A Seamless Multilevel Ensemble Transform Particle Filter

TL;DR

This paper introduces a seamless multilevel ensemble transform particle filter that maintains strong coupling throughout, improving variance decay and computational efficiency in data assimilation tasks.

Contribution

It proposes a novel seamless coupling algorithm for multilevel ensemble transform particle filters, enhancing variance decay and computational efficiency over previous methods.

Findings

Increased variance decay rate between levels

Potential for greater computational cost reductions

Numerical evidence of asymptotic consistency

Abstract

This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combination of optimal coupling transformations between coarse and fine ensembles in difference estimators within a multilevel framework, to minimise estimator variance. It differs from that of Gregory et al. (2016) in that strong coupling between the coarse and fine ensembles is seamlessly maintained during all stages of the assimilation algorithm, instead of using independent transformations to equal weights followed by recoupling with an assignment problem. This modification is found to lead to an increased rate in variance decay between coarse and fine ensembles with level in the hierarchy, a key component of MLMC. This offers the potential for greater computational cost reductions. This is shown, alongside evidence of asymptotic consistency, in numerical examples.