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#+TITLE: Optimal and Robust Complementary Filters for Sensor Fusion
#+TITLE: Robust and Optimal Sensor Fusion
:DRAWER:
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#+LATEX_CLASS_OPTIONS: [9pt, technote, a4paper]
@ -52,6 +52,7 @@
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% Created 2019-08-12 lun. 16:02
% Created 2019-08-21 mer. 13:19
% Intended LaTeX compiler: pdflatex
\documentclass[9pt, technote, a4paper]{ieeeconf}
\usepackage[utf8]{inputenc}
@ -23,11 +23,11 @@
\setcounter{footnote}{1}
\input{config.tex}
\author{\IEEEauthorblockN{Dehaeze Thomas\IEEEauthorrefmark{*} and Collette Christophe} \\ \IEEEauthorblockA{Precision Mechatronics Laboratory, ULB\\ Brussels, Belgium\\ Email: \IEEEauthorrefmark{*}dehaeze.thomas@gmail.com}}
\date{2019-08-12}
\title{On the Design of Complementary Filters for Control}
\date{2019-08-21}
\title{Optimal and Robust Sensor Fusion using Complementary Filters}
\hypersetup{
pdfauthor={\IEEEauthorblockN{Dehaeze Thomas\IEEEauthorrefmark{*} and Collette Christophe} \\ \IEEEauthorblockA{Precision Mechatronics Laboratory, ULB\\ Brussels, Belgium\\ Email: \IEEEauthorrefmark{*}dehaeze.thomas@gmail.com}},
pdftitle={On the Design of Complementary Filters for Control},
pdftitle={Optimal and Robust Sensor Fusion using Complementary Filters},
pdfkeywords={},
pdfsubject={},
pdfcreator={Emacs 26.2 (Org mode 9.2.5)},
@ -46,7 +46,7 @@ complementary filters, h-infinity, feedback control
\end{IEEEkeywords}
\section{Introduction}
\label{sec:orgb15ebed}
\label{sec:org77eabad}
\label{sec:introduction}
The basic idea of a complementary filter involves taking two or more sensors, filtering out unreliable frequencies for each sensor and combining the filtered outputs to get a better estimate throughout the entire bandwidth of the system.
To achieve this, the sensors included in the filter should complement one another by performing better over specific parts of the system bandwidth.
@ -97,7 +97,7 @@ In this paper, we propose
The body of the paper consists of five parts followed by a conclusion.
\section{H-Infinity synthesis of complementary filters}
\label{sec:org303afb5}
\label{sec:org5f39b25}
\label{sec:hinf_filters}
First order complementary filters are easy to synthesize. For instance, one can use the following filters
\begin{equation}
@ -113,7 +113,7 @@ As shown in Sec. \ref{sec:trans_perf}, most of the performance requirements can
Thus, the \(\mathcal{H}_\infty\) framework seems adapted and we here propose a technique to synthesis complementary filters while specifying uppers bounds on their magnitudes.
\subsection{\(\hinf\) problem formulation}
\label{sec:org9dcb2b1}
\label{sec:org9a24692}
\label{sec:hinf_conf}
In this section, we formulate the \(\hinf\) problem for the synthesis of complementary filters.
@ -168,7 +168,7 @@ The stability condition \eqref{eq:hinf_cond_stability} is guaranteed by the \(H_
Using this synthesis method, we are then able to shape at the same time the high pass and low pass filters while ensuring their complementary.
\subsection{Control requirements as \(\mathcal{H}_\infty\) norm of complementary filters}
\label{sec:orgb7d25ea}
\label{sec:org48e11e8}
As presented in Sec. \ref{sec:trans_perf}, almost all the requirements can be specified with upper bounds on the complementary filters.
However, robust performance condition \eqref{eq:robust_perf_a} is not.
@ -181,7 +181,7 @@ With the \(\mathcal{H}_\infty\) synthesis the condition \eqref{eq:hinf_problem}
And thus we have almost robust stability.
\subsection{Choice of the weighting functions}
\label{sec:org2d7aa5b}
\label{sec:orgb8575b8}
\label{sec:hinf_weighting_func}
We here give some advice on the choice of the weighting functions used for the synthesis of the complementary filters.
@ -194,10 +194,10 @@ One should not forget the fundamental limitations of feedback control such that
Similarly, we here have that \(H_L + H_H = 1\) which implies that \(H_L\) and \(H_H\) cannot be made small at the same time.
\subsection{Trade-off between performance and robustness}
\label{sec:org7af3efe}
\label{sec:orgc90eaf9}
\subsection{Analytical formula of complementary filters}
\label{sec:org477b4a4}
\label{sec:org52d63ba}
\label{sec:analytical_complementary_filters}
To simplify the synthesis, one can use already synthesized filters
@ -217,13 +217,13 @@ To simplify the synthesis, one can use already synthesized filters
\end{align}
\section{Discussion}
\label{sec:org4fb9d01}
\label{sec:orgb80d2a2}
\section{Conclusion}
\label{sec:orgecd9d50}
\label{sec:orgdccbd69}
\label{sec:conclusion}
\section{Acknowledgment}
\label{sec:org5cf5157}
\label{sec:org8f4226e}
\bibliography{ref}
\end{document}

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<head>
<!-- 2019-08-14 mer. 12:08 -->
<!-- 2019-08-21 mer. 16:35 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Optimal and Robust Complementary Filters for Sensor Fusion - Tikz Figures</title>
<title>Robust and Optimal Sensor Fusion - Tikz Figures</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Thomas Dehaeze" />
<style type="text/css">
@ -252,23 +252,23 @@ for the JavaScript code in this tag.
|
<a accesskey="H" href="../index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Optimal and Robust Complementary Filters for Sensor Fusion - Tikz Figures</h1>
<h1 class="title">Robust and Optimal Sensor Fusion - Tikz Figures</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org815a564">1. Change some default</a></li>
<li><a href="#org4640d64">2. H-Infinity - Complementary filters - Generalized plant</a></li>
<li><a href="#org0b11ce2">3. H-Infinity - Complementary filters</a></li>
<li><a href="#org958e1e2">4. H-Infinity - Optimal Complementary Filters</a></li>
<li><a href="#org25d9a1b">5. Fusion of two noisy sensors</a></li>
<li><a href="#orga9ed288">6. Fusion of two noisy signals</a></li>
<li><a href="#org22dfd5b">7. Fusion of two noisy sensors with Dynamics</a></li>
<li><a href="#org855fa9e">8. Fusion of two noisy sensors with Dynamics - Bis</a></li>
<li><a href="#org11ffe09">9. Fusion of two sensors with mismatch dynamics</a></li>
<li><a href="#org7af9faf">10. Uncertainty to Phase and Gain variation</a></li>
<li><a href="#orge5f551d">11. Generate Complementary Filters using Feedback Control Architecture</a></li>
<li><a href="#org9ce2a6b">12. H-Infinity Synthesis for Robust Sensor Fusion</a></li>
<li><a href="#org548cc39">1. Change some default</a></li>
<li><a href="#org42c49b0">2. H-Infinity - Complementary filters - Generalized plant</a></li>
<li><a href="#org9a9ee34">3. H-Infinity - Complementary filters</a></li>
<li><a href="#orgaa13075">4. H-Infinity - Optimal Complementary Filters</a></li>
<li><a href="#orgc92348b">5. Fusion of two noisy sensors</a></li>
<li><a href="#org5acbf15">6. Fusion of two noisy signals</a></li>
<li><a href="#org9bf0ed7">7. Fusion of two noisy sensors with Dynamics</a></li>
<li><a href="#org6515349">8. Fusion of two noisy sensors with Dynamics - Bis</a></li>
<li><a href="#org066adab">9. Fusion of two sensors with mismatch dynamics</a></li>
<li><a href="#orga46cc8b">10. Uncertainty to Phase and Gain variation</a></li>
<li><a href="#org1f59e20">11. Generate Complementary Filters using Feedback Control Architecture</a></li>
<li><a href="#org509611f">12. H-Infinity Synthesis for Robust Sensor Fusion</a></li>
</ul>
</div>
</div>
@ -277,11 +277,11 @@ for the JavaScript code in this tag.
Configuration file is accessible <a href="config.html">here</a>.
</p>
<div id="outline-container-org815a564" class="outline-2">
<h2 id="org815a564"><span class="section-number-2">1</span> Change some default</h2>
<div id="outline-container-org548cc39" class="outline-2">
<h2 id="org548cc39"><span class="section-number-2">1</span> Change some default</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-latex" id="org862c935"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.6cm}}
<pre class="src src-latex" id="org7f5b9e0"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.6cm}}
<span class="org-font-latex-sedate">\tikzset</span>{addb/.append style={scale=0.7}}
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<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
@ -293,8 +293,8 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
</div>
<div id="outline-container-org4640d64" class="outline-2">
<h2 id="org4640d64"><span class="section-number-2">2</span> H-Infinity - Complementary filters - Generalized plant</h2>
<div id="outline-container-org42c49b0" class="outline-2">
<h2 id="org42c49b0"><span class="section-number-2">2</span> H-Infinity - Complementary filters - Generalized plant</h2>
<div class="outline-text-2" id="text-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.6cm}}
@ -331,7 +331,7 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
<div id="orgc12e3d2" class="figure">
<div id="org2d1e475" class="figure">
<p><img src="figs/sf_hinf_filters_plant_b.png" alt="sf_hinf_filters_plant_b.png" />
</p>
<p><span class="figure-number">Figure 1: </span>H-Infinity - Complementary filters - Generalized plant (<a href="./figs/sf_hinf_filters_plant_b.png">png</a>, <a href="./figs/sf_hinf_filters_plant_b.pdf">pdf</a>, <a href="./figs/sf_hinf_filters_plant_b.tex">tex</a>).</p>
@ -339,8 +339,8 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
</div>
<div id="outline-container-org0b11ce2" class="outline-2">
<h2 id="org0b11ce2"><span class="section-number-2">3</span> H-Infinity - Complementary filters</h2>
<div id="outline-container-org9a9ee34" class="outline-2">
<h2 id="org9a9ee34"><span class="section-number-2">3</span> H-Infinity - Complementary filters</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.6cm}}
@ -379,7 +379,7 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
<div id="orgd11c746" class="figure">
<div id="org612d916" class="figure">
<p><img src="figs/sf_hinf_filters_b.png" alt="sf_hinf_filters_b.png" />
</p>
<p><span class="figure-number">Figure 2: </span>H-Infinity - Complementary filters (<a href="./figs/sf_hinf_filters_b.png">png</a>, <a href="./figs/sf_hinf_filters_b.pdf">pdf</a>, <a href="./figs/sf_hinf_filters_b.tex">tex</a>).</p>
@ -387,8 +387,8 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
</div>
<div id="outline-container-org958e1e2" class="outline-2">
<h2 id="org958e1e2"><span class="section-number-2">4</span> H-Infinity - Optimal Complementary Filters</h2>
<div id="outline-container-orgaa13075" class="outline-2">
<h2 id="orgaa13075"><span class="section-number-2">4</span> H-Infinity - Optimal Complementary Filters</h2>
<div class="outline-text-2" id="text-4">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/h_infinity_optimal_comp_filters.png">png</a>, <a href="./figs/h_infinity_optimal_comp_filters.pdf">pdf</a> and <a href="./figs/h_infinity_optimal_comp_filters.tex">tex</a>.
@ -433,15 +433,15 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/h_in
</div>
<div id="orgace7a2f" class="figure">
<div id="org7d4df18" class="figure">
<p><img src="figs/h_infinity_optimal_comp_filters.png" alt="h_infinity_optimal_comp_filters.png" />
</p>
<p><span class="figure-number">Figure 3: </span>H-Infinity - Optimal Complementary Filters (<a href="./figs/h_infinity_optimal_comp_filters.png">png</a>, <a href="./figs/h_infinity_optimal_comp_filters.pdf">pdf</a>, <a href="./figs/h_infinity_optimal_comp_filters.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org25d9a1b" class="outline-2">
<h2 id="org25d9a1b"><span class="section-number-2">5</span> Fusion of two noisy sensors</h2>
<div id="outline-container-orgc92348b" class="outline-2">
<h2 id="orgc92348b"><span class="section-number-2">5</span> Fusion of two noisy sensors</h2>
<div class="outline-text-2" id="text-5">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/fusion_two_noisy_sensors.png">png</a>, <a href="./figs/fusion_two_noisy_sensors.pdf">pdf</a> and <a href="./figs/fusion_two_noisy_sensors.tex">tex</a>.
@ -475,15 +475,15 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="org8abe259" class="figure">
<div id="org7fef4e9" class="figure">
<p><img src="figs/fusion_two_noisy_sensors.png" alt="fusion_two_noisy_sensors.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Fusion of two noisy sensors (<a href="./figs/fusion_two_noisy_sensors.png">png</a>, <a href="./figs/fusion_two_noisy_sensors.pdf">pdf</a>, <a href="./figs/fusion_two_noisy_sensors.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-orga9ed288" class="outline-2">
<h2 id="orga9ed288"><span class="section-number-2">6</span> Fusion of two noisy signals</h2>
<div id="outline-container-org5acbf15" class="outline-2">
<h2 id="org5acbf15"><span class="section-number-2">6</span> Fusion of two noisy signals</h2>
<div class="outline-text-2" id="text-6">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/fusion_two_signals.png">png</a>, <a href="./figs/fusion_two_signals.pdf">pdf</a> and <a href="./figs/fusion_two_signals.tex">tex</a>.
@ -505,7 +505,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="orgfca7098" class="figure">
<div id="org319ff6e" class="figure">
<p><img src="figs/fusion_two_signals.png" alt="fusion_two_signals.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Fusion of two noisy sensors (<a href="./figs/fusion_two_signals.png">png</a>, <a href="./figs/fusion_two_signals.pdf">pdf</a>, <a href="./figs/fusion_two_signals.tex">tex</a>).</p>
@ -513,8 +513,8 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
</div>
<div id="outline-container-org22dfd5b" class="outline-2">
<h2 id="org22dfd5b"><span class="section-number-2">7</span> Fusion of two noisy sensors with Dynamics</h2>
<div id="outline-container-org9bf0ed7" class="outline-2">
<h2 id="org9bf0ed7"><span class="section-number-2">7</span> Fusion of two noisy sensors with Dynamics</h2>
<div class="outline-text-2" id="text-7">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/fusion_two_noisy_sensors_with_dyn.png">png</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn.pdf">pdf</a> and <a href="./figs/fusion_two_noisy_sensors_with_dyn.tex">tex</a>.
@ -552,15 +552,15 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="orgbba4705" class="figure">
<div id="orgf0c8eb7" class="figure">
<p><img src="figs/fusion_two_noisy_sensors_with_dyn.png" alt="fusion_two_noisy_sensors_with_dyn.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Fusion of two noisy sensors<sub>with</sub><sub>dyn</sub> (<a href="./figs/fusion_two_noisy_sensors_with_dyn.png">png</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn.pdf">pdf</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org855fa9e" class="outline-2">
<h2 id="org855fa9e"><span class="section-number-2">8</span> Fusion of two noisy sensors with Dynamics - Bis</h2>
<div id="outline-container-org6515349" class="outline-2">
<h2 id="org6515349"><span class="section-number-2">8</span> Fusion of two noisy sensors with Dynamics - Bis</h2>
<div class="outline-text-2" id="text-8">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/fusion_two_noisy_sensors_with_dyn_bis.png">png</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn_bis.pdf">pdf</a> and <a href="./figs/fusion_two_noisy_sensors_with_dyn_bis.tex">tex</a>.
@ -594,7 +594,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="org041e92e" class="figure">
<div id="orgff64b82" class="figure">
<p><img src="figs/fusion_two_noisy_sensors_with_dyn_bis.png" alt="fusion_two_noisy_sensors_with_dyn_bis.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Fusion of two noisy sensors<sub>with</sub><sub>dyn</sub><sub>bis</sub> (<a href="./figs/fusion_two_noisy_sensors_with_dyn_bis.png">png</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn_bis.pdf">pdf</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn_bis.tex">tex</a>).</p>
@ -602,8 +602,8 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
</div>
<div id="outline-container-org11ffe09" class="outline-2">
<h2 id="org11ffe09"><span class="section-number-2">9</span> Fusion of two sensors with mismatch dynamics</h2>
<div id="outline-container-org066adab" class="outline-2">
<h2 id="org066adab"><span class="section-number-2">9</span> Fusion of two sensors with mismatch dynamics</h2>
<div class="outline-text-2" id="text-9">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/fusion_two_signals_with_dyn.png">png</a>, <a href="./figs/fusion_two_signals_with_dyn.pdf">pdf</a> and <a href="./figs/fusion_two_signals_with_dyn.tex">tex</a>.
@ -648,7 +648,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="orgc18d1e5" class="figure">
<div id="org3b33068" class="figure">
<p><img src="figs/fusion_gain_mismatch.png" alt="fusion_gain_mismatch.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Fusion of two noisy sensors<sub>with</sub><sub>dyn</sub> (<a href="./figs/fusion_gain_mismatch.png">png</a>, <a href="./figs/fusion_gain_mismatch.pdf">pdf</a>, <a href="./figs/fusion_gain_mismatch.tex">tex</a>).</p>
@ -656,8 +656,8 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
</div>
<div id="outline-container-org7af9faf" class="outline-2">
<h2 id="org7af9faf"><span class="section-number-2">10</span> Uncertainty to Phase and Gain variation</h2>
<div id="outline-container-orga46cc8b" class="outline-2">
<h2 id="orga46cc8b"><span class="section-number-2">10</span> Uncertainty to Phase and Gain variation</h2>
<div class="outline-text-2" id="text-10">
<p>
The Tikz figure can be downloaded in the following formats: <a href="./figs/uncertainty_gain_phase_variation.png">png</a>, <a href="./figs/uncertainty_gain_phase_variation.pdf">pdf</a> and <a href="./figs/uncertainty_gain_phase_variation.tex">tex</a>.
@ -678,7 +678,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
<div id="org1495cee" class="figure">
<div id="org4d7c276" class="figure">
<p><img src="figs/uncertainty_gain_phase_variation.png" alt="uncertainty_gain_phase_variation.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Uncertainty to Phase and Gain variation (<a href="./figs/uncertainty_gain_phase_variation.png">png</a>, <a href="./figs/uncertainty_gain_phase_variation.pdf">pdf</a>, <a href="./figs/uncertainty_gain_phase_variation.tex">tex</a>).</p>
@ -686,8 +686,8 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
</div>
<div id="outline-container-orge5f551d" class="outline-2">
<h2 id="orge5f551d"><span class="section-number-2">11</span> Generate Complementary Filters using Feedback Control Architecture</h2>
<div id="outline-container-org1f59e20" class="outline-2">
<h2 id="org1f59e20"><span class="section-number-2">11</span> Generate Complementary Filters using Feedback Control Architecture</h2>
<div class="outline-text-2" id="text-11">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
@ -706,7 +706,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
<div id="orge72a5e5" class="figure">
<div id="orgb7a8eef" class="figure">
<p><img src="figs/complementary_filters_feedback_architecture.png" alt="complementary_filters_feedback_architecture.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Generation of Complementary Filters using the feedback architecture (<a href="./figs/complementary_filters_feedback_architecture.png">png</a>, <a href="./figs/complementary_filters_feedback_architecture.pdf">pdf</a>, <a href="./figs/complementary_filters_feedback_architecture.tex">tex</a>).</p>
@ -714,8 +714,8 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
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<h2 id="org9ce2a6b"><span class="section-number-2">12</span> H-Infinity Synthesis for Robust Sensor Fusion</h2>
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<h2 id="org509611f"><span class="section-number-2">12</span> H-Infinity Synthesis for Robust Sensor Fusion</h2>
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The Tikz figure can be downloaded in the following formats: <a href="./figs/h_infinity_robust_fusion.png">png</a>, <a href="./figs/h_infinity_robust_fusion.pdf">pdf</a> and <a href="./figs/h_infinity_robust_fusion.tex">tex</a>.
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<p><img src="figs/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
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<p><span class="figure-number">Figure 11: </span>H-Infinity Synthesis for Robust Sensor Fusion (<a href="./figs/h_infinity_robust_fusion.png">png</a>, <a href="./figs/h_infinity_robust_fusion.pdf">pdf</a>, <a href="./figs/h_infinity_robust_fusion.tex">tex</a>).</p>
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<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-08-14 mer. 12:08</p>
<p class="date">Created: 2019-08-21 mer. 16:35</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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#+TITLE: Robust and Optimal Sensor Fusion - Tikz Figures
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