Iterated Invariant Extended Kalman Filter (IterIEKF)

TL;DR

This paper introduces the Iterated Invariant Extended Kalman Filter (IterIEKF), an enhancement of the IEKF that iteratively refines estimates using Gauss-Newton relinearization, improving accuracy especially in low-noise conditions.

Contribution

The paper proposes the IterIEKF, a novel iterative variant of the IEKF that improves estimation accuracy and exhibits properties similar to the linear Kalman filter in low-noise regimes.

Findings

IterIEKF outperforms IEKF with highly accurate measurements.

IterIEKF exhibits properties akin to the linear Kalman filter in low-noise regimes.

Application to crane payload pose estimation demonstrates practical effectiveness.

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.