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<h1 class="title">LaTeX Configuration for Tikz Figures</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org485d2f8">1. Packages</a></li>
<li><a href="#org8222280">2. Tikz related packages</a></li>
<li><a href="#org983f090">3. Tikz Libraries</a></li>
<li><a href="#org382b6c8">4. PGF Plot libraries and config</a></li>
<li><a href="#orgabed042">5. Setup size of figures</a></li>
<li><a href="#org7ec52e4">6. Setup Arrows style</a></li>
<li><a href="#orgadcf4fa">7. Colors</a></li>
<li><a href="#orgf8644bb">8. Control</a>
<li><a href="#org563923f">1. Packages</a></li>
<li><a href="#orgbba2842">2. Tikz related packages</a></li>
<li><a href="#org78bd760">3. Tikz Libraries</a></li>
<li><a href="#orga2a8c2c">4. PGF Plot libraries and config</a></li>
<li><a href="#orgb16e8c1">5. Setup size of figures</a></li>
<li><a href="#org7a055a0">6. Setup Arrows style</a></li>
<li><a href="#org337891d">7. Colors</a></li>
<li><a href="#org9fba3bd">8. Control</a>
<ul>
<li><a href="#orgb58c271">8.1. Blocks</a></li>
<li><a href="#org30e8430">8.2. <span class="todo TODO">TODO</span> Branches</a></li>
<li><a href="#org53c66b2">8.3. <span class="todo TODO">TODO</span> Hand Writen Style</a></li>
<li><a href="#orgbe652e9">8.4. DAC</a></li>
<li><a href="#orgbc82de4">8.5. ADC</a></li>
<li><a href="#org340b1a4">8.6. <span class="todo TODO">TODO</span> Gain</a></li>
<li><a href="#org275aed0">8.7. Add / Substract / Divide / Multiply block</a></li>
<li><a href="#orgad61177">8.1. Blocks</a></li>
<li><a href="#org747abfd">8.2. Branches</a></li>
<li><a href="#org9eb0276">8.3. Hand Writen Style</a></li>
<li><a href="#org68d7293">8.4. DAC</a></li>
<li><a href="#org703d0a7">8.5. ADC</a></li>
<li><a href="#org525abad">8.6. Gain</a></li>
<li><a href="#orgab3fd46">8.7. Add / Substract / Divide / Multiply block</a></li>
</ul>
</li>
<li><a href="#orga0bb999">9. Plots</a>
<li><a href="#org6dddda4">9. Plots</a>
<ul>
<li><a href="#org335716c">9.1. Grid</a></li>
<li><a href="#org63e134b">9.2. Lines</a></li>
<li><a href="#org14023c7">9.3. Ticks</a></li>
<li><a href="#org97ff77a">9.4. Size</a></li>
<li><a href="#orgbd0ce9a">9.5. Label</a></li>
<li><a href="#org7c80336">9.6. Legend</a></li>
<li><a href="#org882899e">9.7. Upper and Lower bounds</a></li>
<li><a href="#org028ac81">9.8. Pole</a></li>
<li><a href="#org2d51358">9.9. Zero</a></li>
<li><a href="#org5f52280">9.1. Grid</a></li>
<li><a href="#org59e26cb">9.2. Lines</a></li>
<li><a href="#orgbc1d944">9.3. Ticks</a></li>
<li><a href="#org0b17a46">9.4. Size</a></li>
<li><a href="#orge253709">9.5. Label</a></li>
<li><a href="#org0136e6e">9.6. Legend</a></li>
<li><a href="#org6c9488e">9.7. Upper and Lower bounds</a></li>
<li><a href="#org68481dd">9.8. Pole</a></li>
<li><a href="#org4b90ce8">9.9. Zero</a></li>
</ul>
</li>
<li><a href="#org152b1b6">10. Mechanical</a>
<li><a href="#orgddaa691">10. Mechanical</a>
<ul>
<li><a href="#orga9075d9">10.1. Spring</a></li>
<li><a href="#orgc290c7c">10.2. Coil</a></li>
<li><a href="#org642ecab">10.3. Damper</a></li>
<li><a href="#org7603957">10.4. Actuator</a></li>
<li><a href="#orgdcbbf5e">10.5. Ground</a></li>
<li><a href="#org24c87d5">10.6. Force Sensor</a></li>
<li><a href="#org85aab6a">10.7. Inertial Sensor</a></li>
<li><a href="#orgf07d1e3">10.8. Axis Rotator</a></li>
<li><a href="#org091ff6f">10.9. Cross</a></li>
<li><a href="#orgf570b65">10.10. Piezoelectric actuator</a></li>
<li><a href="#org816eebe">10.11. Voice coil</a></li>
<li><a href="#orga04ed0c">10.1. Spring</a></li>
<li><a href="#org5037f72">10.2. Coil</a></li>
<li><a href="#org16357a8">10.3. Damper</a></li>
<li><a href="#orgd56dea9">10.4. Actuator</a></li>
<li><a href="#org39bd1d0">10.5. Ground</a></li>
<li><a href="#org5225a31">10.6. Force Sensor</a></li>
<li><a href="#org6c262c1">10.7. Inertial Sensor</a></li>
<li><a href="#org4071fb1">10.8. Axis Rotator</a></li>
<li><a href="#org66470c0">10.9. Cross</a></li>
<li><a href="#org6eb8134">10.10. Piezoelectric actuator</a></li>
<li><a href="#org6b9bc4d">10.11. Voice coil</a></li>
</ul>
</li>
<li><a href="#orgb095cdb">11. Optics</a></li>
<li><a href="#org06358e3">12. Misc</a></li>
<li><a href="#org69d7a0b">11. Optics</a></li>
<li><a href="#org0283a14">12. Misc</a></li>
<li><a href="#org6860135">13. More Defaults specific to this paper</a></li>
</ul>
</div>
</div>
<div id="outline-container-org485d2f8" class="outline-2">
<h2 id="org485d2f8"><span class="section-number-2">1</span> Packages</h2>
<div id="outline-container-org563923f" class="outline-2">
<h2 id="org563923f"><span class="section-number-2">1</span> Packages</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>[<span class="org-variable-name">utf8</span>]{<span class="org-function-name">inputenc</span>}
@@ -352,8 +122,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-org8222280" class="outline-2">
<h2 id="org8222280"><span class="section-number-2">2</span> Tikz related packages</h2>
<div id="outline-container-orgbba2842" class="outline-2">
<h2 id="orgbba2842"><span class="section-number-2">2</span> Tikz related packages</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"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">tikz</span>} <span class="org-comment">% Tikz</span>
@@ -367,8 +137,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-org983f090" class="outline-2">
<h2 id="org983f090"><span class="section-number-2">3</span> Tikz Libraries</h2>
<div id="outline-container-org78bd760" class="outline-2">
<h2 id="org78bd760"><span class="section-number-2">3</span> Tikz Libraries</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">\usetikzlibrary</span>{arrows} <span class="org-comment">% Arrow tip library</span>
@@ -395,8 +165,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-org382b6c8" class="outline-2">
<h2 id="org382b6c8"><span class="section-number-2">4</span> PGF Plot libraries and config</h2>
<div id="outline-container-orga2a8c2c" class="outline-2">
<h2 id="orga2a8c2c"><span class="section-number-2">4</span> PGF Plot libraries and config</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">\usepgfplotslibrary</span>{patchplots}
@@ -409,8 +179,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-orgabed042" class="outline-2">
<h2 id="orgabed042"><span class="section-number-2">5</span> Setup size of figures</h2>
<div id="outline-container-orgb16e8c1" class="outline-2">
<h2 id="orgb16e8c1"><span class="section-number-2">5</span> Setup size of figures</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">\newlength</span></span>{<span class="org-font-latex-sedate"><span class="org-function-name">\fheight</span></span>}
@@ -423,8 +193,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-org7ec52e4" class="outline-2">
<h2 id="org7ec52e4"><span class="section-number-2">6</span> Setup Arrows style</h2>
<div id="outline-container-org7a055a0" class="outline-2">
<h2 id="org7a055a0"><span class="section-number-2">6</span> Setup Arrows style</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">\tikzset</span>{&gt;=Stealth}
@@ -435,8 +205,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-orgadcf4fa" class="outline-2">
<h2 id="orgadcf4fa"><span class="section-number-2">7</span> Colors</h2>
<div id="outline-container-org337891d" class="outline-2">
<h2 id="org337891d"><span class="section-number-2">7</span> Colors</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">\usepackage</span></span>{<span class="org-function-name">xcolor</span>}<span class="org-comment">% Color extension</span>
@@ -458,12 +228,12 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-orgf8644bb" class="outline-2">
<h2 id="orgf8644bb"><span class="section-number-2">8</span> Control</h2>
<div id="outline-container-org9fba3bd" class="outline-2">
<h2 id="org9fba3bd"><span class="section-number-2">8</span> Control</h2>
<div class="outline-text-2" id="text-8">
</div>
<div id="outline-container-orgb58c271" class="outline-3">
<h3 id="orgb58c271"><span class="section-number-3">8.1</span> Blocks</h3>
<div id="outline-container-orgad61177" class="outline-3">
<h3 id="orgad61177"><span class="section-number-3">8.1</span> Blocks</h3>
<div class="outline-text-3" id="text-8-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -480,8 +250,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-org30e8430" class="outline-3">
<h3 id="org30e8430"><span class="section-number-3">8.2</span> <span class="todo TODO">TODO</span> Branches</h3>
<div id="outline-container-org747abfd" class="outline-3">
<h3 id="org747abfd"><span class="section-number-3">8.2</span> Branches</h3>
<div class="outline-text-3" id="text-8-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
@@ -492,8 +262,8 @@ for the JavaScript code in this tag.
</div>
</div>
<div id="outline-container-org53c66b2" class="outline-3">
<h3 id="org53c66b2"><span class="section-number-3">8.3</span> <span class="todo TODO">TODO</span> Hand Writen Style</h3>
<div id="outline-container-org9eb0276" class="outline-3">
<h3 id="org9eb0276"><span class="section-number-3">8.3</span> Hand Writen Style</h3>
<div class="outline-text-3" id="text-8-3">
<p>
Usefull for schematic plots
@@ -505,8 +275,8 @@ Usefull for schematic plots
</div>
</div>
<div id="outline-container-orgbe652e9" class="outline-3">
<h3 id="orgbe652e9"><span class="section-number-3">8.4</span> DAC</h3>
<div id="outline-container-org68d7293" class="outline-3">
<h3 id="org68d7293"><span class="section-number-3">8.4</span> DAC</h3>
<div class="outline-text-3" id="text-8-4">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -520,8 +290,8 @@ Usefull for schematic plots
</div>
</div>
<div id="outline-container-orgbc82de4" class="outline-3">
<h3 id="orgbc82de4"><span class="section-number-3">8.5</span> ADC</h3>
<div id="outline-container-org703d0a7" class="outline-3">
<h3 id="org703d0a7"><span class="section-number-3">8.5</span> ADC</h3>
<div class="outline-text-3" id="text-8-5">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -536,8 +306,8 @@ Usefull for schematic plots
</div>
</div>
<div id="outline-container-org340b1a4" class="outline-3">
<h3 id="org340b1a4"><span class="section-number-3">8.6</span> <span class="todo TODO">TODO</span> Gain</h3>
<div id="outline-container-org525abad" class="outline-3">
<h3 id="org525abad"><span class="section-number-3">8.6</span> Gain</h3>
<div class="outline-text-3" id="text-8-6">
<p>
Maybe use <code>isosceles</code> instead of regular polygon?
@@ -578,8 +348,8 @@ Maybe use <code>isosceles</code> instead of regular polygon?
</div>
</div>
<div id="outline-container-org275aed0" class="outline-3">
<h3 id="org275aed0"><span class="section-number-3">8.7</span> Add / Substract / Divide / Multiply block</h3>
<div id="outline-container-orgab3fd46" class="outline-3">
<h3 id="orgab3fd46"><span class="section-number-3">8.7</span> Add / Substract / Divide / Multiply block</h3>
<div class="outline-text-3" id="text-8-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">% Add block with Circled operations</span>
@@ -591,7 +361,7 @@ Maybe use <code>isosceles</code> instead of regular polygon?
inner sep = 0pt,
minimum size = 2em,
execute at begin node={<span class="org-font-latex-sedate"><span class="org-keyword">\LARGE</span></span><span class="org-type"> </span><span class="org-type"><span class="org-font-latex-math">$#1$</span></span>},
append after command={<span class="org-font-latex-sedate">\pgfextra</span>{<span class="org-font-latex-sedate">\let\mainnode=\tikzlastnode</span>}
append after command={<span class="org-font-latex-sedate">\pgfextra</span>{<span class="org-font-latex-sedate">\let\mainnode</span>=<span class="org-font-latex-sedate">\tikzlastnode</span>}
<span class="org-font-latex-sedate">\ifx</span>#2<span class="org-font-latex-sedate">\empty\else</span>
node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (<span class="org-font-latex-sedate">\mainnode</span>.west) {<span class="org-font-latex-math">$#2$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
@@ -621,7 +391,7 @@ Maybe use <code>isosceles</code> instead of regular polygon?
inner sep = 0pt,
minimum size = 2em,
execute at begin node={<span class="org-font-latex-sedate"><span class="org-keyword">\LARGE</span></span><span class="org-type"> </span><span class="org-type"><span class="org-font-latex-math">$#1$</span></span>},
append after command={<span class="org-font-latex-sedate">\pgfextra</span>{<span class="org-font-latex-sedate">\let\mainnode=\tikzlastnode</span>}
append after command={<span class="org-font-latex-sedate">\pgfextra</span>{<span class="org-font-latex-sedate">\let\mainnode</span>=<span class="org-font-latex-sedate">\tikzlastnode</span>}
<span class="org-font-latex-sedate">\ifx</span>#2<span class="org-font-latex-sedate">\empty\else</span>
node[outer sep=2pt, inner sep=0pt, above left] at (<span class="org-font-latex-sedate">\mainnode</span>.west) {<span class="org-font-latex-math">$#2$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
@@ -644,12 +414,12 @@ Maybe use <code>isosceles</code> instead of regular polygon?
</div>
</div>
<div id="outline-container-orga0bb999" class="outline-2">
<h2 id="orga0bb999"><span class="section-number-2">9</span> Plots</h2>
<div id="outline-container-org6dddda4" class="outline-2">
<h2 id="org6dddda4"><span class="section-number-2">9</span> Plots</h2>
<div class="outline-text-2" id="text-9">
</div>
<div id="outline-container-org335716c" class="outline-3">
<h3 id="org335716c"><span class="section-number-3">9.1</span> Grid</h3>
<div id="outline-container-org5f52280" class="outline-3">
<h3 id="org5f52280"><span class="section-number-3">9.1</span> Grid</h3>
<div class="outline-text-3" id="text-9-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{grid style={black}}
@@ -662,8 +432,8 @@ Maybe use <code>isosceles</code> instead of regular polygon?
</div>
</div>
<div id="outline-container-org63e134b" class="outline-3">
<h3 id="org63e134b"><span class="section-number-3">9.2</span> Lines</h3>
<div id="outline-container-org59e26cb" class="outline-3">
<h3 id="org59e26cb"><span class="section-number-3">9.2</span> Lines</h3>
<div class="outline-text-3" id="text-9-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{separate axis lines=false} <span class="org-comment">% draw axis as rectangle and not as 4 lines</span>
@@ -677,8 +447,8 @@ Maybe use <code>isosceles</code> instead of regular polygon?
</div>
</div>
<div id="outline-container-org14023c7" class="outline-3">
<h3 id="org14023c7"><span class="section-number-3">9.3</span> Ticks</h3>
<div id="outline-container-orgbc1d944" class="outline-3">
<h3 id="orgbc1d944"><span class="section-number-3">9.3</span> Ticks</h3>
<div class="outline-text-3" id="text-9-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{every y tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}}}
@@ -690,8 +460,8 @@ Maybe use <code>isosceles</code> instead of regular polygon?
</div>
</div>
<div id="outline-container-org97ff77a" class="outline-3">
<h3 id="org97ff77a"><span class="section-number-3">9.4</span> Size</h3>
<div id="outline-container-org0b17a46" class="outline-3">
<h3 id="org0b17a46"><span class="section-number-3">9.4</span> Size</h3>
<div class="outline-text-3" id="text-9-4">
<p>
If <code>scale only axis=false</code> (the default), pgfplots will try to produce the desired width including labels, titles and ticks.
@@ -703,8 +473,8 @@ If <code>scale only axis=false</code> (the default), pgfplots will try to produc
</div>
</div>
<div id="outline-container-orgbd0ce9a" class="outline-3">
<h3 id="orgbd0ce9a"><span class="section-number-3">9.5</span> Label</h3>
<div id="outline-container-orge253709" class="outline-3">
<h3 id="orge253709"><span class="section-number-3">9.5</span> Label</h3>
<div class="outline-text-3" id="text-9-5">
<p>
Used to align all of ylabel of one figure.
@@ -716,8 +486,8 @@ Used to align all of ylabel of one figure.
</div>
</div>
<div id="outline-container-org7c80336" class="outline-3">
<h3 id="org7c80336"><span class="section-number-3">9.6</span> Legend</h3>
<div id="outline-container-org0136e6e" class="outline-3">
<h3 id="org0136e6e"><span class="section-number-3">9.6</span> Legend</h3>
<div class="outline-text-3" id="text-9-6">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-comment-delimiter">% </span><span class="org-comment">https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834</span>
@@ -754,8 +524,8 @@ Used to align all of ylabel of one figure.
</div>
</div>
<div id="outline-container-org882899e" class="outline-3">
<h3 id="org882899e"><span class="section-number-3">9.7</span> Upper and Lower bounds</h3>
<div id="outline-container-org6c9488e" class="outline-3">
<h3 id="org6c9488e"><span class="section-number-3">9.7</span> Upper and Lower bounds</h3>
<div class="outline-text-3" id="text-9-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{upperbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=60}}]
@@ -783,8 +553,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org028ac81" class="outline-3">
<h3 id="org028ac81"><span class="section-number-3">9.8</span> Pole</h3>
<div id="outline-container-org68481dd" class="outline-3">
<h3 id="org68481dd"><span class="section-number-3">9.8</span> Pole</h3>
<div class="outline-text-3" id="text-9-8">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -803,8 +573,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org2d51358" class="outline-3">
<h3 id="org2d51358"><span class="section-number-3">9.9</span> Zero</h3>
<div id="outline-container-org4b90ce8" class="outline-3">
<h3 id="org4b90ce8"><span class="section-number-3">9.9</span> Zero</h3>
<div class="outline-text-3" id="text-9-9">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -824,12 +594,12 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org152b1b6" class="outline-2">
<h2 id="org152b1b6"><span class="section-number-2">10</span> Mechanical</h2>
<div id="outline-container-orgddaa691" class="outline-2">
<h2 id="orgddaa691"><span class="section-number-2">10</span> Mechanical</h2>
<div class="outline-text-2" id="text-10">
</div>
<div id="outline-container-orga9075d9" class="outline-3">
<h3 id="orga9075d9"><span class="section-number-3">10.1</span> Spring</h3>
<div id="outline-container-orga04ed0c" class="outline-3">
<h3 id="orga04ed0c"><span class="section-number-3">10.1</span> Spring</h3>
<div class="outline-text-3" id="text-10-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -850,8 +620,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-orgc290c7c" class="outline-3">
<h3 id="orgc290c7c"><span class="section-number-3">10.2</span> Coil</h3>
<div id="outline-container-org5037f72" class="outline-3">
<h3 id="org5037f72"><span class="section-number-3">10.2</span> Coil</h3>
<div class="outline-text-3" id="text-10-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -872,8 +642,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org642ecab" class="outline-3">
<h3 id="org642ecab"><span class="section-number-3">10.3</span> Damper</h3>
<div id="outline-container-org16357a8" class="outline-3">
<h3 id="org16357a8"><span class="section-number-3">10.3</span> Damper</h3>
<div class="outline-text-3" id="text-10-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -900,8 +670,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org7603957" class="outline-3">
<h3 id="org7603957"><span class="section-number-3">10.4</span> Actuator</h3>
<div id="outline-container-orgd56dea9" class="outline-3">
<h3 id="orgd56dea9"><span class="section-number-3">10.4</span> Actuator</h3>
<div class="outline-text-3" id="text-10-4">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -931,8 +701,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-orgdcbbf5e" class="outline-3">
<h3 id="orgdcbbf5e"><span class="section-number-3">10.5</span> Ground</h3>
<div id="outline-container-org39bd1d0" class="outline-3">
<h3 id="org39bd1d0"><span class="section-number-3">10.5</span> Ground</h3>
<div class="outline-text-3" id="text-10-5">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -954,8 +724,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org24c87d5" class="outline-3">
<h3 id="org24c87d5"><span class="section-number-3">10.6</span> Force Sensor</h3>
<div id="outline-container-org5225a31" class="outline-3">
<h3 id="org5225a31"><span class="section-number-3">10.6</span> Force Sensor</h3>
<div class="outline-text-3" id="text-10-6">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -984,8 +754,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org85aab6a" class="outline-3">
<h3 id="org85aab6a"><span class="section-number-3">10.7</span> Inertial Sensor</h3>
<div id="outline-container-org6c262c1" class="outline-3">
<h3 id="org6c262c1"><span class="section-number-3">10.7</span> Inertial Sensor</h3>
<div class="outline-text-3" id="text-10-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -1013,8 +783,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-orgf07d1e3" class="outline-3">
<h3 id="orgf07d1e3"><span class="section-number-3">10.8</span> Axis Rotator</h3>
<div id="outline-container-org4071fb1" class="outline-3">
<h3 id="org4071fb1"><span class="section-number-3">10.8</span> Axis Rotator</h3>
<div class="outline-text-3" id="text-10-8">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\newcommand</span></span>{<span class="org-font-latex-sedate"><span class="org-function-name">\AxisRotator</span></span>}[<span class="org-variable-name">1</span>][<span class="org-variable-name">rotate=0</span>]{<span class="org-function-name"><span class="org-comment">%</span></span>
@@ -1025,8 +795,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org091ff6f" class="outline-3">
<h3 id="org091ff6f"><span class="section-number-3">10.9</span> Cross</h3>
<div id="outline-container-org66470c0" class="outline-3">
<h3 id="org66470c0"><span class="section-number-3">10.9</span> Cross</h3>
<div class="outline-text-3" id="text-10-9">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{cross}=[path picture={
@@ -1039,8 +809,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-orgf570b65" class="outline-3">
<h3 id="orgf570b65"><span class="section-number-3">10.10</span> Piezoelectric actuator</h3>
<div id="outline-container-org6eb8134" class="outline-3">
<h3 id="org6eb8134"><span class="section-number-3">10.10</span> Piezoelectric actuator</h3>
<div class="outline-text-3" id="text-10-10">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
@@ -1057,7 +827,7 @@ And we add the corresdonding
black,
}]
<span class="org-font-latex-sedate">\foreach</span> <span class="org-font-latex-sedate">\i</span> in {1,...,#3}{
(<span class="org-font-latex-math">${</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i/</span></span><span class="org-font-latex-math">(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.north west)+{(1+#3-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">)/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.south west)+0.1*(#1,0)$</span>) edge (<span class="org-font-latex-math">${</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i/</span></span><span class="org-font-latex-math">(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.north east)+{(1+#3-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">)/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.south east)-0.1*(#1,0)$</span>)
(<span class="org-font-latex-math">${</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.north west)+{(1+#3-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">)/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.south west)+0.1*(#1,0)$</span>) edge (<span class="org-font-latex-math">${</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.north east)+{(1+#3-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">)/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.south east)-0.1*(#1,0)$</span>)
}
}
},
@@ -1068,8 +838,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org816eebe" class="outline-3">
<h3 id="org816eebe"><span class="section-number-3">10.11</span> Voice coil</h3>
<div id="outline-container-org6b9bc4d" class="outline-3">
<h3 id="org6b9bc4d"><span class="section-number-3">10.11</span> Voice coil</h3>
<div class="outline-text-3" id="text-10-11">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\def\voicecoil</span>#1#2#3{
@@ -1080,7 +850,7 @@ And we add the corresdonding
<span class="org-font-latex-sedate">\def\voicecoilh</span>{#2} <span class="org-comment">% Total Height</span>
<span class="org-font-latex-sedate">\def\magnetw</span>{<span class="org-font-latex-sedate">\voicecoilw</span>} <span class="org-comment">% Width of the magnet</span>
<span class="org-font-latex-sedate">\def\magneth</span>{<span class="org-font-latex-sedate">\voicecoilh/1</span>.4} <span class="org-comment">% Height of the magnet</span>
<span class="org-font-latex-sedate">\def\magneth</span>{<span class="org-font-latex-sedate">\voicecoilh</span>/1.4} <span class="org-comment">% Height of the magnet</span>
<span class="org-font-latex-sedate">\def\magnetwb</span>{0.15*<span class="org-font-latex-sedate">\magnetw</span>} <span class="org-comment">% Width of the borders of the magnet</span>
<span class="org-font-latex-sedate">\def\magnetmw</span>{0.15*<span class="org-font-latex-sedate">\magnetw</span>} <span class="org-comment">% Width of the middle part of the magnet</span>
@@ -1095,26 +865,26 @@ And we add the corresdonding
<span class="org-comment">% ======================</span>
<span class="org-comment">% Magnet</span>
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (0, 0) -| ++(0.5*<span class="org-font-latex-sedate">\magnetw</span>, <span class="org-font-latex-sedate">\magneth</span>) -| ++(-0.5*<span class="org-font-latex-sedate">\magnetw+0</span>.5*<span class="org-font-latex-sedate">\magnetwg</span>, -<span class="org-font-latex-sedate">\magnethg</span>) -| (0.5*<span class="org-font-latex-sedate">\magnetw-\magnetwb</span>, <span class="org-font-latex-sedate">\magnethl</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetw+\magnetwb</span>, <span class="org-font-latex-sedate">\magneth-\magnethg</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetwg</span>, <span class="org-font-latex-sedate">\magneth</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetw</span>, 0) -- (cycle);
<span class="org-font-latex-sedate">\draw</span>[fill=white] (0, 0) -| ++(0.5*<span class="org-font-latex-sedate">\magnetw</span>, <span class="org-font-latex-sedate">\magneth</span>) -| ++(-0.5*<span class="org-font-latex-sedate">\magnetw</span>+0.5*<span class="org-font-latex-sedate">\magnetwg</span>, -<span class="org-font-latex-sedate">\magnethg</span>) -| (0.5*<span class="org-font-latex-sedate">\magnetw</span>-<span class="org-font-latex-sedate">\magnetwb</span>, <span class="org-font-latex-sedate">\magnethl</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetw</span>+<span class="org-font-latex-sedate">\magnetwb</span>, <span class="org-font-latex-sedate">\magneth</span>-<span class="org-font-latex-sedate">\magnethg</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetwg</span>, <span class="org-font-latex-sedate">\magneth</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetw</span>, 0) -- (cycle);
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[shift={(0, <span class="org-font-latex-sedate">\magnethl</span>)}]
<span class="org-font-latex-sedate">\draw</span>[fill=red] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 0) rectangle (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-font-latex-sedate">\draw</span>[fill=blue] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>) rectangle (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 2*<span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-comment">% Top conductive Magnet</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 2*<span class="org-font-latex-sedate">\magnetmh</span>) -| (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, -<span class="org-font-latex-sedate">\magnethl+\magneth-\magnethg</span>) -| ++(0.1, <span class="org-font-latex-sedate">\magnethg</span>) -| ++(-0.2-<span class="org-font-latex-sedate">\magnetmw</span>, -<span class="org-font-latex-sedate">\magnethg</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 2*<span class="org-font-latex-sedate">\magnetmh</span>) -| (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, -<span class="org-font-latex-sedate">\magnethl</span>+<span class="org-font-latex-sedate">\magneth</span>-<span class="org-font-latex-sedate">\magnethg</span>) -| ++(0.1, <span class="org-font-latex-sedate">\magnethg</span>) -| ++(-0.2-<span class="org-font-latex-sedate">\magnetmw</span>, -<span class="org-font-latex-sedate">\magnethg</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-comment">% ======================</span>
<span class="org-comment">% ======================</span>
<span class="org-comment">% Coil</span>
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate">\pgfmathsetmacro</span>{<span class="org-font-latex-sedate">\coilwidth</span>}{0.5*0.5*<span class="org-font-latex-sedate">\magnetmw+0</span>.5*0.1+0.25*<span class="org-font-latex-sedate">\magnetwg</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\pgfmathsetmacro</span>{<span class="org-font-latex-sedate">\coilwidth</span>}{0.5*0.5*<span class="org-font-latex-sedate">\magnetmw</span>+0.5*0.1+0.25*<span class="org-font-latex-sedate">\magnetwg</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\draw</span>[] ( <span class="org-font-latex-sedate">\coilwidth</span>, 0.5*<span class="org-font-latex-sedate">\magneth</span>) -- ++(0, 0.7*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\draw</span>[] (-<span class="org-font-latex-sedate">\coilwidth</span>, 0.5*<span class="org-font-latex-sedate">\magneth</span>) -- ++(0, 0.7*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-comment">% Point on the coil</span>
<span class="org-font-latex-sedate">\foreach</span> <span class="org-font-latex-sedate">\x</span> in {0,1,...,9}
{
<span class="org-font-latex-sedate">\node</span>[circle,inner sep=0.6pt,fill] at ( <span class="org-font-latex-sedate">\coilwidth</span>, <span class="org-font-latex-sedate">\x*0</span>.7*<span class="org-font-latex-sedate">\magneth/10+0</span>.5*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\node</span>[circle,inner sep=0.6pt,fill] at (-<span class="org-font-latex-sedate">\coilwidth</span>, <span class="org-font-latex-sedate">\x*0</span>.7*<span class="org-font-latex-sedate">\magneth/10+0</span>.5*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\node</span>[circle,inner sep=0.6pt,fill] at ( <span class="org-font-latex-sedate">\coilwidth</span>, <span class="org-font-latex-sedate">\x</span>*0.7*<span class="org-font-latex-sedate">\magneth</span>/10+0.5*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\node</span>[circle,inner sep=0.6pt,fill] at (-<span class="org-font-latex-sedate">\coilwidth</span>, <span class="org-font-latex-sedate">\x</span>*0.7*<span class="org-font-latex-sedate">\magneth</span>/10+0.5*<span class="org-font-latex-sedate">\magneth</span>);
}
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-0.5*<span class="org-font-latex-sedate">\magnetw</span>, 1.2*<span class="org-font-latex-sedate">\magneth</span>) rectangle ++(<span class="org-font-latex-sedate">\magnetw</span>, <span class="org-font-latex-sedate">\magnethg</span>);
<span class="org-comment">% ======================</span>
@@ -1123,7 +893,7 @@ And we add the corresdonding
<span class="org-comment">% Coordinates</span>
<span class="org-comment">% ======================</span>
<span class="org-comment">% Force</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_force) at (0, <span class="org-font-latex-sedate">\magneth-0</span>.5*<span class="org-font-latex-sedate">\magnethg</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_force) at (0, <span class="org-font-latex-sedate">\magneth</span>-0.5*<span class="org-font-latex-sedate">\magnethg</span>);
<span class="org-comment">% Coil</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_coil) at (0, <span class="org-font-latex-sedate">\voicecoilh</span>);
<span class="org-comment">% Magnet</span>
@@ -1140,8 +910,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-orgb095cdb" class="outline-2">
<h2 id="orgb095cdb"><span class="section-number-2">11</span> Optics</h2>
<div id="outline-container-org69d7a0b" class="outline-2">
<h2 id="org69d7a0b"><span class="section-number-2">11</span> Optics</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">\tikzset</span>{<span class="org-comment">%</span>
@@ -1169,8 +939,8 @@ And we add the corresdonding
</div>
</div>
<div id="outline-container-org06358e3" class="outline-2">
<h2 id="org06358e3"><span class="section-number-2">12</span> Misc</h2>
<div id="outline-container-org0283a14" class="outline-2">
<h2 id="org0283a14"><span class="section-number-2">12</span> Misc</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>{<span class="org-comment">%</span>
@@ -1186,11 +956,22 @@ And we add the corresdonding
</div>
</div>
</div>
<div id="outline-container-org6860135" class="outline-2">
<h2 id="org6860135"><span class="section-number-2">13</span> More Defaults specific to this paper</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}
</pre>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-08-01 jeu. 17:46</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2020-11-12 jeu. 10:41</p>
</div>
</body>
</html>

11
tikz/config.org
View File

@@ -1,11 +1,10 @@
#+TITLE: LaTeX Configuration for Tikz Figures
:DRAWER:
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
#+HTML_HEAD: <script src="../js/jquery.min.js"></script>
#+HTML_HEAD: <script src="../js/bootstrap.min.js"></script>
#+HTML_HEAD: <script src="../js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script src="../js/readtheorg.js"></script>
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
#+PROPERTY: header-args:latex+ :tangle config.tex
#+PROPERTY: header-args:latex+ :exports code

677
tikz/index.html
View File

@@ -3,17 +3,13 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-08-17 lun. 17:49 -->
<!-- 2020-11-12 jeu. 10:42 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Robust and Optimal Sensor Fusion - Tikz Figures</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Thomas Dehaeze" />
<link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
<link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
<script src="../js/jquery.min.js"></script>
<script src="../js/bootstrap.min.js"></script>
<script src="../js/jquery.stickytableheaders.min.js"></script>
<script src="../js/readtheorg.js"></script>
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
<script>MathJax = {
tex: {
tags: 'ams',
@@ -34,13 +30,16 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org4e2a932">1. Sensor Fusion Architecture</a></li>
<li><a href="#org1353381">2. Architecture used for \(\mathcal{H}_2\) synthesis of complementary filters</a></li>
<li><a href="#org1189340">3. Sensor fusion architecture with sensor dynamics uncertainty</a></li>
<li><a href="#org635364c">4. Uncertainty set of the super sensor dynamics</a></li>
<li><a href="#org8471952">5. Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</a></li>
<li><a href="#orgd2abe63">6. Sensor fusion architecture with sensor dynamics uncertainty and noise</a></li>
<li><a href="#org25fbe7c">7. Mixed H2/H-Infinity Synthesis</a></li>
<li><a href="#orgde691cc">1. Sensor Model - Noise</a></li>
<li><a href="#org3e09ccd">2. Sensor Fusion Architecture</a></li>
<li><a href="#org98e222d">3. Architecture used for \(\mathcal{H}_2\) synthesis of complementary filters</a></li>
<li><a href="#org7b2be36">4. Sensor Model - Uncertainty</a></li>
<li><a href="#org201b812">5. Sensor fusion architecture with sensor dynamics uncertainty</a></li>
<li><a href="#org295dc2a">6. Uncertainty set of the super sensor dynamics</a></li>
<li><a href="#orgff8ec60">7. Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</a></li>
<li><a href="#org77a9624">8. Sensor Model - Noise and Uncertainty</a></li>
<li><a href="#org194f17b">9. Sensor fusion architecture with sensor dynamics uncertainty and noise</a></li>
<li><a href="#org92adb06">10. Mixed H2/H-Infinity Synthesis</a></li>
</ul>
</div>
</div>
@@ -48,360 +47,504 @@
Configuration file is accessible <a href="config.html">here</a>.
</p>
<div id="outline-container-org4e2a932" class="outline-2">
<h2 id="org4e2a932"><span class="section-number-2">1</span> Sensor Fusion Architecture</h2>
<div id="outline-container-orgde691cc" class="outline-2">
<h2 id="orgde691cc"><span class="section-number-2">1</span> Sensor Model - Noise</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[block, above right=1.0 and 0.5 of x](G1){$G_1(s)$};
\node[block, below right=1.0 and 0.5 of x](G2){$G_2(s)$};
\node[addb, right=0.4 of G1](add1){};
\node[addb, right=0.4 of G2](add2){};
\node[block, right=1.1 of add1](H1){$H_1(s)$};
\node[block, right=1.1 of add2](H2){$H_2(s)$};
\node[block, above=0.5 of add1](N1){$N_1(s)$};
\node[block, above=0.5 of add2](N2){$N_2(s)$};
\node[addb, right=4.8 of x](add){};
<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](add1){};
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add1](G1){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.8 of G1](Ginv1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add1](N1){<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[-&gt;] (x.center) |- (G1.west);
\draw[-&gt;] (x.center) |- (G2.west);
\draw[-&gt;] (G1.east) -- (add1.west);
\draw[-&gt;] (G2.east) -- (add2.west);
\draw[-&gt;] (N1.south) -- (add1.north)node[above right]{$n_1$};
\draw[-&gt;] (N2.south) -- (add2.north)node[above right]{$n_2$};
\draw[&lt;-] (N1.north) -- ++(0, 0.6)node[below right](n1){$\tilde{n}_1$};
\draw[&lt;-] (N2.north) -- ++(0, 0.6)node[below right](n2){$\tilde{n}_2$};
\draw[-&gt;] (add1.east) -- (H1.west)node[above left]{$\hat{x}_1$};
\draw[-&gt;] (add2.east) -- (H2.west)node[above left]{$\hat{x}_2$};
\draw[-&gt;] (H1) -| (add.north);
\draw[-&gt;] (H2) -| (add.south);
\draw[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (add1.west) -- ++(-1.0, 0) node[above right]{<span class="org-font-latex-math">$x$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N1.south) -- (add1.north)node[above left]{<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (N1.north)node[above left](n1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>} -- ++(0, 0.4);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (Ginv1.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv1.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
\begin{scope}[on background layer]
\node[fit={($(G2.south-|x)+(-0.2, -0.3)$) ($(n1.north east-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
\node[below left] at (supersensor.north east) {Super Sensor};
\node[fit={($(G1.south west)+(-0.3, -0.1)$) ($(n1.north east)+(0.1, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
\node[below right] at (sensor1.north west) {Sensor 1};
\node[fit={($(G2.south west)+(-0.3, -0.1)$) ($(n2.north east)+(0.1, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
\node[below right] at (sensor2.north west) {Sensor 2};
\end{scope}
\end{tikzpicture}
<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">$(G1.south east)+(0.15, -0.15)$</span>) (<span class="org-font-latex-math">$(n1.north west)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below left, align=right] at (sensor1.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="orge2c7af4" class="figure">
<p><img src="figs/sensor_fusion_noise_arch.png" alt="sensor_fusion_noise_arch.png" />
<div id="org540adfc" class="figure">
<p><img src="figs/sensor_model_noise.png" alt="sensor_model_noise.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Sensor Fusion Architecture (<a href="./figs/sensor_fusion_noise_arch.png">png</a>, <a href="./figs/sensor_fusion_noise_arch.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 1: </span>Sensor Model (<a href="./figs/sensor_model_noise.png">png</a>, <a href="./figs/sensor_model_noise.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org1353381" class="outline-2">
<h2 id="org1353381"><span class="section-number-2">2</span> Architecture used for \(\mathcal{H}_2\) synthesis of complementary filters</h2>
<div id="outline-container-org3e09ccd" class="outline-2">
<h2 id="org3e09ccd"><span class="section-number-2">2</span> Sensor Fusion Architecture</h2>
<div class="outline-text-2" id="text-2">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\node[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
<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=1.05 and 0.6 of x](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, below right=1.05 and 0.6 of x](add2){};
<span class="org-font-latex-sedate">\node</span>[block, right=0.4 of add1](G1){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.4 of add2](G2){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.7 of G1](Ginv1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.7 of G2](Ginv2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.6 of Ginv1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.6 of Ginv2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add1](N1){<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add2](N2){<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=5.3 of x](add){};
\coordinate[] (inputw) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.35!(P.north west) + (-0.7, 0)$);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add2.east) -- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N1.south) -- (add1.north)node[above left]{<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N2.south) -- (add2.north)node[above left]{<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (N1.north)node[above left](n1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>} -- ++(0, 0.4);
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (N2.north)node[above left](n2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>} -- ++(0, 0.4);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (Ginv1.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G2.east) -- (Ginv2.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv1.east) -- (H1.west)node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv2.east) -- (H2.west)node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H1) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
\coordinate[] (output1) at ($(P.south east)!0.75!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.35!(P.north east) + ( 0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( 0.7, 0)$);
<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">$(G2.south-|x)+(-0.2, -0.3)$</span>) (<span class="org-font-latex-math">$(n1.north east-|add.east)+(0.2, 0.2)$</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};
\node[block, left=1.4 of output1] (N1){$N_1(s)$};
\node[block, left=1.4 of output2] (N2){$N_2(s)$};
\node[addb={+}{}{}{}{-}, left=of N1] (sub) {};
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G1.south east)+(0.15, -0.15)$</span>) (<span class="org-font-latex-math">$(n1.north west)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor1.north east) {Sensor 1};
\node[block, below=0.3 of P] (H2) {$H_2(s)$};
\draw[-&gt;] (inputw) node[above right]{$w$} -- (sub.west);
\draw[-&gt;] (H2.west) -| ($(inputu)+(0.35, 0)$) node[above]{$u$} -- (N2.west);
\draw[-&gt;] (inputu-|sub) node[branch]{} -- (sub.south);
\draw[-&gt;] (sub.east) -- (N1.west);
\draw[-&gt;] ($(sub.west)+(-0.6, 0)$) node[branch]{} |- ($(outputv)+(-0.35, 0)$) node[above]{$v$} |- (H2.east);
\draw[-&gt;] (N1.east) -- (output1)node[above left]{$z_1$};
\draw[-&gt;] (N2.east) -- (output2)node[above left]{$z_2$};
\end{tikzpicture}
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G2.south east)+(0.15, -0.15)$</span>) (<span class="org-font-latex-math">$(n2.north west)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor2.north east) {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="org8ddefad" class="figure">
<p><img src="figs/h_two_optimal_fusion.png" alt="h_two_optimal_fusion.png" />
<div id="org896d2c3" class="figure">
<p><img src="figs/sensor_fusion_noise_arch.png" alt="sensor_fusion_noise_arch.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (<a href="./figs/h_two_optimal_fusion.png">png</a>, <a href="./figs/h_two_optimal_fusion.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 2: </span>Sensor Fusion Architecture (<a href="./figs/sensor_fusion_noise_arch.png">png</a>, <a href="./figs/sensor_fusion_noise_arch.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org1189340" class="outline-2">
<h2 id="org1189340"><span class="section-number-2">3</span> Sensor fusion architecture with sensor dynamics uncertainty</h2>
<div id="outline-container-org98e222d" class="outline-2">
<h2 id="org98e222d"><span class="section-number-2">3</span> Architecture used for \(\mathcal{H}_2\) synthesis of complementary filters</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[addb, above right=0.8 and 4 of x](add1){};
\node[addb, below right=0.8 and 4 of x](add2){};
\node[block, above left=0.2 and 0.1 of add1](delta1){$\Delta_1(s)$};
\node[block, above left=0.2 and 0.1 of add2](delta2){$\Delta_2(s)$};
\node[block, left=0.5 of delta1](W1){$w_1(s)$};
\node[block, left=0.5 of delta2](W2){$w_2(s)$};
\node[block, right=0.5 of add1](H1){$H_1(s)$};
\node[block, right=0.5 of add2](H2){$H_2(s)$};
\node[addb, right=6 of x](add){};
<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>[block={3.5cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">{</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2}$</span>};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[-&gt;] (x.center) |- (add1.west);
\draw[-&gt;] (x.center) |- (add2.west);
\draw[-&gt;] ($(add1-|W1.west)+(-0.5, 0)$)node[branch](S1){} |- (W1.west);
\draw[-&gt;] ($(add2-|W2.west)+(-0.5, 0)$)node[branch](S1){} |- (W2.west);
\draw[-&gt;] (W1.east) -- (delta1.west);
\draw[-&gt;] (W2.east) -- (delta2.west);
\draw[-&gt;] (delta1.east) -| (add1.north);
\draw[-&gt;] (delta2.east) -| (add2.north);
\draw[-&gt;] (add1.east) -- (H1.west);
\draw[-&gt;] (add2.east) -- (H2.west);
\draw[-&gt;] (H1.east) -| (add.north);
\draw[-&gt;] (H2.east) -| (add.south);
\draw[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.8!(P.north west) + (-0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.5!(P.north west) + (-0.7, 0)$</span>);
\begin{scope}[on background layer]
\node[fit={($(H2.south-|x)+(-0.2, -0.3)$) ($(delta1.north east-|add.east)+(0.2, 0.4)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
\node[below left] at (supersensor.north east) {Super Sensor};
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(P.south east)!0.8!(P.north east) + ( 0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(P.south east)!0.5!(P.north east) + ( 0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.2!(P.north east) + ( 0.7, 0)$</span>);
\node[block, fit={($(W1.north-|S1)+(-0.2, 0.2)$) ($(add1.south east)+(0.2, -0.3)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
\node[above right] at (sensor1.south west) {Sensor 1};
\node[block, fit={($(W2.north-|S1)+(-0.2, 0.2)$) ($(add2.south east)+(0.2, -0.3)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
\node[above right] at (sensor2.south west) {Sensor 2};
\end{scope}
\end{tikzpicture}
<span class="org-font-latex-sedate">\node</span>[block, left=0.9 of output1] (N1){<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.9 of output2] (N2){<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of N1] (sub) {};
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H2) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2.west) -| (<span class="org-font-latex-math">$(inputu)+(0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$u$</span>} -- (N2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (inputu-|sub) node[branch]{} -- (sub.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (sub.east) -- (N1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(sub.west)+(-0.6, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$v$</span>} |- (H2.east);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N1.east) -- (output1)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</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="org6316ce9" class="figure">
<p><img src="figs/sensor_fusion_arch_uncertainty.png" alt="sensor_fusion_arch_uncertainty.png" />
<div id="orgc47567c" class="figure">
<p><img src="figs/h_two_optimal_fusion.png" alt="h_two_optimal_fusion.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_arch_uncertainty.png">png</a>, <a href="./figs/sensor_fusion_arch_uncertainty.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 3: </span>Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (<a href="./figs/h_two_optimal_fusion.png">png</a>, <a href="./figs/h_two_optimal_fusion.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org635364c" class="outline-2">
<h2 id="org635364c"><span class="section-number-2">4</span> Uncertainty set of the super sensor dynamics</h2>
<div id="outline-container-org7b2be36" class="outline-2">
<h2 id="org7b2be36"><span class="section-number-2">4</span> Sensor Model - Uncertainty</h2>
<div class="outline-text-2" id="text-4">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\begin{scope}[shift={(4, 0)}]
<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](b1){};
<span class="org-font-latex-sedate">\node</span>[block, above right=0.3 and 0.25 of b1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of W1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.3 of b1-|delta1](add1){};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of add1](G1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.7 of G1](Ginv1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
% Uncertainty Circle
\node[draw, circle, fill=black!20!white, minimum size=3.6cm] (c) at (0, 0) {};
\path[draw, dotted] (0, 0) circle [radius=1.0];
\path[draw, dashed] (135:1.0) circle [radius=0.8];
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(g1)+(-0.6,0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (g1) |- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta1.east) -| (add1.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (Ginv1.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv1.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
% Center of Circle
\node[below] at (0, 0){$1$};
\draw[&lt;-&gt;, dashed] (0, 0) node[branch]{} -- coordinate[midway](r1) ++(45:1.0);
\draw[&lt;-&gt;, dashed] (135:1.0)node[branch]{} -- coordinate[midway](r2) ++(90:0.8);
\node[] (l1) at (2, 1.5) {$|w_1 H_1|$};
\draw[-&gt;, dashed, out=-90, in=0] (l1.south) to (r1);
\node[] (l2) at (-2.5, 1.5) {$|w_2 H_2|$};
\draw[-&gt;, dashed, out=0, in=-180] (l2.east) to (r2);
\draw[&lt;-&gt;, dashed] (0, 0) -- coordinate[near end](r3) ++(200:1.8);
\node[] (l3) at (-2.5, -1.5) {$|w_1 H_1| + |w_2 H_2|$};
\draw[-&gt;, dashed, out=90, in=-90] (l3.north) to (r3);
\end{scope}
% Real and Imaginary Axis
\draw[-&gt;] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
\draw[-&gt;] (0, -1.7) -- (0, 1.7) node[below left]{Im};
\draw[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=2);
\draw[dashed] (1, 0) arc (0:28:1) node[midway, right]{$\Delta \phi$};
\end{tikzpicture}
<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>[block, fit={(<span class="org-font-latex-math">$(b1|-W1.north) + (-0.15, 0.15)$</span>) (<span class="org-font-latex-math">$(G1.south east)+(0.15, -0.15)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor1.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="orgdf90733" class="figure">
<p><img src="figs/uncertainty_set_super_sensor.png" alt="uncertainty_set_super_sensor.png" />
<div id="org3c8c032" class="figure">
<p><img src="figs/sensor_model_uncertainty.png" alt="sensor_model_uncertainty.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Uncertainty region of the super sensor dynamics in the complex plane (solid circle), of the sensor 1 (dotted circle) and of the sensor 2 (dashed circle) (<a href="./figs/uncertainty_set_super_sensor.png">png</a>, <a href="./figs/uncertainty_set_super_sensor.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 4: </span>Sensor Model including dynamical uncertainty (<a href="./figs/sensor_model_uncertainty.png">png</a>, <a href="./figs/sensor_model_uncertainty.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org8471952" class="outline-2">
<h2 id="org8471952"><span class="section-number-2">5</span> Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</h2>
<div id="outline-container-org201b812" class="outline-2">
<h2 id="org201b812"><span class="section-number-2">5</span> Sensor fusion architecture with sensor dynamics uncertainty</h2>
<div class="outline-text-2" id="text-5">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\node[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
<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>[branch, above right=0.8 and 0.2 of x](b1){};
<span class="org-font-latex-sedate">\node</span>[branch, below right=0.8 and 0.2 of x](b2){};
<span class="org-font-latex-sedate">\node</span>[block, above right=0.3 and 0.25 of b1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above right=0.3 and 0.25 of b2](W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of W1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of W2](delta2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.3 of b1-|delta1](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.3 of b2-|delta2](add2){};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of add1](G1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of add2](G2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.7 of G1](Ginv1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.7 of G2](Ginv2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.35 of Ginv1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.35 of Ginv2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=6.8 of x](add){};
\coordinate[] (inputw) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.35!(P.north west) + (-0.7, 0)$);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add2.east) -- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (b1) |- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (b2) |- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W2.east) -- (delta2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta1.east) -| (add1.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta2.east) -| (add2.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (Ginv1.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G2.east) -- (Ginv2.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H1.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2.east) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
\coordinate[] (output1) at ($(P.south east)!0.75!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.35!(P.north east) + ( 0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( 0.7, 0)$);
<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">$(H2.south-|x)+(-0.2, -0.3)$</span>) (<span class="org-font-latex-math">$(delta1.north east-|add.east)+(0.2, 0.3)$</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};
\node[block, left=1.4 of output1] (W1){$W_1(s)$};
\node[block, left=1.4 of output2] (W2){$W_2(s)$};
\node[addb={+}{}{}{}{-}, left=of W1] (sub) {};
\node[block, below=0.3 of P] (H2) {$H_2(s)$};
\draw[-&gt;] (inputw) node[above right]{$w$} -- (sub.west);
\draw[-&gt;] (H2.west) -| ($(inputu)+(0.35, 0)$) node[above]{$u$} -- (W2.west);
\draw[-&gt;] (inputu-|sub) node[branch]{} -- (sub.south);
\draw[-&gt;] (sub.east) -- (W1.west);
\draw[-&gt;] ($(sub.west)+(-0.6, 0)$) node[branch]{} |- ($(outputv)+(-0.35, 0)$) node[above]{$v$} |- (H2.east);
\draw[-&gt;] (W1.east) -- (output1)node[above left]{$z_1$};
\draw[-&gt;] (W2.east) -- (output2)node[above left]{$z_2$};
\end{tikzpicture}
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(b1|-W1.north) + (-0.15, 0.15)$</span>) (<span class="org-font-latex-math">$(G1.south east)+(0.15, -0.15)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor1.north east) {Sensor 1};
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(b2|-W2.north) + (-0.15, 0.15)$</span>) (<span class="org-font-latex-math">$(G2.south east)+(0.15, -0.15)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor2.north east) {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="orgc7070d9" class="figure">
<p><img src="figs/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
<div id="org4ef6676" class="figure">
<p><img src="figs/sensor_fusion_arch_uncertainty.png" alt="sensor_fusion_arch_uncertainty.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (<a href="./figs/h_infinity_robust_fusion.png">png</a>, <a href="./figs/h_infinity_robust_fusion.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 5: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_arch_uncertainty.png">png</a>, <a href="./figs/sensor_fusion_arch_uncertainty.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-orgd2abe63" class="outline-2">
<h2 id="orgd2abe63"><span class="section-number-2">6</span> Sensor fusion architecture with sensor dynamics uncertainty and noise</h2>
<div id="outline-container-org295dc2a" class="outline-2">
<h2 id="org295dc2a"><span class="section-number-2">6</span> Uncertainty set of the super sensor dynamics</h2>
<div class="outline-text-2" id="text-6">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[addb, above right=1.2 and 3.7 of x](add1){};
\node[addb, below right=1.2 and 3.7 of x](add2){};
\node[block, above left=0.2 and 0.1 of add1](delta1){$\Delta_1(s)$};
\node[block, above left=0.2 and 0.1 of add2](delta2){$\Delta_2(s)$};
\node[block, left=0.5 of delta1](W1){$w_1(s)$};
\node[block, left=0.5 of delta2](W2){$w_2(s)$};
\node[addb, right=0.5 of add1](addn1){};
\node[addb, right=0.5 of add2](addn2){};
\node[block, above=0.5 of addn1](N1) {$N_1(s)$};
\node[block, above=0.5 of addn2](N2) {$N_2(s)$};
\node[block, right=1.2 of addn1](H1){$H_1(s)$};
\node[block, right=1.2 of addn2](H2){$H_2(s)$};
\node[addb, right=7.5 of x](add){};
<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"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[shift={(4, 0)}]
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[-&gt;] (x.center) |- (add1.west);
\draw[-&gt;] (x.center) |- (add2.west);
\draw[-&gt;] ($(add1-|W1.west)+(-0.5, 0)$)node[branch](S1){} |- (W1.west);
\draw[-&gt;] ($(add2-|W2.west)+(-0.5, 0)$)node[branch](S2){} |- (W2.west);
\draw[-&gt;] (W1.east) -- (delta1.west);
\draw[-&gt;] (W2.east) -- (delta2.west);
\draw[-&gt;] (delta1.east) -| (add1.north);
\draw[-&gt;] (delta2.east) -| (add2.north);
\draw[-&gt;] (add1.east) -- (addn1.west);
\draw[-&gt;] (add2.east) -- (addn2.west);
\draw[-&gt;] (addn1.east) -- (H1.west)node[above left]{$\hat{x}_1$};
\draw[-&gt;] (addn2.east) -- (H2.west)node[above left]{$\hat{x}_2$};
\draw[-&gt;] ($(N1.north)+(0,0.7)$) node[below right](n1){$\tilde{n}_1$} -- (N1.north);
\draw[-&gt;] ($(N2.north)+(0,0.7)$) node[below right](n2){$\tilde{n}_2$} -- (N2.north);
\draw[-&gt;] (N1.south) -- (addn1.north)node[above right]{$n_1$};
\draw[-&gt;] (N2.south) -- (addn2.north)node[above right]{$n_2$};
\draw[-&gt;] (H1.east) -| (add.north);
\draw[-&gt;] (H2.east) -| (add.south);
\draw[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
<span class="org-comment">% Uncertainty Circle</span>
<span class="org-font-latex-sedate">\node</span>[draw, circle, fill=black!20!white, minimum size=3.6cm] (c) at (0, 0) {};
<span class="org-font-latex-sedate">\path</span>[draw, dotted] (0, 0) circle [radius=1.0];
<span class="org-font-latex-sedate">\path</span>[draw, dashed] (135:1.0) circle [radius=0.8];
\begin{scope}[on background layer]
\node[fit={($(add2.south-|x)+(-0.2, -0.4)$) ($(n1.north-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
\node[below left] at (supersensor.north east) {Super Sensor};
\node[block, fit={($(S1|-add1.south)+(-0.2, -0.2)$) ($(n1.north-|N1.east)+(0.2, 0.1)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
\node[below right] at (sensor1.north west) {Sensor 1};
\node[block, fit={($(S2|-add2.south)+(-0.2, -0.2)$) ($(n2.north-|N2.east)+(0.2, 0.1)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
\node[below right] at (sensor2.north west) {Sensor 2};
\end{scope}
\end{tikzpicture}
<span class="org-comment">% Center of Circle</span>
<span class="org-font-latex-sedate">\node</span>[below] at (0, 0){<span class="org-font-latex-math">$1$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-&gt;, dashed] (0, 0) node[branch]{} -- coordinate[midway](r1) ++(45:1.0);
<span class="org-font-latex-sedate">\draw</span>[&lt;-&gt;, dashed] (135:1.0)node[branch]{} -- coordinate[midway](r2) ++(90:0.8);
<span class="org-font-latex-sedate">\node</span>[] (l1) at (2, 1.5) {<span class="org-font-latex-math">$|W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1|$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;, dashed, out=-90, in=0] (l1.south) to (r1);
<span class="org-font-latex-sedate">\node</span>[] (l2) at (-2.5, 1.5) {<span class="org-font-latex-math">$|W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2|$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;, dashed, out=0, in=-180] (l2.east) to (r2);
<span class="org-font-latex-sedate">\draw</span>[&lt;-&gt;, dashed] (0, 0) -- coordinate[near end](r3) ++(200:1.8);
<span class="org-font-latex-sedate">\node</span>[] (l3) at (-2.5, -1.5) {<span class="org-font-latex-math">$|W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1| + |W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2|$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;, dashed, out=90, in=-90] (l3.north) to (r3);
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-comment">% Real and Imaginary Axis</span>
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, -1.7) -- (0, 1.7) node[below left]{Im};
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=2);
<span class="org-font-latex-sedate">\draw</span>[dashed] (1, 0) arc (0:28:1) 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-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org2a7478b" class="figure">
<p><img src="figs/sensor_fusion_arch_full.png" alt="sensor_fusion_arch_full.png" />
<div id="orgb4e2baf" class="figure">
<p><img src="figs/uncertainty_set_super_sensor.png" alt="uncertainty_set_super_sensor.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_arch_full.png">png</a>, <a href="./figs/sensor_fusion_arch_full.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 6: </span>Uncertainty region of the super sensor dynamics in the complex plane (solid circle), of the sensor 1 (dotted circle) and of the sensor 2 (dashed circle) (<a href="./figs/uncertainty_set_super_sensor.png">png</a>, <a href="./figs/uncertainty_set_super_sensor.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org25fbe7c" class="outline-2">
<h2 id="org25fbe7c"><span class="section-number-2">7</span> Mixed H2/H-Infinity Synthesis</h2>
<div id="outline-container-orgff8ec60" class="outline-2">
<h2 id="orgff8ec60"><span class="section-number-2">7</span> Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</h2>
<div class="outline-text-2" id="text-7">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
\node[block={5.0cm}{5.0cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
<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>[block={4.2cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">{</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\infty</span></span><span class="org-font-latex-math">}$</span>};
\coordinate[] (inputw) at ($(P.south west)!0.85!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.35!(P.north west) + (-0.7, 0)$);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.8!(P.north west) + (-0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.5!(P.north west) + (-0.7, 0)$</span>);
\coordinate[] (output1) at ($(P.south east)!0.85!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.7!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output3) at ($(P.south east)!0.5!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output4) at ($(P.south east)!0.35!(P.north east) + ( 0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.15!(P.north east) + ( 0.7, 0)$);
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(P.south east)!0.8!(P.north east) + ( 0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(P.south east)!0.5!(P.north east) + ( 0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.2!(P.north east) + ( 0.7, 0)$</span>);
\node[block, left=1.4 of output1] (W1){$W_1(s)$};
\node[block, left=1.4 of output2] (W2){$W_2(s)$};
\node[addb={+}{}{}{}{-}, left=1.6 of W1] (sub1) {};
<span class="org-font-latex-sedate">\node</span>[block, left=0.9 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.9 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.4 of W1] (Wu1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.4 of W2] (Wu2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>};
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of Wu1] (sub) {};
\node[block, left=1.4 of output3] (N1){$N_1(s)$};
\node[block, left=1.4 of output4] (N2){$N_2(s)$};
\node[addb={+}{}{}{}{-}, left=1 of N1] (sub2) {};
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H2) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
\node[block, below=0.3 of P] (H2) {$H_2(s)$};
\draw[-&gt;] (inputw) node[above right]{$w$} -- (sub1.west);
\draw[-&gt;] (H2.west) -| ($(inputu)+(0.35, 0)$) node[above]{$u$} -- (N2.west);
\draw[-&gt;] (inputu-|sub1) node[branch]{} -- (sub1.south);
\draw[-&gt;] (inputu-|sub2) node[branch]{} -- (sub2.south);
\draw[-&gt;] (sub1|-W2) node[branch]{} -- (W2.west);
\draw[-&gt;] (sub1.east) -- (W1.west);
\draw[-&gt;] (sub2.east) -- (N1.west);
\draw[-&gt;] ($(sub1.west)+(-0.6, 0)$) node[branch](w_branch){} |- ($(outputv)+(-0.35, 0)$) node[above]{$v$} |- (H2.east);
\draw[-&gt;] (w_branch|-sub2) node[branch]{} -- (sub2.west);
\draw[-&gt;] (W1.east) -- (output1)node[above left]{$z_1$};
\draw[-&gt;] (W2.east) -- (output2)node[above left]{$z_2$};
\draw[-&gt;] (N1.east) -- (output3)node[above left]{$z_3$};
\draw[-&gt;] (N2.east) -- (output4)node[above left]{$z_4$};
\end{tikzpicture}
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2.west) -| (<span class="org-font-latex-math">$(inputu)+(0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$u$</span>} -- (Wu2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (inputu-|sub) node[branch]{} -- (sub.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (sub.east) -- (Wu1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(sub.west)+(-0.6, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$v$</span>} |- (H2.east);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Wu1.east) -- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Wu2.east) -- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W1.east) -- (output1)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</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="org855c0bc" class="figure">
<div id="orgcfbd978" class="figure">
<p><img src="figs/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (<a href="./figs/h_infinity_robust_fusion.png">png</a>, <a href="./figs/h_infinity_robust_fusion.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org77a9624" class="outline-2">
<h2 id="org77a9624"><span class="section-number-2">8</span> Sensor Model - Noise and Uncertainty</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>[addb](add1){};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of add1](N1){<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[branch, right=0.4 of add1](b1){};
<span class="org-font-latex-sedate">\node</span>[block, above right=0.3 and 0.25 of b1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of W1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.3 of b1-|delta1](addu){};
<span class="org-font-latex-sedate">\node</span>[block, right=0.3 of addu](G1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.7 of G1](Ginv1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">^</span></span><span class="org-font-latex-math">{-1}$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (add1.west) -- ++(-1.0, 0) node[above right]{<span class="org-font-latex-math">$x$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (addu.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (b1) |- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta1.east) -| (addu.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (addu.east) -- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (N1.south) -- (add1.north)node[above left]{<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (N1.north)node[above left](n1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tilde</span></span><span class="org-font-latex-math">{n}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>} -- ++(0, 0.4);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (Ginv1.west)node[above left]{<span class="org-font-latex-math">$v</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ginv1.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">i$</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">$(G1.south east)+(0.15, -0.15)$</span>) (<span class="org-font-latex-math">$(n1.north west)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below left, align=right] at (sensor1.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="org121d2ed" class="figure">
<p><img src="figs/sensor_model_noise_uncertainty.png" alt="sensor_model_noise_uncertainty.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Sensor Model (<a href="./figs/sensor_model_noise_uncertainty.png">png</a>, <a href="./figs/sensor_model_noise_uncertainty.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org194f17b" class="outline-2">
<h2 id="org194f17b"><span class="section-number-2">9</span> Sensor fusion architecture with sensor dynamics uncertainty and noise</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"><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=1.0 and 0.6 of x](addn1){};
<span class="org-font-latex-sedate">\node</span>[addb, below right=1.0 and 0.6 of x](addn2){};
<span class="org-font-latex-sedate">\node</span>[addb, right=2.6 of addn1](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=2.6 of addn2](add2){};
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0 of add1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0 of add2](delta2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.4 of delta1](W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.4 of delta2](W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
<span class="org-font-latex-sedate">\node</span>[block, above=0.5 of addn1](N1) {<span class="org-font-latex-math">$N</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
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<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">$(H2.south-|x)+(-0.2, -0.3)$</span>) (<span class="org-font-latex-math">$(n1.north east-|add.east)+(0.2, 0.3)$</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>[fit={(n1.north west) (<span class="org-font-latex-math">$(add1.south -| add1.east) + (0.1, -0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor1.north east) {Sensor 1};
<span class="org-font-latex-sedate">\node</span>[fit={(n2.north west) (<span class="org-font-latex-math">$(add2.south -| add2.east) + (0.1, -0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (sensor2.north east) {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="org257652d" class="figure">
<p><img src="figs/sensor_fusion_arch_full.png" alt="sensor_fusion_arch_full.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_arch_full.png">png</a>, <a href="./figs/sensor_fusion_arch_full.pdf">pdf</a>).</p>
</div>
</div>
</div>
<div id="outline-container-org92adb06" class="outline-2">
<h2 id="org92adb06"><span class="section-number-2">10</span> Mixed H2/H-Infinity Synthesis</h2>
<div class="outline-text-2" id="text-10">
<div class="org-src-container">
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</pre>
</div>
<div id="org7166204" class="figure">
<p><img src="figs/mixed_h2_hinf_synthesis.png" alt="mixed_h2_hinf_synthesis.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Mixed H2/H-Infinity Synthesis (<a href="./figs/mixed_h2_hinf_synthesis.png">png</a>, <a href="./figs/mixed_h2_hinf_synthesis.pdf">pdf</a>).</p>
<p><span class="figure-number">Figure 10: </span>Mixed H2/H-Infinity Synthesis (<a href="./figs/mixed_h2_hinf_synthesis.png">png</a>, <a href="./figs/mixed_h2_hinf_synthesis.pdf">pdf</a>).</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2020-08-17 lun. 17:49</p>
<p class="date">Created: 2020-11-12 jeu. 10:42</p>
</div>
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