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Add many figures about sensor fusion / noise / dynamic uncertainty

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Thomas Dehaeze 2019-08-29 11:21:07 +02:00
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commit ab1d026898
26 changed files with 2501 additions and 98 deletions
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tikz/index.html
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-08-21 mer. 16:35 -->
<!-- 2019-08-29 jeu. 11:21 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Robust and Optimal Sensor Fusion - Tikz Figures</title>
@ -257,18 +257,25 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<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>
<li><a href="#org942e687">1. Change some default</a></li>
<li><a href="#orge1eca0e">2. H-Infinity - Complementary filters - Generalized plant</a></li>
<li><a href="#orgb6b40a8">3. H-Infinity - Complementary filters</a></li>
<li><a href="#orgdc216d7">4. H-Infinity - Optimal Complementary Filters</a></li>
<li><a href="#org8178630">5. Fusion of two noisy sensors</a></li>
<li><a href="#orgb1a2881">6. Fusion of two noisy signals</a></li>
<li><a href="#orgb70e68a">7. Fusion of two noisy sensors with Dynamics</a></li>
<li><a href="#org329b1aa">8. Fusion of two noisy sensors with Dynamics - Bis</a></li>
<li><a href="#org63f0fd9">9. Fusion of two sensors with mismatch dynamics</a></li>
<li><a href="#org91e15b3">10. Uncertainty to Phase and Gain variation</a></li>
<li><a href="#org3a28dde">11. Generate Complementary Filters using Feedback Control Architecture</a></li>
<li><a href="#org3bfc326">12. H-Infinity Synthesis for Robust Sensor Fusion</a></li>
<li><a href="#org25da4e5">13. Sensor fusion architecture with sensor dynamics uncertainty and noise</a></li>
<li><a href="#orgcc1d2ba">14. Equivalent super sensor</a></li>
<li><a href="#org36a14ee">15. One sensor with noise</a></li>
<li><a href="#org69ecf2e">16. One sensor with normalized noise</a></li>
<li><a href="#org94c7648">17. One sensor with dynamic uncertainty</a></li>
<li><a href="#orgab2cd5c">18. One sensor with dynamic uncertainty and noise</a></li>
<li><a href="#org7356a2a">19. Huddle Test</a></li>
</ul>
</div>
</div>
@ -277,11 +284,11 @@ for the JavaScript code in this tag.
Configuration file is accessible <a href="config.html">here</a>.
</p>
<div id="outline-container-org548cc39" class="outline-2">
<h2 id="org548cc39"><span class="section-number-2">1</span> Change some default</h2>
<div id="outline-container-org942e687" class="outline-2">
<h2 id="org942e687"><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="org7f5b9e0"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.6cm}}
<pre class="src src-latex" id="org60d2887"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
@ -293,8 +300,8 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
</div>
<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 id="outline-container-orge1eca0e" class="outline-2">
<h2 id="orge1eca0e"><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 +338,7 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
<div id="org2d1e475" class="figure">
<div id="org4cc8a00" 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 +346,8 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
</div>
<div id="outline-container-org9a9ee34" class="outline-2">
<h2 id="org9a9ee34"><span class="section-number-2">3</span> H-Infinity - Complementary filters</h2>
<div id="outline-container-orgb6b40a8" class="outline-2">
<h2 id="orgb6b40a8"><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 +386,7 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
<div id="org612d916" class="figure">
<div id="orgae2446b" 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>
@ -387,13 +394,9 @@ Configuration file is accessible <a href="config.html">here</a>.
</div>
</div>
<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 id="outline-container-orgdc216d7" class="outline-2">
<h2 id="orgdc216d7"><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>.
</p>
<div class="org-src-container">
<pre class="src src-latex"><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}}
@ -433,20 +436,16 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/h_in
</div>
<div id="org7d4df18" class="figure">
<div id="orgd4a1bec" 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-orgc92348b" class="outline-2">
<h2 id="orgc92348b"><span class="section-number-2">5</span> Fusion of two noisy sensors</h2>
<div id="outline-container-org8178630" class="outline-2">
<h2 id="org8178630"><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>.
</p>
<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>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
@ -475,20 +474,16 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="org7fef4e9" class="figure">
<div id="org933620b" 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-org5acbf15" class="outline-2">
<h2 id="org5acbf15"><span class="section-number-2">6</span> Fusion of two noisy signals</h2>
<div id="outline-container-orgb1a2881" class="outline-2">
<h2 id="orgb1a2881"><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>.
</p>
<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>}
<span class="org-font-latex-sedate">\node</span>[addb] (add) at (0, 0){};
@ -505,7 +500,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="org319ff6e" class="figure">
<div id="orgb511654" 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>
@ -513,13 +508,9 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
</div>
<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 id="outline-container-orgb70e68a" class="outline-2">
<h2 id="orgb70e68a"><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>.
</p>
<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>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
@ -552,20 +543,16 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="orgf0c8eb7" class="figure">
<div id="org264bbc5" 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-org6515349" class="outline-2">
<h2 id="org6515349"><span class="section-number-2">8</span> Fusion of two noisy sensors with Dynamics - Bis</h2>
<div id="outline-container-org329b1aa" class="outline-2">
<h2 id="org329b1aa"><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>.
</p>
<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>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
@ -594,7 +581,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="orgff64b82" class="figure">
<div id="orgae0bd65" 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>
@ -602,13 +589,9 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
</div>
<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 id="outline-container-org63f0fd9" class="outline-2">
<h2 id="org63f0fd9"><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>.
</p>
<div class="org-src-container">
<pre class="src src-latex"><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}}
@ -648,7 +631,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
<div id="org3b33068" class="figure">
<div id="orgecd13d0" 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>
@ -656,13 +639,9 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/fusi
</div>
</div>
<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 id="outline-container-org91e15b3" class="outline-2">
<h2 id="org91e15b3"><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>.
</p>
<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>}
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-0.5, 0) -- (7, 0) node[below left]{Real};
@ -678,7 +657,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
<div id="org4d7c276" class="figure">
<div id="org88614a3" 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 +665,8 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
</div>
<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 id="outline-container-org3a28dde" class="outline-2">
<h2 id="org3a28dde"><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 +685,7 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
<div id="orgb7a8eef" class="figure">
<div id="orgb320104" 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>
@ -714,13 +693,9 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/unce
</div>
</div>
<div id="outline-container-org509611f" class="outline-2">
<h2 id="org509611f"><span class="section-number-2">12</span> H-Infinity Synthesis for Robust Sensor Fusion</h2>
<div id="outline-container-org3bfc326" class="outline-2">
<h2 id="org3bfc326"><span class="section-number-2">12</span> H-Infinity Synthesis for Robust Sensor Fusion</h2>
<div class="outline-text-2" id="text-12">
<p>
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>.
</p>
<div class="org-src-container">
<pre class="src src-latex"><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}}
@ -758,17 +733,344 @@ The Tikz figure can be downloaded in the following formats: <a href="./figs/h_in
</div>
<div id="org0a4ff4a" class="figure">
<div id="org672dec4" class="figure">
<p><img src="figs/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
</p>
<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>
</div>
</div>
</div>
<div id="outline-container-org25da4e5" class="outline-2">
<h2 id="org25da4e5"><span class="section-number-2">13</span> Sensor fusion architecture with sensor dynamics uncertainty and noise</h2>
<div class="outline-text-2" id="text-13">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
<span class="org-font-latex-sedate">\node</span>[addb, above right=1.2 and 3.7 of x](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, below right=1.2 and 3.7 of x](add2){};
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0.1 of add1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0.1 of add2](delta2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.5 of delta1](W1){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.5 of delta2](W2){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.5 of add1](addn1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.5 of add2](addn2){};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of addn1](N1) {<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of addn2](N2) {<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1.2 of addn1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1.2 of addn2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=7.5 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(add1-|W1.west)+(-0.5, 0)$</span>)node[branch](S1){} |- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(add2-|W2.west)+(-0.5, 0)$</span>)node[branch](S2){} |- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W2.east) -- (delta2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta1.east) -| (add1.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta2.east) -| (add2.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (addn1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add2.east) -- (addn2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (addn1.east) -- (H1.west)node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (addn2.east) -- (H2.west)node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(N1.north)+(0,0.7)$</span>) node[below right](n1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>} -- (N1.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(N2.north)+(0,0.7)$</span>) node[below right](n2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>} -- (N2.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N1.south) -- (addn1.north)node[above right]{<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N2.south) -- (addn2.north)node[above right]{<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H1.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2.east) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(add2.south-|x)+(-0.2, -0.4)$</span>) (<span class="org-font-latex-math">$(n1.north-|add.east)+(0.2, 0.3)$</span>)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (supersensor.north east) {Super Sensor};
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(S1|-add1.south)+(-0.2, -0.2)$</span>) (<span class="org-font-latex-math">$(n1.north-|N1.east)+(0.2, 0.1)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor1.north west) {Sensor 1};
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(S2|-add2.south)+(-0.2, -0.2)$</span>) (<span class="org-font-latex-math">$(n2.north-|N2.east)+(0.2, 0.1)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor2.north west) {Sensor 2};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orga0d661d" class="figure">
<p><img src="figs/sensor_fusion_full.png" alt="sensor_fusion_full.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_full.png">png</a>, <a href="./figs/sensor_fusion_full.pdf">pdf</a>, <a href="./figs/sensor_fusion_full.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-orgcc1d2ba" class="outline-2">
<h2 id="orgcc1d2ba"><span class="section-number-2">14</span> Equivalent super sensor</h2>
<div class="outline-text-2" id="text-14">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
<span class="org-font-latex-sedate">\node</span>[block, above right=0.6 and 0.4 of x](Wss){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_{ss}</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of Wss](delta){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb](add) at (<span class="org-font-latex-math">$(delta.east|-x) + (0.5, 0)$</span>){};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.5 of add](addn){};
<span class="org-font-latex-sedate">\node</span>[block](Nss) at (delta-|addn) {<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_{ss}</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (Wss);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Wss.east) -- (delta.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- (addn.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(Nss.north)+(0,0.7)$</span>) node[below right](nss){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{n}$</span>} -- (Nss.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Nss.south) -- (addn.north) node[above right]{<span class="org-font-latex-math">$n$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (addn.east) -- ++(1.1, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(add.south-|x)+(-0.2, -0.2)$</span>) (<span class="org-font-latex-math">$(Nss.east|-nss.north)+(0.2, 0.2)$</span>)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (supersensor.north west) {Super Sensor};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org405feac" class="figure">
<p><img src="figs/sensor_fusion_equivalent.png" alt="sensor_fusion_equivalent.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_equivalent.png">png</a>, <a href="./figs/sensor_fusion_equivalent.pdf">pdf</a>, <a href="./figs/sensor_fusion_equivalent.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org36a14ee" class="outline-2">
<h2 id="org36a14ee"><span class="section-number-2">15</span> One sensor with noise</h2>
<div class="outline-text-2" id="text-15">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[block] (G) at (0, 0) {<span class="org-font-latex-math">$G(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.8 of G] (add) {};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(G.west) + (-0.8, 0)$</span>)node[above right]{<span class="org-font-latex-math">$x$</span>} -- (G.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G.east) -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(add.north) + (0, 0.8)$</span>)node[below right](n){<span class="org-font-latex-math">$n$</span>} -- (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(0.8, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G.south west)+(-0.3, -0.1)$</span>) (<span class="org-font-latex-math">$(n.north east)+(0.0, 0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor.north west) {Sensor};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org2b94710" class="figure">
<p><img src="figs/one_sensor_noise.png" alt="one_sensor_noise.png" />
</p>
<p><span class="figure-number">Figure 14: </span>One sensor with Noise (<a href="./figs/one_sensor_noise.png">png</a>, <a href="./figs/one_sensor_noise.pdf">pdf</a>, <a href="./figs/one_sensor_noise.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org69ecf2e" class="outline-2">
<h2 id="org69ecf2e"><span class="section-number-2">16</span> One sensor with normalized noise</h2>
<div class="outline-text-2" id="text-16">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[block] (G) at (0, 0) {<span class="org-font-latex-math">$G(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.8 of G] (add) {};
<span class="org-font-latex-sedate">\node</span>[block, above=0.6 of add] (N) {<span class="org-font-latex-math">$N(s)$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(G.west) + (-0.8, 0)$</span>)node[above right]{<span class="org-font-latex-math">$x$</span>} -- (G.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G.east) -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(N.north) + (0, 0.8)$</span>)node[below right](ntilde){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}$</span>} -- (N.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N.south) -- (add.north)node[above right](n){<span class="org-font-latex-math">$n$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(1.0, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G.south west)+(-0.3, -0.2)$</span>) (<span class="org-font-latex-math">$(ntilde.north-|N.east)+(0.2, 0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor.north west) {Sensor};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org0741f37" class="figure">
<p><img src="figs/one_sensor_normalized_noise.png" alt="one_sensor_normalized_noise.png" />
</p>
<p><span class="figure-number">Figure 15: </span>One sensor with normalized noise (<a href="./figs/one_sensor_normalized_noise.png">png</a>, <a href="./figs/one_sensor_normalized_noise.pdf">pdf</a>, <a href="./figs/one_sensor_normalized_noise.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org94c7648" class="outline-2">
<h2 id="org94c7648"><span class="section-number-2">17</span> One sensor with dynamic uncertainty</h2>
<div class="outline-text-2" id="text-17">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0) {};
<span class="org-font-latex-sedate">\node</span>[block, above right=0.4 and 0.4 of x](W){<span class="org-font-latex-math">$w(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.4 of W](delta){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb](add) at (<span class="org-font-latex-math">$(delta.east|-x) + (0.4, 0)$</span>) {};
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add](G){<span class="org-font-latex-math">$G(s)$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(x.west) + (-0.8, 0)$</span>)node[above right]{<span class="org-font-latex-math">$x$</span>} -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (W.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W.east) -- (delta.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- (G.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G.east) -- ++(0.8, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(x.west|-G.south)+(-0.2, -0.2)$</span>) (<span class="org-font-latex-math">$(delta.north-|G.east)+(0.2, 0.2)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor.north east) {Sensor};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org99f65af" class="figure">
<p><img src="figs/one_sensor_dyn_uncertainty.png" alt="one_sensor_dyn_uncertainty.png" />
</p>
<p><span class="figure-number">Figure 16: </span>One sensor with dynamic uncertainty (<a href="./figs/one_sensor_dyn_uncertainty.png">png</a>, <a href="./figs/one_sensor_dyn_uncertainty.pdf">pdf</a>, <a href="./figs/one_sensor_dyn_uncertainty.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-orgab2cd5c" class="outline-2">
<h2 id="orgab2cd5c"><span class="section-number-2">18</span> One sensor with dynamic uncertainty and noise</h2>
<div class="outline-text-2" id="text-18">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0) {};
<span class="org-font-latex-sedate">\node</span>[block, above right=0.4 and 0.4 of x](W){<span class="org-font-latex-math">$w(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.4 of W](delta){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb](add) at (<span class="org-font-latex-math">$(delta.east|-x) + (0.4, 0)$</span>) {};
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add](G){<span class="org-font-latex-math">$G(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.5 of G] (addn) {};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(x.west) + (-0.8, 0)$</span>)node[above right]{<span class="org-font-latex-math">$x$</span>} -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (W.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W.east) -- (delta.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- (G.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G.east) -- (addn.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(addn.north)+(0, 0.8)$</span>) node[below right]{<span class="org-font-latex-math">$n$</span>} -- (addn.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (addn.east) -- ++(0.8, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(x.west|-G.south)+(-0.2, -0.2)$</span>) (<span class="org-font-latex-math">$(delta.north-|addn.east)+(0.2, 0.2)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
<span class="org-font-latex-sedate">\node</span>[above right] at (sensor.south west) {Sensor};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orge2a5263" class="figure">
<p><img src="figs/one_sensor_dyn_uncertainty_noise.png" alt="one_sensor_dyn_uncertainty_noise.png" />
</p>
<p><span class="figure-number">Figure 17: </span>One sensor with dynamic uncertainty (<a href="./figs/one_sensor_dyn_uncertainty_noise.png">png</a>, <a href="./figs/one_sensor_dyn_uncertainty_noise.pdf">pdf</a>, <a href="./figs/one_sensor_dyn_uncertainty_noise.tex">tex</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org7356a2a" class="outline-2">
<h2 id="org7356a2a"><span class="section-number-2">19</span> Huddle Test</h2>
<div class="outline-text-2" id="text-19">
<div class="org-src-container">
<pre class="src src-latex"><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}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate">\def\cdist</span>{0.7}
<span class="org-font-latex-sedate">\definecolor</span>{T}{rgb}{0.230, 0.299, 0.754}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\definecolor</span>{S}{rgb}{0.706, 0.016, 0.150}<span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
<span class="org-font-latex-sedate">\node</span>[block, above right=0.5 and 0.5 of x](G1){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, below right=0.5 and 0.5 of x](G2){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.8 of G1](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.8 of G2](add2){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G2.east) -- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (add1.north) -- ++(0, 0.8)node[below right](n1){<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (add2.north) -- ++(0, 0.8)node[below right](n2){<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- ++(1, 0)node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add2.east) -- ++(1, 0)node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[fit={($(G2.south-|x)+(-0.2, -0.3)$) ($(n1.north east-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};</span>
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below left] at (supersensor.north east) {Super Sensor};</span>
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G1.south west)+(-0.3, -0.1)$</span>) (<span class="org-font-latex-math">$(n1.north east)+(0.0, 0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor1.north west) {Sensor 1};
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G2.south west)+(-0.3, -0.1)$</span>) (<span class="org-font-latex-math">$(n2.north east)+(0.0, 0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor2.north west) {Sensor 2};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org25f2d34" class="figure">
<p><img src="figs/huddle_test.png" alt="huddle_test.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Huddle Test (<a href="./figs/huddle_test.png">png</a>, <a href="./figs/huddle_test.pdf">pdf</a>, <a href="./figs/huddle_test.tex">tex</a>).</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-08-21 mer. 16:35</p>
<p class="date">Created: 2019-08-29 jeu. 11:21</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

252
tikz/index.org
View File

@ -105,8 +105,6 @@ Configuration file is accessible [[file:config.org][here]].
[[file:figs/sf_hinf_filters_b.png]]
* H-Infinity - Optimal Complementary Filters
The Tikz figure can be downloaded in the following formats: [[./figs/h_infinity_optimal_comp_filters.png][png]], [[./figs/h_infinity_optimal_comp_filters.pdf][pdf]] and [[./figs/h_infinity_optimal_comp_filters.tex][tex]].
#+begin_src latex :file h_infinity_optimal_comp_filters.pdf :tangle figs/h_infinity_optimal_comp_filters.tex
<<tikz_default>>
\begin{tikzpicture}
@ -143,8 +141,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/h_infinity_
#+RESULTS:
[[file:figs/h_infinity_optimal_comp_filters.png]]
* Fusion of two noisy sensors
The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_noisy_sensors.png][png]], [[./figs/fusion_two_noisy_sensors.pdf][pdf]] and [[./figs/fusion_two_noisy_sensors.tex][tex]].
#+begin_src latex :file fusion_two_noisy_sensors.pdf :tangle figs/fusion_two_noisy_sensors.tex
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
@ -176,8 +172,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_
#+RESULTS:
[[file:figs/fusion_two_noisy_sensors.png]]
* Fusion of two noisy signals
The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_signals.png][png]], [[./figs/fusion_two_signals.pdf][pdf]] and [[./figs/fusion_two_signals.tex][tex]].
#+begin_src latex :file fusion_two_signals.pdf :tangle figs/fusion_two_signals.tex
\begin{tikzpicture}
\node[addb] (add) at (0, 0){};
@ -198,8 +192,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_
[[file:figs/fusion_two_signals.png]]
* Fusion of two noisy sensors with Dynamics
The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_noisy_sensors_with_dyn.png][png]], [[./figs/fusion_two_noisy_sensors_with_dyn.pdf][pdf]] and [[./figs/fusion_two_noisy_sensors_with_dyn.tex][tex]].
#+begin_src latex :file fusion_two_noisy_sensors_with_dyn.pdf :tangle figs/fusion_two_noisy_sensors_with_dyn.tex
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
@ -235,8 +227,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_
#+RESULTS:
[[file:figs/fusion_two_noisy_sensors_with_dyn.png]]
* Fusion of two noisy sensors with Dynamics - Bis
The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_noisy_sensors_with_dyn_bis.png][png]], [[./figs/fusion_two_noisy_sensors_with_dyn_bis.pdf][pdf]] and [[./figs/fusion_two_noisy_sensors_with_dyn_bis.tex][tex]].
#+begin_src latex :file fusion_two_noisy_sensors_with_dyn_bis.pdf :tangle figs/fusion_two_noisy_sensors_with_dyn_bis.tex
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
@ -269,8 +259,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_
[[file:figs/fusion_two_noisy_sensors_with_dyn_bis.png]]
* Fusion of two sensors with mismatch dynamics
The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_signals_with_dyn.png][png]], [[./figs/fusion_two_signals_with_dyn.pdf][pdf]] and [[./figs/fusion_two_signals_with_dyn.tex][tex]].
#+begin_src latex :file fusion_gain_mismatch.pdf :tangle figs/fusion_gain_mismatch.tex
<<tikz_default>>
\begin{tikzpicture}
@ -308,8 +296,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/fusion_two_
[[file:figs/fusion_gain_mismatch.png]]
* Uncertainty to Phase and Gain variation
The Tikz figure can be downloaded in the following formats: [[./figs/uncertainty_gain_phase_variation.png][png]], [[./figs/uncertainty_gain_phase_variation.pdf][pdf]] and [[./figs/uncertainty_gain_phase_variation.tex][tex]].
#+begin_src latex :file uncertainty_gain_phase_variation.pdf :tangle figs/uncertainty_gain_phase_variation.tex :exports both
\begin{tikzpicture}
\draw[->] (-0.5, 0) -- (7, 0) node[below left]{Real};
@ -350,8 +336,6 @@ The Tikz figure can be downloaded in the following formats: [[./figs/uncertainty
[[file:figs/complementary_filters_feedback_architecture.png]]
* H-Infinity Synthesis for Robust Sensor Fusion
The Tikz figure can be downloaded in the following formats: [[./figs/h_infinity_robust_fusion.png][png]], [[./figs/h_infinity_robust_fusion.pdf][pdf]] and [[./figs/h_infinity_robust_fusion.tex][tex]].
#+begin_src latex :file h_infinity_robust_fusion.pdf :tangle figs/h_infinity_robust_fusion.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
@ -385,3 +369,239 @@ The Tikz figure can be downloaded in the following formats: [[./figs/h_infinity_
#+caption: H-Infinity Synthesis for Robust Sensor Fusion ([[./figs/h_infinity_robust_fusion.png][png]], [[./figs/h_infinity_robust_fusion.pdf][pdf]], [[./figs/h_infinity_robust_fusion.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_robust_fusion.png]]
* Sensor fusion architecture with sensor dynamics uncertainty and noise
#+begin_src latex :file sensor_fusion_full.pdf :tangle figs/sensor_fusion_full.tex
<<tikz_default>>
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[addb, above right=1.2 and 3.7 of x](add1){};
\node[addb, below right=1.2 and 3.7 of x](add2){};
\node[block, above left=0.2 and 0.1 of add1](delta1){$\Delta_1(s)$};
\node[block, above left=0.2 and 0.1 of add2](delta2){$\Delta_2(s)$};
\node[block, left=0.5 of delta1](W1){$w_1(s)$};
\node[block, left=0.5 of delta2](W2){$w_2(s)$};
\node[addb, right=0.5 of add1](addn1){};
\node[addb, right=0.5 of add2](addn2){};
\node[block, above=0.5 of addn1](N1) {$N_1(s)$};
\node[block, above=0.5 of addn2](N2) {$N_2(s)$};
\node[block, right=1.2 of addn1](H1){$H_1(s)$};
\node[block, right=1.2 of addn2](H2){$H_2(s)$};
\node[addb, right=7.5 of x](add){};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[->] (x.center) |- (add1.west);
\draw[->] (x.center) |- (add2.west);
\draw[->] ($(add1-|W1.west)+(-0.5, 0)$)node[branch](S1){} |- (W1.west);
\draw[->] ($(add2-|W2.west)+(-0.5, 0)$)node[branch](S2){} |- (W2.west);
\draw[->] (W1.east) -- (delta1.west);
\draw[->] (W2.east) -- (delta2.west);
\draw[->] (delta1.east) -| (add1.north);
\draw[->] (delta2.east) -| (add2.north);
\draw[->] (add1.east) -- (addn1.west);
\draw[->] (add2.east) -- (addn2.west);
\draw[->] (addn1.east) -- (H1.west)node[above left]{$\hat{x}_1$};
\draw[->] (addn2.east) -- (H2.west)node[above left]{$\hat{x}_2$};
\draw[->] ($(N1.north)+(0,0.7)$) node[below right](n1){$\tilde{n}_1$} -- (N1.north);
\draw[->] ($(N2.north)+(0,0.7)$) node[below right](n2){$\tilde{n}_2$} -- (N2.north);
\draw[->] (N1.south) -- (addn1.north)node[above right]{$n_1$};
\draw[->] (N2.south) -- (addn2.north)node[above right]{$n_2$};
\draw[->] (H1.east) -| (add.north);
\draw[->] (H2.east) -| (add.south);
\draw[->] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(add2.south-|x)+(-0.2, -0.4)$) ($(n1.north-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
\node[below left] at (supersensor.north east) {Super Sensor};
\node[block, fit={($(S1|-add1.south)+(-0.2, -0.2)$) ($(n1.north-|N1.east)+(0.2, 0.1)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
\node[below right] at (sensor1.north west) {Sensor 1};
\node[block, fit={($(S2|-add2.south)+(-0.2, -0.2)$) ($(n2.north-|N2.east)+(0.2, 0.1)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
\node[below right] at (sensor2.north west) {Sensor 2};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:sensor_fusion_full
#+caption: Sensor fusion architecture with sensor dynamics uncertainty ([[./figs/sensor_fusion_full.png][png]], [[./figs/sensor_fusion_full.pdf][pdf]], [[./figs/sensor_fusion_full.tex][tex]]).
#+RESULTS:
[[file:figs/sensor_fusion_full.png]]
* Equivalent super sensor
#+begin_src latex :file sensor_fusion_equivalent.pdf :tangle figs/sensor_fusion_equivalent.tex
<<tikz_default>>
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[block, above right=0.6 and 0.4 of x](Wss){$w_{ss}(s)$};
\node[block, right=0.5 of Wss](delta){$\Delta(s)$};
\node[addb](add) at ($(delta.east|-x) + (0.5, 0)$){};
\node[addb, right=0.5 of add](addn){};
\node[block](Nss) at (delta-|addn) {$N_{ss}(s)$};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (add.west);
\draw[->] (x.center) |- (Wss);
\draw[->] (Wss.east) -- (delta.west);
\draw[->] (delta.east) -| (add.north);
\draw[->] (add.east) -- (addn.west);
\draw[->] ($(Nss.north)+(0,0.7)$) node[below right](nss){$\hat{n}$} -- (Nss.north);
\draw[->] (Nss.south) -- (addn.north) node[above right]{$n$};
\draw[->] (addn.east) -- ++(1.1, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(add.south-|x)+(-0.2, -0.2)$) ($(Nss.east|-nss.north)+(0.2, 0.2)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
\node[below right] at (supersensor.north west) {Super Sensor};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:sensor_fusion_equivalent
#+caption: Sensor fusion architecture with sensor dynamics uncertainty ([[./figs/sensor_fusion_equivalent.png][png]], [[./figs/sensor_fusion_equivalent.pdf][pdf]], [[./figs/sensor_fusion_equivalent.tex][tex]]).
#+RESULTS:
[[file:figs/sensor_fusion_equivalent.png]]
* One sensor with noise
#+begin_src latex :file one_sensor_noise.pdf :tangle figs/huddle_test.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[block] (G) at (0, 0) {$G(s)$};
\node[addb, right=0.8 of G] (add) {};
\draw[->] ($(G.west) + (-0.8, 0)$)node[above right]{$x$} -- (G.west);
\draw[->] (G.east) -- (add.west);
\draw[->] ($(add.north) + (0, 0.8)$)node[below right](n){$n$} -- (add.north);
\draw[->] (add.east) -- ++(0.8, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(G.south west)+(-0.3, -0.1)$) ($(n.north east)+(0.0, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
\node[below right] at (sensor.north west) {Sensor};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:one_sensor_noise
#+caption: One sensor with Noise ([[./figs/one_sensor_noise.png][png]], [[./figs/one_sensor_noise.pdf][pdf]], [[./figs/one_sensor_noise.tex][tex]]).
#+RESULTS:
[[file:figs/one_sensor_noise.png]]
* One sensor with normalized noise
#+begin_src latex :file one_sensor_normalized_noise.pdf :tangle figs/huddle_test.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[block] (G) at (0, 0) {$G(s)$};
\node[addb, right=0.8 of G] (add) {};
\node[block, above=0.6 of add] (N) {$N(s)$};
\draw[->] ($(G.west) + (-0.8, 0)$)node[above right]{$x$} -- (G.west);
\draw[->] (G.east) -- (add.west);
\draw[->] ($(N.north) + (0, 0.8)$)node[below right](ntilde){$\tilde{n}$} -- (N.north);
\draw[->] (N.south) -- (add.north)node[above right](n){$n$};
\draw[->] (add.east) -- ++(1.0, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(G.south west)+(-0.3, -0.2)$) ($(ntilde.north-|N.east)+(0.2, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
\node[below right] at (sensor.north west) {Sensor};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:one_sensor_normalized_noise
#+caption: One sensor with normalized noise ([[./figs/one_sensor_normalized_noise.png][png]], [[./figs/one_sensor_normalized_noise.pdf][pdf]], [[./figs/one_sensor_normalized_noise.tex][tex]]).
#+RESULTS:
[[file:figs/one_sensor_normalized_noise.png]]
* One sensor with dynamic uncertainty
#+begin_src latex :file one_sensor_dyn_uncertainty.pdf :tangle figs/huddle_test.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[branch] (x) at (0, 0) {};
\node[block, above right=0.4 and 0.4 of x](W){$w(s)$};
\node[block, right=0.4 of W](delta){$\Delta(s)$};
\node[addb](add) at ($(delta.east|-x) + (0.4, 0)$) {};
\node[block, right=0.5 of add](G){$G(s)$};
\draw[->] ($(x.west) + (-0.8, 0)$)node[above right]{$x$} -- (add.west);
\draw[->] (x.center) |- (W.west);
\draw[->] (W.east) -- (delta.west);
\draw[->] (delta.east) -| (add.north);
\draw[->] (add.east) -- (G.west);
\draw[->] (G.east) -- ++(0.8, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(x.west|-G.south)+(-0.2, -0.2)$) ($(delta.north-|G.east)+(0.2, 0.2)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
\node[below left] at (sensor.north east) {Sensor};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:one_sensor_dyn_uncertainty
#+caption: One sensor with dynamic uncertainty ([[./figs/one_sensor_dyn_uncertainty.png][png]], [[./figs/one_sensor_dyn_uncertainty.pdf][pdf]], [[./figs/one_sensor_dyn_uncertainty.tex][tex]]).
#+RESULTS:
[[file:figs/one_sensor_dyn_uncertainty.png]]
* One sensor with dynamic uncertainty and noise
#+begin_src latex :file one_sensor_dyn_uncertainty_noise.pdf :tangle figs/huddle_test.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[branch] (x) at (0, 0) {};
\node[block, above right=0.4 and 0.4 of x](W){$w(s)$};
\node[block, right=0.4 of W](delta){$\Delta(s)$};
\node[addb](add) at ($(delta.east|-x) + (0.4, 0)$) {};
\node[block, right=0.5 of add](G){$G(s)$};
\node[addb, right=0.5 of G] (addn) {};
\draw[->] ($(x.west) + (-0.8, 0)$)node[above right]{$x$} -- (add.west);
\draw[->] (x.center) |- (W.west);
\draw[->] (W.east) -- (delta.west);
\draw[->] (delta.east) -| (add.north);
\draw[->] (add.east) -- (G.west);
\draw[->] (G.east) -- (addn.west);
\draw[->] ($(addn.north)+(0, 0.8)$) node[below right]{$n$} -- (addn.north);
\draw[->] (addn.east) -- ++(0.8, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(x.west|-G.south)+(-0.2, -0.2)$) ($(delta.north-|addn.east)+(0.2, 0.2)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
\node[above right] at (sensor.south west) {Sensor};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:one_sensor_dyn_uncertainty_noise
#+caption: One sensor with dynamic uncertainty ([[./figs/one_sensor_dyn_uncertainty_noise.png][png]], [[./figs/one_sensor_dyn_uncertainty_noise.pdf][pdf]], [[./figs/one_sensor_dyn_uncertainty_noise.tex][tex]]).
#+RESULTS:
[[file:figs/one_sensor_dyn_uncertainty_noise.png]]
* Huddle Test
#+begin_src latex :file huddle_test.pdf :tangle figs/huddle_test.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[block, above right=0.5 and 0.5 of x](G1){$G_1(s)$};
\node[block, below right=0.5 and 0.5 of x](G2){$G_2(s)$};
\node[addb, right=0.8 of G1](add1){};
\node[addb, right=0.8 of G2](add2){};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[->] (x.center) |- (G1.west);
\draw[->] (x.center) |- (G2.west);
\draw[->] (G1.east) -- (add1.west);
\draw[->] (G2.east) -- (add2.west);
\draw[<-] (add1.north) -- ++(0, 0.8)node[below right](n1){$n_1$};
\draw[<-] (add2.north) -- ++(0, 0.8)node[below right](n2){$n_2$};
\draw[->] (add1.east) -- ++(1, 0)node[above left]{$\hat{x}_1$};
\draw[->] (add2.east) -- ++(1, 0)node[above left]{$\hat{x}_2$};
\begin{scope}[on background layer]
% \node[fit={($(G2.south-|x)+(-0.2, -0.3)$) ($(n1.north east-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
% \node[below left] at (supersensor.north east) {Super Sensor};
\node[fit={($(G1.south west)+(-0.3, -0.1)$) ($(n1.north east)+(0.0, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
\node[below right] at (sensor1.north west) {Sensor 1};
\node[fit={($(G2.south west)+(-0.3, -0.1)$) ($(n2.north east)+(0.0, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
\node[below right] at (sensor2.north west) {Sensor 2};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:huddle_test
#+caption: Huddle Test ([[./figs/huddle_test.png][png]], [[./figs/huddle_test.pdf][pdf]], [[./figs/huddle_test.tex][tex]]).
#+RESULTS:
[[file:figs/huddle_test.png]]