基于组合导航系统的非线性高斯滤波算法

Gaussian non-linear filter algorithm based on integrated navigation system

由于组合导航系统具有强非线性和模型不确定性的特点,工程中扩展卡尔曼滤波无法满足组合导航系统实际应用的要求.为此,针对贝叶斯框架下高斯类非线性滤波算法的估计性能给出具体分析.首先,在估计点处对非线性函数进行泰勒展开获得泰勒近似,通过一阶矩和二阶矩分析滤波算法的近似精度;然后,通过数值稳定性对非线性滤波算法进行分析;最后,分别采用低维和高维模型对各滤波算法进行对比分析,为组合导航系统的实践提供借鉴.

Because of the strong nonlinearity and model uncertainty in the integrated navigation system, the classical extended Kalman filter cannot satisfy the actual application requirement of the integrated navigation system. The concrete analysis of the estimation performance of the Gaussian nonlinear filter under Bayes framework is given. Firstly, the Taylor approximation is obtained by the Taylor expansion of the nonlinear function at the estimation points, and the approximate precision of the filter algorithm is analyzed by the first and second moment. Then, the nonlinear filter algorithm is analyzed by the numerical stability. Finally, the low-dimensional and the high-dimensional test model is used to analyze and compare several Gaussian filter algorithms. The results provide reference for the practice of the integrated navigation system.