GHQF精度分析及其在组合导航中的应用

Precision analysis of GHQF and its application in integrated navigation

针对非线性滤波算法在组合导航系统中的应用问题,利用泰勒级数展开对无味卡尔曼滤波(UKF)、容积卡尔曼滤波(CKF)和高斯厄米特积分滤波(GHQF)三种非线性高斯滤波算法的性能进行了比较分析;基于泰勒展开的精度分析表明,UKF和CKF从四阶项开始出现截断误差,而GHQF可以逼近任意阶精度的非线性系统的后验均值;以CNS/SAR/SINS非线性组合导航系统为应用背景,对三种滤波算法的精度进行了仿真验证。数学仿真结果表明,与UKF和CKF相比,GHQF具有更高的滤波估计精度。

In view of the applicability of nonlinear filters in integrated navigation, Unscented Kalman fil- ter （UKF）, Cubature Kalman filter （CKF） and Gauss-Hermite quadrature filter （GHQF） are analyzed and compared utilizing the Taylor expansion of function. Taylor expansion analyses demonstrate that GHQF can approximate posterior mean of nonlinear system at any order expansions, but UKF and CKF produce truncation error since the fourth order term. The three methods were used to CNS/SAR/SINS nonlinear integrated navigation system to verify their performance and the simulation results show that the GHQF is more accurate than the UKF and CKF.