Multilevel ensemble Kalman filtering

TL;DR

This paper introduces a multilevel Monte Carlo approach into the ensemble Kalman filter to improve computational efficiency in estimating signals governed by stochastic differential equations, demonstrating theoretical and numerical advantages.

Contribution

It develops a multilevel ensemble Kalman filter that outperforms standard EnKF in computational cost for a given accuracy, with rigorous theoretical proof and numerical validation.

Findings

Multilevel EnKF reduces computational cost compared to standard EnKF.

Theoretical proof of asymptotic efficiency gain.

Numerical experiments confirm improved performance.

Abstract

This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.