High-Order Unscented Transformation Based on the Bayesian Learning for Nonlinear Systems with Non-Gaussian Noises

Abstract

In this paper, a new high-order unscented Kalman particle filter (HUPF) is proposed to solve the state estimation problems for nonlinear systems with non-Gaussian process noises and different measurement noises scheme. Based on a high-order Unscented Transformation (UT) method, the accuracy of importance density function (IDF) and the rationality of prior distribution are guaranteed, and it is substituted into the framework of Bayesian learning. The proposed HUPF has the higher computational complexity than existing filters, such as standard extended Kalman filter (EKF), unscented Kalman filter (UKF) and particle filter (PF). The superior performance of the proposed HUPF as compared with existing methods is illustrated in a numerical example concerning strong nonlinearity with non-Gaussian noises.