Algorithm of Gaussian Sum Filter based on High-order UKF for Dynamic State Estimation

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. A new version of Gaussian sum estimation algorithm is developed here based on high-order unscented Kalman filter (HUKF). A sigma point selection method, high-order unscented transformation (HUT) technique is proposed for the HUKF, which can approximate the Gaussian distributions more accurately. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We then go on to extend the use of the HUKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. The resulting filtering algorithm, called the Gaussian sum high-order unscented Kalman filter (GS-HUKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. It is corroborated in the theoretical analysis and the simulation that the proposed Gaussian sum HUKF has integrated advantages with respect to computational accuracy and time complexity for nonlinear non-Gaussian filtering problems.