METHOD FOR SOLVING HIGH-DIMENSIONAL NONLINEAR FILTERING PROBLEM

摘要

A method for solving high-dimensional nonlinear filtering problems is revealed. The method uses a fast computational module to solve an equation and get approximate numerical solutions of a signal-observation model. The equation-solving process of the fast computational module is speeded up by a transformation module and the computational stability is further improved. D-dimensional nonlinear filtering problems are solved and approximate numerical solutions are obtained based on Yau-Yau filtering theory. A Quasi-Implicit Euler Method (QIEM) is applied to solve the Kolmogorov equations and estimate approximate numerical solutions of the signal-observation model. Moreover, QIEM is more efficient and the numerical solutions are more stable by Fast Fourier transformation (FFT) acceleration.