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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2021-09-01 mer. 11:36 --> <!-- 2021-09-01 mer. 17:04 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis</title> <title>Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis</title>
<meta name="author" content="Thomas Dehaeze" /> <meta name="author" content="Thomas Dehaeze" />
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</p> </p>
<p> <p>
For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using 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;.
This paper presents a method for designing these complementary filters using \(\mathcal{H}_\infty\) synthesis that allows to shape the filter norms. 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.
This method is shown to be easily applicable for the synthesis of complex complementary filters. 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> </p>
</blockquote> </blockquote>
<div id="outline-container-orgafee5c3" class="outline-2"> <div id="outline-container-org1d8b653" class="outline-2">
<h2 id="orgafee5c3">Paper (<a href="journal/dehaeze21_desig_compl_filte.pdf">link</a>)</h2> <h2 id="org1d8b653">Journal Article (<a href="journal/dehaeze21_desig_compl_filte.pdf">link</a>)</h2>
<div class="outline-text-2" id="text-orgafee5c3"> <div class="outline-text-2" id="text-org1d8b653">
<p> <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>. 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>
<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> </div>
<div id="outline-container-orgb8fb429" class="outline-2"> <div id="outline-container-org6ba84bc" class="outline-2">
<h2 id="orgb8fb429">Matlab Scripts (<a href="matlab/dehaeze21_desig_compl_filte_matlab.html">link</a>)</h2> <h2 id="org6ba84bc">Matlab Scripts (<a href="matlab/dehaeze21_desig_compl_filte_matlab.html">link</a>)</h2>
<div class="outline-text-2" id="text-orgb8fb429"> <div class="outline-text-2" id="text-org6ba84bc">
<p> <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. 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>
<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> </div>
<div id="outline-container-org0ecd5c8" class="outline-2"> <div id="outline-container-org827f683" class="outline-2">
<h2 id="org0ecd5c8">Tikz Figures (<a href="tikz/dehaeze21_desig_compl_filte_tikz.html">link</a>)</h2> <h2 id="org827f683">Tikz Figures (<a href="tikz/dehaeze21_desig_compl_filte_tikz.html">link</a>)</h2>
<div class="outline-text-2" id="text-org0ecd5c8"> <div class="outline-text-2" id="text-org827f683">
<p> <p>
All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>. All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>.
</p> </p>

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@ -15,37 +15,69 @@
#+begin_quote #+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. 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".
This paper presents a method for designing these complementary filters using $\mathcal{H}_\infty$ synthesis that allows to shape the filter norms. The obtained "super sensor" can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
This method is shown to be easily applicable for the synthesis of complex complementary filters. 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 #+end_quote
* Paper ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]]) * Journal Article ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]])
:PROPERTIES: :PROPERTIES:
:UNNUMBERED: t :UNNUMBERED: t
:END: :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]]. 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]].
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]]) * Matlab Scripts ([[file:matlab/dehaeze21_desig_compl_filte_matlab.org][link]])
:PROPERTIES: :PROPERTIES:
:UNNUMBERED: t :UNNUMBERED: t
:END: :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: :PROPERTIES:
:UNNUMBERED: t :UNNUMBERED: t
:END: :END:
All the figures for the paper have been generated using [[https://sourceforge.net/projects/pgf/][TikZ]]. 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

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@ -1442,6 +1442,4 @@ H1 = 1 - H2;
#+end_src #+end_src
* Bibliography :ignore: * Bibliography :ignore:
bibliography:ref.bib
#+latex: \printbibliography #+latex: \printbibliography