#+TITLE: A new method of designing complementary filters for sensor fusion using the $\mathcal{H}_\infty$ synthesis
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#+SUBTITLE: Dehaeze Thomas, Verma Mohit and Collette Christophe

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#+begin_quote
*Abstract*:

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".
The obtained "super sensor" can combine the benefits of the individual sensors provided that the complementary filters used in the fusion are well designed.
Indeed, properties of the super sensor are linked to the magnitude of the complementary filters.
Properly shaping the magnitude of complementary filters is a difficult and time-consuming task.
In this study, we address this issue and propose a new method for designing complementary filters.
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.
The proper choice of the weighting functions is discussed, and the effectiveness and simplicity of the design method is highlighted using several examples.
Such synthesis method is further extended for the shaping of more than two complementary filters.
#+end_quote

* Journal Article ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]])
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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]].

To cite this paper use the following BibTeX code.
#+begin_src bibtex
@article{dehaeze21_new_method_desig_compl_filter,
  author          = {Dehaeze, Thomas and Vermat, Mohit and Collette, Christophe},
  title           = {A New Method of Designing Complementary Filters for Sensor
                  Fusion Using the $\mathcal{H}_\infty$ Synthesis},
  journal         = {Mechanical Systems and Signal Processing},
  year            = 2021,
  month           = {Nov},
}
#+end_src

You can also use the formatted citation below.
#+begin_quote
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).
#+end_quote

* Matlab Scripts ([[file:matlab/dehaeze21_desig_compl_filte_matlab.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.
The source code is hosted on [[https://zenodo.org/record/5361920][Zenodo]].

If you use this code and want to refer to it in a publication, you can use the following BibTeX reference:
#+begin_src bibtex
@misc{dehaeze21_new_method_desig_compl_filter_code,
  author          = {Dehaeze, Thomas},
  doi             = {10.5281/zenodo.5361943},
  howpublished    = {Source code on Zenodo},
  month           = sep,
  title           = {{A New Method of Designing Complementary Filters for Sensor
                  Fusion Using the $\mathcal{H}_\infty$ Synthesis}},
  year            = 2021,
}
#+end_src

You can also use the formatted citation below.
#+begin_quote
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
#+end_quote

* Tikz Figures ([[file:tikz/dehaeze21_desig_compl_filte_tikz.org][link]])
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All the figures for the paper have been generated using [[https://sourceforge.net/projects/pgf/][TikZ]].