摘要
基于SINS初始对准误差参数计算精度要求,利用Gauss-Hermite积分和Gauss-Lagerre积分数值逼近方法,证明了Bayesian最优估计理论的高阶球面径向联合积分数值逼近的五阶SRC-KF算法.通过状态向量坐标变换开展高阶球面径向数值积分逼近计算,根据获得2n2个球面径向采样点,利用高阶矩匹配方法设计采样点权值展开系统状态后验概率密度函数逼近计算,来达到非线性系统状态参数五阶SRC-KF最优估计算法高精度计算目的.采用四元数姿态建模方法构建新型SINS初始对准非线性误差模型,引入Lagrangian乘子算法计算四元数估计加权均值,最后利用SINS粗对准实验数据开展初始对准高阶SRC-KF模型算法仿真验证研究.通过UKF、CKF和五阶SRC-KF算法估计数据比较,五阶SRC-KF算法计算精度较高,数值计算稳定性好,验证了五阶SRC-KF算法的可行性及计算精度优势.
Based on the higher-accuracy calculation requirement of SINS＇initial alignment,with GaussHermite Quadrature and Gauss-Lagerre Quadrature numerical approximation method, the fifth-order spherical radial joint integral numerical approximation of higher-order SRC-KF algorithm in Bayesian optimal estimation theory was proved. Through developing higher-order spherical radial numerical integral approximation calculation with state vector transformation of coordinates,the obtained 2n2 spherical radial sampling points,and the higher-order moment matching method in designing the sampling points ＇weights,the aim of high accuracy calculation of system state and parameters with the fifth-order SRC-KF algorithm was achieved. Based on attitude quaternion modeling method,the new nonlinear error model of SINS＇initial alignment was constructed. With Lagrangian operator,the weighted average of estimated quaternion was calculated. Finally,with the SINS＇coarse alignment experiment data,the higher-order SRC-KF algorithms simulation validation studies of SINS＇initial alignment were carried out. By the comparison of UKF,CKF and the fifth-order SRC-KF algorithms,it was shown that fifth-order SRC-KF algorithm＇s calculation accuracy was higher than others,and it had better numerical stability. The feasibility and calculation accuracy of the fifth-order SRC-KF algorithm were verified.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2014年第4期33-39,共7页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金资助项目
编号U1204603
郑州轻工业学院博士基金项目
编号2011BSJJ00048
