Gaussian-mixture based ensemble Kalman filter

The Ensemble Kalman Filter (EnKF) is a Kalman based particle filter which was introduced to solve large scale data assimilation problems where the state space is of very large dimensionality. It also achieves good results when applied to a target tracking problem, however, due to its Gaussian assumption for the prior density, the performance can be improved by introducing Gaussian mixtures. In this paper, a new derivation of the EnKF is presented which is based on a duality between Gaussian products and particle densities. A relaxation of the Gaussian assumption is then achieved by introducing a particle clustering into Gaussian Mixtures by means of the Expectation Maximization (EM) algorithm and to apply the EnKF on the clusters. The soft assignment of the EM allows all Gaussian components to contribute to each of the particles. It is shown that the EM-EnKF performs better than a standard particle filter while having less computation time.