137 lines
6.2 KiB
HTML
137 lines
6.2 KiB
HTML
<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-09-01 mer. 17:04 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis</title>
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<meta name="author" content="Thomas Dehaeze" />
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<meta name="generator" content="Org Mode" />
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<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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MathJax = {
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svg: {
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scale: 1,
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fontCache: "global"
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},
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tex: {
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tags: "ams",
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multlineWidth: "%MULTLINEWIDTH",
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tagSide: "right",
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macros: {bm: ["\\boldsymbol{#1}",1],},
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tagIndent: ".8em"
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};
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</script>
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<script id="MathJax-script" async
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src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content" class="content">
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<h1 class="title">Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis
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<br />
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<span class="subtitle">Dehaeze Thomas, Verma Mohit and Collette Christophe</span>
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</h1>
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<blockquote>
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<p>
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<b>Abstract</b>:
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</p>
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<p>
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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”.
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The obtained “super sensor” can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
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Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
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Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
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In this study, we address this issue and propose a new method for designing complementary filters.
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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.
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The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
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Such synthesis method is further extended for the shaping of more than two complementary filters.
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</p>
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</blockquote>
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<div id="outline-container-org1d8b653" class="outline-2">
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<h2 id="org1d8b653">Journal Article (<a href="journal/dehaeze21_desig_compl_filte.pdf">link</a>)</h2>
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<div class="outline-text-2" id="text-org1d8b653">
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<p>
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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>.
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</p>
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<p>
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To cite this paper use the following BibTeX code.
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</p>
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<div class="org-src-container">
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<pre class="src src-bibtex"><span class="org-function-name">@article</span>{<span class="org-constant">dehaeze21_new_method_desig_compl_filter</span>,
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<span class="org-variable-name">author</span> = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
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<span class="org-variable-name">title</span> = {A New Method of Designing Complementary Filters for Sensor
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Fusion Using the <span class="org-string">$\mathcal{H}_\infty$</span> Synthesis},
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<span class="org-variable-name">journal</span> = {Mechanical Systems and Signal Processing},
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<span class="org-variable-name">year</span> = 2021,
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<span class="org-variable-name">month</span> = {Nov},
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}
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</pre>
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</div>
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<p>
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You can also use the formatted citation below.
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</p>
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<blockquote>
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<p>
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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).
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-org6ba84bc" class="outline-2">
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<h2 id="org6ba84bc">Matlab Scripts (<a href="matlab/dehaeze21_desig_compl_filte_matlab.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org6ba84bc">
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<p>
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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.
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The source code is hosted on <a href="https://zenodo.org/record/5361920">Zenodo</a>.
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</p>
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<p>
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If you use this code and want to refer to it in a publication, you can use the following BibTeX reference:
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</p>
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<div class="org-src-container">
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<pre class="src src-bibtex"><span class="org-function-name">@misc</span>{<span class="org-constant">dehaeze21_new_method_desig_compl_filter_code</span>,
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<span class="org-variable-name">author</span> = {Dehaeze, Thomas},
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<span class="org-variable-name">doi</span> = {<span class="org-button">10.5281/zenodo.5361943</span>},
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<span class="org-variable-name">howpublished</span> = {Source code on Zenodo},
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<span class="org-variable-name">month</span> = sep,
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<span class="org-variable-name">title</span> = {{A New Method of Designing Complementary Filters for Sensor
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Fusion Using the <span class="org-string">$\mathcal{H}_\infty$</span> Synthesis}},
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<span class="org-variable-name">year</span> = 2021,
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}
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</pre>
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</div>
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<p>
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You can also use the formatted citation below.
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</p>
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<blockquote>
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<p>
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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
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-org827f683" class="outline-2">
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<h2 id="org827f683">Tikz Figures (<a href="tikz/dehaeze21_desig_compl_filte_tikz.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org827f683">
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<p>
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All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>.
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</p>
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</div>
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</div>
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</div>
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</body>
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