Version 1
: Received: 13 September 2024 / Approved: 13 September 2024 / Online: 16 September 2024 (14:24:05 CEST)
How to cite:
Choukroun, D.; Cooper, L.; Berman, N. Stochastic H∞ Filtering of the Attitude Quaternion. Preprints2024, 2024091245. https://doi.org/10.20944/preprints202409.1245.v1
Choukroun, D.; Cooper, L.; Berman, N. Stochastic H∞ Filtering of the Attitude Quaternion. Preprints 2024, 2024091245. https://doi.org/10.20944/preprints202409.1245.v1
Choukroun, D.; Cooper, L.; Berman, N. Stochastic H∞ Filtering of the Attitude Quaternion. Preprints2024, 2024091245. https://doi.org/10.20944/preprints202409.1245.v1
APA Style
Choukroun, D., Cooper, L., & Berman, N. (2024). Stochastic H∞ Filtering of the Attitude Quaternion. Preprints. https://doi.org/10.20944/preprints202409.1245.v1
Chicago/Turabian Style
Choukroun, D., Lotan Cooper and Nadav Berman. 2024 "Stochastic H∞ Filtering of the Attitude Quaternion" Preprints. https://doi.org/10.20944/preprints202409.1245.v1
Abstract
Several stochastic H∞ filters for estimating the attitude of a rigid body from line-of-sight measurements and rate gyro readings are developed. The measurements are corrupted by white noise with unknown variances. Our approach consists of estimating the quaternion while attenuating the transmission gain from the unknown variances and initial errors to the current estimation error. The time-varying H∞ gains are computed through differential and algebraic linear matrix inequalities whose parameters are independent of the state. The case of a gyro drift is addressed, too. Extensive Monte Carlo simulations show that the proposed stochastic H∞ quaternion filters perform well for a wide range of noise variances. The actual attenuation, which improves with the noise level and is worst in the noise-free case, is better than the guaranteed attenuation by one order of magnitude. The proposed stochastic H∞ filter produces smaller biases than a standard quaternion Kalman filter and similar standard deviations at large noise levels. An essential advantage of this H∞ filter is that the gains are independent of the quaternion, which makes it insensitive to modeling errors. This desired feature is illustrated by comparing its performances against those of unmatched Kalman filters. When provided with too high or too low noise variances the Kalman filter is outperformed by the $H_\infty$ filter, which essentially delivers identical error magnitudes.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
