摘要
A fast U D factorization based Kalman filter for the 21 state integrated global positioning system and inertial navigation system (GPS/INS) is developed from the point of engineering implementation. The conventional Kalman filter is widely used for integration of GPS/INS, however, due to the model and numerical computation errors, the Kalman filter may diverge in engineering implementation. In order to solve this problem, an extended Kalman filter based on the U D factorization is proposed. Moreover, the high order integrated system suffers from the problem of long computation time, leading to difficulties in real time applications. An algorithmic approach is developed to improve the computational speed. A typical aircraft trajectory is simulated to compare the improvement in the computational speed and the navigation accuracy using the conventional Kalman filter and the fast Kalman filter based on the U D factorization. The results indicate that the methods proposed in this paper are very effective in overcoming these problems for the high dynamic integrated GPS/INS system.
研究了基于Ｕ－Ｄ分解的快速Ｋａｌｍａｎ滤波算法，并将它应用到一个２１状态的ＧＰＳ／ＩＮＳ组合导航系统工程实现中。常规的Ｋａｌｍａｎ滤波器已广泛应用于ＧＰＳ／ＩＮＳ组合系统，但由于系统建模误差和计算舍入误差，Ｋａｌｍａｎ滤波器在工程应用中会出现发散现象。为了解决这个问题，本文推导了一个基于Ｕ－Ｄ的扩展Ｋａｌｍａｎ滤波器。此外，由于高阶组合系统计算量大，导致基于Ｕ－Ｄ分解的滤波器在实时应用中有困难，为此，本文提出了一种快速的滤波算法来节省计算时间。文中设计了一条近于实际的飞机航迹来仿真。结果表明，本文所提的滤波算法能有效地克服组合系统滤波器发散问题，并减少计算时间近６９％。
