An optimal control approach to particle filtering on Lie groups

TL;DR

This paper introduces a novel particle filtering algorithm on Lie groups using stochastic control and duality principles, improving performance in satellite attitude estimation tasks.

Contribution

It presents a new particle filtering method based on optimal control and duality, enhancing robustness against sample degeneracy in Lie group filtering problems.

Findings

Reduced sample degeneracy compared to existing methods

Effective in satellite attitude estimation over SO(3)

Utilizes iLQR for approximate optimal control solution

Abstract

We study the filtering problem over a Lie group that plays an important role in robotics and aerospace applications. We present a new particle filtering algorithm based on stochastic control. In particular, our algorithm is based on a duality between smoothing and optimal control. Leveraging this duality, we reformulate the smoothing problem into an optimal control problem, and by approximately solving it (using, e.g., iLQR) we establish a superior proposal for particle smoothing. Combining it with a suitably designed sliding window mechanism, we obtain a particle filtering algorithm that suffers less from sample degeneracy compared with existing methods. The efficacy of our algorithm is illustrated by a filtering problem over SO(3) for satellite attitude estimation.