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.