Accurate Smoothing for Continuous-Discrete Nonlinear Systems With Non-Gaussian Noise

In this letter, an accurate Gaussian sum-smoothing approach is derived for the continuous-discrete systems, where the dynamics can be modeled with nonlinear Ito-type stochastic differential equations and the measurements are obtained at discrete sampling times with non-Gaussian noise. The proposed smoothing method is derived by applying a bank of parallel accurate continuous-discrete extended-cubature Kalman filters used in the classical Gaussian state estimation to approximate the non-Gaussian estimation densities as a finite number of weighted sums of Gaussian densities. The performances of the proposed method are compared with the recently presented filters based on the maximum correntropy criterion in a simulated application and the numerical results show that the new approach is more accurate and robust than others.