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2019-08-21 16:35:08 +02:00
< h1 class = "title" > Robust and Optimal Sensor Fusion - Tikz Figures< / h1 >
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< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org942e687" > 1. Change some default< / a > < / li >
< li > < a href = "#orge1eca0e" > 2. H-Infinity - Complementary filters - Generalized plant< / a > < / li >
< li > < a href = "#orgb6b40a8" > 3. H-Infinity - Complementary filters< / a > < / li >
< li > < a href = "#orgdc216d7" > 4. H-Infinity - Optimal Complementary Filters< / a > < / li >
< li > < a href = "#org8178630" > 5. Fusion of two noisy sensors< / a > < / li >
< li > < a href = "#orgb1a2881" > 6. Fusion of two noisy signals< / a > < / li >
< li > < a href = "#orgb70e68a" > 7. Fusion of two noisy sensors with Dynamics< / a > < / li >
< li > < a href = "#org329b1aa" > 8. Fusion of two noisy sensors with Dynamics - Bis< / a > < / li >
< li > < a href = "#org63f0fd9" > 9. Fusion of two sensors with mismatch dynamics< / a > < / li >
< li > < a href = "#org91e15b3" > 10. Uncertainty to Phase and Gain variation< / a > < / li >
< li > < a href = "#org3a28dde" > 11. Generate Complementary Filters using Feedback Control Architecture< / a > < / li >
< li > < a href = "#org3bfc326" > 12. H-Infinity Synthesis for Robust Sensor Fusion< / a > < / li >
< li > < a href = "#org25da4e5" > 13. Sensor fusion architecture with sensor dynamics uncertainty and noise< / a > < / li >
< li > < a href = "#orgcc1d2ba" > 14. Equivalent super sensor< / a > < / li >
< li > < a href = "#org36a14ee" > 15. One sensor with noise< / a > < / li >
< li > < a href = "#org69ecf2e" > 16. One sensor with normalized noise< / a > < / li >
< li > < a href = "#org94c7648" > 17. One sensor with dynamic uncertainty< / a > < / li >
< li > < a href = "#orgab2cd5c" > 18. One sensor with dynamic uncertainty and noise< / a > < / li >
< li > < a href = "#org7356a2a" > 19. Huddle Test< / a > < / li >
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Configuration file is accessible < a href = "config.html" > here< / a > .
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< h2 id = "org942e687" > < span class = "section-number-2" > 1< / span > Change some default< / h2 >
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< h2 id = "orge1eca0e" > < span class = "section-number-2" > 2< / span > H-Infinity - Complementary filters - Generalized plant< / h2 >
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< p > < span class = "figure-number" > Figure 1: < / span > H-Infinity - Complementary filters - Generalized plant (< a href = "./figs/sf_hinf_filters_plant_b.png" > png< / a > , < a href = "./figs/sf_hinf_filters_plant_b.pdf" > pdf< / a > , < a href = "./figs/sf_hinf_filters_plant_b.tex" > tex< / a > ).< / p >
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< div id = "orgae2446b" class = "figure" >
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< p > < img src = "figs/sf_hinf_filters_b.png" alt = "sf_hinf_filters_b.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > H-Infinity - Complementary filters (< a href = "./figs/sf_hinf_filters_b.png" > png< / a > , < a href = "./figs/sf_hinf_filters_b.pdf" > pdf< / a > , < a href = "./figs/sf_hinf_filters_b.tex" > tex< / a > ).< / p >
< / div >
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< div id = "outline-container-orgdc216d7" class = "outline-2" >
< h2 id = "orgdc216d7" > < span class = "section-number-2" > 4< / span > H-Infinity - Optimal Complementary Filters< / h2 >
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< div id = "orgd4a1bec" class = "figure" >
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< p > < img src = "figs/h_infinity_optimal_comp_filters.png" alt = "h_infinity_optimal_comp_filters.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > H-Infinity - Optimal Complementary Filters (< a href = "./figs/h_infinity_optimal_comp_filters.png" > png< / a > , < a href = "./figs/h_infinity_optimal_comp_filters.pdf" > pdf< / a > , < a href = "./figs/h_infinity_optimal_comp_filters.tex" > tex< / a > ).< / p >
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< div id = "outline-container-org8178630" class = "outline-2" >
< h2 id = "org8178630" > < span class = "section-number-2" > 5< / span > Fusion of two noisy sensors< / h2 >
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< div id = "org933620b" class = "figure" >
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< p > < img src = "figs/fusion_two_noisy_sensors.png" alt = "fusion_two_noisy_sensors.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Fusion of two noisy sensors (< a href = "./figs/fusion_two_noisy_sensors.png" > png< / a > , < a href = "./figs/fusion_two_noisy_sensors.pdf" > pdf< / a > , < a href = "./figs/fusion_two_noisy_sensors.tex" > tex< / a > ).< / p >
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< h2 id = "orgb1a2881" > < span class = "section-number-2" > 6< / span > Fusion of two noisy signals< / h2 >
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< div id = "orgb511654" class = "figure" >
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< p > < img src = "figs/fusion_two_signals.png" alt = "fusion_two_signals.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Fusion of two noisy sensors (< a href = "./figs/fusion_two_signals.png" > png< / a > , < a href = "./figs/fusion_two_signals.pdf" > pdf< / a > , < a href = "./figs/fusion_two_signals.tex" > tex< / a > ).< / p >
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< h2 id = "orgb70e68a" > < span class = "section-number-2" > 7< / span > Fusion of two noisy sensors with Dynamics< / h2 >
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< p > < img src = "figs/fusion_two_noisy_sensors_with_dyn.png" alt = "fusion_two_noisy_sensors_with_dyn.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Fusion of two noisy sensors< sub > with< / sub > < sub > dyn< / sub > (< a href = "./figs/fusion_two_noisy_sensors_with_dyn.png" > png< / a > , < a href = "./figs/fusion_two_noisy_sensors_with_dyn.pdf" > pdf< / a > , < a href = "./figs/fusion_two_noisy_sensors_with_dyn.tex" > tex< / a > ).< / p >
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< h2 id = "org329b1aa" > < span class = "section-number-2" > 8< / span > Fusion of two noisy sensors with Dynamics - Bis< / h2 >
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< p > < img src = "figs/fusion_two_noisy_sensors_with_dyn_bis.png" alt = "fusion_two_noisy_sensors_with_dyn_bis.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Fusion of two noisy sensors< sub > with< / sub > < sub > dyn< / sub > < sub > bis< / sub > (< a href = "./figs/fusion_two_noisy_sensors_with_dyn_bis.png" > png< / a > , < a href = "./figs/fusion_two_noisy_sensors_with_dyn_bis.pdf" > pdf< / a > , < a href = "./figs/fusion_two_noisy_sensors_with_dyn_bis.tex" > tex< / a > ).< / p >
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< h2 id = "org63f0fd9" > < span class = "section-number-2" > 9< / span > Fusion of two sensors with mismatch dynamics< / h2 >
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< p > < img src = "figs/fusion_gain_mismatch.png" alt = "fusion_gain_mismatch.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > Fusion of two noisy sensors< sub > with< / sub > < sub > dyn< / sub > (< a href = "./figs/fusion_gain_mismatch.png" > png< / a > , < a href = "./figs/fusion_gain_mismatch.pdf" > pdf< / a > , < a href = "./figs/fusion_gain_mismatch.tex" > tex< / a > ).< / p >
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< h2 id = "org91e15b3" > < span class = "section-number-2" > 10< / span > Uncertainty to Phase and Gain variation< / h2 >
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< p > < img src = "figs/uncertainty_gain_phase_variation.png" alt = "uncertainty_gain_phase_variation.png" / >
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< p > < span class = "figure-number" > Figure 9: < / span > Uncertainty to Phase and Gain variation (< a href = "./figs/uncertainty_gain_phase_variation.png" > png< / a > , < a href = "./figs/uncertainty_gain_phase_variation.pdf" > pdf< / a > , < a href = "./figs/uncertainty_gain_phase_variation.tex" > tex< / a > ).< / p >
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< h2 id = "org3a28dde" > < span class = "section-number-2" > 11< / span > Generate Complementary Filters using Feedback Control Architecture< / h2 >
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< div class = "outline-text-2" id = "text-11" >
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< / pre >
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< div id = "orgb320104" class = "figure" >
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< p > < img src = "figs/complementary_filters_feedback_architecture.png" alt = "complementary_filters_feedback_architecture.png" / >
< / p >
< p > < span class = "figure-number" > Figure 10: < / span > Generation of Complementary Filters using the feedback architecture (< a href = "./figs/complementary_filters_feedback_architecture.png" > png< / a > , < a href = "./figs/complementary_filters_feedback_architecture.pdf" > pdf< / a > , < a href = "./figs/complementary_filters_feedback_architecture.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org3bfc326" class = "outline-2" >
< h2 id = "org3bfc326" > < span class = "section-number-2" > 12< / span > H-Infinity Synthesis for Robust Sensor Fusion< / h2 >
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< div class = "outline-text-2" id = "text-12" >
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< div id = "org672dec4" class = "figure" >
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< p > < img src = "figs/h_infinity_robust_fusion.png" alt = "h_infinity_robust_fusion.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > H-Infinity Synthesis for Robust Sensor Fusion (< a href = "./figs/h_infinity_robust_fusion.png" > png< / a > , < a href = "./figs/h_infinity_robust_fusion.pdf" > pdf< / a > , < a href = "./figs/h_infinity_robust_fusion.tex" > tex< / a > ).< / p >
< / div >
< / div >
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< div id = "outline-container-org25da4e5" class = "outline-2" >
< h2 id = "org25da4e5" > < span class = "section-number-2" > 13< / span > Sensor fusion architecture with sensor dynamics uncertainty and noise< / h2 >
< div class = "outline-text-2" id = "text-13" >
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< / div >
< div id = "orga0d661d" class = "figure" >
< p > < img src = "figs/sensor_fusion_full.png" alt = "sensor_fusion_full.png" / >
< / p >
< p > < span class = "figure-number" > Figure 12: < / span > Sensor fusion architecture with sensor dynamics uncertainty (< a href = "./figs/sensor_fusion_full.png" > png< / a > , < a href = "./figs/sensor_fusion_full.pdf" > pdf< / a > , < a href = "./figs/sensor_fusion_full.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-orgcc1d2ba" class = "outline-2" >
< h2 id = "orgcc1d2ba" > < span class = "section-number-2" > 14< / span > Equivalent super sensor< / h2 >
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< p > < img src = "figs/sensor_fusion_equivalent.png" alt = "sensor_fusion_equivalent.png" / >
< / p >
< p > < span class = "figure-number" > Figure 13: < / span > Sensor fusion architecture with sensor dynamics uncertainty (< a href = "./figs/sensor_fusion_equivalent.png" > png< / a > , < a href = "./figs/sensor_fusion_equivalent.pdf" > pdf< / a > , < a href = "./figs/sensor_fusion_equivalent.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-org36a14ee" class = "outline-2" >
< h2 id = "org36a14ee" > < span class = "section-number-2" > 15< / span > One sensor with noise< / h2 >
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< p > < img src = "figs/one_sensor_noise.png" alt = "one_sensor_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 14: < / span > One sensor with Noise (< a href = "./figs/one_sensor_noise.png" > png< / a > , < a href = "./figs/one_sensor_noise.pdf" > pdf< / a > , < a href = "./figs/one_sensor_noise.tex" > tex< / a > ).< / p >
< / div >
< / div >
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< div id = "outline-container-org69ecf2e" class = "outline-2" >
< h2 id = "org69ecf2e" > < span class = "section-number-2" > 16< / span > One sensor with normalized noise< / h2 >
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< p > < img src = "figs/one_sensor_normalized_noise.png" alt = "one_sensor_normalized_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 15: < / span > One sensor with normalized noise (< a href = "./figs/one_sensor_normalized_noise.png" > png< / a > , < a href = "./figs/one_sensor_normalized_noise.pdf" > pdf< / a > , < a href = "./figs/one_sensor_normalized_noise.tex" > tex< / a > ).< / p >
< / div >
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< div id = "outline-container-org94c7648" class = "outline-2" >
< h2 id = "org94c7648" > < span class = "section-number-2" > 17< / span > One sensor with dynamic uncertainty< / h2 >
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< p > < img src = "figs/one_sensor_dyn_uncertainty.png" alt = "one_sensor_dyn_uncertainty.png" / >
< / p >
< p > < span class = "figure-number" > Figure 16: < / span > One sensor with dynamic uncertainty (< a href = "./figs/one_sensor_dyn_uncertainty.png" > png< / a > , < a href = "./figs/one_sensor_dyn_uncertainty.pdf" > pdf< / a > , < a href = "./figs/one_sensor_dyn_uncertainty.tex" > tex< / a > ).< / p >
< / div >
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< div id = "outline-container-orgab2cd5c" class = "outline-2" >
< h2 id = "orgab2cd5c" > < span class = "section-number-2" > 18< / span > One sensor with dynamic uncertainty and noise< / h2 >
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (W.east) -- (delta.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (delta.east) -| (add.north);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (add.east) -- (G.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (G.east) -- (addn.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (< span class = "org-font-latex-math" > $(addn.north)+(0, 0.8)$< / span > ) node[below right]{< span class = "org-font-latex-math" > $n$< / span > } -- (addn.north);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (addn.east) -- ++(0.8, 0) node[above left]{< span class = "org-font-latex-math" > $< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \hat< / span > < / span > < span class = "org-font-latex-math" > {x}$< / span > };
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > scope< / span > }[on background layer]
< span class = "org-font-latex-sedate" > \node< / span > [fit={(< span class = "org-font-latex-math" > $(x.west|-G.south)+(-0.2, -0.2)$< / span > ) (< span class = "org-font-latex-math" > $(delta.north-|addn.east)+(0.2, 0.2)$< / span > )}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor) {};
< span class = "org-font-latex-sedate" > \node< / span > [above right] at (sensor.south west) {Sensor};
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > scope< / span > }
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
< / div >
< div id = "orge2a5263" class = "figure" >
< p > < img src = "figs/one_sensor_dyn_uncertainty_noise.png" alt = "one_sensor_dyn_uncertainty_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 17: < / span > One sensor with dynamic uncertainty (< a href = "./figs/one_sensor_dyn_uncertainty_noise.png" > png< / a > , < a href = "./figs/one_sensor_dyn_uncertainty_noise.pdf" > pdf< / a > , < a href = "./figs/one_sensor_dyn_uncertainty_noise.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-org7356a2a" class = "outline-2" >
< h2 id = "org7356a2a" > < span class = "section-number-2" > 19< / span > Huddle Test< / h2 >
< div class = "outline-text-2" id = "text-19" >
< div class = "org-src-container" >
< pre class = "src src-latex" > < span class = "org-font-latex-sedate" > \tikzset< / span > {block/.default={0.8cm}{0.6cm}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {addb/.append style={scale=0.7}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {node distance=0.6}
< span class = "org-font-latex-sedate" > \def\cdist< / span > {0.7}
< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
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< span class = "org-font-latex-sedate" > \node< / span > [block, below right=0.5 and 0.5 of x](G2){< span class = "org-font-latex-math" > $G< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _2< / span > < / span > < span class = "org-font-latex-math" > (s)$< / span > };
< span class = "org-font-latex-sedate" > \node< / span > [addb, right=0.8 of G1](add1){};
< span class = "org-font-latex-sedate" > \node< / span > [addb, right=0.8 of G2](add2){};
< span class = "org-font-latex-sedate" > \draw< / span > [] (< span class = "org-font-latex-math" > $(x)+(-0.7, 0)$< / span > ) node[above right]{< span class = "org-font-latex-math" > $x$< / span > } -- (x.center);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (x.center) |- (G1.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (x.center) |- (G2.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (G1.east) -- (add1.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (G2.east) -- (add2.west);
< span class = "org-font-latex-sedate" > \draw< / span > [< -] (add1.north) -- ++(0, 0.8)node[below right](n1){< span class = "org-font-latex-math" > $n< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _1< / span > < / span > < span class = "org-font-latex-math" > $< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [< -] (add2.north) -- ++(0, 0.8)node[below right](n2){< span class = "org-font-latex-math" > $n< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _2< / span > < / span > < span class = "org-font-latex-math" > $< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (add1.east) -- ++(1, 0)node[above left]{< span class = "org-font-latex-math" > $< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \hat< / span > < / span > < span class = "org-font-latex-math" > {x}< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _1< / span > < / span > < span class = "org-font-latex-math" > $< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (add2.east) -- ++(1, 0)node[above left]{< span class = "org-font-latex-math" > $< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \hat< / span > < / span > < span class = "org-font-latex-math" > {x}< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _2< / span > < / span > < span class = "org-font-latex-math" > $< / span > };
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > scope< / span > }[on background layer]
< span class = "org-comment" > % < / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \node< / span > < / span > < span class = "org-comment" > [fit={($(G2.south-|x)+(-0.2, -0.3)$) ($(n1.north east-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};< / span >
< span class = "org-comment" > % < / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \node< / span > < / span > < span class = "org-comment" > [below left] at (supersensor.north east) {Super Sensor};< / span >
< span class = "org-font-latex-sedate" > \node< / span > [fit={(< span class = "org-font-latex-math" > $(G1.south west)+(-0.3, -0.1)$< / span > ) (< span class = "org-font-latex-math" > $(n1.north east)+(0.0, 0.1)$< / span > )}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
< span class = "org-font-latex-sedate" > \node< / span > [below right] at (sensor1.north west) {Sensor 1};
< span class = "org-font-latex-sedate" > \node< / span > [fit={(< span class = "org-font-latex-math" > $(G2.south west)+(-0.3, -0.1)$< / span > ) (< span class = "org-font-latex-math" > $(n2.north east)+(0.0, 0.1)$< / span > )}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
< span class = "org-font-latex-sedate" > \node< / span > [below right] at (sensor2.north west) {Sensor 2};
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > scope< / span > }
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
< / div >
< div id = "org25f2d34" class = "figure" >
< p > < img src = "figs/huddle_test.png" alt = "huddle_test.png" / >
< / p >
< p > < span class = "figure-number" > Figure 18: < / span > Huddle Test (< a href = "./figs/huddle_test.png" > png< / a > , < a href = "./figs/huddle_test.pdf" > pdf< / a > , < a href = "./figs/huddle_test.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
2019-08-14 12:08:30 +02:00
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Thomas Dehaeze< / p >
2019-08-29 11:21:07 +02:00
< p class = "date" > Created: 2019-08-29 jeu. 11:21< / p >
2019-08-14 12:08:30 +02:00
< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
