Solving 2-dimensional navigation stochastic differential model based on finite element

Abstract

A new method applying finite element is proposed in this paper to approximate probability density function of the state of a navigation system. The weak solution of navigation stochastic differential model is denoted by the Kolmogorov's forward equation, which it is very difficult to be obtained. The solution is approached through finite element to obtain a prior probability density function of the state, then a posterior probability density function is gained through Bayesian formula, By taking the underwater vehicle integrated navigation system as the instance and carrying out the contrastive analysis with Particle Filter, the feasibility of solving of navigation stochastic differential model with the help of finite element is confirmed through simulating experiment results.