Ensemble Kalman Filters with Resampling

TL;DR

This paper introduces a resampling step into ensemble Kalman filters, enhancing their theoretical understanding and practical performance in high-dimensional state estimation tasks.

Contribution

It proposes a novel resampling approach within ensemble Kalman filters, enabling rigorous analysis and improved numerical results.

Findings

Resampling breaks particle dependence, facilitating theoretical analysis.

The new algorithm performs well in numerical experiments.

Extended theoretical guarantees for ensemble Kalman filters with resampling.

Abstract

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice. These algorithms rely on an ensemble of interacting particles to sequentially estimate the state as new observations become available. Despite the practical success of ensemble Kalman filters, theoretical understanding is hindered by the intricate dependence structure of the interacting particles. This paper investigates ensemble Kalman filters that incorporate an additional resampling step to break the dependency between particles. The new algorithm is amenable to a theoretical analysis that extends and improves upon those available for filters without resampling, while also performing well in numerical examples.