-For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using complementary filters. -This paper presents a method for designing these complementary filters using \(\mathcal{H}_\infty\) synthesis that allows to shape the filter norms. -This method is shown to be easily applicable for the synthesis of complex complementary filters. +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.
-The paper has been created Org Mode (generating LaTeX code) under Emacs.
+ ++To cite this paper use the following BibTeX code. +
+@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}, +} ++
+You can also use the formatted citation below. +
+++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). +
+
All the Matlab code that was used for the paper are accessible so that all the results are reproducible. +The source code is hosted on Zenodo.
+ ++If you use this code and want to refer to it in a publication, you can use the following BibTeX reference: +
+@misc{dehaeze21_new_method_desig_compl_filter_code, + author = {Dehaeze, Thomas}, + doi = {}, + 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, +} ++
+You can also use the formatted citation below. +
+++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 +
+
All the figures for the paper have been generated using TikZ.
diff --git a/index.org b/index.org index 27ee2b0..befcc13 100644 --- a/index.org +++ b/index.org @@ -13,39 +13,71 @@ :END: #+begin_quote - *Abstract*: +*Abstract*: - For many applications, large bandwidth and dynamic ranges are requiring to use several sensors, whose signals are combined using complementary filters. - This paper presents a method for designing these complementary filters using $\mathcal{H}_\infty$ synthesis that allows to shape the filter norms. - This method is shown to be easily applicable for the synthesis of complex complementary filters. +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 -* Paper ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]]) +* Journal Article ([[file:journal/dehaeze21_desig_compl_filte.pdf][link]]) :PROPERTIES: :UNNUMBERED: t :END: + 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]]) :PROPERTIES: :UNNUMBERED: t :END: -All the [[https://fr.mathworks.com/][Matlab]] code that was used for the paper are accessible so that all the results are reproducible. -* Tikz Figures ([[file:tikz/index.org][link]]) +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]]) :PROPERTIES: :UNNUMBERED: t :END: All the figures for the paper have been generated using [[https://sourceforge.net/projects/pgf/][TikZ]]. -* Cite this paper :noexport: -:PROPERTIES: -:UNNUMBERED: t -:END: -To cite this paper use the following bibtex code. -#+begin_src bibtex -#+end_src - -You can also use the formatted citation below. -#+begin_quote -#+end_quote diff --git a/matlab/dehaeze21_desig_compl_filte_matlab.org b/matlab/dehaeze21_desig_compl_filte_matlab.org index 5245d26..e0c761e 100644 --- a/matlab/dehaeze21_desig_compl_filte_matlab.org +++ b/matlab/dehaeze21_desig_compl_filte_matlab.org @@ -1442,6 +1442,4 @@ H1 = 1 - H2; #+end_src * Bibliography :ignore: -bibliography:ref.bib - #+latex: \printbibliography