The Ensemble Kalman Update is an Empirical Matheron Update

TL;DR

This paper reveals that the ensemble update step in the Ensemble Kalman Filter is equivalent to an empirical Matheron update used in Gaussian process regression, linking data assimilation and modern GP sampling.

Contribution

It uncovers a fundamental connection between the Ensemble Kalman Filter and the Matheron update, providing insights into their equivalence and potential for cross-disciplinary applications.

Findings

EnKF update step is an empirical Matheron update.

Links data assimilation techniques with Gaussian process regression.

Provides accessible definitions and source code for the connection.

Abstract

The Ensemble Kalman Filter (EnKF) is a widely used method for data assimilation in high-dimensional systems, with an ensemble update step equivalent to an empirical version of the Matheron update popular in Gaussian process regression -- a connection that links half a century of data-assimilation engineering to modern path-wise GP sampling. This paper provides a compact introduction to this simple but under-exploited connection, with necessary definitions accessible to all fields involved. Source code is available at https://github.com/danmackinlay/paper_matheron_equals_enkf .