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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-09-01 mer. 11:36 -->
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<!-- 2021-09-01 mer. 17:04 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis</title>
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<meta name="author" content="Thomas Dehaeze" />
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</p>
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<p>
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For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using complementary filters.
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This paper presents a method for designing these complementary filters using \(\mathcal{H}_\infty\) synthesis that allows to shape the filter norms.
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This method is shown to be easily applicable for the synthesis of complex complementary filters.
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In order to obtain a better estimate of a quantity being measured, several sensors having different characteristics can be merged with a technique called “sensor fusion”.
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The obtained “super sensor” can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
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Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
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Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
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In this study, we address this issue and propose a new method for designing complementary filters.
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This method uses weighting functions to specify the wanted shape of the complementary filter that are then easily obtained using the standard \(\mathcal{H}_\infty\) synthesis.
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The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
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Such synthesis method is further extended for the shaping of more than two complementary filters.
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</p>
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</blockquote>
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<div id="outline-container-orgafee5c3" class="outline-2">
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<h2 id="orgafee5c3">Paper (<a href="journal/dehaeze21_desig_compl_filte.pdf">link</a>)</h2>
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<div class="outline-text-2" id="text-orgafee5c3">
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<div id="outline-container-org1d8b653" class="outline-2">
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<h2 id="org1d8b653">Journal Article (<a href="journal/dehaeze21_desig_compl_filte.pdf">link</a>)</h2>
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<div class="outline-text-2" id="text-org1d8b653">
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<p>
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The paper has been created <a href="https://orgmode.org/">Org Mode</a> (generating <a href="https://www.latex-project.org/">LaTeX</a> code) under <a href="https://www.gnu.org/software/emacs/">Emacs</a>.
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</p>
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<p>
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To cite this paper use the following BibTeX code.
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</p>
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<div class="org-src-container">
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<pre class="src src-bibtex"><span class="org-function-name">@article</span>{<span class="org-constant">dehaeze21_new_method_desig_compl_filter</span>,
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<span class="org-variable-name">author</span> = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
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<span class="org-variable-name">title</span> = {A New Method of Designing Complementary Filters for Sensor
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Fusion Using the <span class="org-string">$\mathcal{H}_\infty$</span> Synthesis},
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<span class="org-variable-name">journal</span> = {Mechanical Systems and Signal Processing},
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<span class="org-variable-name">year</span> = 2021,
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<span class="org-variable-name">month</span> = {Nov},
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}
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</pre>
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</div>
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<p>
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You can also use the formatted citation below.
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</p>
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<blockquote>
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<p>
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Dehaeze, T., Vermat, M., & Collette, C., A new method of designing complementary filters for sensor fusion using the \(H_\infty\) synthesis, Mechanical Systems and Signal Processing, (2021).
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-orgb8fb429" class="outline-2">
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<h2 id="orgb8fb429">Matlab Scripts (<a href="matlab/dehaeze21_desig_compl_filte_matlab.html">link</a>)</h2>
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<div class="outline-text-2" id="text-orgb8fb429">
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<div id="outline-container-org6ba84bc" class="outline-2">
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<h2 id="org6ba84bc">Matlab Scripts (<a href="matlab/dehaeze21_desig_compl_filte_matlab.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org6ba84bc">
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<p>
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All the <a href="https://fr.mathworks.com/">Matlab</a> code that was used for the paper are accessible so that all the results are reproducible.
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The source code is hosted on <a href="https://zenodo.org/record/5361920">Zenodo</a>.
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</p>
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<p>
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If you use this code and want to refer to it in a publication, you can use the following BibTeX reference:
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</p>
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<div class="org-src-container">
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<pre class="src src-bibtex"><span class="org-function-name">@misc</span>{<span class="org-constant">dehaeze21_new_method_desig_compl_filter_code</span>,
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<span class="org-variable-name">author</span> = {Dehaeze, Thomas},
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<span class="org-variable-name">doi</span> = {<span class="org-button">10.5281/zenodo.5361943</span>},
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<span class="org-variable-name">howpublished</span> = {Source code on Zenodo},
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<span class="org-variable-name">month</span> = sep,
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<span class="org-variable-name">title</span> = {{A New Method of Designing Complementary Filters for Sensor
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Fusion Using the <span class="org-string">$\mathcal{H}_\infty$</span> Synthesis}},
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<span class="org-variable-name">year</span> = 2021,
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}
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</pre>
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</div>
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<p>
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You can also use the formatted citation below.
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</p>
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<blockquote>
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<p>
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Dehaeze Thomas. (2021). A New Method of Designing Complementary Filters for Sensor Fusion Using the H-Infinity Synthesis. Source code on Zenodo. 10.5281/zenodo.5361943
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-org0ecd5c8" class="outline-2">
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<h2 id="org0ecd5c8">Tikz Figures (<a href="tikz/dehaeze21_desig_compl_filte_tikz.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org0ecd5c8">
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<div id="outline-container-org827f683" class="outline-2">
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<h2 id="org827f683">Tikz Figures (<a href="tikz/dehaeze21_desig_compl_filte_tikz.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org827f683">
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<p>
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All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>.
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</p>
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68
index.org
68
index.org
@ -13,39 +13,71 @@
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:END:
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#+begin_quote
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*Abstract*:
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*Abstract*:
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For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using complementary filters.
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This paper presents a method for designing these complementary filters using $\mathcal{H}_\infty$ synthesis that allows to shape the filter norms.
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This method is shown to be easily applicable for the synthesis of complex complementary filters.
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In order to obtain a better estimate of a quantity being measured, several sensors having different characteristics can be merged with a technique called "sensor fusion".
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The obtained "super sensor" can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
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Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
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Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
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In this study, we address this issue and propose a new method for designing complementary filters.
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This method uses weighting functions to specify the wanted shape of the complementary filter that are then easily obtained using the standard $\mathcal{H}_\infty$ synthesis.
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The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
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Such synthesis method is further extended for the shaping of more than two complementary filters.
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#+end_quote
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* Paper ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]])
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* Journal Article ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]])
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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The paper has been created [[https://orgmode.org/][Org Mode]] (generating [[https://www.latex-project.org/][LaTeX]] code) under [[https://www.gnu.org/software/emacs/][Emacs]].
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To cite this paper use the following BibTeX code.
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#+begin_src bibtex
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@article{dehaeze21_new_method_desig_compl_filter,
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author = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
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title = {A New Method of Designing Complementary Filters for Sensor
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Fusion Using the $\mathcal{H}_\infty$ Synthesis},
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journal = {Mechanical Systems and Signal Processing},
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year = 2021,
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month = {Nov},
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}
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#+end_src
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You can also use the formatted citation below.
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#+begin_quote
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Dehaeze, T., Vermat, M., & Collette, C., A new method of designing complementary filters for sensor fusion using the $H_\infty$ synthesis, Mechanical Systems and Signal Processing, (2021).
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#+end_quote
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* Matlab Scripts ([[file:matlab/dehaeze21_desig_compl_filte_matlab.org][link]])
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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All the [[https://fr.mathworks.com/][Matlab]] code that was used for the paper are accessible so that all the results are reproducible.
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* Tikz Figures ([[file:tikz/index.org][link]])
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All the [[https://fr.mathworks.com/][Matlab]] code that was used for the paper are accessible so that all the results are reproducible.
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The source code is hosted on [[https://zenodo.org/record/5361920][Zenodo]].
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If you use this code and want to refer to it in a publication, you can use the following BibTeX reference:
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#+begin_src bibtex
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@misc{dehaeze21_new_method_desig_compl_filter_code,
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author = {Dehaeze, Thomas},
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doi = {10.5281/zenodo.5361943},
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howpublished = {Source code on Zenodo},
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month = sep,
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title = {{A New Method of Designing Complementary Filters for Sensor
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Fusion Using the $\mathcal{H}_\infty$ Synthesis}},
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year = 2021,
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}
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#+end_src
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You can also use the formatted citation below.
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#+begin_quote
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Dehaeze Thomas. (2021). A New Method of Designing Complementary Filters for Sensor Fusion Using the H-Infinity Synthesis. Source code on Zenodo. 10.5281/zenodo.5361943
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#+end_quote
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* Tikz Figures ([[file:tikz/dehaeze21_desig_compl_filte_tikz.org][link]])
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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All the figures for the paper have been generated using [[https://sourceforge.net/projects/pgf/][TikZ]].
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* Cite this paper :noexport:
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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To cite this paper use the following bibtex code.
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#+begin_src bibtex
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#+end_src
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You can also use the formatted citation below.
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#+begin_quote
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#+end_quote
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@ -1442,6 +1442,4 @@ H1 = 1 - H2;
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#+end_src
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* Bibliography :ignore:
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bibliography:ref.bib
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#+latex: \printbibliography
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