Invariant Kalman Filtering with Noise-Free Pseudo-Measurements

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

1 CAOR - Centre de Robotique

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 pseudomeasurements. 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.

Domaines: Sciences de l'ingénieur [physics]

Sven Goffin, Silvère Bonnabel, Olivier Brüls, Pierre Sacré. Invariant Kalman Filtering with Noise-Free Pseudo-Measurements. 2023 IEEE 62nd Conference on Decision and Control (CDC), Dec 2023, Singapore (SG), Singapore. ⟨hal-04398694⟩