Improve the autonomy of the SE2(3) group based Extended Kalman Filter for Integrated Navigation: Theoretical Analysis

TL;DR

This paper analyzes the limitations of current SE2(3) Lie group-based extended Kalman filters in high-precision navigation, proposing a new modeling approach to enhance error propagation autonomy considering earth rotation and inertial biases.

Contribution

The paper provides a theoretical analysis of SE2(3) group navigation models in high-precision contexts and introduces a construction method to improve autonomy by addressing Coriolis force effects.

Findings

Traditional SE2(3) models are limited by Coriolis force effects.

The proposed construction method enhances model autonomy.

Analysis applies to inertial, earth, and world frames.

Abstract

One of core advantages of the SE2(3) Lie group framework for navigation modeling lies in the autonomy of error propagation. Current research on Lie group based extended Kalman filters has demonstrated that error propagation autonomy holds in low-precision applications, such as in micro electromechanical system (MEMS) based integrated navigation without considering earth rotation and inertial device biases. However, in high-precision navigation state estimation, maintaining autonomy is extremely difficult when considering with earth rotation and inertial device biases. This paper presents the theoretical analysis on the autonomy of SE2(3) group based high-precision navigation models under inertial, earth and world frame respectively. Through theoretical analysis, we find that the limitation of the traditional, trivial SE2(3) group navigation modeling method is that the presence of Coriolis force terms introduced by velocity in non-inertial frame. Therefore, a construction method for SE2(3) group navigation models is proposed, which brings the navigation models closer to full autonomy.