A sparse matrix formulation of model-based ensemble Kalman filter

TL;DR

This paper presents a computationally efficient variant of the ensemble Kalman filter that leverages sparse precision matrices and block updates, enabling faster processing of high-dimensional problems with minimal approximation error.

Contribution

It introduces a novel sparse precision matrix formulation and block updating scheme for the ensemble Kalman filter, improving scalability and efficiency.

Findings

Substantial speedup for high-dimensional state vectors.

Negligible approximation error from block updating.

Effective application demonstrated in simulation example.

Abstract

We introduce a computationally efficient variant of the model-based ensemble Kalman filter (EnKF). We propose two changes to the original formulation. First, we phrase the setup in terms of precision matrices instead of covariance matrices, and introduce a new prior for the precision matrix which ensures it to be sparse. Second, we propose to split the state vector into several blocks and formulate an approximate updating procedure for each of these blocks. We study in a simulation example the computational speedup and the approximation error resulting from using the proposed approach. The speedup is substantial for high dimensional state vectors, allowing the proposed filter to be run on much larger problems than can be done with the original formulation. In the simulation example the approximation error resulting from using the introduced block updating is negligible compared to the Monte Carlo variability inherent in both the original and the proposed procedures.