776 lines
61 KiB
HTML
776 lines
61 KiB
HTML
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Optimal and Robust Complementary Filters for Sensor Fusion - Tikz Figures</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org815a564">1. Change some default</a></li>
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<li><a href="#org4640d64">2. H-Infinity - Complementary filters - Generalized plant</a></li>
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<li><a href="#org0b11ce2">3. H-Infinity - Complementary filters</a></li>
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<li><a href="#org958e1e2">4. H-Infinity - Optimal Complementary Filters</a></li>
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<li><a href="#org25d9a1b">5. Fusion of two noisy sensors</a></li>
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<li><a href="#orga9ed288">6. Fusion of two noisy signals</a></li>
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<li><a href="#org22dfd5b">7. Fusion of two noisy sensors with Dynamics</a></li>
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<li><a href="#org855fa9e">8. Fusion of two noisy sensors with Dynamics - Bis</a></li>
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<li><a href="#org11ffe09">9. Fusion of two sensors with mismatch dynamics</a></li>
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<li><a href="#org7af9faf">10. Uncertainty to Phase and Gain variation</a></li>
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<li><a href="#orge5f551d">11. Generate Complementary Filters using Feedback Control Architecture</a></li>
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<li><a href="#org9ce2a6b">12. H-Infinity Synthesis for Robust Sensor Fusion</a></li>
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</ul>
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Configuration file is accessible <a href="config.html">here</a>.
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<h2 id="org815a564"><span class="section-number-2">1</span> Change some default</h2>
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<div class="outline-text-2" id="text-1">
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<div class="org-src-container">
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<pre class="src src-latex" id="org862c935"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.6cm}}
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<div id="outline-container-org4640d64" class="outline-2">
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<h2 id="org4640d64"><span class="section-number-2">2</span> H-Infinity - Complementary filters - Generalized plant</h2>
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<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgc12e3d2" 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-org0b11ce2" class="outline-2">
|
|
<h2 id="org0b11ce2"><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}}
|
|
<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] (WL){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_L</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=2*<span class="org-font-latex-sedate">\cdist</span> of outputh] (WH){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_H</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of WH] (sub) {};
|
|
|
|
<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="orgd11c746" 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-org958e1e2" class="outline-2">
|
|
<h2 id="org958e1e2"><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}}
|
|
<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="orgace7a2f" class="figure">
|
|
<p><img src="figs/h_infinity_optimal_comp_filters.png" alt="h_infinity_optimal_comp_filters.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>H-Infinity - Optimal Complementary Filters (<a href="./figs/h_infinity_optimal_comp_filters.png">png</a>, <a href="./figs/h_infinity_optimal_comp_filters.pdf">pdf</a>, <a href="./figs/h_infinity_optimal_comp_filters.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org25d9a1b" class="outline-2">
|
|
<h2 id="org25d9a1b"><span class="section-number-2">5</span> Fusion of two noisy sensors</h2>
|
|
<div 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);
|
|
<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="org8abe259" class="figure">
|
|
<p><img src="figs/fusion_two_noisy_sensors.png" alt="fusion_two_noisy_sensors.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Fusion of two noisy sensors (<a href="./figs/fusion_two_noisy_sensors.png">png</a>, <a href="./figs/fusion_two_noisy_sensors.pdf">pdf</a>, <a href="./figs/fusion_two_noisy_sensors.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orga9ed288" class="outline-2">
|
|
<h2 id="orga9ed288"><span class="section-number-2">6</span> Fusion of two noisy signals</h2>
|
|
<div 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){};
|
|
<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="orgfca7098" 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-org22dfd5b" class="outline-2">
|
|
<h2 id="org22dfd5b"><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);
|
|
<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="orgbba4705" class="figure">
|
|
<p><img src="figs/fusion_two_noisy_sensors_with_dyn.png" alt="fusion_two_noisy_sensors_with_dyn.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Fusion of two noisy sensors<sub>with</sub><sub>dyn</sub> (<a href="./figs/fusion_two_noisy_sensors_with_dyn.png">png</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn.pdf">pdf</a>, <a href="./figs/fusion_two_noisy_sensors_with_dyn.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org855fa9e" class="outline-2">
|
|
<h2 id="org855fa9e"><span class="section-number-2">8</span> Fusion of two noisy sensors with Dynamics - Bis</h2>
|
|
<div 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);
|
|
<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="org041e92e" 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-org11ffe09" class="outline-2">
|
|
<h2 id="org11ffe09"><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}}
|
|
<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="orgc18d1e5" 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-org7af9faf" class="outline-2">
|
|
<h2 id="org7af9faf"><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>[->] (-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>
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|
|
|
|
|
<div id="org1495cee" class="figure">
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<p><img src="figs/uncertainty_gain_phase_variation.png" alt="uncertainty_gain_phase_variation.png" />
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</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>
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</div>
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</div>
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</div>
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|
<div id="outline-container-orge5f551d" class="outline-2">
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<h2 id="orge5f551d"><span class="section-number-2">11</span> Generate Complementary Filters using Feedback Control Architecture</h2>
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|
<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){};
|
|
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|
<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="orge72a5e5" 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-org9ce2a6b" class="outline-2">
|
|
<h2 id="org9ce2a6b"><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}}
|
|
<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="orgcd478e3" 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>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Thomas Dehaeze</p>
|
|
<p class="date">Created: 2019-08-14 mer. 12:08</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|