Rename paper files

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=('dehaeze22_optim_robus_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 = 1;  # 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
+$bibtex     = "bibtex %S";
+
+# ======================================================================================
+# Auxiliary Files
+# ======================================================================================
+
+# Let latexmk know about generated files, so they can be used to detect if a
+# rerun is required, or be deleted in a cleanup.
+# loe: List of Examples (KOMAScript)
+# lol: List of Listings (`listings` and `minted` packages)
+# run.xml: biber runs
+# glg: glossaries log
+# glstex: generated from glossaries-extra
+push @generated_exts, 'loe', 'lol', 'run.xml', 'glg', 'glstex';
+
+# Also delete the *.glstex files from package glossaries-extra. Problem is,
+# that that package generates files of the form "basename-digit.glstex" if
+# multiple glossaries are present. Latexmk looks for "basename.glstex" and so
+# does not find those. For that purpose, use wildcard.
+# Also delete files generated by gnuplot/pgfplots contour plots
+# (.dat, .script, .table).
+$clean_ext = "%R-*.glstex %R_contourtmp*.*";

journal/dehaeze22_optim_robus_compl_filte.org

@@ -1,7 +1,7 @@
 #+TITLE: Optimal and Robust Sensor Fusion
 :DRAWER:
 #+LATEX_CLASS: IEEEtran
-#+LATEX_CLASS_OPTIONS: [conference]
+#+LATEX_CLASS_OPTIONS: [10pt,final,journal,a4paper]
 #+OPTIONS: toc:nil todo:nil
 #+STARTUP: overview
 
@@ -45,40 +45,44 @@
 #+LATEX_HEADER_EXTRA: \usepackage{showframe}
 
 #+LATEX_HEADER: \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
-
-\bibliographystyle{IEEEtran}
 :END:
 
-* LaTeX Config                                                      :noexport:
-#+begin_src latex :tangle config.tex
-#+end_src
-
 * Build                                                             :noexport:
 #+NAME: startblock
 #+BEGIN_SRC emacs-lisp :results none
-  (add-to-list 'org-latex-classes
+(add-to-list 'org-latex-classes
-               '("IEEEtran"
+             '("IEEEtran"
-                 "\\documentclass{IEEEtran}"
+               "\\documentclass{IEEEtran}"
-                 ("\\section{%s}" . "\\section*{%s}")
+               ("\\section{%s}" . "\\section*{%s}")
-                 ("\\subsection{%s}" . "\\subsection*{%s}")
+               ("\\subsection{%s}" . "\\subsection*{%s}")
-                 ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
+               ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
-                 ("\\paragraph{%s}" . "\\paragraph*{%s}")
+               ("\\paragraph{%s}" . "\\paragraph*{%s}")
-                 ("\\subparagraph{%s}" . "\\subparagraph*{%s}"))
+               ("\\subparagraph{%s}" . "\\subparagraph*{%s}"))
-               )
+             )
 
-  (defun delete-org-comments (backend)
+;; Remove automatic org headings
-    (loop for comment in (reverse (org-element-map (org-element-parse-buffer)
+(defun my-latex-filter-removeOrgAutoLabels (text backend info)
-                                      'comment 'identity))
+  "Org-mode automatically generates labels for headings despite explicit use of `#+LABEL`. This filter forcibly removes all automatically generated org-labels in headings."
-          do
+  (when (org-export-derived-backend-p backend 'latex)
-          (setf (buffer-substring (org-element-property :begin comment)
+    (replace-regexp-in-string "\\\\label{sec:org[a-f0-9]+}\n" "" text)))
-                                  (org-element-property :end comment))
-                "")))
 
-  ;; add to export hook
+(add-to-list 'org-export-filter-headline-functions
-  (add-hook 'org-export-before-processing-hook 'delete-org-comments)
+             'my-latex-filter-removeOrgAutoLabels)
 
-  ;; Remove hypersetup
+;; Automatic delete org org-comments
-  (setq org-latex-with-hyperref nil)
+(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
 
 * Abstract                                                            :ignore:
@@ -94,6 +98,8 @@
 * Introduction
 <<sec:introduction>>
 
+cite:mahony08_nonlin_compl_filter_special_orthog_group
+
 - Section ref:sec:optimal_fusion
 - Section ref:sec:robust_fusion
 - Section ref:sec:optimal_robust_fusion
@@ -518,4 +524,10 @@ The synthesis objective is to:
 * Acknowledgment
 
 * Bibliography                                                       :ignore:
+\bibliographystyle{IEEEtran}
 \bibliography{ref}
+
+* Local Variables                                                   :noexport:
+# Local Variables:
+# org-latex-packages-alist: nil
+# End:

journal/dehaeze22_optim_robus_compl_filte.tex

@@ -1,6 +1,6 @@
-% Created 2020-10-26 lun. 18:25
+% Created 2021-09-10 ven. 10:25
 % Intended LaTeX compiler: pdflatex
-\documentclass[conference]{IEEEtran}
+\documentclass[final,journal,a4paper]{IEEEtran}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{graphicx}
@@ -14,12 +14,6 @@
 \usepackage{amssymb}
 \usepackage{capt-of}
 \usepackage{hyperref}
-\usepackage[most]{tcolorbox}
-\usepackage{bm}
-\usepackage{booktabs}
-\usepackage{tabularx}
-\usepackage{array}
-\usepackage{siunitx}
 \IEEEoverridecommandlockouts
 \usepackage{cite}
 \usepackage{amsmath,amssymb,amsfonts}
@@ -35,7 +29,7 @@
 \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
 \usepackage{showframe}
 \author{\IEEEauthorblockN{Dehaeze Thomas} \IEEEauthorblockA{\textit{European Synchrotron Radiation Facility} \\ Grenoble, France\\ \textit{Precision Mechatronics Laboratory} \\ \textit{University of Liege}, Belgium \\ thomas.dehaeze@esrf.fr }\and \IEEEauthorblockN{Verma Mohit} \IEEEauthorblockA{\textit{BEAMS Department}\\ \textit{Free University of Brussels}, Belgium\\ \textit{Precision Mechatronics Laboratory} \\ \textit{University of Liege}, Belgium \\ mohitverma.serc@csir.res.in }\and \IEEEauthorblockN{Collette Christophe} \IEEEauthorblockA{\textit{BEAMS Department}\\ \textit{Free University of Brussels}, Belgium\\ \textit{Precision Mechatronics Laboratory} \\ \textit{University of Liege}, Belgium \\ ccollett@ulb.ac.be }}
-\date{2020-10-26}
+\date{2021-09-10}
 \title{Optimal and Robust Sensor Fusion}
 \begin{document}
 
@@ -50,9 +44,10 @@ Complementary Filters, Sensor Fusion, H-Infinity Synthesis
 \end{IEEEkeywords}
 
 \section{Introduction}
-\label{sec:org2820158}
 \label{sec:introduction}
 
+\cite{mahony08_nonlin_compl_filter_special_orthog_group}
+
 \begin{itemize}
 \item Section \ref{sec:optimal_fusion}
 \item Section \ref{sec:robust_fusion}
@@ -61,11 +56,9 @@ Complementary Filters, Sensor Fusion, H-Infinity Synthesis
 \end{itemize}
 
 \section{Optimal Super Sensor Noise: \(\mathcal{H}_2\) Synthesis}
-\label{sec:org2513ad9}
 \label{sec:optimal_fusion}
 
 \subsection{Sensor Model}
-\label{sec:orgbcc6cb6}
 Let's consider a sensor measuring a physical quantity \(x\) (Figure \ref{fig:sensor_model_noise}).
 The sensor has an internal dynamics which is here modelled with a Linear Time Invariant (LTI) system transfer function \(G_i(s)\).
 
@@ -96,19 +89,18 @@ In order to obtain an estimate \(\hat{x}_i\) of \(x\), a model \(\hat{G}_i\) of
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensor_model_noise.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensor_model_noise.pdf}
 \caption{\label{fig:sensor_model_noise}Sensor Model}
 \end{figure}
 
 \subsection{Sensor Fusion Architecture}
-\label{sec:orgdb526ec}
 Let's now consider two sensors measuring the same physical quantity \(x\) but with different dynamics \((G_1, G_2)\) and noise characteristics \((N_1, N_2)\) (Figure \ref{fig:sensor_fusion_noise_arch}).
 
 The noise sources \(\tilde{n}_1\) and \(\tilde{n}_2\) are considered to be uncorrelated.
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensor_fusion_noise_arch.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensor_fusion_noise_arch.pdf}
 \caption{\label{fig:sensor_fusion_noise_arch}Sensor Fusion Architecture with sensor noise}
 \end{figure}
 
@@ -138,7 +130,6 @@ In such case, the super sensor estimate \(\hat{x}\) is equal to \(x\) plus the n
 \end{equation}
 
 \subsection{Super Sensor Noise}
-\label{sec:org48c0d52}
 Let's note \(n\) the super sensor noise.
 \begin{equation}
   n = \left( H_1 N_1 \right) \tilde{n}_1 + \left( H_2 N_2 \right) \tilde{n}_2
@@ -152,7 +143,6 @@ As the noise of both sensors are considered to be uncorrelated, the PSD of the s
 It is clear that the PSD of the super sensor depends on the norm of the complementary filters.
 
 \subsection{\(\mathcal{H}_2\) Synthesis of Complementary Filters}
-\label{sec:org0d9384e}
 The goal is to design \(H_1(s)\) and \(H_2(s)\) such that the effect of the noise sources \(\tilde{n}_1\) and \(\tilde{n}_2\) has the smallest possible effect on the noise \(n\) of the estimation \(\hat{x}\).
 
 And the goal is the minimize the Root Mean Square (RMS) value of \(n\):
@@ -191,67 +181,63 @@ We then have that the \(\mathcal{H}_2\) synthesis applied on \(P_{\mathcal{H}_2}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/h_two_optimal_fusion.pdf}
+\includegraphics[scale=1,scale=1]{figs/h_two_optimal_fusion.pdf}
 \caption{\label{fig:h_two_optimal_fusion}Generalized plant \(P_{\mathcal{H}_2}\) used for the \(\mathcal{H}_2\) synthesis of complementary filters}
 \end{figure}
 
 \subsection{Example}
-\label{sec:org99002de}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensors_nominal_dynamics.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensors_nominal_dynamics.pdf}
 \caption{\label{fig:sensors_nominal_dynamics}Sensor nominal dynamics from the velocity of the object to the output voltage}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensors_noise.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensors_noise.pdf}
 \caption{\label{fig:sensors_noise}Amplitude spectral density of the sensors \(\sqrt{\Phi_{n_i}(\omega)} = |N_i(j\omega)|\)}
 \end{figure}
 
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/htwo_comp_filters.pdf}
+\includegraphics[scale=1,scale=1]{figs/htwo_comp_filters.pdf}
 \caption{\label{fig:htwo_comp_filters}Obtained complementary filters using the \(\mathcal{H}_2\) Synthesis}
 \end{figure}
 
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/psd_sensors_htwo_synthesis.pdf}
+\includegraphics[scale=1,scale=1]{figs/psd_sensors_htwo_synthesis.pdf}
 \caption{\label{fig:psd_sensors_htwo_synthesis}Power Spectral Density of the estimated \(\hat{x}\) using the two sensors alone and using the optimally fused signal}
 \end{figure}
 
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/super_sensor_time_domain_h2.pdf}
+\includegraphics[scale=1,scale=1]{figs/super_sensor_time_domain_h2.pdf}
 \caption{\label{fig:super_sensor_time_domain_h2}Noise of individual sensors and noise of the super sensor}
 \end{figure}
 
 \subsection{Robustness Problem}
-\label{sec:org262893f}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensors_nominal_dynamics_and_uncertainty.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensors_nominal_dynamics_and_uncertainty.pdf}
 \caption{\label{fig:sensors_nominal_dynamics_and_uncertainty}Nominal Sensor Dynamics \(\hat{G}_i\) (solid lines) as well as the spread of the dynamical uncertainty (background color)}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/super_sensor_dynamical_uncertainty_H2.pdf}
+\includegraphics[scale=1,scale=1]{figs/super_sensor_dynamical_uncertainty_H2.pdf}
 \caption{\label{fig:super_sensor_dynamical_uncertainty_H2}Super sensor dynamical uncertainty when using the \(\mathcal{H}_2\) Synthesis}
 \end{figure}
 
 \section{Robust Sensor Fusion: \(\mathcal{H}_\infty\) Synthesis}
-\label{sec:org7c9047e}
 \label{sec:robust_fusion}
 
 \subsection{Representation of Sensor Dynamical Uncertainty}
-\label{sec:org7bd4379}
 
 In Section \ref{sec:optimal_fusion}, the model \(\hat{G}_i(s)\) of the sensor was considered to be perfect.
 In reality, there are always uncertainty (neglected dynamics) associated with the estimation of the sensor dynamics.
@@ -266,12 +252,11 @@ The sensor can then be represented as shown in Figure \ref{fig:sensor_model_unce
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensor_model_uncertainty.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensor_model_uncertainty.pdf}
 \caption{\label{fig:sensor_model_uncertainty}Sensor Model including Dynamical Uncertainty}
 \end{figure}
 
 \subsection{Sensor Fusion Architecture}
-\label{sec:org0b8ce2b}
 Let's consider the sensor fusion architecture shown in Figure \ref{fig:sensor_fusion_arch_uncertainty} where the dynamical uncertainties of both sensors are included.
 
 The super sensor estimate is then:
@@ -291,12 +276,11 @@ As \(H_1\) and \(H_2\) are complementary filters, we finally have:
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensor_fusion_arch_uncertainty.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensor_fusion_arch_uncertainty.pdf}
 \caption{\label{fig:sensor_fusion_arch_uncertainty}Sensor Fusion Architecture with sensor model uncertainty}
 \end{figure}
 
 \subsection{Super Sensor Dynamical Uncertainty}
-\label{sec:org725af92}
 The uncertainty set of the transfer function from \(\hat{x}\) to \(x\) at frequency \(\omega\) is bounded in the complex plane by a circle centered on 1 and 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}.
 
 
@@ -304,14 +288,13 @@ And we can see that the dynamical uncertainty of the super sensor is equal to th
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/uncertainty_set_super_sensor.pdf}
+\includegraphics[scale=1,scale=1]{figs/uncertainty_set_super_sensor.pdf}
 \caption{\label{fig:uncertainty_set_super_sensor}Super Sensor model uncertainty displayed in the complex plane}
 \end{figure}
 
 At frequencies where \(\left|W_i(j\omega)\right| > 1\) the uncertainty exceeds \(100\%\) and sensor fusion is impossible.
 
 \subsection{\(\mathcal{H_\infty}\) Synthesis of Complementary Filters}
-\label{sec:org941ed72}
 In order for the fusion to be ``robust'', meaning no phase drop will be induced in the super sensor dynamics,
 
 The goal is to design two complementary filters \(H_1(s)\) and \(H_2(s)\) such that the super sensor noise uncertainty is kept reasonably small.
@@ -352,51 +335,48 @@ The \(\mathcal{H}_\infty\) norm of Eq. \eqref{eq:Hinf_norm} is equals to \(\sigm
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/h_infinity_robust_fusion.pdf}
+\includegraphics[scale=1,scale=1]{figs/h_infinity_robust_fusion.pdf}
 \caption{\label{fig:h_infinity_robust_fusion}Generalized plant \(P_{\mathcal{H}_\infty}\) used for the \(\mathcal{H}_\infty\) synthesis of complementary filters}
 \end{figure}
 
 \subsection{Example}
-\label{sec:org7df520f}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensors_uncertainty_weights.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensors_uncertainty_weights.pdf}
 \caption{\label{fig:sensors_uncertainty_weights}Magnitude of the multiplicative uncertainty weights \(|W_i(j\omega)|\)}
 \end{figure}
 
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/weight_uncertainty_bounds_Wu.pdf}
+\includegraphics[scale=1,scale=1]{figs/weight_uncertainty_bounds_Wu.pdf}
 \caption{\label{fig:weight_uncertainty_bounds_Wu}Uncertainty region of the two sensors as well as the wanted maximum uncertainty of the super sensor (dashed lines)}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/hinf_comp_filters.pdf}
+\includegraphics[scale=1,scale=1]{figs/hinf_comp_filters.pdf}
 \caption{\label{fig:hinf_comp_filters}Obtained complementary filters using the \(\mathcal{H}_\infty\) Synthesis}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/super_sensor_dynamical_uncertainty_Hinf.pdf}
+\includegraphics[scale=1,scale=1]{figs/super_sensor_dynamical_uncertainty_Hinf.pdf}
 \caption{\label{fig:super_sensor_dynamical_uncertainty_Hinf}Super sensor dynamical uncertainty (solid curve) when using the \(\mathcal{H}_\infty\) Synthesis}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/psd_sensors_hinf_synthesis.pdf}
+\includegraphics[scale=1,scale=1]{figs/psd_sensors_hinf_synthesis.pdf}
 \caption{\label{fig:psd_sensors_hinf_synthesis}Power Spectral Density of the estimated \(\hat{x}\) using the two sensors alone and using the \(\mathcal{H}_\infty\) synthesis}
 \end{figure}
 
 
 \section{Optimal and Robust Sensor Fusion: Mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) Synthesis}
-\label{sec:org75a038a}
 \label{sec:optimal_robust_fusion}
 
 \subsection{Sensor with noise and model uncertainty}
-\label{sec:org3810d6b}
 We wish now to combine the two previous synthesis, that is to say
 
 The sensors are now modelled by a white noise with unitary PSD \(\tilde{n}_i\) shaped by a LTI transfer function \(N_i(s)\).
@@ -412,12 +392,11 @@ Multiplying by the inverse of the nominal model of the sensor dynamics gives an
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensor_model_noise_uncertainty.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensor_model_noise_uncertainty.pdf}
 \caption{\label{fig:sensor_model_noise_uncertainty}Sensor Model including Noise and Dynamical Uncertainty}
 \end{figure}
 
 \subsection{Sensor Fusion Architecture}
-\label{sec:org3758b1e}
 
 For reason of space, the blocks \(\hat{G}_i\) and \(\hat{G}_i^{-1}\) are omitted.
 
@@ -439,12 +418,11 @@ The estimate \(\hat{x}\) of \(x\)
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/sensor_fusion_arch_full.pdf}
+\includegraphics[scale=1,scale=1]{figs/sensor_fusion_arch_full.pdf}
 \caption{\label{fig:sensor_fusion_arch_full}Super Sensor Fusion with both sensor noise and sensor model uncertainty}
 \end{figure}
 
 \subsection{Mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) Synthesis}
-\label{sec:org06317f4}
 
 The synthesis objective is to generate two complementary filters \(H_1(s)\) and \(H_2(s)\) such that the uncertainty associated with the super sensor is kept reasonably small and such that the RMS value of super sensors noise is minimized.
 
@@ -474,59 +452,52 @@ The synthesis objective is to:
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/mixed_h2_hinf_synthesis.pdf}
+\includegraphics[scale=1,scale=1]{figs/mixed_h2_hinf_synthesis.pdf}
 \caption{\label{fig:mixed_h2_hinf_synthesis}Generalized plant \(P_{\mathcal{H}_2/\matlcal{H}_\infty}\) used for the mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) synthesis of complementary filters}
 \end{figure}
 
 \subsection{Example}
-\label{sec:org42ee165}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/htwo_hinf_comp_filters.pdf}
+\includegraphics[scale=1,scale=1]{figs/htwo_hinf_comp_filters.pdf}
 \caption{\label{fig:htwo_hinf_comp_filters}Obtained complementary filters after mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) synthesis}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/psd_sensors_htwo_hinf_synthesis.pdf}
+\includegraphics[scale=1,scale=1]{figs/psd_sensors_htwo_hinf_synthesis.pdf}
 \caption{\label{fig:psd_sensors_htwo_hinf_synthesis}Power Spectral Density of the Super Sensor obtained with the mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) synthesis}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/super_sensor_time_domain_h2_hinf.pdf}
+\includegraphics[scale=1,scale=1]{figs/super_sensor_time_domain_h2_hinf.pdf}
 \caption{\label{fig:super_sensor_time_domain_h2_hinf}Noise of individual sensors and noise of the super sensor}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/super_sensor_dynamical_uncertainty_Htwo_Hinf.pdf}
+\includegraphics[scale=1,scale=1]{figs/super_sensor_dynamical_uncertainty_Htwo_Hinf.pdf}
 \caption{\label{fig:super_sensor_dynamical_uncertainty_Htwo_Hinf}Super sensor dynamical uncertainty (solid curve) when using the mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) Synthesis}
 \end{figure}
 
 \section{Experimental Validation}
-\label{sec:orge381a2a}
 \label{sec:experimental_validation}
 
 \subsection{Experimental Setup}
-\label{sec:org473ab00}
 
 \subsection{Sensor Noise and Dynamical Uncertainty}
-\label{sec:orgebcb65d}
 
 \subsection{Mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) Synthesis}
-\label{sec:org0259d19}
 
 \subsection{Super Sensor Noise and Dynamical Uncertainty}
-\label{sec:orgdb5d29f}
 
 \section{Conclusion}
-\label{sec:org07df454}
 \label{sec:conclusion}
 
 \section{Acknowledgment}
-\label{sec:org7b7e461}
 
+\bibliographystyle{IEEEtran}
 \bibliography{ref}
 \end{document}

paper/config.tex

@@ -1,28 +0,0 @@
-% H Infini
-\newcommand{\hinf}{\mathcal{H}_\infty}
-
-% H 2
-\newcommand{\htwo}{\mathcal{H}_2}
-
-% Omega
-\newcommand{\w}{\omega}
-
-% H-Infinity Norm
-\newcommand{\hnorm}[1]{\left\|#1\right\|_{\infty}}
-
-% H-2 Norm
-\newcommand{\normtwo}[1]{\left\|#1\right\|_{2}}
-
-% Norm
-\newcommand{\norm}[1]{\left\|#1\right\|}
-
-% Absolute value
-\newcommand{\abs}[1]{\left\lvert #1 \right\lvert}
-
-% Minimum Subscript
-\newcommand{\smin}{_{\text{min}}}
-
-% Maximum Subscript
-\newcommand{\smax}{_{\text{max}}}
-
-\newcommand*\colvec[1]{\begin{bmatrix}#1\end{bmatrix}}