Multilevel Ensemble Transform Particle Filtering

TL;DR

This paper introduces a multilevel ensemble transform particle filtering method that leverages optimal transport to reduce variance and computational costs in nonlinear filtering tasks.

Contribution

It extends multilevel Monte Carlo techniques to the Ensemble Transform Particle Filter using optimal transport for improved correlation control.

Findings

Significant reduction in computational costs demonstrated

Effective variance control via optimal transport methods

Proof of concept shown through numerical examples

Abstract

This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.