Abstract:

For modern engineering systems, the nonlinear state estimation is a crucial and important problem. A method applying the finite element method to approximate the probability density function of the nonlinear system state is proposed. The approximate solution of the stochastic differential model is denoted by the Kolmogorov's forward equation, but it is very difficult to be obtained. This article constructs its interpolating point through the finite element method, then it approaches its solution through the interpolation function to obtain a prior probability density function of the state, then, a posterior probability density function is gained through Bayesian formula. Finally, by taking the inertia terrainaided integrated navigation system as the background and performing the comparison analysis with the particle filter, the feasibility of this method is verified by numerical simulation.