基于有限单元的贝叶斯滤波估计算法

摘要

现代工程系统具有较强的非线性特性,针对这类非线性系统的状态估计问题,提出基于有限单元的贝叶斯原理估计的非线性滤波方法.采用有限单元法逼近系统状态的先验概率解,即前向Kolmogorov方程的解,通过贝叶斯估计得到状态的后验信息.将其方法应用到惯性/地形组合导航系统中,仿真结果表明该方法的可行性.%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.