What are You Weighting For? Improved Weights for Gaussian Mixture Filtering With Application to Cislunar Orbit Determination

TL;DR

This paper introduces a new method for computing weights in Gaussian mixture filters by linearizing measurement models around each component's posterior, leading to improved accuracy in nonlinear scenarios, especially in cislunar orbit determination.

Contribution

It proposes a novel weight computation approach for Gaussian mixture filters that enhances performance in nonlinear measurement models, supported by theoretical proofs and empirical validation.

Findings

Improved filter accuracy in nonlinear cases.

Enhanced consistency demonstrated in cislunar tracking.

Theoretical equivalence with traditional methods for linear models.

Abstract

This work focuses on the critical aspect of accurate weight computation during the measurement incorporation phase of Gaussian mixture filters. The proposed novel approach computes weights by linearizing the measurement model about each component's posterior estimate rather than the the prior, as traditionally done. This work proves equivalence with traditional methods for linear models, provides novel sigma-point extensions to the traditional and proposed methods, and empirically demonstrates improved performance in nonlinear cases. Two illustrative examples, the Avocado and a cislunar single target tracking scenario, serve to highlight the advantages of the new weight computation technique by analyzing filter accuracy and consistency through varying the number of Gaussian mixture components.