Iterated Invariant Extended Kalman Filter (IterIEKF)

Abstract

We study the mathematical properties of the Invariant Extended Kalman Filter (IEKF) when iterating on the measurement update step, following the principles of the well-known Iterated Extended Kalman Filter. This iterative variant of the IEKF (IterIEKF) systematically improves its accuracy through Gauss-Newton-based relinearization, and exhibits additional theoretical properties, particularly in the low-noise regime, that resemble those of the linear Kalman filter. We apply the proposed approach to the problem of estimating the extended pose of a crane payload using an inertial measurement unit. Our results suggest that the IterIEKF significantly outperforms the IEKF when measurements are highly accurate.