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<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="#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>
<p>
Configuration file is accessible <a href="config.html">here</a>.
</p>
<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="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}
<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>
</pre>
</div>
</div>
</div>
<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}}
<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>
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</pre>
</div>
<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>
</div>
</div>
</div>
<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}}
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<span class="org-font-latex-sedate">\node</span>[block, below=<span class="org-font-latex-sedate">\cdist</span> of P] (HL) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_L</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
<span class="org-font-latex-sedate">\draw</span>[->] (HL.west) -| (<span class="org-font-latex-math">$(inputu)+(0.5*</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>) -- (WL.west);
<span class="org-font-latex-sedate">\draw</span>[->] (inputu-|sub) node[branch]{} -- (sub.south);
<span class="org-font-latex-sedate">\draw</span>[->] (sub.east) -- (WH.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(inputw)+(2*</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.5*</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>) |- (HL.east);
<span class="org-font-latex-sedate">\draw</span>[->] (WH.east) -- (outputh)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_H</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (WL.east) -- (outputl)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_L</span></span><span class="org-font-latex-math">$</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="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>
</div>
</div>
</div>
<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">
<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={5.0cm}{3.0cm}, dashed] (P) {};
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P$</span>};
<span class="org-font-latex-sedate">\coordinate</span>[] (inputn1) at (<span class="org-font-latex-math">$(P.south west)!0.8!(P.north west) + (-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputn2) at (<span class="org-font-latex-math">$(P.south west)!0.5!(P.north west) + (-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.2!(P.north west) + (-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputx) at (<span class="org-font-latex-math">$(P.south east)!0.5!(P.north east) + ( </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.1!(P.north east) + ( </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\node</span>[block, right=1.5 of inputn1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1.5 of inputn2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, right=of W1] (sub) {};
<span class="org-font-latex-sedate">\node</span>[addb, right=2 of W2] (add) {};
<span class="org-font-latex-sedate">\node</span>[block, below=of P] (H1) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (inputn1)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>} -- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (inputn2)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>} -- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W1) -- (sub.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W2) -| (sub.south);
<span class="org-font-latex-sedate">\draw</span>[->] (W2-|sub.south) node[branch]{} -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[->] (sub.east) -- ++(0.5, 0) |- (<span class="org-font-latex-math">$(outputv) + (-0.3, 0)$</span>) |- (H1.east);
<span class="org-font-latex-sedate">\draw</span>[->] (H1.west) -| (<span class="org-font-latex-math">$(inputu) + (0.3, 0)$</span>) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (add.east) -- (outputx) 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">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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-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">
<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);
<span class="org-font-latex-sedate">\node</span>[addb, above right=1.5 and 1 of x](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, below right=1.5 and 1 of x](add2){};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add2](W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=4 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-1, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W1.south) -- (add1.north);
<span class="org-font-latex-sedate">\draw</span>[->] (W2.south) -- (add2.north);
<span class="org-font-latex-sedate">\draw</span>[<-] (W1.north) -- ++(0, 0.8)node[below 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>[<-] (W2.north) -- ++(0, 0.8)node[below 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>[->] (add1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (H1) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (H2) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (add.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-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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-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">
<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){};
<span class="org-font-latex-sedate">\node</span>[block, above left=0.5 and 0.8 of add] (H1) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, below left=0.5 and 0.8 of add] (H2) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(H1.west)+(-1.5, 0)$</span>)node[above right]{<span class="org-font-latex-math">$x + n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>} -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(H2.west)+(-1.5, 0)$</span>)node[above right]{<span class="org-font-latex-math">$x + n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>} -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (H1) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (H2) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (add.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-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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>
</div>
</div>
</div>
<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">
<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);
<span class="org-font-latex-sedate">\node</span>[block, above right=1.5 and 0.5 of x](G1){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, below right=1.5 and 0.5 of x](G2){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=1 of G1](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=1 of G2](add2){};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add2](W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=6 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-1, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G1.east) -- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G2.east) -- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W1.south) -- (add1.north);
<span class="org-font-latex-sedate">\draw</span>[->] (W2.south) -- (add2.north);
<span class="org-font-latex-sedate">\draw</span>[<-] (W1.north) -- ++(0, 0.8)node[below 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>[<-] (W2.north) -- ++(0, 0.8)node[below 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>[->] (add1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (H1) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (H2) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (add.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-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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-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">
<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);
<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">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</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">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=1 of G1](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=1 of G2](add2){};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=6 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-1, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G1.east) -- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G2.east) -- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[<-] (add1.north) -- ++(0, 0.8)node[below 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>[<-] (add2.north) -- ++(0, 0.8)node[below 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>[->] (add1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (H1) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (H2) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (add.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-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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>
</div>
</div>
</div>
<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">
<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 and 3.5 of x](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, below right=1 and 3.5 of x](add2){};
<span class="org-font-latex-sedate">\node</span>[block, above left= of add1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above left= of add2](delta2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left= of delta1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left= of delta2](W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right= of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right= of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=5.5 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-1, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (x) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(add1-|W1.west)+(-0.5, 0)$</span>)node[branch]{} |- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(add2-|W2.west)+(-0.5, 0)$</span>)node[branch]{} |- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (delta2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (delta1.east) -| (add1.north);
<span class="org-font-latex-sedate">\draw</span>[->] (delta2.east) -| (add2.north);
<span class="org-font-latex-sedate">\draw</span>[->] (add1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (H1.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (H2.east) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (add.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-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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>
</div>
</div>
</div>
<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">
<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>[->] (-0.5, 0) -- (7, 0) node[below left]{Real};
<span class="org-font-latex-sedate">\draw</span>[->] (0, -1) -- (0, 1) node[left]{Im};
<span class="org-font-latex-sedate">\node</span>[branch] (1) at (5, 0){};
<span class="org-font-latex-sedate">\node</span>[below] at (1){<span class="org-font-latex-math">$1$</span>};
<span class="org-font-latex-sedate">\node</span>[circle, draw] (c) at (1)[minimum size=2cm]{};
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=2) -- node[midway, right]{<span class="org-font-latex-math">$|H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_i</span></span><span class="org-font-latex-math"> W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_i</span></span><span class="org-font-latex-math">|$</span>} (1);
<span class="org-font-latex-sedate">\draw</span>[dashed] (2, 0) arc (0:23:1) node[midway, right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"> </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\phi</span></span><span class="org-font-latex-math">$</span>};
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\draw</span></span><span class="org-comment">[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=1) coordinate(cbot);</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="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>
</div>
</div>
</div>
<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>}
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
<span class="org-font-latex-sedate">\node</span>[block, right=1 of addfb] (L){<span class="org-font-latex-math">$L$</span>};
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{}, right=1 of L] (adddy){};
<span class="org-font-latex-sedate">\draw</span>[<-] (addfb.west) -- ++(-1, 0) node[above right]{<span class="org-font-latex-math">$y</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (addfb.east) -- (L.west);
<span class="org-font-latex-sedate">\draw</span>[->] (L.east) -- (adddy.west);
<span class="org-font-latex-sedate">\draw</span>[->] (adddy.east) -- ++(1, 0) node[above left]{<span class="org-font-latex-math">$y</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_s</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(adddy.east) + (0.5, 0)$</span>) node[branch]{} -- ++(0, -1) -| (addfb.south);
<span class="org-font-latex-sedate">\draw</span>[<-] (adddy.north) -- ++(0, 1) node[below right]{<span class="org-font-latex-math">$y</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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>
</div>
</div>
</div>
<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">
<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={4.0cm}{3.0cm}, dashed] (P) {};
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P$</span>};
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.8!(P.north west) + (-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.4!(P.north west) + (-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputh) at (<span class="org-font-latex-math">$(P.south east)!0.8!(P.north east) + ( </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputl) at (<span class="org-font-latex-math">$(P.south east)!0.4!(P.north east) + ( </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.1!(P.north east) + ( </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>);
<span class="org-font-latex-sedate">\node</span>[block, left=2*<span class="org-font-latex-sedate">\cdist</span> of outputl] (W1){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=2*<span class="org-font-latex-sedate">\cdist</span> of outputh] (W2){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of W2] (sub) {};
<span class="org-font-latex-sedate">\node</span>[block, below=<span class="org-font-latex-sedate">\cdist</span> of P] (H1) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
<span class="org-font-latex-sedate">\draw</span>[->] (H1.west) -| (<span class="org-font-latex-math">$(inputu)+(0.5*</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>) -- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (inputu-|sub) node[branch]{} -- (sub.south);
<span class="org-font-latex-sedate">\draw</span>[->] (sub.east) -- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(inputw)+(2*</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.5*</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\cdist</span></span><span class="org-font-latex-math">, 0)$</span>) |- (H1.east);
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (outputh)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (outputl)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<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>[->] (x.center) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (x.center) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<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>[->] (<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>[->] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (delta2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (delta1.east) -| (add1.north);
<span class="org-font-latex-sedate">\draw</span>[->] (delta2.east) -| (add2.north);
<span class="org-font-latex-sedate">\draw</span>[->] (add1.east) -- (addn1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (addn2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (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>[->] (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>[->] (<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>[->] (<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>[->] (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>[->] (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>[->] (H1.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (H2.east) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[->] (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>[->] (x.center) |- (Wss);
<span class="org-font-latex-sedate">\draw</span>[->] (Wss.east) -- (delta.west);
<span class="org-font-latex-sedate">\draw</span>[->] (delta.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (add.east) -- (addn.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<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>[->] (Nss.south) -- (addn.north) node[above right]{<span class="org-font-latex-math">$n$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (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>[->] (<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>[->] (G.east) -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<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>[->] (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>[->] (<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>[->] (G.east) -- (add.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<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>[->] (N.south) -- (add.north)node[above right](n){<span class="org-font-latex-math">$n$</span>};
<span class="org-font-latex-sedate">\draw</span>[->] (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>[->] (<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>[->] (x.center) |- (W.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W.east) -- (delta.west);
<span class="org-font-latex-sedate">\draw</span>[->] (delta.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (add.east) -- (G.west);
<span class="org-font-latex-sedate">\draw</span>[->] (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>[->] (<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>[->] (x.center) |- (W.west);
<span class="org-font-latex-sedate">\draw</span>[->] (W.east) -- (delta.west);
<span class="org-font-latex-sedate">\draw</span>[->] (delta.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[->] (add.east) -- (G.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G.east) -- (addn.west);
<span class="org-font-latex-sedate">\draw</span>[->] (<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>[->] (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>[->] (x.center) |- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (x.center) |- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G1.east) -- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[->] (G2.east) -- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[<-] (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>[<-] (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>[->] (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>[->] (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: 2019-08-29 jeu. 11:21</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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</html>