usually normalized to simplify the fusion.
-This normalization consists of first obtaining an estimate \(\hat{G}_i(s)\) of the sensor dynamics \(G_i(s)\).
-It is supposed that the estimate of the sensor dynamics \(\hat{G}_i(s)\) can be inverted and that its inverse \(\hat{G}_i^{-1}(s)\) is proper and stable.
-The raw output of the sensor \(\tilde{x}_i\) is then passed through \(\hat{G}_i^{-1}(s)\) as shown in Figure \ref{fig:sensor_model_calibrated}.
-This way, the units of the estimates \(\hat{x}_i\) are equal to the units of the physical quantity \(x\).
-The sensor dynamics estimate \(\hat{G}_1(s)\) can be a simple gain or more complex transfer functions.
-
-\begin{figure}[htbp]
-\begin{subfigure}[b]{0.49\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model.pdf}
-\caption{\label{fig:sensor_model} Basic sensor model consisting of a noise input $n_i$ and a dynamics $G_i(s)$}
-\end{subfigure}
-\hfill
-\begin{subfigure}[b]{0.49\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model_calibrated.pdf}
-\caption{\label{fig:sensor_model_calibrated} Calibrated sensors using the inverse of an estimate $\hat{G}_1(s)$ of the sensor dynamics}
-\end{subfigure}
-\caption{\label{fig:sensor_models}Sensor models with an without normalization}
-\centering
-\end{figure}
-
-Two calibrated sensors and then combined to form a super sensor as shown in Figure \ref{fig:fusion_super_sensor}.
-
-The two sensors are measuring the same physical quantity \(x\) with dynamics \(G_1(s)\) and \(G_2(s)\), and with \emph{uncorrelated} noises \(n_1\) and \(n_2\).
-The normalized signals from both calibrated sensors are fed into two complementary filters \(H_1(s)\) and \(H_2(s)\) and then combined to yield an estimate \(\hat{x}\) of \(x\) as shown in Fig. \ref{fig:fusion_super_sensor}.
-
-The super sensor output is therefore equal to:
-\begin{equation}
-\label{eq:comp_filter_estimate}
-  \hat{x} = \Big( H_1(s) \hat{G}_1^{-1}(s) G_1(s) + H_2(s) \hat{G}_2^{-1}(s) G_2(s) \Big) x + H_1(s) \hat{G}_1^{-1}(s) G_1(s) n_1 + H_2(s) \hat{G}_2^{-1}(s) G_2(s) n_2
-\end{equation}
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/fusion_super_sensor.pdf}
-\caption{\label{fig:fusion_super_sensor}Sensor fusion architecture}
-\end{figure}
-
-\subsection{Noise Sensor Filtering}
-\label{sec:org5397108}
-\label{sec:noise_filtering}
-
-In this section, it is supposed that all the sensors are perfectly calibrated, such that:
-\begin{equation}
-\label{eq:perfect_dynamics}
-  \frac{\hat{x}_i}{x} = \hat{G}_i(s) G_i(s) = 1
-\end{equation}
-
-The effect of a non-perfect normalization will be discussed in the next section.
-
-The super sensor output \(\hat{x}\) is then:
-\begin{equation}
-\label{eq:estimate_perfect_dyn}
-  \hat{x} = x + H_1(s) n_1 + H_2(s) n_2
-\end{equation}
-
-From \eqref{eq:estimate_perfect_dyn}, the complementary filters \(H_1(s)\) and \(H_2(s)\) are shown to only operate on the sensor's noises.
-Thus, this sensor fusion architecture permits to filter the noise of both sensors without introducing any distortion in the physical quantity to be measured.
-
-The estimation error \(\delta x\), defined as the difference between the sensor output \(\hat{x}\) and the measured quantity \(x\), is computed for the super sensor \eqref{eq:estimate_error}.
-\begin{equation}
-\label{eq:estimate_error}
-  \delta x \triangleq \hat{x} - x = H_1(s) n_1 + H_2(s) n_2
-\end{equation}
-
-As shown in \eqref{eq:noise_filtering_psd}, the Power Spectral Density (PSD) of the estimation error \(\Phi_{\delta x}\) depends both on the norm of the two complementary filters and on the PSD of the noise sources \(\Phi_{n_1}\) and \(\Phi_{n_2}\).
-\begin{equation}
-\label{eq:noise_filtering_psd}
-  \Phi_{\delta x}(\omega) = \left|H_1(j\omega)\right|^2 \Phi_{n_1}(\omega) + \left|H_2(j\omega)\right|^2 \Phi_{n_2}(\omega)
-\end{equation}
-
-If the two sensors have identical noise characteristics (\(\Phi_{n_1}(\omega) = \Phi_{n_2}(\omega)\)), a simple averaging (\(H_1(s) = H_2(s) = 0.5\)) is what would minimize the super sensor noise.
-This the simplest form of sensor fusion with complementary filters.
-
-However, the two sensors have usually high noise levels over distinct frequency regions.
-In such case, to lower the noise of the super sensor, the value of the norm \(|H_1|\) has to be lowered when \(\Phi_{n_1}\) is larger than \(\Phi_{n_2}\) and that of \(|H_2|\) lowered when \(\Phi_{n_2}\) is larger than \(\Phi_{n_1}\).
-Therefore, by properly shaping the norm of the complementary filters, it is possible to minimize the noise of the super sensor noise.
-
-\subsection{Sensor Fusion Robustness}
-\label{sec:org6cbe7ea}
-\label{sec:fusion_robustness}
-
-In practical systems the sensor normalization is not perfect and condition \eqref{eq:perfect_dynamics} is not verified.
-
-In order to study such imperfection, a multiplicative input uncertainty is added to the sensor dynamics (Figure \ref{fig:sensor_model_uncertainty}), where the nominal model is taken as the estimated model for the normalization \(\hat{G}_i(s)\), \(\Delta_i\) is any stable transfer function satisfying \(|\Delta_i(j\omega)| \le 1,\ \forall\omega\), and \(w_i(s)\) is a weight representing the magnitude of the uncertainty.
-
-The weight \(w_i(s)\) is chosen such that the real sensor dynamics is always contained in the uncertain region represented by a circle centered on \(1\) and with a radius equal to \(|w_i(j\omega)|\).
-
-As the nominal sensor dynamics is taken as the normalized filter, the normalized sensor can be further simplified as shown in Figure \ref{fig:sensor_model_uncertainty_simplified}.
-
-\begin{figure}[htbp]
-\begin{subfigure}[b]{0.59\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model_uncertainty.pdf}
-\caption{\label{fig:sensor_model_uncertainty} Sensor with multiplicative input uncertainty}
-\end{subfigure}
-\hfill
-\begin{subfigure}[b]{0.39\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_model_uncertainty_simplified.pdf}
-\caption{\label{fig:sensor_model_uncertainty_simplified} Simplified sensor model}
-\end{subfigure}
-\hfill
-\caption{\label{fig:sensor_models_uncertainty}Sensor models with dynamical uncertainty}
-\centering
-\end{figure}
-
-A sensor fusion architecture with two sensors with dynamical uncertainty is shown in Figure \ref{fig:sensor_fusion_dynamic_uncertainty}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1]{figs/sensor_fusion_dynamic_uncertainty.pdf}
-\caption{\label{fig:sensor_fusion_dynamic_uncertainty}Sensor fusion architecture with sensor dynamics uncertainty}
-\end{figure}
-
-The super sensor dynamics \eqref{eq:super_sensor_dyn_uncertainty} is no longer equal to \(1\) and now depends on the sensor dynamics uncertainty weights \(w_i(s)\) as well as on the complementary filters \(H_i(s)\).
-\begin{equation}
-\label{eq:super_sensor_dyn_uncertainty}
-  \frac{\hat{x}}{x} = 1 + w_1(s) H_1(s) \Delta_1(s) + w_2(s) H_2(s) \Delta_2(s)
-\end{equation}
-
-The dynamical uncertainty of the super sensor can be graphically represented in the complex plane by a circle centered on \(1\) with a radius equal to \(|w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)|\) as shown in Figure \ref{fig:uncertainty_set_super_sensor}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1]{figs/uncertainty_set_super_sensor.pdf}
-\caption{\label{fig:uncertainty_set_super_sensor}Uncertainty region of the super sensor dynamics in the complex plane (solid circle). The contribution of both sensors 1 and 2 to the uncertainty are represented respectively by a blue circle and a red circle. The frequency dependency \(\omega\) is here omitted.}
-\end{figure}
-
-The super sensor dynamical uncertainty (i.e. the robustness of the fusion) clearly depends on the complementary filters norms.
-For instance, the phase uncertainty \(\Delta\phi(\omega)\) added by the super sensor dynamics at frequency \(\omega\) can be found by drawing a tangent from the origin to the uncertainty circle of super sensor (Figure \ref{fig:uncertainty_set_super_sensor}) and is bounded by \eqref{eq:max_phase_uncertainty}.
-
-\begin{equation}
-\label{eq:max_phase_uncertainty}
-    \Delta\phi(\omega) < \arcsin\big( |w_1(j\omega) H_1(j\omega)| + |w_2(j\omega) H_2(j\omega)| \big)
-\end{equation}
-
-As it is generally desired to limit the maximum phase added by the super sensor, \(H_1(s)\) and \(H_2(s)\) should be designed such that \(\Delta \phi\) is bounded to acceptable values.
-Typically, the norm of the complementary filter \(|H_i(j\omega)|\) should be made small when \(|w_i(j\omega)|\) is large, i.e., at frequencies where the sensor dynamics is uncertain.
-
-\section{Complementary Filters Shaping}
-\label{sec:org3fcce50}
-\label{sec:hinf_method}
-As shown in Section \ref{sec:requirements}, the noise and robustness of the ``super sensor'' are determined by the complementary filters norms.
-Therefore, a complementary filters synthesis method that allows to shape their norms would be of great use.
-
-In this section, such synthesis is proposed by expressing this problem as a \(\mathcal{H}_\infty\) norm optimization.
-\subsection{Synthesis Objective}
-\label{sec:org006154f}
-\label{sec:synthesis_objective}
-
-The synthesis objective is to shape the norm of two filters \(H_1(s)\) and \(H_2(s)\) while ensuring their complementary property \eqref{eq:comp_filter}.
-This is equivalent as to finding proper and stable transfer functions \(H_1(s)\) and \(H_2(s)\) such that conditions \eqref{eq:comp_filter_problem_form} are satisfied.
-
-\begin{subequations}
-\label{eq:comp_filter_problem_form}
-  \begin{align}
-  & H_1(s) + H_2(s) = 1 \label{eq:hinf_cond_complementarity} \\
-  & |H_1(j\omega)| \le \frac{1}{|W_1(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h1} \\
-  & |H_2(j\omega)| \le \frac{1}{|W_2(j\omega)|} \quad \forall\omega \label{eq:hinf_cond_h2}
-  \end{align}
-\end{subequations}
-where \(W_1(s)\) and \(W_2(s)\) are two weighting transfer functions that are chosen to specify the maximum wanted norms of the complementary filters during the synthesis.
-
-\subsection{Shaping of Complementary Filters using \(\mathcal{H}_\infty\) synthesis}
-\label{sec:orgd8cba14}
-\label{sec:hinf_synthesis}
-
-In this section, it is shown that the synthesis objective can be easily expressed as a standard \(\mathcal{H}_\infty\) optimal control problem and therefore solved using convenient tools readily available.
-
-Consider the generalized plant \(P(s)\) shown in Figure \ref{fig:h_infinity_robust_fusion} and mathematically described by \eqref{eq:generalized_plant}.
-
-\begin{equation}
-\label{eq:generalized_plant}
-  \begin{bmatrix} z_1 \\ z_2 \\ v \end{bmatrix} = P(s) \begin{bmatrix} w\\u \end{bmatrix}; \quad P(s) = \begin{bmatrix}W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) \\  1 & 0 \end{bmatrix}
-\end{equation}
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/h_infinity_robust_fusion.pdf}
-\caption{\label{fig:h_infinity_robust_fusion}Generalized plant used for \(\mathcal{H}_\infty\) synthesis of complementary filters}
-\end{figure}
-
-Applying the standard \(\mathcal{H}_\infty\) synthesis on the generalized plant \(P(s)\) is then equivalent as finding a stable filter \(H_2(s)\) which based on \(v\), generates a signal \(u\) such that the \(\mathcal{H}_\infty\) norm from \(w\) to \([z_1, \ z_2]\) is less than one \eqref{eq:hinf_syn_obj}.
-\begin{equation}
-\label{eq:hinf_syn_obj}
-  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
-\end{equation}
-
-By then defining \(H_1(s)\) to be the complementary of \(H_2(s)\) \eqref{eq:definition_H1}, the \(\mathcal{H}_\infty\) synthesis objective becomes equivalent to \eqref{eq:hinf_problem} which ensure that \eqref{eq:hinf_cond_h1} and \eqref{eq:hinf_cond_h2} are satisfied.
-
-\begin{equation}
-\label{eq:definition_H1}
-  H_1(s) \triangleq 1 - H_2(s)
-\end{equation}
-
-\begin{equation}
-\label{eq:hinf_problem}
-  \left\|\begin{matrix} H_1(s) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \le 1
-\end{equation}
-
-Therefore, applying the \(\mathcal{H}_\infty\) synthesis on the standard plant \(P(s)\) \eqref{eq:generalized_plant} will generate two filters \(H_2(s)\) and \(H_1(s) \triangleq 1 - H_2(s)\) that are complementary \eqref{eq:comp_filter_problem_form} and such that there norms are bellow specified bounds \eqref{eq:hinf_cond_h1},\eqref{eq:hinf_cond_h2}.
-
-The above optimization problem can be efficiently solved in Matlab \cite{matlab20} using the Robust Control Toolbox.
-
-\subsection{Weighting Functions Design}
-\label{sec:org7aa4ffb}
-\label{sec:hinf_weighting_func}
-
-Weighting functions are used during the synthesis to specify what is the maximum allowed norms of the complementary filters.
-The proper design of these weighting functions is of primary importance for the success of the presented complementary filters \(\mathcal{H}_\infty\) synthesis.
-
-First, only proper and stable transfer functions should be used.
-Second, the order of the weighting functions should stay reasonably small in order to reduce the computational costs associated with the solving of the optimization problem and for the physical implementation of the filters (the order of the synthesized filters being equal to the sum of the weighting functions order).
-Third, one should not forget the fundamental limitations imposed by the complementary property \eqref{eq:comp_filter}.
-This implies for instance that \(|H_1(j\omega)|\) and \(|H_2(j\omega)|\) cannot be made small at the same frequency.
-
-
-When designing complementary filters, it is usually desired to specify its slope, its crossover frequency and its maximum gain at low and high frequency.
-To help with the design of the weighting functions such that the above specification can be easily expressed, the formula \eqref{eq:weight_formula} is proposed.
-
-\begin{equation}
-\label{eq:weight_formula}
-  W(s) = \left( \frac{
-           \hfill{} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{G_0}{G_c}\right)^{\frac{1}{n}}
-         }{
-           \left(\frac{1}{G_\infty}\right)^{\frac{1}{n}} \frac{1}{\omega_c} \sqrt{\frac{1 - \left(\frac{G_0}{G_c}\right)^{\frac{2}{n}}}{1 - \left(\frac{G_c}{G_\infty}\right)^{\frac{2}{n}}}} s + \left(\frac{1}{G_c}\right)^{\frac{1}{n}}
-         }\right)^n
-\end{equation}
-
-The parameters in formula \eqref{eq:weight_formula} are:
-\begin{itemize}
-\item \(G_0 = lim_{\omega \to 0} |W(j\omega)|\): the low frequency gain
-\item \(G_\infty = lim_{\omega \to \infty} |W(j\omega)|\): the high frequency gain
-\item \(G_c = |W(j\omega_c)|\): the gain at \(\omega_c\)
-\item \(n\): the slope between high and low frequency. It is also the order of the weighting function.
-\end{itemize}
-
-The parameters \(G_0\), \(G_c\) and \(G_\infty\) should either satisfy condition \eqref{eq:cond_formula_1} or \eqref{eq:cond_formula_2}.
-\begin{subequations}
-\label{eq:condition_params_formula}
-  \begin{align}
-    G_0 < 1 < G_\infty \text{ and } G_0 < G_c < G_\infty \label{eq:cond_formula_1}\\
-    G_\infty < 1 < G_0 \text{ and } G_\infty < G_c < G_0 \label{eq:cond_formula_2}
-  \end{align}
-\end{subequations}
-
-The typical shape of a weighting function generated using \eqref{eq:weight_formula} is shown in Figure \ref{fig:weight_formula}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/weight_formula.pdf}
-\caption{\label{fig:weight_formula}Magnitude of a weighting function generated using the proposed formula \eqref{eq:weight_formula}, \(G_0 = 1e^{-3}\), \(G_\infty = 10\), \(\omega_c = \SI{10}{Hz}\), \(G_c = 2\), \(n = 3\)}
-\end{figure}
-
-\subsection{Validation of the proposed synthesis method}
-\label{sec:orgb562cf2}
-\label{sec:hinf_example}
-
-The proposed methodology for the design of complementary filters is now applied on a simple example where two complementary filters \(H_1(s)\) and \(H_2(s)\) have to be designed such that:
-\begin{itemize}
-\item the merging frequency is around \(\SI{10}{Hz}\)
-\item the slope of \(|H_1(j\omega)|\) is \(-2\) above \(\SI{10}{Hz}\)
-\item the slope of \(|H_2(j\omega)|\) is \(+3\) below \(\SI{10}{Hz}\)
-\item the maximum gain of both filters is \(10^{-3}\) away from the merging frequency
-\end{itemize}
-
-The first step is to design weighting functions that translate the above requirements.
-They are here designed using \eqref{eq:weight_formula} with parameters summarized in table \ref{tab:weights_params}.
-The magnitudes of the weighting functions are shown by dashed lines in Figure \ref{fig:hinf_filters_results}.
-
-\begin{table}[htbp]
-\caption{\label{tab:weights_params}Parameters used for weighting functions \(W_1(s)\) and \(W_2(s)\) using \eqref{eq:weight_formula}}
-\centering
-\begin{tabularx}{0.29\linewidth}{ccc}
-\toprule
-Parameters & \(W_1(s)\) & \(W_2(s)\)\\
-\midrule
-\(G_0\) & \(0.1\) & \(1000\)\\
-\(G_\infty\) & \(1000\) & \(0.1\)\\
-\(\omega_c\) & \(2\pi\cdot10\) & \(2\pi\cdot10\)\\
-\(G_c\) & \(0.45\) & \(0.45\)\\
-\(n\) & \(2\) & \(3\)\\
-\bottomrule
-\end{tabularx}
-\end{table}
-
-The \(\mathcal{H}_\infty\) synthesis is applied on the generalized plant of Figure \ref{fig:h_infinity_robust_fusion} using the Matlab \texttt{hinfsyn} command.
-The synthesized filter \(H_2(s)\) is such that \(\mathcal{H}_\infty\) norm between \(w\) and \([z_1,\ z_2]^T\) is minimized and here found close to one \eqref{eq:hinf_synthesis_result}.
-
-\begin{equation}
-\label{eq:hinf_synthesis_result}
-  \left\|\begin{matrix} \left(1 - H_2(s)\right) W_1(s) \\ H_2(s) W_2(s) \end{matrix}\right\|_\infty \approx 1
-\end{equation}
-
-The bode plots of the obtained complementary filters are shown by solid lines in Figure \ref{fig:hinf_filters_results} and their transfer functions in the Laplace domain are given in \eqref{eq:hinf_synthesis_result_tf}.
-
-\begin{subequations}
-\label{eq:hinf_synthesis_result_tf}
-  \begin{align}
-    H_2(s) &= \frac{(s+6.6e^4) (s+160) (s+4)^3}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)} \\
-    H_1(s) &\triangleq H_2(s) - 1 = \frac{10^{-8} (s+6.6e^9) (s+3450)^2 (s^2 + 49s + 895)}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)}
-  \end{align}
-\end{subequations}
-
-The obtained transfer functions are of order \(5\) as expected (sum of the weighting functions orders), and their magnitudes are bellow the maximum specified ones as ensured by \eqref{eq:hinf_synthesis_result}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1]{figs/hinf_filters_results.pdf}
-\caption{\label{fig:hinf_filters_results}Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis}
-\end{figure}
-
-This simple example illustrates the fact that the proposed methodology for complementary filters shaping is quite easy to use and effective.
-A more complex real life example is taken up in the next section.
-
-\section{Application: Design of Complementary Filters used in the Active Vibration Isolation System at the LIGO}
-\label{sec:org60805ba}
-\label{sec:application_ligo}
-Sensor fusion using complementary filters are widely used in active vibration isolation systems in gravitational wave detectors such at the LIGO \cite{matichard15_seism_isolat_advan_ligo,hua05_low_ligo}, the VIRGO \cite{lucia18_low_frequen_optim_perfor_advan,heijningen18_low} and the KAGRA \cite{akutsu21_vibrat_isolat_system_beam_split}.
-
-In the first isolation stage at the LIGO, two sets of complementary filters are used and included in a feedback loop \cite{hua04_low_ligo}.
-A set of complementary filters (\(L_2,H_2\)) is first used to fuse a seismometer and a geophone.
-Then, another set of complementary filters (\(L_1,H_1\)) is used to merge the output of the first ``inertial super sensor'' with a position sensor.
-A simplified block diagram of the sensor fusion architecture is shown in Figure \ref{fig:ligo_super_sensor_architecture}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/ligo_super_sensor_architecture.pdf}
-\caption{\label{fig:ligo_super_sensor_architecture}Simplified block diagram of the sensor blending strategy for the first stage at the LIGO \cite{hua04_low_ligo}}
-\end{figure}
-
-The fusion of the position sensor at low frequency with the ``inertial super sensor'' at high frequency using the complementary filters (\(L_1,H_1\)) is done for several reasons, first of which is to give the super sensor a DC sensibility and therefore allow the feedback loop to have authority at zero frequency.
-The requirements on those filters are very tight and thus their design is complex and should be expressed as an optimization problem.
-
-The approach used in \cite{hua05_low_ligo} is to use FIR complementary filters and to write the synthesis as a convex optimization problem.
-After synthesis, the obtained FIR filters were found to be compliant with the requirements.
-However they are of very high order so their implementation is quite complex.
-In this section, the effectiveness of the proposed complementary filter synthesis strategy is demonstrated on the same set of requirements.
-\subsection{Complementary Filters Specifications}
-\label{sec:orgfdd63d0}
-\label{sec:ligo_specifications}
-The specifications for the set of complementary filters (\(L_1,H_1\)) used at the LIGO are summarized below (for further details, refer to \cite{hua04_polyp_fir_compl_filter_contr_system}):
-\begin{itemize}
-\item From \(0\) to \(\SI{0.008}{Hz}\), the magnitude \(|L_1(j\omega)|\) should be less or equal to \(8 \times 10^{-4}\)
-\item Between \(\SI{0.008}{Hz}\) to \(\SI{0.04}{Hz}\), the filter \(L_1(s)\) should attenuate the input signal proportional to frequency cubed
-\item Between \(\SI{0.04}{Hz}\) to \(\SI{0.1}{Hz}\), the magnitude \(|L_1(j\omega)|\) should be less than \(3\)
-\item Above \(\SI{0.1}{Hz}\), the magnitude \(|H_1(j\omega)|\) should be less than \(0.045\)
-\end{itemize}
-
-These specifications are therefore upper bounds on the complementary filters' magnitudes.
-They are physically represented in Figure \ref{fig:fir_filter_ligo} as well as the obtained magnitude of the FIR filters in \cite{hua05_low_ligo}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/fir_filter_ligo.pdf}
-\caption{\label{fig:fir_filter_ligo}Specifications and Bode plot of the obtained FIR filters in \cite{hua05_low_ligo}}
-\end{figure}
-
-\subsection{Weighting Functions Design}
-\label{sec:org916b9d5}
-\label{sec:ligo_weights}
-The weighting functions should be designed such that their inverse magnitude is as close as possible to the specifications in order to not over-constrain the synthesis problem.
-However, the order of each weight should stay reasonably small in order to reduce the computational costs of the optimization problem as well as for the physical implementation of the filters.
-
-A Type I Chebyshev filter of order \(20\) is used as the weighting transfer function \(w_L(s)\) corresponding to the low pass filter.
-For the one corresponding to the high pass filter \(w_H(s)\), a \(7^{\text{th}}\) order transfer function is designed.
-The magnitudes of the weighting functions are shown in Fig. \ref{fig:ligo_weights}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/ligo_weights.pdf}
-\caption{\label{fig:ligo_weights}Specifications and weighting functions magnitudes}
-\end{figure}
-
-\subsection{\(\mathcal{H}_\infty\) Synthesis}
-\label{sec:orgab74bf1}
-\label{sec:ligo_results}
-\(\mathcal{H}_\infty\) synthesis is performed using the architecture shown in Fig. \ref{eq:generalized_plant}.
-The complementary filters obtained are of order \(27\).
-In Fig. \ref{fig:comp_fir_ligo_hinf}, their bode plot is compared with the FIR filters of order 512 obtained in \cite{hua05_low_ligo}.
-They are found to be very close to each other and this shows the effectiveness of the proposed synthesis method.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/comp_fir_ligo_hinf.pdf}
-\caption{\label{fig:comp_fir_ligo_hinf}Comparison of the FIR filters (solid) designed in \cite{hua05_low_ligo} with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)}
-\end{figure}
-
-\section{Discussion}
-\label{sec:org5bc126e}
-\label{sec:discussion}
-\subsection{``Closed-Loop'' complementary filters}
-\label{sec:org8731218}
-\label{sec:closed_loop_complementary_filters}
-It is possible to use the fundamental properties of a feedback architecture to generate complementary filters.
-
-It has been proposed by:
-\begin{itemize}
-\item \cite{plummer06_optim_compl_filter_their_applic_motion_measur} use H-Infinity to optimize complementary filters (flatten the super sensor noise spectral density)
-\item \cite{jensen13_basic_uas} design of complementary filters with classical control theory, PID
-\item Maybe also cite \cite{mahony05_compl_filter_desig_special_orthog}
-\end{itemize}
-
-Consider the feedback architecture of Figure \ref{fig:feedback_sensor_fusion}, with two inputs \(\hat{x}_1\) and \(\hat{x}_2\), and one output \(\hat{x}\).
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/feedback_sensor_fusion.pdf}
-\caption{\label{fig:feedback_sensor_fusion}``Closed-Loop'' complementary filters}
-\end{figure}
-
-The output \(\hat{x}\) is described by \eqref{eq:closed_loop_complementary_filters}.
-
-\begin{equation}
-\label{eq:closed_loop_complementary_filters}
-\hat{x} = \underbrace{\frac{1}{1 + L(s)}}_{S(s)} \hat{x}_1 + \underbrace{\frac{L(s)}{1 + L(s)}}_{T(s)} \hat{x}_2
-\end{equation}
-
-with the famous relationship
-\begin{equation}
-T(s) + S(s) = 1
-\end{equation}
-
-Provided that the closed-loop system is stable, this indeed forms two complementary filters.
-Therefore, two filters can be merged as shown in Figure \ref{fig:feedback_sensor_fusion_arch}.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/feedback_sensor_fusion_arch.pdf}
-\caption{\label{fig:feedback_sensor_fusion_arch}Classical feedback architecture for sensor fusion}
-\end{figure}
-
-One of the main advantage of this configuration is that standard tools of the linear control theory can be applied.
-If one want to shape both the transfer functions \(\frac{\hat{x}}{\hat{x}_1}(s) = S(s)\) and \(\frac{\hat{x}}{\hat{x}_2}(s) = T(s)\), this corresponds to the \(\mathcal{H}_\infty\) mixed-sensitivity synthesis.
-
-The \(\mathcal{H}_\infty\) mixed-sensitivity synthesis can be perform by applying the \(\mathcal{H}_\infty\) synthesis to the generalized plant \(P_L(s)\) shown in Figure \ref{fig:feedback_synthesis_architecture_generalized_plant} and described by \eqref{eq:generalized_plant_mixed_sensitivity} where \(W_1(s)\) and \(W_2(s)\) are weighting functions used to respectively shape \(S(s)\) and \(T(s)\).
-
-\begin{equation}
-\label{eq:generalized_plant_mixed_sensitivity}
-  \begin{bmatrix} z \\ v \end{bmatrix} = P_L(s) \begin{bmatrix} w_1 \\ w_2 \\ u \end{bmatrix}; \quad P_L(s) = \begin{bmatrix}
-    \phantom{+}W_1(s) & 0      & \phantom{+}1 \\
-              -W_1(s) & W_2(s) &           -1
-  \end{bmatrix}
-\end{equation}
-
-This is equivalent as to find a filter \(L(s)\) such that \eqref{eq:comp_filters_feedback_obj} is verified.
-
-\begin{equation}
-\label{eq:comp_filters_feedback_obj}
-  \left\|\begin{matrix} \frac{1}{1 + L(s)} W_1(s) \\ \frac{L(s)}{1 + L(s)} W_2(s) \end{matrix}\right\|_\infty \le 1
-\end{equation}
-
-The sensor fusion can be implemented as shown in Figure \ref{fig:feedback_sensor_fusion_arch} using the feedback architecture or more classically as shown in Figure \ref{fig:sensor_fusion_overview} using \eqref{eq:comp_filters_feedback}.
-
-\begin{equation}
-\label{eq:comp_filters_feedback}
-H_1(s) = \frac{1}{1 + L(s)}; \quad H_2(s) = \frac{L(s)}{1 + L(s)}
-\end{equation}
-
-The two being equivalent considering only the inputs/outputs relationships.
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/feedback_synthesis_architecture_generalized_plant.pdf}
-\caption{\label{fig:feedback_synthesis_architecture_generalized_plant}Generalized plant for the \(\mathcal{H}_\infty\) mixed-sensitivity synthesis}
-\end{figure}
-Example: same weights as in \ref{tab:weights_params}.
-
-Therefore, complementary filter design is very similar to mixed-sensitivity synthesis.
-
-They are actually equivalent by taking
-\begin{equation}
-L = H_H^{-1} - 1
-\end{equation}
-(provided \(H_H\) is invertible, therefore bi-proper)
-
-\subsection{Imposing zero at origin / roll-off}
-\label{sec:orgdea775a}
-\label{sec:add_features_in_filters}
-
-3 methods:
-
-Link to literature about doing that with mixed sensitivity
-
-\subsection{Synthesis of Three Complementary Filters}
-\label{sec:org6446998}
-\label{sec:hinf_three_comp_filters}
-Some applications may require to merge more than two sensors.
-For instance at the LIGO, three sensors (an LVDT, a seismometer and a geophone) are merged to form a super sensor (Figure \ref{fig:ligo_super_sensor_architecture}). \par
-When merging \(n>2\) sensors using complementary filters, two architectures can be used as shown in Figure \ref{fig:sensor_fusion_three}.
-
-The fusion can either be done in a ``sequential'' way where \(n-1\) sets of two complementary filters are used (Figure \ref{fig:sensor_fusion_three_sequential}), or in a ``parallel'' way where one set of \(n\) complementary filters is used (Figure \ref{fig:sensor_fusion_three_parallel}).
-
-In the first case, typical sensor fusion synthesis techniques can be used.
-However, when a parallel architecture is used, a new synthesis method for a set of more than two complementary filters is required.
-Such synthesis method is presented in this section. \par
-
-\begin{center}
-\fbox{
-\begin{minipage}[c]{.6\textwidth}
-Say possible advantages of parallel architecture
-
-\end{minipage}
-}
-\end{center}
-
-\begin{figure}[htbp]
-\begin{subfigure}[b]{0.59\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_fusion_three_sequential.pdf}
-\caption{\label{fig:sensor_fusion_three_sequential}Sequential fusion}
-\end{subfigure}
-\hfill
-\begin{subfigure}[b]{0.39\linewidth}
-\centering
-\includegraphics[scale=1]{figs/sensor_fusion_three_parallel.pdf}
-\caption{\label{fig:sensor_fusion_three_parallel}Parallel fusion}
-\end{subfigure}
-\caption{\label{fig:sensor_fusion_three}Sensor fusion architecture with more than two sensors}
-\centering
-\end{figure}
-The synthesis objective is to compute a set of \(n\) stable transfer functions \([H_1(s),\ H_2(s),\ \dots,\ H_n(s)]\) such that \eqref{eq:hinf_problem_gen} is satisfied.
-\begin{subequations}
-\label{eq:hinf_problem_gen}
-  \begin{align}
-  & \sum_{i=0}^n H_i(s) = 1 \label{eq:hinf_cond_compl_gen} \\
-  & \left| H_i(j\omega) \right| < \frac{1}{\left| W_i(j\omega) \right|}, \quad \forall \omega,\ i = 1 \dots n \label{eq:hinf_cond_perf_gen}
-  \end{align}
-\end{subequations}
-where \([W_1(s),\ W_2(s),\ \dots,\ W_n(s)]\) are weighting transfer functions that are chosen to specify the maximum wanted norms of the complementary filters during the synthesis.
-
-Such synthesis objective is very close to the one described in Section \ref{sec:synthesis_objective}, and indeed the proposed synthesis architecture is also very similar. \par
-Consider the generalized plant \(P_3(s)\) shown in Figure \ref{fig:comp_filter_three_hinf} which is also described by \eqref{eq:generalized_plant_three_filters}.
-
-\begin{equation}
-\label{eq:generalized_plant_three_filters}
-  \begin{bmatrix} z_1 \\ z_2 \\ z_3 \\ v \end{bmatrix} = P_3(s) \begin{bmatrix} w \\ u_1 \\ u_2 \end{bmatrix}; \quad P_3(s) = \begin{bmatrix}W_1(s) & -W_1(s) & -W_1(s) \\ 0 & \phantom{+}W_2(s) & 0 \\ 0 & 0 & \phantom{+}W_3(s) \\ 1 & 0 & 0 \end{bmatrix}
-\end{equation}
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/comp_filter_three_hinf.pdf}
-\caption{\label{fig:comp_filter_three_hinf}Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters}
-\end{figure}
-
-Applying the \(\mathcal{H}_\infty\) synthesis on the generalized plant \(P_3(s)\) is equivalent as to find two stable filters \([H_2(s),\ H_3(s)]\) (shown in Figure \ref{fig:comp_filter_three_hinf}) such that the \(\mathcal{H}_\infty\) norm of the transfer function from \(w\) to \([z_1,\ z_2, \ z_3]\) is less than one \eqref{eq:hinf_syn_obj_three}.
-
-\begin{equation}
-\label{eq:hinf_syn_obj_three}
-  \left\| \begin{matrix} \left[1 - H_2(s) - H_3(s)\right] W_1(s) \\ H_2(s) W_2(s) \\ H_3(s) W_3(s) \end{matrix} \right\|_\infty \le 1
-\end{equation}
-
-By defining \(H_1(s) \triangleq 1 - H_2(s) - H_3(s)\), the proposed \(\mathcal{H}_\infty\) synthesis solves the design problem \eqref{eq:hinf_problem_gen} with \(n=3\). \par
-An example is given to validate the method where three sensors are used in different frequency bands (up to \(\SI{1}{Hz}\), from \(1\) to \(\SI{10}{Hz}\) and above \(\SI{10}{Hz}\) respectively).
-Three weighting functions are designed using \eqref{eq:weight_formula} and shown by dashed curves in Fig. \ref{fig:three_complementary_filters_results}.
-The bode plots of the obtained complementary filters are shown in Fig. \ref{fig:three_complementary_filters_results}. \par
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,scale=1]{figs/three_complementary_filters_results.pdf}
-\caption{\label{fig:three_complementary_filters_results}Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis}
-\end{figure}
-Such synthesis method can be generalized to a set of \(n\) complementary filters, even though there might not be any practical application for \(n>3\).
-
-\begin{equation}
-\label{eq:generalized_plant_n_filters}
-  \begin{bmatrix} z_1 \\ \vdots \\ z_n \\ v \end{bmatrix} = P_n(s) \begin{bmatrix} w \\ u_1 \\ \vdots \\ u_{n-1} \end{bmatrix}; \quad
-  P_n(s) = \begin{bmatrix}
-    W_1    & -W_1   & \dots  & \dots  & -W_1 \\
-    0      &  W_2   & 0      & \dots  & 0 \\
-    \vdots & \ddots & \ddots & \ddots & \vdots \\
-    \vdots &        & \ddots & \ddots & 0 \\
-    0      & \dots  & \dots  & 0      & W_n \\
-    1      & 0      & \dots  & \dots  & 0
-    \end{bmatrix}
-\end{equation}
-
-\section{Conclusion}
-\label{sec:orgcba6c13}
-\label{sec:conclusion}
-This paper has shown how complementary filters can be used to combine multiple sensors in order to obtain a super sensor.
-Typical specification on the super sensor noise and on the robustness of the sensor fusion has been shown to be linked to the norm of the complementary filters.
-Therefore, a synthesis method that permits the shaping of the complementary filters norms has been proposed and has been successfully applied for the design of complex filters.
-Future work will aim at further developing this synthesis method for the robust and optimal synthesis of complementary filters used in sensor fusion.
-
-\section*{Acknowledgment}
-\label{sec:orgf175dee}
-This research benefited from a FRIA grant from the French Community of Belgium.
-
-\bibliographystyle{elsarticle-num}
-\bibliography{ref}
-\end{document}
--- a/journal/ref.bib
+++ b/journal/ref.bib
@@ -7,7 +7,6 @@
  pages           = {1-21},
  year            = 2015,
  doi             = {10.1016/j.jsv.2015.01.006},
-  url             = {https://doi.org/10.1016/j.jsv.2015.01.006},
 }

@phdthesis{hua05_low_ligo,
@@ -15,15 +14,14 @@
  doi             = {10.1117/12.552518},
  school          = {stanford university},
  title           = {Low frequency vibration isolation and alignment system for
-                  advanced LIGO},
-  url             = {https://doi.org/10.1117/12.552518},
+                  {Advanced LIGO}},
  year            = 2005,
 }

@inproceedings{hua04_polyp_fir_compl_filter_contr_system,
  author          = {Hua, Wensheng and Debra, B. and Hardham, T. and Lantz, T.
                  and Giaime, A.},
-  title           = {Polyphase FIR Complementary Filters for Control Systems},
+  title           = {Polyphase {FIR} Complementary Filters for Control Systems},
  booktitle       = {Proceedings of ASPE Spring Topical Meeting on Control of
                  Precision Systems},
  year            = 2004,
@@ -33,7 +31,7 @@
@article{matichard15_seism_isolat_advan_ligo,
  author          = {Matichard, F and Lantz, B and Mittleman, R and Mason, K and
                  Kissel, J and others},
-  title           = {Seismic Isolation of Advanced Ligo: Review of Strategy,
+  title           = {Seismic Isolation of {Advanced LIGO}: Review of Strategy,
                  Instrumentation and Performance},
  journal         = {Classical and Quantum Gravity},
  volume          = 32,
@@ -41,7 +39,6 @@
  pages           = 185003,
  year            = 2015,
  doi             = {10.1088/0264-9381/32/18/185003},
-  url             = {https://doi.org/10.1088/0264-9381/32/18/185003},
  publisher       = {IOP Publishing},
 }

@@ -55,7 +52,6 @@
  pages           = {43-51},
  year            = 2004,
  doi             = {10.1002/rob.10127},
-  url             = {https://doi.org/10.1002/rob.10127},
 }

@inproceedings{jensen13_basic_uas,
@@ -66,7 +62,6 @@
                  (ICUAS)},
  year            = 2013,
  doi             = {10.1109/ICUAS.2013.6564726 },
-  url             = {https://doi.org/10.1109/ICUAS.2013.6564726 },
  month           = 5,
 }

@@ -77,38 +72,22 @@
  booktitle       = {Guidance, Navigation, and Control Conference and Exhibit},
  year            = 1999,
  doi             = {10.1109/7.892661},
-  url             = {https://doi.org/10.1109/7.892661},
 }

@article{zimmermann92_high_bandw_orien_measur_contr,
-  author          = {M. Zimmermann and W. Sulzer},
+  author          = {Zimmermann, M and Sulzer, W},
  title           = {High Bandwidth Orientation Measurement and Control Based on
                  Complementary Filtering},
-  journal         = {Robot Control 1991},
-  pages           = {525-530},
+  journal         = {Robot Control},
  year            = 1992,
  doi             = {10.1016/B978-0-08-041276-4.50093-5},
-  url             = {https://doi.org/10.1016/B978-0-08-041276-4.50093-5},
  publisher       = {Elsevier},
  series          = {Robot Control 1991},
 }

-@article{mahony08_nonlin_compl_filter_special_orthog_group,
-  author          = {Robert Mahony and Tarek Hamel and Jean-Michel Pflimlin},
-  title           = {Nonlinear Complementary Filters on the Special Orthogonal
-                  Group},
-  journal         = {IEEE Transactions on Automatic Control},
-  volume          = 53,
-  number          = 5,
-  pages           = {1203-1218},
-  year            = 2008,
-  doi             = {10.1109/TAC.2008.923738},
-  url             = {https://doi.org/10.1109/TAC.2008.923738},
-}
-
@article{sturm99_using_sedum,
  author          = {Sturm, Jos F},
-  title           = {Using Sedumi 1.02, a Matlab Toolbox for Optimization Over
+  title           = {Using {SeDuMi} 1.02, a Matlab Toolbox for Optimization Over
                  Symmetric Cones},
  journal         = {Optimization methods and software},
  volume          = 11,
@@ -116,25 +95,9 @@
  pages           = {625--653},
  year            = 1999,
  doi             = {10.1080/10556789908805766},
-  url             = {https://doi.org/10.1080/10556789908805766},
  publisher       = {Taylor \& Francis},
 }

-@article{cao20_adapt_compl_filter_based_post,
-  author          = {Cao, Mingcong and Hu, Chuan and Wang, Jinxiang and Wang,
-                  Rongrong and Chen, Nan},
-  title           = {Adaptive Complementary Filter-Based Post-Impact Control for
-                  Independently-Actuated and Differentially-Steered Autonomous
-                  Vehicles},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 144,
-  pages           = 106852,
-  year            = 2020,
-  doi             = {10.1016/j.ymssp.2020.106852},
-  url             = {https://doi.org/10.1016/j.ymssp.2020.106852},
-  publisher       = {Elsevier},
-}
-
@article{tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip,
  author          = {Tjepkema, D and van Dijk, Johannes and Soemers, HMJR},
  title           = {Sensor Fusion for Active Vibration Isolation in Precision
@@ -145,38 +108,9 @@
  pages           = {735--749},
  year            = 2012,
  doi             = {10.1016/j.jsv.2011.09.022},
-  url             = {https://doi.org/10.1016/j.jsv.2011.09.022},
  publisher       = {Elsevier},
 }

-@article{verma21_virtual_sensor_fusion_high_precis_contr,
-  author          = {Verma, Mohit and Dehaeze, Thomas and Zhao, Guoying and
-                  Watchi, Jennifer and Collette, Christophe},
-  title           = {Virtual Sensor Fusion for High Precision Control},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 150,
-  pages           = 107241,
-  year            = 2021,
-  doi             = {10.1016/j.ymssp.2020.107241},
-  url             = {https://doi.org/10.1016/j.ymssp.2020.107241},
-  publisher       = {Elsevier},
-}
-
-@article{ma04_frequen_weigh_adapt_contr_simul,
-  author          = {Ma, Kougen and Ghasemi-Nejhad, Mehrdad N},
-  title           = {Frequency-Weighted Adaptive Control for Simultaneous
-                  Precision Positioning and Vibration Suppression of Smart
-                  Structures},
-  journal         = {Smart materials and structures},
-  volume          = 13,
-  number          = 5,
-  pages           = 1143,
-  year            = 2004,
-  doi             = {10.1088/0964-1726/13/5/019},
-  url             = {https://doi.org/10.1088/0964-1726/13/5/019},
-  publisher       = {IOP Publishing},
-}
-
@article{anderson53_instr_approac_system_steer_comput,
  author          = {Anderson, WG and Fritze, EH},
  title           = {Instrument Approach System Steering Computer},
@@ -186,7 +120,6 @@
  pages           = {219--228},
  year            = 1953,
  doi             = {10.1109/JRPROC.1953.274209},
-  url             = {https://doi.org/10.1109/JRPROC.1953.274209},
  publisher       = {IEEE},
 }

@@ -200,92 +133,9 @@
  pages           = {23--38},
  year            = 1990,
  doi             = {10.1016/0888-3270(90)90038-M},
-  url             = {https://doi.org/10.1016/0888-3270(90)90038-M},
  publisher       = {Elsevier},
 }

-@inproceedings{baerveldt97,
-  author          = {Baerveldt, A-J and Klang, Robert},
-  title           = {A low-cost and low-weight attitude estimation system for an
-                  autonomous helicopter},
-  booktitle       = {Proceedings of IEEE International Conference on Intelligent
-                  Engineering Systems},
-  year            = 1997,
-  pages           = {391--395},
-  doi             = {10.1109/INES.1997.632450},
-  url             = {https://doi.org/10.1109/INES.1997.632450},
-  organization    = {IEEE},
-}
-
-@inproceedings{roberts03_low,
-  author          = {Roberts, Jonathan M and Corke, Peter I and Buskey, Gregg},
-  title           = {Low-cost flight control system for a small autonomous
-                  helicopter},
-  booktitle       = {2003 IEEE International Conference on Robotics and
-                  Automation (Cat. No. 03CH37422)},
-  year            = 2003,
-  volume          = 1,
-  pages           = {546--551},
-  doi             = {10.1109/ROBOT.2003.1241651},
-  url             = {https://doi.org/10.1109/ROBOT.2003.1241651},
-  organization    = {IEEE},
-}
-
-@inproceedings{bachmann03_desig_marg_dof,
-  author          = {Bachmann, Eric R and Yun, Xiaoping and McKinney, Doug and
-                  McGhee, Robert B and Zyda, Michael J},
-  title           = {Design and implementation of MARG sensors for 3-DOF
-                  orientation measurement of rigid bodies},
-  booktitle       = {2003 IEEE International Conference on Robotics and
-                  Automation (Cat. No. 03CH37422)},
-  year            = 2003,
-  volume          = 1,
-  pages           = {1171--1178},
-  doi             = {10.1109/ROBOT.2003.1241751},
-  url             = {https://doi.org/10.1109/ROBOT.2003.1241751},
-  organization    = {IEEE},
-}
-
-@article{salcudean91_global_conver_angul_veloc_obser,
-  author          = {Salcudean, S},
-  title           = {A Globally Convergent Angular Velocity Observer for Rigid
-                  Body Motion},
-  journal         = {IEEE transactions on Automatic Control},
-  volume          = 36,
-  number          = 12,
-  pages           = {1493--1497},
-  year            = 1991,
-  doi             = {10.1109/9.106169},
-  url             = {https://doi.org/10.1109/9.106169},
-  publisher       = {IEEE},
-}
-
-@article{pascoal00_navig_system_desig_using_time,
-  author          = {Pascoal, Antonio and Kaminer, Isaac and Oliveira, Paulo},
-  title           = {Navigation System Design Using Time-Varying Complementary
-                  Filters},
-  journal         = {IEEE Transactions on Aerospace and Electronic Systems},
-  volume          = 36,
-  number          = 4,
-  pages           = {1099--1114},
-  year            = 2000,
-  doi             = {10.1109/7.892661},
-  url             = {https://doi.org/10.1109/7.892661},
-  publisher       = {IEEE},
-}
-
-@inproceedings{ryzhkov18_compl,
-  author          = {Ryzhkov, L},
-  title           = {Complementary filter design for attitude determination},
-  booktitle       = {2018 IEEE 5th International Conference on Methods and
-                  Systems of Navigation and Motion Control (MSNMC)},
-  year            = 2018,
-  pages           = {214--217},
-  doi             = {10.1109/MSNMC.2018.8576177},
-  url             = {https://doi.org/10.1109/MSNMC.2018.8576177},
-  organization    = {IEEE},
-}
-
@article{plummer06_optim_compl_filter_their_applic_motion_measur,
  author          = {Plummer, AR},
  title           = {Optimal Complementary Filters and Their Application in
@@ -297,7 +147,6 @@
  pages           = {489--507},
  year            = 2006,
  doi             = {10.1243/09596518JSCE229},
-  url             = {https://doi.org/10.1243/09596518JSCE229},
  publisher       = {Sage Publications Sage UK: London, England},
 }

@@ -311,70 +160,9 @@
  pages           = {569--589},
  year            = 2018,
  doi             = {10.1016/j.ymssp.2018.03.053},
-  url             = {https://doi.org/10.1016/j.ymssp.2018.03.053},
  publisher       = {Elsevier},
 }

-@article{ren19_integ_gnss_hub_motion_estim,
-  author          = {Ren, Zhengru and Skjetne, Roger and Jiang, Zhiyu and Gao,
-                  Zhen and Verma, Amrit Shankar},
-  title           = {Integrated Gnss/imu Hub Motion Estimator for Offshore Wind
-                  Turbine Blade Installation},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 123,
-  pages           = {222--243},
-  year            = 2019,
-  doi             = {10.1016/j.ymssp.2019.01.008},
-  url             = {https://doi.org/10.1016/j.ymssp.2019.01.008},
-  publisher       = {Elsevier},
-}
-
-@article{faria19_sensor_fusion_rotat_motion_recon,
-  author          = {Faria, CT},
-  title           = {Sensor Fusion and Rotational Motion Reconstruction Via
-                  Nonlinear State-Observers},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 114,
-  pages           = {571--578},
-  year            = 2019,
-  doi             = {10.1016/j.ymssp.2018.05.021},
-  url             = {https://doi.org/10.1016/j.ymssp.2018.05.021},
-  publisher       = {Elsevier},
-}
-
-@article{liu18_innov_infor_fusion_method_with,
-  author          = {Liu, Yahui and Fan, Xiaoqian and Lv, Chen and Wu, Jian and
-                  Li, Liang and Ding, Dawei},
-  title           = {An Innovative Information Fusion Method With Adaptive
-                  Kalman Filter for Integrated Ins/gps Navigation of Autonomous
-                  Vehicles},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 100,
-  pages           = {605--616},
-  year            = 2018,
-  doi             = {10.1016/j.ymssp.2017.07.051},
-  url             = {https://doi.org/10.1016/j.ymssp.2017.07.051},
-  publisher       = {Elsevier},
-}
-
-@book{boyd94_linear,
-  author          = {Boyd, Stephen P and El Ghaoui, Laurent and Feron, Eric and
-                  Balakrishnan, Venkataramanan},
-  title           = {Linear matrix inequalities in system and control theory},
-  year            = 1994,
-  publisher       = {SIAM},
-  isbn            = {0-89871-334-X},
-  volume          = 15,
-}
-
-@book{boyd91_linear,
-  author          = {Boyd, Stephen P and Barratt, Craig H},
-  title           = {Linear controller design: limits of performance},
-  year            = 1991,
-  publisher       = {Prentice Hall Englewood Cliffs, NJ},
-  isbn            = {0-13-538687-X},
-}
-
@book{matlab20,
  author          = {MATLAB},
  title           = {version 9.9.0 (R2020b)},
@@ -383,34 +171,6 @@
  address         = {Natick, Massachusetts},
 }

-@article{abdel15_const_low_cost_gps_filter,
-  author          = {Abdel Hafez, Mamoun F and Saadeddin, Kamal and Jarrah,
-                  Mohammad Amin},
-  title           = {Constrained Low-Cost Gps/ins Filter With Encoder Bias
-                  Estimation for Ground Vehicles Applications},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 58,
-  pages           = {285--297},
-  year            = 2015,
-  doi             = {10.1016/j.ymssp.2014.12.012},
-  url             = {https://doi.org/10.1016/j.ymssp.2014.12.012},
-  publisher       = {Elsevier},
-}
-
-@article{biondi17_attit_recov_from_featur_track,
-  author          = {Biondi, Gabriele and Mauro, S and Mohtar, T and Pastorelli,
-                  S and Sorli, M},
-  title           = {Attitude Recovery From Feature Tracking for Estimating
-                  Angular Rate of Non-Cooperative Spacecraft},
-  journal         = {Mechanical Systems and Signal Processing},
-  volume          = 83,
-  pages           = {321--336},
-  year            = 2017,
-  doi             = {10.1016/j.ymssp.2016.06.017},
-  url             = {https://doi.org/10.1016/j.ymssp.2016.06.017},
-  publisher       = {Elsevier},
-}
-
@article{brown72_integ_navig_system_kalman_filter,
  author          = {R. G. Brown},
  title           = {Integrated Navigation Systems and Kalman Filtering: a
@@ -421,7 +181,6 @@
  pages           = {355-362},
  year            = 1972,
  doi             = {10.1002/j.2161-4296.1972.tb01706.x},
-  url             = {https://doi.org/10.1002/j.2161-4296.1972.tb01706.x},
 }

@article{moore19_capac_instr_sensor_fusion_high_bandw_nanop,
@@ -434,7 +193,6 @@
  pages           = {1-3},
  year            = 2019,
  doi             = {10.1109/lsens.2019.2933065},
-  url             = {https://doi.org/10.1109/lsens.2019.2933065},
 }

@article{higgins75_compar_compl_kalman_filter,
@@ -445,8 +203,6 @@
  pages           = {321--325},
  year            = 1975,
  doi             = {10.1109/TAES.1975.308081},
-  url             = {https://doi.org/10.1109/TAES.1975.308081},
-  keywords        = {sensor fusion, complementary filters},
  publisher       = {IEEE},
 }

@@ -456,8 +212,12 @@
                  with Matlab Exercises},
  year            = 2012,
  publisher       = {Wiley},
+  day             = 07,
  edition         = 4,
  isbn            = {978-0-470-60969-9},
+  month           = 02,
+  note            = {isbn:978-0-470-60969-9},
+  pagecount       = 400,
 }

@inproceedings{becker15_compl_filter_desig_three_frequen_bands,
@@ -469,9 +229,8 @@
                  Competitions},
  year            = 2015,
  doi             = {10.1109/ICARSC.2015.34},
-  url             = {https://doi.org/10.1109/ICARSC.2015.34},
  isbn            = {978-1-4673-6991-6},
-  keywords        = {complementary filters},
+  note            = {isbn:978-1-4673-6991-6},
  page            = {204--209},
 }

@@ -484,7 +243,6 @@
  pages           = "184 - 192",
  year            = 2016,
  doi             = {10.1016/j.sna.2016.06.042},
-  url             = {https://doi.org/10.1016/j.sna.2016.06.042},
  issn            = "0924-4247",
 }

@@ -495,10 +253,7 @@
  booktitle       = {Proceedings of IEEE International Conference on Intelligent
                  Engineering Systems},
  year            = 1997,
-  pages           = {nil},
  doi             = {10.1109/ines.1997.632450},
-  url             = {https://doi.org/10.1109/ines.1997.632450},
-  keywords        = {complementary filters},
  month           = {-},
 }

@@ -512,8 +267,6 @@
  pages           = {483--497},
  year            = 2001,
  doi             = {10.1177/095965180121500505},
-  url             = {https://doi.org/10.1177/095965180121500505},
-  keywords        = {sensor fusion, complementary filters},
  publisher       = {SAGE Publications Sage UK: London, England},
 }

@@ -524,7 +277,6 @@
  journal         = {IRE Transactions on Circuit Theory},
  year            = 1957,
  doi             = {10.1109/tct.1957.1086345},
-  url             = {https://doi.org/10.1109/tct.1957.1086345},
  page            = {--},
 }

@@ -533,7 +285,7 @@
                  Giaime, Joseph A and Hammond, Giles Dominic and Hardham, C and
                  Hennessy, Mike and How, Jonathan P and Lantz, Brian T and
                  Macinnis, M and others},
-  title           = {Low-frequency active vibration isolation for advanced LIGO},
+  title           = {Low-frequency active vibration isolation for {Advanced LIGO}},
  booktitle       = {Gravitational Wave and Particle Astrophysics Detectors},
  year            = 2004,
  volume          = 5500,
@@ -541,21 +293,6 @@
  organization    = {International Society for Optics and Photonics},
 }

-@article{akutsu21_vibrat_isolat_system_beam_split,
-  author          = {Akutsu, T and Ando, M and Arai, K and Arai, Y and Araki, S
-                  and Araya, A and Aritomi, N and Asada, H and Aso, Y and Bae, S
-                  and others},
-  title           = {Vibration Isolation Systems for the Beam Splitter and
-                  Signal Recycling Mirrors of the Kagra Gravitational Wave
-                  Detector},
-  journal         = {Classical and Quantum Gravity},
-  volume          = 38,
-  number          = 6,
-  pages           = 065011,
-  year            = 2021,
-  publisher       = {IOP Publishing},
-}
-
@phdthesis{heijningen18_low,
  author          = {van Heijningen, JV},
  school          = {Vrije Universiteit},
@@ -566,10 +303,10 @@
 }

@phdthesis{lucia18_low_frequen_optim_perfor_advan,
-  author          = {Trozzo Lucia},
+  author          = {L. Trozzo},
  school          = {University of Siena},
-  title           = {Low Frequency Optimization and Performance of Advanced
-                  Virgo Seismic Isolation System},
+  title           = {Low Frequency Optimization and Performance of {Advanced
+                  Virgo} Seismic Isolation System},
  year            = 2018,
 }

@@ -580,8 +317,82 @@
  booktitle       = {Proceedings of the 44th IEEE Conference on Decision and
                  Control},
  year            = 2005,
-  pages           = {nil},
  doi             = {10.1109/cdc.2005.1582367},
-  url             = {https://doi.org/10.1109/cdc.2005.1582367},
  month           = {-},
 }
+
+@article{min15_compl_filter_desig_angle_estim,
+  author          = {Min, Hyung Gi and Jeung, Eun Tae},
+  title           = {Complementary Filter Design for Angle Estimation Using Mems
+                  Accelerometer and Gyroscope},
+  journal         = {Department of Control and Instrumentation, Changwon
+                  National University, Changwon, Korea},
+  pages           = {641--773},
+  year            = 2015,
+}
+
+@article{batista10_optim_posit_veloc_navig_filter_auton_vehic,
+  author          = {Batista, Pedro and Silvestre, Carlos and Oliveira, Paulo},
+  title           = {Optimal Position and Velocity Navigation Filters for
+                  Autonomous Vehicles},
+  journal         = {Automatica},
+  volume          = 46,
+  number          = 4,
+  pages           = {767--774},
+  year            = 2010,
+  doi             = {10.1016/j.automatica.2010.02.004},
+  publisher       = {Elsevier},
+}
+
+@phdthesis{sekiguchi16_study_low_frequen_vibrat_isolat_system,
+  author          = {Sekiguchi, Takanori},
+  school          = {University of Tokyo},
+  title           = {A Study of Low Frequency Vibration Isolation System for
+                  large scale gravitational wave detectors},
+  year            = 2016,
+}
+
+@article{yeh05_model_contr_hydraul_actuat_two,
+  author          = {T-J Yeh and C-Y Su and W-J Wang},
+  title           = {Modelling and Control of a Hydraulically Actuated
+                  Two-Degree-Of-Freedom Inertial Platform},
+  journal         = {Proceedings of the Institution of Mechanical Engineers,
+                  Part I: Journal of Systems and Control Engineering},
+  volume          = 219,
+  number          = 6,
+  pages           = {405-417},
+  year            = 2005,
+  doi             = {10.1243/095965105x33527},
+}
+
+@inproceedings{dehaeze19_compl_filter_shapin_using_synth,
+  author          = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
+  title           = {Complementary Filters Shaping Using $\mathcal{H}_\infty$
+                  Synthesis},
+  booktitle       = {7th International Conference on Control, Mechatronics and
+                  Automation (ICCMA)},
+  year            = 2019,
+  pages           = {459-464},
+  doi             = {10.1109/ICCMA46720.2019.8988642},
+  language        = {english},
+}
+
+@misc{dehaeze21_new_method_desig_compl_filter_code,
+  author          = {Dehaeze, Thomas},
+  doi             = {10.5281/zenodo.5361943},
+  howpublished    = {Source code on Zenodo},
+  month           = sep,
+  title           = {{A New Method of Designing Complementary Filters for Sensor
+                  Fusion Using the $\mathcal{H}_\infty$ Synthesis}},
+  year            = 2021,
+}
+
+@book{skogestad07_multiv_feedb_contr,
+  author          = {Skogestad, Sigurd and Postlethwaite, Ian},
+  title           = {Multivariable Feedback Control: Analysis and Design -
+                  Second Edition},
+  year            = 2007,
+  publisher       = {John Wiley},
+  isbn            = {978-0470011683},
+  note            = {isbn:978-0470011683},
+}
--- a/matlab/.latexmkrc
+++ b/matlab/.latexmkrc
@@ -0,0 +1,98 @@
+#!/bin/env perl
+
+# Shebang is only to get syntax highlighting right across GitLab, GitHub and IDEs.
+# This file is not meant to be run, but read by `latexmk`.
+
+# ======================================================================================
+# Perl `latexmk` configuration file
+# ======================================================================================
+
+# ======================================================================================
+# PDF Generation/Building/Compilation
+# ======================================================================================
+
+@default_files=('dehaeze21_desig_compl_filte_matlab.tex');
+
+# PDF-generating modes are:
+# 1: pdflatex, as specified by $pdflatex variable (still largely in use)
+# 2: postscript conversion, as specified by the $ps2pdf variable (useless)
+# 3: dvi conversion, as specified by the $dvipdf variable (useless)
+# 4: lualatex, as specified by the $lualatex variable (best)
+# 5: xelatex, as specified by the $xelatex variable (second best)
+$pdf_mode = 1;
+
+# Treat undefined references and citations as well as multiply defined references as
+# ERRORS instead of WARNINGS.
+# This is only checked in the *last* run, since naturally, there are undefined references
+# in initial runs.
+# This setting is potentially annoying when debugging/editing, but highly desirable
+# in the CI pipeline, where such a warning should result in a failed pipeline, since the
+# final document is incomplete/corrupted.
+#
+# However, I could not eradicate all warnings, so that `latexmk` currently fails with
+# this option enabled.
+# Specifically, `microtype` fails together with `fontawesome`/`fontawesome5`, see:
+# https://tex.stackexchange.com/a/547514/120853
+# The fix in that answer did not help.
+# Setting `verbose=silent` to mute `microtype` warnings did not work.
+# Switching between `fontawesome` and `fontawesome5` did not help.
+$warnings_as_errors = 0;
+
+# Show used CPU time. Looks like: https://tex.stackexchange.com/a/312224/120853
+$show_time = 1;
+
+# Default is 5; we seem to need more owed to the complexity of the document.
+# Actual documents probably don't need this many since they won't use all features,
+# plus won't be compiling from cold each time.
+$max_repeat=7;
+
+# --shell-escape option (execution of code outside of latex) is required for the
+#'svg' package.
+# It converts raw SVG files to the PDF+PDF_TEX combo using InkScape.
+#
+# SyncTeX allows to jump between source (code) and output (PDF) in IDEs with support
+# (many have it). A value of `1` is enabled (gzipped), `-1` is enabled but uncompressed,
+# `0` is off.
+# Testing in VSCode w/ LaTeX Workshop only worked for the compressed version.
+# Adjust this as needed. Of course, only relevant for local use, no effect on a remote
+# CI pipeline (except for slower compilation, probably).
+#
+# %O and %S will forward Options and the Source file, respectively, given to latexmk.
+#
+# `set_tex_cmds` applies to all *latex commands (latex, xelatex, lualatex, ...), so
+# no need to specify these each. This allows to simply change `$pdf_mode` to get a
+# different engine. Check if this works with `latexmk --commands`.
+set_tex_cmds("--shell-escape -interaction=nonstopmode --synctex=1 %O %S");
+
+# Use default pdf viewer
+$pdf_previewer = 'zathura';
+
+# option 2 is same as 1 (run biber when necessary), but also deletes the
+# regeneratable bbl-file in a clenaup (`latexmk -c`). Do not use if original
+# bib file is not available!
+$bibtex_use = 2;  # default: 1
+
+# Change default `biber` call, help catch errors faster/clearer. See
+# https://web.archive.org/web/20200526101657/https://www.semipol.de/2018/06/12/latex-best-practices.html#database-entries
+$biber = "biber --validate-datamodel %O %S";
+
+# ======================================================================================
+# Auxiliary Files
+# ======================================================================================
+
+# Let latexmk know about generated files, so they can be used to detect if a
+# rerun is required, or be deleted in a cleanup.
+# loe: List of Examples (KOMAScript)
+# lol: List of Listings (`listings` and `minted` packages)
+# run.xml: biber runs
+# glg: glossaries log
+# glstex: generated from glossaries-extra
+push @generated_exts, 'loe', 'lol', 'run.xml', 'glg', 'glstex';
+
+# Also delete the *.glstex files from package glossaries-extra. Problem is,
+# that that package generates files of the form "basename-digit.glstex" if
+# multiple glossaries are present. Latexmk looks for "basename.glstex" and so
+# does not find those. For that purpose, use wildcard.
+# Also delete files generated by gnuplot/pgfplots contour plots
+# (.dat, .script, .table).
+$clean_ext = "%R-*.glstex %R_contourtmp*.*";
--- a/matlab/dehaeze21_desig_compl_filte_matlab.html
+++ b/matlab/dehaeze21_desig_compl_filte_matlab.html
--- a/matlab/dehaeze21_desig_compl_filte_matlab.org
+++ b/matlab/dehaeze21_desig_compl_filte_matlab.org
--- a/matlab/dehaeze21_desig_compl_filte_matlab.pdf
+++ b/matlab/dehaeze21_desig_compl_filte_matlab.pdf
--- a/matlab/dehaeze21_desig_compl_filte_matlab.tex
+++ b/matlab/dehaeze21_desig_compl_filte_matlab.tex
--- a/matlab/figs-journal
+++ b/matlab/figs-journal
--- a/matlab/figs/comp_fir_ligo_hinf.pdf
+++ b/matlab/figs/comp_fir_ligo_hinf.pdf
--- a/matlab/figs/comp_fir_ligo_hinf.png
+++ b/matlab/figs/comp_fir_ligo_hinf.png
--- a/matlab/figs/fir_filter_ligo.pdf
+++ b/matlab/figs/fir_filter_ligo.pdf
--- a/matlab/figs/fir_filter_ligo.png
+++ b/matlab/figs/fir_filter_ligo.png
--- a/matlab/figs/hinf_filters_results.pdf
+++ b/matlab/figs/hinf_filters_results.pdf
--- a/matlab/figs/hinf_filters_results.png
+++ b/matlab/figs/hinf_filters_results.png
--- a/matlab/figs/hinf_filters_results_mixed_sensitivity.pdf
+++ b/matlab/figs/hinf_filters_results_mixed_sensitivity.pdf
--- a/matlab/figs/hinf_filters_results_mixed_sensitivity.png
+++ b/matlab/figs/hinf_filters_results_mixed_sensitivity.png
--- a/journal/figs/hinf_synthesis_ligo_results.pdf
+++ b/journal/figs/hinf_synthesis_ligo_results.pdf
--- a/journal/figs/hinf_synthesis_ligo_results.png
+++ b/journal/figs/hinf_synthesis_ligo_results.png
--- a/journal/figs/ligo_specifications.pdf
+++ b/journal/figs/ligo_specifications.pdf
--- a/matlab/figs/ligo_specifications.png
+++ b/matlab/figs/ligo_specifications.png
--- a/matlab/figs/ligo_weights.pdf
+++ b/matlab/figs/ligo_weights.pdf
--- a/matlab/figs/ligo_weights.png
+++ b/matlab/figs/ligo_weights.png
--- a/matlab/figs/three_complementary_filters_results.pdf
+++ b/matlab/figs/three_complementary_filters_results.pdf
--- a/matlab/figs/three_complementary_filters_results.png
+++ b/matlab/figs/three_complementary_filters_results.png
--- a/matlab/figs/three_weighting_functions.pdf
+++ b/matlab/figs/three_weighting_functions.pdf
--- a/matlab/figs/three_weighting_functions.png
+++ b/matlab/figs/three_weighting_functions.png
--- a/matlab/figs/weight_formula.pdf
+++ b/matlab/figs/weight_formula.pdf
--- a/matlab/figs/weight_formula.png
+++ b/matlab/figs/weight_formula.png
--- a/matlab/figs/weights_W1_W2.pdf
+++ b/matlab/figs/weights_W1_W2.pdf
--- a/matlab/figs/weights_W1_W2.png
+++ b/matlab/figs/weights_W1_W2.png
--- a/matlab/index.html
+++ b/matlab/index.html
--- a/matlab/index.org
+++ b/matlab/index.org
--- a/matlab/index.pdf
+++ b/matlab/index.pdf
--- a/matlab/matlab.zip
+++ b/matlab/matlab.zip
--- a/matlab/matlab/1_synthesis_complementary_filters.m
+++ b/matlab/matlab/1_synthesis_complementary_filters.m
@@ -0,0 +1,120 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize Frequency Vector
+freqs = logspace(-1, 3, 1000);
+
+%% Weighting Function Design
+% Parameters
+n = 3; w0 = 2*pi*10; G0 = 1e-3; G1 = 1e1; Gc = 2;
+
+% Formulas
+W = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
+
+%% Magnitude of the weighting function with parameters
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(W, freqs, 'Hz'))), 'k-');
+
+plot([1e-3 1e0], [G0 G0], 'k--', 'LineWidth', 1)
+text(1e0, G0, '$\quad G_0$')
+
+plot([1e1 1e3], [G1 G1], 'k--', 'LineWidth', 1)
+text(1e1,G1,'$G_{\infty}\quad$','HorizontalAlignment', 'right')
+
+plot([w0/2/pi w0/2/pi], [1 2*Gc], 'k--', 'LineWidth', 1)
+text(w0/2/pi,1,'$\omega_c$','VerticalAlignment', 'top', 'HorizontalAlignment', 'center')
+
+plot([w0/2/pi/2  2*w0/2/pi], [Gc Gc], 'k--', 'LineWidth', 1)
+text(w0/2/pi/2, Gc, '$G_c \quad$','HorizontalAlignment', 'right')
+
+text(w0/5/pi/2, abs(evalfr(W, j*w0/5)), 'Slope: $n \quad$', 'HorizontalAlignment', 'right')
+
+text(w0/2/pi, abs(evalfr(W, j*w0)), '$\bullet$', 'HorizontalAlignment', 'center')
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude');
+hold off;
+xlim([freqs(1), freqs(end)]);
+ylim([5e-4, 20]);
+yticks([1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1]);
+
+%% Design of the Weighting Functions
+W1 = generateWF('n', 3, 'w0', 2*pi*10, 'G0', 1000, 'Ginf', 1/10, 'Gc', 0.45);
+W2 = generateWF('n', 2, 'w0', 2*pi*10, 'G0', 1/10, 'Ginf', 1000, 'Gc', 0.45);
+
+%% Plot of the Weighting function magnitude
+figure;
+tiledlayout(1, 1, 'TileSpacing', 'None', 'Padding', 'None');
+ax1 = nexttile();
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]', 'FontSize', 10); ylabel('Magnitude', 'FontSize', 10);
+hold off;
+xlim([freqs(1), freqs(end)]);
+xticks([0.1, 1, 10, 100, 1000]);
+ylim([8e-4, 20]);
+yticks([1e-3, 1e-2, 1e-1, 1, 1e1]);
+yticklabels({'', '$10^{-2}$', '', '$10^0$', ''});
+ax1.FontSize = 9;
+leg = legend('location', 'south', 'FontSize', 8);
+leg.ItemTokenSize(1) = 18;
+
+%% Generalized Plant
+P = [W1 -W1;
+     0   W2;
+     1   0];
+
+%% H-Infinity Synthesis
+[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
+
+%% Define H1 to be the complementary of H2
+H1 = 1 - H2;
+
+%% Bode plot of the complementary filters
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+% Magnitude
+ax1 = nexttile([2, 1]);
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
+
+set(gca,'ColorOrderIndex',1)
+plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]); ylabel('Magnitude');
+ylim([8e-4, 20]);
+yticks([1e-3, 1e-2, 1e-1, 1, 1e1]);
+yticklabels({'', '$10^{-2}$', '', '$10^0$', ''})
+leg = legend('location', 'south', 'FontSize', 8, 'NumColumns', 2);
+leg.ItemTokenSize(1) = 18;
+
+% Phase
+ax2 = nexttile;
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*phase(squeeze(freqresp(H1, freqs, 'Hz'))), '-');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, 180/pi*phase(squeeze(freqresp(H2, freqs, 'Hz'))), '-');
+hold off;
+set(gca, 'XScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+yticks([-180:90:180]);
+ylim([-180, 200])
+yticklabels({'-180', '', '0', '', '180'})
+
+linkaxes([ax1,ax2],'x');
+xlim([freqs(1), freqs(end)]);
--- a/matlab/matlab/2_ligo_complementary_filters.m
+++ b/matlab/matlab/2_ligo_complementary_filters.m
@@ -0,0 +1,255 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize Frequency Vector
+freqs = logspace(-3, 0, 1000);
+
+%% Upper bounds for the complementary filters
+figure;
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot([0.0001, 0.008], [8e-3, 8e-3], ':', 'DisplayName', 'Spec. on $H_H$');
+set(gca,'ColorOrderIndex',1)
+plot([0.008 0.04], [8e-3, 1], ':', 'HandleVisibility', 'off');
+set(gca,'ColorOrderIndex',1)
+plot([0.04 0.1], [3, 3], ':', 'HandleVisibility', 'off');
+set(gca,'ColorOrderIndex',2)
+plot([0.1, 10], [0.045, 0.045], ':', 'DisplayName', 'Spec. on $H_L$');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude');
+hold off;
+xlim([freqs(1), freqs(end)]);
+ylim([1e-4, 10]);
+leg = legend('location', 'southeast', 'FontSize', 8);
+leg.ItemTokenSize(1) = 18;
+
+%% Initialized CVX
+cvx_startup;
+cvx_solver sedumi;
+
+%% Frequency vectors
+w1 = 0:4.06e-4:0.008;
+w2 = 0.008:4.06e-4:0.04;
+w3 = 0.04:8.12e-4:0.1;
+w4 = 0.1:8.12e-4:0.83;
+
+%% Filter order
+n = 512;
+
+%% Initialization of filter responses
+A1 = [ones(length(w1),1),  cos(kron(w1'.*(2*pi),[1:n-1]))];
+A2 = [ones(length(w2),1),  cos(kron(w2'.*(2*pi),[1:n-1]))];
+A3 = [ones(length(w3),1),  cos(kron(w3'.*(2*pi),[1:n-1]))];
+A4 = [ones(length(w4),1),  cos(kron(w4'.*(2*pi),[1:n-1]))];
+
+B1 = [zeros(length(w1),1), sin(kron(w1'.*(2*pi),[1:n-1]))];
+B2 = [zeros(length(w2),1), sin(kron(w2'.*(2*pi),[1:n-1]))];
+B3 = [zeros(length(w3),1), sin(kron(w3'.*(2*pi),[1:n-1]))];
+B4 = [zeros(length(w4),1), sin(kron(w4'.*(2*pi),[1:n-1]))];
+
+%% Convex optimization
+cvx_begin
+
+variable y(n+1,1)
+
+% t
+maximize(-y(1))
+
+for i = 1:length(w1)
+    norm([0 A1(i,:); 0 B1(i,:)]*y) <= 8e-3;
+end
+
+for  i = 1:length(w2)
+    norm([0 A2(i,:); 0 B2(i,:)]*y) <= 8e-3*(2*pi*w2(i)/(0.008*2*pi))^3;
+end
+
+for i = 1:length(w3)
+    norm([0 A3(i,:); 0 B3(i,:)]*y) <= 3;
+end
+
+for i = 1:length(w4)
+    norm([[1 0]'- [0 A4(i,:); 0 B4(i,:)]*y]) <= y(1);
+end
+
+cvx_end
+
+h = y(2:end);
+
+%% Combine the frequency vectors to form the obtained filter
+w = [w1 w2 w3 w4];
+H = [exp(-j*kron(w'.*2*pi,[0:n-1]))]*h;
+
+%% Bode plot of the obtained complementary filters
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+% Magnitude
+ax1 = nexttile([2, 1]);
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot(w, abs(1-H), '-', 'DisplayName', '$L_1$');
+plot([0.1, 10], [0.045, 0.045], 'k:', 'DisplayName', 'Spec. on $L_1$');
+
+set(gca,'ColorOrderIndex',2)
+plot(w, abs(H), '-', 'DisplayName', '$H_1$');
+plot([0.0001, 0.008], [8e-3, 8e-3], 'k--', 'DisplayName', 'Spec. on $H_1$');
+plot([0.008 0.04], [8e-3, 1],       'k--', 'HandleVisibility', 'off');
+plot([0.04 0.1], [3, 3],            'k--', 'HandleVisibility', 'off');
+
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]); ylabel('Magnitude');
+hold off;
+ylim([5e-3, 10]);
+leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
+leg.ItemTokenSize(1) = 16;
+
+% Phase
+ax2 = nexttile;
+hold on;
+plot(w, 180/pi*unwrap(angle(1-H)), '-');
+plot(w, 180/pi*unwrap(angle(H)), '-');
+hold off;
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+set(gca, 'XScale', 'log');
+yticks([-360:180:180]); ylim([-380, 200]);
+
+linkaxes([ax1,ax2],'x');
+xlim([1e-3, 1]);
+
+%% Design of the weight for the high pass filter
+w1 = 2*pi*0.008; x1 = 0.35;
+w2 = 2*pi*0.04;  x2 = 0.5;
+w3 = 2*pi*0.05;  x3 = 0.5;
+
+% Slope of +3 from w1
+wH = 0.008*(s^2/w1^2 + 2*x1/w1*s + 1)*(s/w1 + 1);
+% Little bump from w2 to w3
+wH = wH*(s^2/w2^2 + 2*x2/w2*s + 1)/(s^2/w3^2 + 2*x3/w3*s + 1);
+% No Slope at high frequencies
+wH = wH/(s^2/w3^2 + 2*x3/w3*s + 1)/(s/w3 + 1);
+% Little bump between w2 and w3
+w0 = 2*pi*0.045; xi = 0.1; A = 2; n = 1;
+wH = wH*((s^2 + 2*w0*xi*A^(1/n)*s + w0^2)/(s^2 + 2*w0*xi*s + w0^2))^n;
+
+wH = 1/wH;
+wH = minreal(ss(wH));
+
+%% Design of the weight for the low pass filter
+n = 20; % Filter order
+Rp = 1; % Peak to peak passband ripple
+Wp = 2*pi*0.102; % Edge frequency
+
+% Chebyshev Type I filter design
+[b,a] = cheby1(n, Rp, Wp, 'high', 's');
+wL = 0.04*tf(a, b);
+
+wL = 1/wL;
+wL = minreal(ss(wL));
+
+%% Magnitude of the designed Weights and initial specifications
+figure;
+hold on;
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(inv(wL), freqs, 'Hz'))), '-', 'DisplayName', '$|W_L|^{-1}$');
+plot([0.1, 10], [0.045, 0.045],     'k:',  'DisplayName', 'Spec. on $L_1$');
+
+set(gca,'ColorOrderIndex',2);
+plot(freqs, abs(squeeze(freqresp(inv(wH), freqs, 'Hz'))), '-', 'DisplayName', '$|W_H|^{-1}$');
+plot([0.0001, 0.008], [8e-3, 8e-3], 'k--', 'DisplayName', 'Spec. on $H_1$');
+plot([0.008 0.04], [8e-3, 1],       'k--', 'HandleVisibility', 'off');
+plot([0.04 0.1], [3, 3],            'k--', 'HandleVisibility', 'off');
+
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude');
+hold off;
+xlim([freqs(1), freqs(end)]);
+ylim([5e-3, 10]);
+leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
+leg.ItemTokenSize(1) = 16;
+
+%% Generalized plant for the H-infinity Synthesis
+P = [0   wL;
+     wH -wH;
+     1   0];
+
+%% Standard H-Infinity synthesis
+[Hl, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
+
+%% High pass filter as the complementary of the low pass filter
+Hh = 1 - Hl;
+
+%% Minimum realization of the filters
+Hh = minreal(Hh);
+Hl = minreal(Hl);
+
+%% Bode plot of the obtained filters and comparison with the upper bounds
+figure;
+hold on;
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(Hl, freqs, 'Hz'))), '-', 'DisplayName', '$L_1^\prime$');
+plot([0.1, 10], [0.045, 0.045],     'k:',  'DisplayName', 'Spec. on $L_1$');
+
+set(gca,'ColorOrderIndex',2);
+plot(freqs, abs(squeeze(freqresp(Hh, freqs, 'Hz'))), '-', 'DisplayName', '$H_1^\prime$');
+plot([0.0001, 0.008], [8e-3, 8e-3], 'k--', 'DisplayName', 'Spec. on $H_1$');
+plot([0.008 0.04], [8e-3, 1],       'k--', 'HandleVisibility', 'off');
+plot([0.04 0.1], [3, 3],            'k--', 'HandleVisibility', 'off');
+
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude');
+hold off;
+xlim([freqs(1), freqs(end)]);
+ylim([5e-3, 10]);
+leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
+leg.ItemTokenSize(1) = 16;
+
+%% Comparison of the complementary filters obtained with H-infinity and with CVX
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+% Magnitude
+ax1 = nexttile([2, 1]);
+hold on;
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(Hl, freqs, 'Hz'))), '-', ...
+     'DisplayName', '$L_1(s)$ - $\mathcal{H}_\infty$');
+set(gca,'ColorOrderIndex',2);
+plot(freqs, abs(squeeze(freqresp(Hh, freqs, 'Hz'))), '-', ...
+     'DisplayName', '$H_1(s)$ - $\mathcal{H}_\infty$');
+
+set(gca,'ColorOrderIndex',1);
+plot(w, abs(1-H), '--', ...
+     'DisplayName', '$L_1(s)$ - FIR');
+set(gca,'ColorOrderIndex',2);
+plot(w, abs(H), '--', ...
+     'DisplayName', '$H_1(s)$ - FIR');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Magnitude');
+set(gca, 'XTickLabel',[]);
+ylim([5e-3, 10]);
+leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
+leg.ItemTokenSize(1) = 16;
+
+% Phase
+ax2 = nexttile;
+hold on;
+set(gca,'ColorOrderIndex',1);
+plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Hl, freqs, 'Hz')))), '-');
+set(gca,'ColorOrderIndex',2);
+plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Hh, freqs, 'Hz')))), '-');
+
+set(gca,'ColorOrderIndex',1);
+plot(w, 180/pi*unwrap(angle(1-H)), '--');
+set(gca,'ColorOrderIndex',2);
+plot(w, 180/pi*unwrap(angle(H)), '--');
+set(gca, 'XScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+hold off;
+yticks([-360:180:180]); ylim([-380, 200]);
+
+linkaxes([ax1,ax2],'x');
+xlim([freqs(1), freqs(end)]);
--- a/matlab/matlab/3_closed_loop_complementary_filters.m
+++ b/matlab/matlab/3_closed_loop_complementary_filters.m
@@ -0,0 +1,68 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize Frequency Vector
+freqs = logspace(-1, 3, 1000);
+
+%% Design of the Weighting Functions
+W1 = generateWF('n', 3, 'w0', 2*pi*10, 'G0', 1000, 'Ginf', 1/10, 'Gc', 0.45);
+W2 = generateWF('n', 2, 'w0', 2*pi*10, 'G0', 1/10, 'Ginf', 1000, 'Gc', 0.45);
+
+%% Generalized plant for "closed-loop" complementary filter synthesis
+P = [ W1 0   1;
+     -W1 W2 -1];
+
+%% Standard H-Infinity Synthesis
+[L, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
+
+%% Complementary filters
+H1 = inv(1 + L);
+H2 = 1 - H1;
+
+%% Bode plot of the obtained Complementary filters with upper-bounds
+freqs = logspace(-1, 3, 1000);
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+% Magnitude
+ax1 = nexttile([2, 1]);
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
+
+set(gca,'ColorOrderIndex',1)
+plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
+
+plot(freqs, abs(squeeze(freqresp(L, freqs, 'Hz'))), 'k--', 'DisplayName', '$|L|$');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]); ylabel('Magnitude');
+ylim([1e-3, 1e3]);
+yticks([1e-3, 1e-2, 1e-1, 1, 1e1, 1e2, 1e3]);
+yticklabels({'', '$10^{-2}$', '', '$10^0$', '', '$10^2$', ''});
+leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 3);
+leg.ItemTokenSize(1) = 18;
+
+% Phase
+ax2 = nexttile;
+hold on;
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*phase(squeeze(freqresp(H1, freqs, 'Hz'))), '-');
+set(gca,'ColorOrderIndex',2)
+plot(freqs, 180/pi*phase(squeeze(freqresp(H2, freqs, 'Hz'))), '-');
+hold off;
+set(gca, 'XScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+yticks([-180:90:180]);
+ylim([-180, 200])
+yticklabels({'-180', '', '0', '', '180'})
+
+linkaxes([ax1,ax2],'x');
+xlim([freqs(1), freqs(end)]);
--- a/matlab/matlab/4_three_complementary_filters.m
+++ b/matlab/matlab/4_three_complementary_filters.m
@@ -4,21 +4,14 @@ clear; close all; clc;
 %% Intialize Laplace variable
 s = zpk('s');

-freqs = logspace(-2, 4, 1000);
-
-addpath('./src');
-
-% Weights
-% First we define the weights.
-
-n = 2; w0 = 2*pi*1; G0 = 1/10; G1 = 1000; Gc = 1/2;
-W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
+freqs = logspace(-2, 3, 1000);

+%% Design of the Weighting Functions
+W1 = generateWF('n', 2, 'w0', 2*pi*1, 'G0', 1/10, 'Ginf', 1000, 'Gc', 0.5);
 W2 = 0.22*(1 + s/2/pi/1)^2/(sqrt(1e-4) + s/2/pi/1)^2*(1 + s/2/pi/10)^2/(1 + s/2/pi/1000)^2;
+W3 = generateWF('n', 3, 'w0', 2*pi*10, 'G0', 1000, 'Ginf', 1/10, 'Gc', 0.5);

-n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 1/2;
-W3 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
-
+%% Inverse magnitude of the weighting functions
 figure;
 hold on;
 set(gca,'ColorOrderIndex',1)
@@ -34,27 +27,23 @@ xlim([freqs(1), freqs(end)]); ylim([2e-4, 1.3e1])
 leg = legend('location', 'northeast', 'FontSize', 8);
 leg.ItemTokenSize(1) = 18;

-% H-Infinity Synthesis
-% Then we create the generalized plant =P=.
-
+%% Generalized plant for the synthesis of 3 complementary filters
 P = [W1 -W1 -W1;
     0   W2  0 ;
     0   0   W3;
     1   0   0];

-
-
-% And we do the $\mathcal{H}_\infty$ synthesis.
-
+%% Standard H-Infinity Synthesis
 [H, ~, gamma, ~] = hinfsyn(P, 1, 2,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');

-% Obtained Complementary Filters
-% The obtained filters are:
-
+%% Synthesized H2 and H3 filters
 H2 = tf(H(1));
 H3 = tf(H(2));
+
+%% H1 is defined as the complementary filter of H2 and H3
 H1 = 1 - H2 - H3;

+%% Bode plot of the obtained complementary filters
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');

@@ -79,7 +68,7 @@ set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
 ylabel('Magnitude');
 set(gca, 'XTickLabel',[]);
 ylim([1e-4, 20]);
-leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
+leg = legend('location', 'northeast', 'FontSize', 8);
 leg.ItemTokenSize(1) = 18;

 % Phase
@@ -94,7 +83,7 @@ plot(freqs, 180/pi*phase(squeeze(freqresp(H3, freqs, 'Hz'))));
 hold off;
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 set(gca, 'XScale', 'log');
-yticks([-360:90:360]); ylim([-270, 270]);
+yticks([-180:90:180]); ylim([-220, 220]);

 linkaxes([ax1,ax2],'x');
 xlim([freqs(1), freqs(end)]);
--- a/matlab/matlab/comp_filters_ligo.m
+++ b/matlab/matlab/comp_filters_ligo.m
@@ -1,410 +0,0 @@
-%% Clear Workspace and Close figures
-clear; close all; clc;
-
-%% Intialize Laplace variable
-s = zpk('s');
-
-freqs = logspace(-3, 0, 1000);
-
-addpath('./src');
-
-% Specifications
-% The specifications for the filters are:
-% 1. From $0$ to $0.008\text{ Hz}$,the magnitude of the filter’s transfer function should be less than or equal to $8 \times 10^{-3}$
-% 2. From $0.008\text{ Hz}$ to $0.04\text{ Hz}$, it attenuates the input signal proportional to frequency cubed
-% 3. Between $0.04\text{ Hz}$ and $0.1\text{ Hz}$, the magnitude of the transfer function should be less than 3
-% 4. Above $0.1\text{ Hz}$, the maximum of the magnitude of the complement filter should be as close to zero as possible. In our system, we would like to have the magnitude of the complementary filter to be less than $0.1$. As the filters obtained in cite:hua05_low_ligo have a magnitude of $0.045$, we will set that as our requirement
-
-% The specifications are translated in upper bounds of the complementary filters are shown on figure [[fig:ligo_specifications]].
-
-
-figure;
-hold on;
-set(gca,'ColorOrderIndex',1)
-plot([0.0001, 0.008], [8e-3, 8e-3], ':', 'DisplayName', 'Spec. on $H_H$');
-set(gca,'ColorOrderIndex',1)
-plot([0.008 0.04], [8e-3, 1], ':', 'HandleVisibility', 'off');
-set(gca,'ColorOrderIndex',1)
-plot([0.04 0.1], [3, 3], ':', 'HandleVisibility', 'off');
-set(gca,'ColorOrderIndex',2)
-plot([0.1, 10], [0.045, 0.045], ':', 'DisplayName', 'Spec. on $H_L$');
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Magnitude');
-hold off;
-xlim([freqs(1), freqs(end)]);
-ylim([1e-4, 10]);
-leg = legend('location', 'southeast', 'FontSize', 8);
-leg.ItemTokenSize(1) = 18;
-
-% FIR Filter
-% We here try to implement the FIR complementary filter synthesis as explained in cite:hua05_low_ligo.
-% For that, we use the [[http://cvxr.com/cvx/][CVX matlab Toolbox]].
-
-% We setup the CVX toolbox and use the =SeDuMi= solver.
-
-cvx_startup;
-cvx_solver sedumi;
-
-
-
-% We define the frequency vectors on which we will constrain the norm of the FIR filter.
-
-w1 = 0:4.06e-4:0.008;
-w2 = 0.008:4.06e-4:0.04;
-w3 = 0.04:8.12e-4:0.1;
-w4 = 0.1:8.12e-4:0.83;
-
-
-
-% We then define the order of the FIR filter.
-
-n = 512;
-
-A1 = [ones(length(w1),1),  cos(kron(w1'.*(2*pi),[1:n-1]))];
-A2 = [ones(length(w2),1),  cos(kron(w2'.*(2*pi),[1:n-1]))];
-A3 = [ones(length(w3),1),  cos(kron(w3'.*(2*pi),[1:n-1]))];
-A4 = [ones(length(w4),1),  cos(kron(w4'.*(2*pi),[1:n-1]))];
-
-B1 = [zeros(length(w1),1), sin(kron(w1'.*(2*pi),[1:n-1]))];
-B2 = [zeros(length(w2),1), sin(kron(w2'.*(2*pi),[1:n-1]))];
-B3 = [zeros(length(w3),1), sin(kron(w3'.*(2*pi),[1:n-1]))];
-B4 = [zeros(length(w4),1), sin(kron(w4'.*(2*pi),[1:n-1]))];
-
-
-
-% We run the convex optimization.
-
-cvx_begin
-
-variable y(n+1,1)
-
-% t
-maximize(-y(1))
-
-for i = 1:length(w1)
-    norm([0 A1(i,:); 0 B1(i,:)]*y) <= 8e-3;
-end
-
-for  i = 1:length(w2)
-    norm([0 A2(i,:); 0 B2(i,:)]*y) <= 8e-3*(2*pi*w2(i)/(0.008*2*pi))^3;
-end
-
-for i = 1:length(w3)
-    norm([0 A3(i,:); 0 B3(i,:)]*y) <= 3;
-end
-
-for i = 1:length(w4)
-    norm([[1 0]'- [0 A4(i,:); 0 B4(i,:)]*y]) <= y(1);
-end
-
-cvx_end
-
-h = y(2:end);
-
-
-
-% #+RESULTS:
-% #+begin_example
-% cvx_begin
-% variable y(n+1,1)
-% % t
-% maximize(-y(1))
-% for i = 1:length(w1)
-%     norm([0 A1(i,:); 0 B1(i,:)]*y) <= 8e-3;
-% end
-% for  i = 1:length(w2)
-%     norm([0 A2(i,:); 0 B2(i,:)]*y) <= 8e-3*(2*pi*w2(i)/(0.008*2*pi))^3;
-% end
-% for i = 1:length(w3)
-%     norm([0 A3(i,:); 0 B3(i,:)]*y) <= 3;
-% end
-% for i = 1:length(w4)
-%     norm([[1 0]'- [0 A4(i,:); 0 B4(i,:)]*y]) <= y(1);
-% end
-% cvx_end
-
-% Calling SeDuMi 1.34: 4291 variables, 1586 equality constraints
-%    For improved efficiency, SeDuMi is solving the dual problem.
-% ------------------------------------------------------------
-% SeDuMi 1.34 (beta) by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
-% Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
-% eqs m = 1586, order n = 3220, dim = 4292, blocks = 1073
-% nnz(A) = 1100727 + 0, nnz(ADA) = 1364794, nnz(L) = 683190
-%  it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
-%   0 :            4.11E+02 0.000
-%   1 :  -2.58E+00 1.25E+02 0.000 0.3049 0.9000 0.9000   4.87  1  1  3.0E+02
-%   2 :  -2.36E+00 3.90E+01 0.000 0.3118 0.9000 0.9000   1.83  1  1  6.6E+01
-%   3 :  -1.69E+00 1.31E+01 0.000 0.3354 0.9000 0.9000   1.76  1  1  1.5E+01
-%   4 :  -8.60E-01 7.10E+00 0.000 0.5424 0.9000 0.9000   2.48  1  1  4.8E+00
-%   5 :  -4.91E-01 5.44E+00 0.000 0.7661 0.9000 0.9000   3.12  1  1  2.5E+00
-%   6 :  -2.96E-01 3.88E+00 0.000 0.7140 0.9000 0.9000   2.62  1  1  1.4E+00
-%   7 :  -1.98E-01 2.82E+00 0.000 0.7271 0.9000 0.9000   2.14  1  1  8.5E-01
-%   8 :  -1.39E-01 2.00E+00 0.000 0.7092 0.9000 0.9000   1.78  1  1  5.4E-01
-%   9 :  -9.99E-02 1.30E+00 0.000 0.6494 0.9000 0.9000   1.51  1  1  3.3E-01
-%  10 :  -7.57E-02 8.03E-01 0.000 0.6175 0.9000 0.9000   1.31  1  1  2.0E-01
-%  11 :  -5.99E-02 4.22E-01 0.000 0.5257 0.9000 0.9000   1.17  1  1  1.0E-01
-%  12 :  -5.28E-02 2.45E-01 0.000 0.5808 0.9000 0.9000   1.08  1  1  5.9E-02
-%  13 :  -4.82E-02 1.28E-01 0.000 0.5218 0.9000 0.9000   1.05  1  1  3.1E-02
-%  14 :  -4.56E-02 5.65E-02 0.000 0.4417 0.9045 0.9000   1.02  1  1  1.4E-02
-%  15 :  -4.43E-02 2.41E-02 0.000 0.4265 0.9004 0.9000   1.01  1  1  6.0E-03
-%  16 :  -4.37E-02 8.90E-03 0.000 0.3690 0.9070 0.9000   1.00  1  1  2.3E-03
-%  17 :  -4.35E-02 3.24E-03 0.000 0.3641 0.9164 0.9000   1.00  1  1  9.5E-04
-%  18 :  -4.34E-02 1.55E-03 0.000 0.4788 0.9086 0.9000   1.00  1  1  4.7E-04
-%  19 :  -4.34E-02 8.77E-04 0.000 0.5653 0.9169 0.9000   1.00  1  1  2.8E-04
-%  20 :  -4.34E-02 5.05E-04 0.000 0.5754 0.9034 0.9000   1.00  1  1  1.6E-04
-%  21 :  -4.34E-02 2.94E-04 0.000 0.5829 0.9136 0.9000   1.00  1  1  9.9E-05
-%  22 :  -4.34E-02 1.63E-04 0.015 0.5548 0.9000 0.0000   1.00  1  1  6.6E-05
-%  23 :  -4.33E-02 9.42E-05 0.000 0.5774 0.9053 0.9000   1.00  1  1  3.9E-05
-%  24 :  -4.33E-02 6.27E-05 0.000 0.6658 0.9148 0.9000   1.00  1  1  2.6E-05
-%  25 :  -4.33E-02 3.75E-05 0.000 0.5972 0.9187 0.9000   1.00  1  1  1.6E-05
-%  26 :  -4.33E-02 1.89E-05 0.000 0.5041 0.9117 0.9000   1.00  1  1  8.6E-06
-%  27 :  -4.33E-02 9.72E-06 0.000 0.5149 0.9050 0.9000   1.00  1  1  4.5E-06
-%  28 :  -4.33E-02 2.94E-06 0.000 0.3021 0.9194 0.9000   1.00  1  1  1.5E-06
-%  29 :  -4.33E-02 9.73E-07 0.000 0.3312 0.9189 0.9000   1.00  2  2  5.3E-07
-%  30 :  -4.33E-02 2.82E-07 0.000 0.2895 0.9063 0.9000   1.00  2  2  1.6E-07
-%  31 :  -4.33E-02 8.05E-08 0.000 0.2859 0.9049 0.9000   1.00  2  2  4.7E-08
-%  32 :  -4.33E-02 1.43E-08 0.000 0.1772 0.9059 0.9000   1.00  2  2  8.8E-09
-
-% iter seconds digits       c*x               b*y
-%  32     49.4   6.8 -4.3334083581e-02 -4.3334090214e-02
-% |Ax-b| =   3.7e-09, [Ay-c]_+ =   1.1E-10, |x|=  1.0e+00, |y|=  2.6e+00
-
-% Detailed timing (sec)
-%    Pre          IPM          Post
-% 3.902E+00    4.576E+01    1.035E-02
-% Max-norms: ||b||=1, ||c|| = 3,
-% Cholesky |add|=0, |skip| = 0, ||L.L|| = 4.26267.
-% ------------------------------------------------------------
-% Status: Solved
-% Optimal value (cvx_optval): -0.0433341
-% h = y(2:end);
-% #+end_example
-
-% Finally, we compute the filter response over the frequency vector defined and the result is shown on figure [[fig:fir_filter_ligo]] which is very close to the filters obtain in cite:hua05_low_ligo.
-
-
-w = [w1 w2 w3 w4];
-H = [exp(-j*kron(w'.*2*pi,[0:n-1]))]*h;
-
-figure;
-tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
-
-% Magnitude
-ax1 = nexttile([2, 1]);
-hold on;
-plot(w, abs(H), 'k-');
-plot(w, abs(1-H), 'k--');
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Magnitude');
-set(gca, 'XTickLabel',[]);
-ylim([5e-3, 5]);
-
-% Phase
-ax2 = nexttile;
-hold on;
-plot(w, 180/pi*unwrap(angle(H)), 'k-');
-plot(w, 180/pi*unwrap(angle(1-H)), 'k--');
-hold off;
-xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
-set(gca, 'XScale', 'log');
-yticks([-450:90:180]); ylim([-450, 200]);
-
-linkaxes([ax1,ax2],'x');
-xlim([1e-3, 1]);
-
-% Weights
-% We design weights that will be used for the $\mathcal{H}_\infty$ synthesis of the complementary filters.
-% These weights will determine the order of the obtained filters.
-% Here are the requirements on the filters:
-% - reasonable order
-% - to be as close as possible to the specified upper bounds
-% - stable minimum phase
-
-% The bode plot of the weights is shown on figure [[fig:ligo_weights]].
-
-
-w1 = 2*pi*0.008; x1 = 0.35;
-w2 = 2*pi*0.04;  x2 = 0.5;
-w3 = 2*pi*0.05;  x3 = 0.5;
-
-% Slope of +3 from w1
-wH = 0.008*(s^2/w1^2 + 2*x1/w1*s + 1)*(s/w1 + 1);
-% Little bump from w2 to w3
-wH = wH*(s^2/w2^2 + 2*x2/w2*s + 1)/(s^2/w3^2 + 2*x3/w3*s + 1);
-% No Slope at high frequencies
-wH = wH/(s^2/w3^2 + 2*x3/w3*s + 1)/(s/w3 + 1);
-% Little bump between w2 and w3
-w0 = 2*pi*0.045; xi = 0.1; A = 2; n = 1;
-wH = wH*((s^2 + 2*w0*xi*A^(1/n)*s + w0^2)/(s^2 + 2*w0*xi*s + w0^2))^n;
-
-wH = 1/wH;
-wH = minreal(ss(wH));
-
-n = 20; Rp = 1; Wp = 2*pi*0.102;
-[b,a] = cheby1(n, Rp, Wp, 'high', 's');
-wL = 0.04*tf(a, b);
-
-wL = 1/wL;
-wL = minreal(ss(wL));
-
-figure;
-hold on;
-set(gca,'ColorOrderIndex',1);
-plot(freqs, abs(squeeze(freqresp(inv(wH), freqs, 'Hz'))), '-', 'DisplayName', '$|w_H|^{-1}$');
-set(gca,'ColorOrderIndex',2);
-plot(freqs, abs(squeeze(freqresp(inv(wL), freqs, 'Hz'))), '-', 'DisplayName', '$|w_L|^{-1}$');
-
-plot([0.0001, 0.008], [8e-3, 8e-3], 'k--', 'DisplayName', 'Spec.');
-plot([0.008 0.04], [8e-3, 1], 'k--', 'HandleVisibility', 'off');
-plot([0.04 0.1], [3, 3], 'k--', 'HandleVisibility', 'off');
-plot([0.1, 10], [0.045, 0.045], 'k--', 'HandleVisibility', 'off');
-
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Magnitude');
-hold off;
-xlim([freqs(1), freqs(end)]);
-ylim([1e-3, 10]);
-leg = legend('location', 'southeast', 'FontSize', 8);
-leg.ItemTokenSize(1) = 18;
-
-% H-Infinity Synthesis
-% We define the generalized plant as shown on figure [[fig:h_infinity_robst_fusion]].
-
-P = [0   wL;
-     wH -wH;
-     1   0];
-
-
-
-% And we do the $\mathcal{H}_\infty$ synthesis using the =hinfsyn= command.
-
-[Hl, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
-
-
-
-% #+RESULTS:
-% #+begin_example
-% [Hl, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
-% Resetting value of Gamma min based on D_11, D_12, D_21 terms
-
-% Test bounds:      0.3276 <  gamma  <=      1.8063
-
-%   gamma    hamx_eig  xinf_eig  hamy_eig   yinf_eig   nrho_xy   p/f
-%     1.806   1.4e-02 -1.7e-16   3.6e-03   -4.8e-12    0.0000    p
-%     1.067   1.3e-02 -4.2e-14   3.6e-03   -1.9e-12    0.0000    p
-%     0.697   1.3e-02 -3.0e-01#  3.6e-03   -3.5e-11    0.0000    f
-%     0.882   1.3e-02 -9.5e-01#  3.6e-03   -1.2e-34    0.0000    f
-%     0.975   1.3e-02 -2.7e+00#  3.6e-03   -1.6e-12    0.0000    f
-%     1.021   1.3e-02 -8.7e+00#  3.6e-03   -4.5e-16    0.0000    f
-%     1.044   1.3e-02 -6.5e-14   3.6e-03   -3.0e-15    0.0000    p
-%     1.032   1.3e-02 -1.8e+01#  3.6e-03    0.0e+00    0.0000    f
-%     1.038   1.3e-02 -3.8e+01#  3.6e-03    0.0e+00    0.0000    f
-%     1.041   1.3e-02 -8.3e+01#  3.6e-03   -2.9e-33    0.0000    f
-%     1.042   1.3e-02 -1.9e+02#  3.6e-03   -3.4e-11    0.0000    f
-%     1.043   1.3e-02 -5.3e+02#  3.6e-03   -7.5e-13    0.0000    f
-
-%  Gamma value achieved:     1.0439
-% #+end_example
-
-% The high pass filter is defined as $H_H = 1 - H_L$.
-
-Hh = 1 - Hl;
-
-Hh = minreal(Hh);
-Hl = minreal(Hl);
-
-
-
-% The size of the filters is shown below.
-
-
-size(Hh), size(Hl)
-
-
-
-% #+RESULTS:
-% #+begin_example
-% size(Hh), size(Hl)
-% State-space model with 1 outputs, 1 inputs, and 27 states.
-% State-space model with 1 outputs, 1 inputs, and 27 states.
-% #+end_example
-
-% The bode plot of the obtained filters as shown on figure [[fig:hinf_synthesis_ligo_results]].
-
-
-figure;
-hold on;
-set(gca,'ColorOrderIndex',1);
-plot([0.0001, 0.008], [8e-3, 8e-3], ':', 'DisplayName', 'Spec. on $H_H$');
-set(gca,'ColorOrderIndex',1);
-plot([0.008 0.04], [8e-3, 1], ':', 'HandleVisibility', 'off');
-set(gca,'ColorOrderIndex',1);
-plot([0.04 0.1], [3, 3], ':', 'HandleVisibility', 'off');
-
-set(gca,'ColorOrderIndex',2);
-plot([0.1, 10], [0.045, 0.045], ':', 'DisplayName', 'Spec. on $H_L$');
-
-set(gca,'ColorOrderIndex',1);
-plot(freqs, abs(squeeze(freqresp(Hh, freqs, 'Hz'))), '-', 'DisplayName', '$H_H$');
-set(gca,'ColorOrderIndex',2);
-plot(freqs, abs(squeeze(freqresp(Hl, freqs, 'Hz'))), '-', 'DisplayName', '$H_L$');
-
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Magnitude');
-hold off;
-xlim([freqs(1), freqs(end)]);
-ylim([1e-3, 10]);
-leg = legend('location', 'southeast', 'FontSize', 8);
-leg.ItemTokenSize(1) = 18;
-
-% Compare FIR and H-Infinity Filters
-% Let's now compare the FIR filters designed in cite:hua05_low_ligo and the one obtained with the $\mathcal{H}_\infty$ synthesis on figure [[fig:comp_fir_ligo_hinf]].
-
-
-figure;
-tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
-
-% Magnitude
-ax1 = nexttile([2, 1]);
-hold on;
-set(gca,'ColorOrderIndex',1);
-plot(freqs, abs(squeeze(freqresp(Hh, freqs, 'Hz'))), '-', ...
-     'DisplayName', '$H_H(s)$ - $\mathcal{H}_\infty$');
-set(gca,'ColorOrderIndex',2);
-plot(freqs, abs(squeeze(freqresp(Hl, freqs, 'Hz'))), '-', ...
-     'DisplayName', '$H_L(s)$ - $\mathcal{H}_\infty$');
-
-set(gca,'ColorOrderIndex',1);
-plot(w, abs(H), '--', ...
-     'DisplayName', '$H_H(s)$ - FIR');
-set(gca,'ColorOrderIndex',2);
-plot(w, abs(1-H), '--', ...
-     'DisplayName', '$H_L(s)$ - FIR');
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Magnitude');
-set(gca, 'XTickLabel',[]);
-ylim([5e-3, 10]);
-leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
-leg.ItemTokenSize(1) = 16;
-
-% Phase
-ax2 = nexttile;
-hold on;
-set(gca,'ColorOrderIndex',1);
-plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Hh, freqs, 'Hz')))), '-');
-set(gca,'ColorOrderIndex',2);
-plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Hl, freqs, 'Hz')))), '-');
-
-set(gca,'ColorOrderIndex',1);
-plot(w, 180/pi*unwrap(angle(H)), '--');
-set(gca,'ColorOrderIndex',2);
-plot(w, 180/pi*unwrap(angle(1-H)), '--');
-set(gca, 'XScale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
-hold off;
-yticks([-450:90:180]); ylim([-450, 200]);
-
-linkaxes([ax1,ax2],'x');
-xlim([freqs(1), freqs(end)]);
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Thomas Dehaeze	8cba417317	First LIGO review	2021-09-14 13:46:28 +02:00
Thomas Dehaeze	369454f877	Review	2021-09-08 10:56:25 +02:00
Thomas Dehaeze	6a65ed51a5	Add comments by Mohit and Christophe	2021-09-02 10:04:30 +02:00
Thomas Dehaeze	572e1d5abd	Update title	2021-09-02 10:04:16 +02:00
Thomas Dehaeze	504f0d7935	First review	2021-09-02 10:02:12 +02:00
Thomas Dehaeze	d424d56143	Remove Mohit's folder	2021-09-01 17:05:20 +02:00
Thomas Dehaeze	f34ae9b8c4	Update main page	2021-09-01 17:04:48 +02:00
Thomas Dehaeze	4568a119a2	Update bibtex for source code	2021-09-01 17:03:27 +02:00
Thomas Dehaeze	4769d4b57f	Last update before submission	2021-09-01 17:00:12 +02:00
Thomas Dehaeze	616652f67a	Update matlab scripts	2021-09-01 16:50:18 +02:00
Thomas Dehaeze	946ae5f977	Update journal file	2021-09-01 15:00:34 +02:00
Thomas Dehaeze	b1517f1c35	Update license date	2021-09-01 15:00:22 +02:00
Thomas Dehaeze	5592f7a37d	Completely rework matlab files	2021-09-01 15:00:04 +02:00
Thomas Dehaeze	c073d945d1	Add main bib file	2021-09-01 11:36:08 +02:00
Thomas Dehaeze	0d33958b17	Update links to files	2021-09-01 11:36:05 +02:00
Thomas Dehaeze	4836b9e254	Update bib file for matlab	2021-09-01 11:35:32 +02:00
Thomas Dehaeze	2b5757bb09	Update tangled files	2021-09-01 11:35:25 +02:00
Thomas Dehaeze	c520f7903e	Update all matlab figures	2021-09-01 11:35:13 +02:00
Thomas Dehaeze	10e9c17a60	Delete unused figures	2021-09-01 11:34:32 +02:00
Thomas Dehaeze	6ce027cf8a	Reworked tikz figures	2021-09-01 10:16:26 +02:00
Thomas Dehaeze	eb57832eb7	Rename main orgmode matlab file	2021-09-01 09:56:37 +02:00
Thomas Dehaeze	84b224ce38	Rework abstract	2021-09-01 09:56:26 +02:00
Thomas Dehaeze	e82e86486e	Rework matlab functions	2021-09-01 09:56:11 +02:00
Thomas Dehaeze	c6d715734f	Reworked all sections / add many figures Sent for first internal review	2021-08-31 14:19:41 +02:00
Thomas Dehaeze	f57207d529	Change paper filename	2021-08-27 11:28:24 +02:00
Thomas Dehaeze	23cdb386f2	Now compile with latexmk	2021-08-27 11:28:09 +02:00
Thomas Dehaeze	bc3efd689d	Rework introduction and cleaned BIB file	2021-08-27 11:27:59 +02:00