The Ensemble Kalman Update is an Empirical Matheron Update
This clarifies a theoretical connection for researchers in data assimilation and Gaussian processes, but it is incremental as it primarily explains an existing equivalence.
The paper shows that the Ensemble Kalman Filter update step is equivalent to an empirical version of the Matheron update from Gaussian process regression, linking decades of data assimilation engineering to modern GP sampling techniques.
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 .