On Ensemble Kalman Filter, Particle Filter, and Gaussian Particle Filter

Abstract

In this paper, we clarify theoretical aspects of the representative non-Gaussian filters: the ensem- ble Kalman filter (EnKF) and the particle filter (PF). We first show that the EnKF is a realization algorithm of the linear optimal filter for nonlinear problems. We also show that under the Gaussian assumption for the predicted state, the EnKF provides a realization algorithm of the Gaussian filter. We next propose the multiple distribution estimation approach which is a novel framework for designing non-Gaussian filters and show that the PFs are special cases. We then propose a new PF algorithm to address the particle impoverishment problem inherent in the standard PF algorithms. We also show that by applying the proposed algorithm, we can improve the filtering accuracy of the Gaussian particle filter. We finally confirm the performance of each filter using two benchmark simulation models.