The application of Monte Carlo methods to the nonlinear filtering problem

The minimum variance estimates of state variables in a noisy, nonlinear discrete-time system are evaluated by a Monte Carlo method. The a posteriori probability density function for state variables conditioned upon measurement data sequence is expanded into a series of orthonormal Hermite functions and numerically determined in a recursive form. The numerical results indicate that the proposed method can markedly improve the accuracy by using the quasi-random numbers.