Equivariant Filtering Framework for Inertial-Integrated Navigation

TL;DR

This paper introduces an equivariant filtering framework for inertial navigation that leverages Lie group symmetries to improve state estimation accuracy and robustness.

Contribution

It develops a novel equivariant filter based on Lie group symmetries for inertial-integrated navigation, extending invariant EKF methods.

Findings

Enhanced state estimation accuracy

Utilizes Lie group symmetries for filter design

Provides analytic state transition matrices

Abstract

This paper proposes a equivariant filtering (EqF) framework for the inertial-integrated state estimation problem. As the kinematic system of the inertial-integrated navigation can be naturally modeling on the matrix Lie group $SE_2(3)$, the symmetry of the Lie group can be exploited to design a equivariant filter which extends the invariant extended Kalman filtering on the group affine system. Furthermore, details of the analytic state transition matrices for left invariant error and right invariant error are given.