Discrete update pose filter on the special Euclidean group SE(3)

Abstract

This paper proposes two variants of the Geometric Approximate Minimum Energy (GAME) filter on the Special Euclidean Group SE(3) in the case that exteroceptive measurements are obtained in discrete time. Continuous-discrete versions of the GAME filter are provided that near-continuously predict pose and its covariance using high frequency interoceptive measurements and then update these estimates utilizing low frequency exteroceptive measurements obtained in discrete time. The two variants of the proposed filter are differentiated in their derivation due to the choice of affine connection used on SE(3). The proposed discrete update filters are derived based on first principles of deterministic minimum-energy filtering extended for discrete time measurements and derived directly on SE(3). The performance of the proposed filters is demonstrated and compared in simulations with a short discussion of practical implications of the choice of affine connection.