State Estimation of Nonlinear Systems Using Gaussian-Sum Cubature Kalman Filter Based-on Spherical Simplex-Radial Rule

In this paper, a new algorithm of Gaussian sum filters for state estimation of nonlinear systems is presented. The proposed method consists of several parallel Cubature Kalman filters each of which is implemented according to the simplex spherical-radial rule. In this method, the probability density function is the sum of the weights of several Gaussian functions. The mean value, covariance, and weight coefficients of these Gaussian functions are calculated recursively over time, and each of the Cubature Kalman filters are responsible for updating one of these functions. Finally, the performance of the proposed filter is investigated using two nonlinear state estimation problems and the results are compared with conventional nonlinear filters. The simulation results show the appropriate accuracy of the proposed algorithm in state estimation of nonlinear systems.