Deterministic Optimal Transport-based Gaussian Mixture Particle Filtering for Verifiable Applications

TL;DR

This paper introduces a deterministic resampling method based on optimal transport for Gaussian mixture particle filters, improving efficiency and accuracy in state estimation tasks, including space object tracking.

Contribution

It proposes a novel optimal transport-based resampling procedure that enhances particle filter performance and reduces particle requirements.

Findings

Significantly reduces particles needed for accurate estimation in toy problems

Improves state estimation of space objects in lunar orbit scenarios

Demonstrates effectiveness over traditional stochastic resampling methods

Abstract

Mixture-model particle filters such as the ensemble Gaussian mixture filter require a resampling procedure in order to converge to exact Bayesian inference. Canonically, stochastic resampling is performed, which provides useful samples with no guarantee of usefulness for a finite ensemble. We propose a new resampling procedure based on optimal transport that deterministically selects optimal resampling points. We show on a toy 3-variable problem that it significantly reduces the amount of particles required for useful state estimation. Finally, we show that this filter improves the state estimation of a seldomly-observed space object in an NRHO around the moon.