Symmetries in observer design: review of some recent results and applications to EKF-based SLAM

TL;DR

This paper reviews symmetry-preserving observer theory and applies it to develop a new EKF-based SLAM algorithm with proven convergence properties, enhancing robustness in nonlinear localization tasks.

Contribution

It introduces a symmetry-preserving EKF for SLAM that guarantees convergence, combining recent symmetry theory with practical filtering applications.

Findings

New symmetry-preserving EKF for SLAM with convergence guarantees

Global exponential convergence achieved through specific gain choices

Application of symmetry theory to improve observer design in nonlinear systems

Abstract

In this paper, we first review the theory of symmetry-preserving observers and we mention some recent results. Then, we apply the theory to Extended Kalman Filter-based Simultaneous Localization and Mapping (EKF SLAM). It allows to derive a new (symmetry-preserving) Extended Kalman Filter for the non-linear SLAM problem that possesses convergence properties. We also prove a special choice of the gains ensures global exponential convergence.