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. In this paper, we show that the ensemble update step of the EnKF is equivalent to an empirical version of the Matheron update popular in the study of Gaussian process regression. While this connection is simple, it seems not to be widely known, the literature about each technique seems distinct, and connections between the methods are not exploited. This paper exists to provide an informal introduction to the connection, with the necessary definitions so that it is intelligible to as broad an audience as possible.