A novel high order unscented transform (HUT) mechanism is proposed to improve the approximation accuracy of the nonlinear transformation.The HUT is adopted to select the Sigma points which can be used to approximate the posterior probability density of state variable by numerical integration.Thus the high order unscented Kalman filtering (HUKF) algorithm can be made up.Further

to solve the state estimation problem for nonlinear/non-Gaussian system

Gaussian sum high order unscented Kalman filter (GS-HUKF) is proposed by combining the HUKF and Gaussian sum filter (GSF).The basic idea of the GS-HUKF is that a cluster of Gaussian distribution is used to approximate the posterior probability density of state variable.At the mean time

each separated Gaussian distribution is estimated by HUKF.Numerical simulation results demonstrate that the proposed HUT has higher estimation precision than ordinary unscented transform (UT) method.The GS-HUKF has integrated advantages with respect to estimation accuracy and computational complexity and its performance is superior to the existing Gaussian sum filters.