Multilevel ensemble Kalman filtering for spatio-temporal processes

TL;DR

This paper introduces a multilevel ensemble Kalman filter (MLEnKF) tailored for infinite-dimensional spatio-temporal processes, combining multilevel Monte Carlo techniques with ensemble filtering to improve efficiency in high-dimensional settings.

Contribution

The paper develops and analyzes a novel multilevel ensemble Kalman filter that leverages hierarchical sampling to enhance efficiency for complex spatio-temporal models.

Findings

MLEnKF outperforms traditional EnKF in efficiency for weak approximations.

Theoretical analysis confirms asymptotic efficiency gains under regularity conditions.

Numerical experiments validate the theoretical advantages of MLEnKF.

Abstract

We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensional spatio-temporal process. We consider underlying models that needs to be simulated by numerical methods, with discretization in both space and time. The multilevel Monte Carlo (MLMC) sampling strategy, achieving variance reduction through pairwise coupling of ensemble particles on neighboring resolutions, is used in the sample-moment step of MLEnKF to produce an efficient hierarchical filtering method for spatio-temporal models. Under sufficient regularity, MLEnKF is proven to be more efficient for weak approximations than EnKF, asymptotically in the large-ensemble and fine-numerical-resolution limit. Numerical examples support our theoretical findings.