Robust Nonlinear Filter Using Adaptive Edgeworth Expansion

Edgeworth expansion is an effective method to approximate a non-Gaussian distribution by utilizing higher order cumulants of the statistics, which can be obtained from corresponding moments. The higher order moments can be calculated by numerical integration rules. In this paper, a new nonlinear filtering method that combines higher order moment approximation with the Edgeworth expansion is proposed. The Edgeworth expansion is utilized to correct the weights on the quadrature points in the Gauss-Hermite quadrature filter. This new filter can provide the robustness to non-Gaussianity for nonlinear filters. An adaptive mechanism is adopted in the filtering algorithm to determine which orders of moments need to be used in the Edgeworth expansion based on the measure of non-Gaussianity. The simulation results demonstrate the enhanced performance of this new filter compared with the conventional nonlinear Gaussian filters.