Invariant Kalman Filtering with Noise-Free Pseudo-Measurements

Sven Goffin (1) , Silvère Bonnabel (2) , Olivier Brüls (3) , Pierre Sacré (1)

1 Institut Montefiore - Department of Electrical Engineering and Computer Science
2 CAOR - Centre de Robotique
3 LTAS - Aerospace and Mechanical Engineering Department [Liège]

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.

Keywords: Kalman filtering; Kalman filtering

Domains: Systems and Control [cs.SY]

Sven Goffin, Silvère Bonnabel, Olivier Brüls, Pierre Sacré. Invariant Kalman Filtering with Noise-Free Pseudo-Measurements. 2023 62nd IEEE Conference on Decision and Control (CDC), Dec 2023, Singapore, Singapore. pp.8665-8671, ⟨10.1109/cdc49753.2023.10383262⟩. ⟨hal-04409333⟩