Invariant Kalman Filtering with Noise-Free Pseudo-Measurements
<|reference_start|>Invariant Kalman Filtering with Noise-Free Pseudo-Measurements: In this paper, we focus on developing an Invariant Extended Kalman Filter (IEKF) for extended pose estimation for a noisy system with state equality constraints. We treat those constraints as noise-free pseudo-measurements. To this aim, we provide a formula for the Kalman gain in the limit of noise-free measurements and rank-deficient covariance matrix. We relate the constraints to group-theoretic properties and study the behavior of the IEKF in the presence of such noise-free measurements. We illustrate this perspective on the estimation of the motion of the load of an overhead crane, when a wireless inertial measurement unit is mounted on the hook.<|reference_end|>
@article{goffin2024invariant,
    title={Invariant Kalman Filtering with Noise-Free Pseudo-Measurements},
    author={Sven Goffin, Silv`ere Bonnabel, Olivier Br"uls, and Pierre Sacr'e},
    journal={62nd IEEE Conference on Decision and Control (CDC), Singapore,
  Singapore, 2023, pp. 8665-8671},
    year={2024},
    doi={10.1109/CDC49753.2023.10383262},
    archivePrefix={arXiv},
    eprint={2404.10687},
    primaryClass={eess.SY cs.SY}
}