Abridged Gaussian sum extended Kalman filter for nonlinear state estimation under non-Gaussian process uncertainties

Abstract

Studies on Extended Kalman Filter (EKF) that explicitly consider non-Gaussian process uncertainties are scarce in the literature. In the current study, a novel approach referred to as Abridged Gaussian Sum-Extended Kalman Filter (AGS-EKF) is developed to improve EKF performance for such systems. AGS-EKF performs a modified version of the EKF formulation that accounts for non-zero mean process uncertainties. Contrary to the conventional Gaussian Sum Filter (GSF), the process uncertainties involved in the prior estimation step of AGS-EKF follow an overall Gaussian mixture model that approximates the actual non-Gaussian process uncertainty distribution. Hence, AGS-EKF computes the EKF calculation only once thus avoiding the need to perform multiple EKFs to capture all the Gaussian components in the mixture as in GSF approach. Since AGS-EKF considers the overall Gaussian mixture of the process uncertainties, the method avoids the biased estimations that may appear in GSF. In addition to AGS-EKF, an adaptation in the GSF framework is proposed to improve the estimation accuracy of GSF. Case studies have shown that AGS-EKF offers higher accuracy of the estimation in comparison with GSF in shorter computational times.