The Ensemble Kalman Update is an Empirical Matheron Update

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 .