Invariant Smoothing on Lie Groups

TL;DR

This paper introduces a non-linear smoothing algorithm tailored for group-affine observation systems on Lie groups, leveraging their structure to improve estimation efficiency and reduce relinearization needs, validated through robot localization experiments.

Contribution

The paper presents a novel invariant smoothing algorithm for Lie group-based systems that minimizes relinearization by exploiting problem structure, enhancing estimation robustness.

Findings

Effective in simulation and real robot localization data.

Reduces need for relinearization compared to traditional methods.

Demonstrates improved estimation accuracy on Lie group systems.

Abstract

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the proposed algorithm is based on a maximum a posteriori estimator, determined by optimization. But owing to the specific properties of the considered class of problems, the involved linearizations are proved to have a form of independence with respect to the current estimates, leveraged to avoid (partially or sometimes totally) the need to relinearize. The method is validated on a robot localization example, both in simulations and on real experimental data.