为了避免扩展Kalman滤波算法中的矩阵微分计算,提高计算效率,降低非线性函数线性化逼近中的高阶截断误差影响,文中分别利用一阶和二阶Stirling多项式插值逼近公式计算系统状态变量均值和方差矩阵,按照EKF滤波算法计算流程建立非线性系统一阶和二阶插值滤波算法。基于大失准角传递对准非线性系统滤波实时性和精确性要求,应用一阶和二阶插值滤波算法对其实现系统状态滤波研究。从仿真结果可以看出,与EKF算法相比,插值滤波算法计算量小,有效提高了传递对准非线性系统滤波精度,其中二阶插值滤波算法估计性能最好。

In order to avoid the calculation of matrix differentiation in extended Kalman filtering algorithm and improve the calculation efficiency, and as the same time, decrease the impact of the higher-order truncation error in which nonlinear function is operated by linearization processing, with the first-order and the second-order Stirling polynomial interpolation approximation formulas this paper calculates the mean and estimation error variance matrix of system state variables, according to the calculation procedure of EKF algorithm, and constructs the first-order and second-order divided difference filtering algorithm of nonlinear system. Based on the real-time and accuracy requirements of the large initial misalignment transfer alignment system, its estimation performance is studied with DDFI algorithm, DDFII algorithm, and EKF algorithms. With the comparison of the simulation results, it verifies that the estimation precision of DDFII and DDFI algorithms, which don't decrease the real-time of the transfer alignment system, is superior to the EKF algorithm because of their lesser calculation burden. As the same time the DDFII algorithm's estimation performance has better than DDFI.