Invariant extended Kalman filter on matrix Lie groups

TL;DR

This paper introduces a symmetry-preserving invariant extended Kalman filter on matrix Lie groups that simplifies derivation, improves convergence, and outperforms traditional EKFs in attitude estimation tasks.

Contribution

It presents a novel IEKF derived using minimal differential geometry tools, with error dynamics on the Lie algebra, enhancing simplicity and performance.

Findings

IEKF is computationally less intensive than EKF.

IEKF provides more accurate state estimates.

Numerical experiments demonstrate superior performance of IEKF.

Abstract

We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the group configuration which, in turn, provides a uniform estimate of the region of convergence. The proposed IEKF differs from existing techniques in literature on the account that it is derived using minimal tools from differential geometry that simplifies its representation and derivation to a large extent. The filter error dynamics is defined on the Lie algebra directly instead of identifying the Lie algebra with an Euclidean space or defining the error dynamics in local coordinates using exponential map, and the associated differential Riccati equations are described on the corresponding space of linear operators using tensor algebra. The proposed filter is implemented for the attitude dynamics of the rigid body, which is a benchmark problem in control, and its performance is compared against a conventional extended Kalman filter (EKF). Numerical experiments support that the IEKF is computationally less intensive and gives better performance than the EKF.