Accurate Gaussian Sum-filter for Continuous-discrete Nonlinear Systems with Non-Gaussian Noise

In this paper, an accurate Gaussian sum-filtering method is developed theoretically and tested experimentally for the continuous-discrete nonlinear systems with non-Gaussian noise. The state dynamics of the systems are modeled with nonlinear Itô-type stochastic differential equations (SDEs) and the measurements are obtained at discrete time instants with non-Gaussian noise. We first show how the recently developed accurate continuous-discrete extended-cubature Kalman filter (ACD-ECKF) can be applied to classical continuous-discrete Gaussian state estimation. Then, we derive the square-root version of the Gaussian sum-ACD-ECKF for continuous-discrete models with non-Gaussian noise. The Gaussian sum-filter applies a bank of parallel ACD-ECKFs to approximate the predicted and posterior densities as a finite number of weighted sums of Gaussian densities and the corresponding weights are obtained from the residuals of ACD-ECKFs. The performances of the proposed method are compared with the recently presented filters based on the Maximum Correntropy Criterion (MCC) in a simulated application and the numerical results show that the presented approach is more accurate and robust than other algorithms.