Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis
Dehaeze Thomas, Verma Mohit and Collette Christophe

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.

@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},
}

@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,
}