Bayesian unscented Kalman filter for state estimation of nonlinear and non-Gaussian systems

Abstract

This paper proposes a Bayesian unscented Kalman filter with simplified Gaussian mixtures (BUKF-SGM) for dynamic state space estimation of nonlinear and non-Gaussian systems. In the BUKF-SGM, the state and noise densities are approximated as finite Gaussian mixtures, in which the mean and covariance for each component are recursively estimated using the UKF. To avoid the exponential growth of mixture components, a Gaussian mixture simplification algorithm is employed to reduce the number of mixture components, which leads to lower complexity in comparing with conventional resampling and clustering techniques. Experimental results show that the proposed BUKF-SGM can achieve better performance compared with the particle filter (PF)-based algorithms. This provides an attractive alternative for nonlinear state estimation problem.