区间卡尔曼滤波算法在高动态导航的研究

Interval Kalman Filtering Algorithm for High Dynamic Navigation and Positioning

针对卡尔曼滤波算法中动力学系统模型以及噪声模型不能精确已知,导致卡尔曼滤波算法在实际中不能实现最优估计。首先分析了传统卡尔曼滤波算法中各种误差源的影响,以及区间矩阵运算的影响,经分析得到,区间运算可以保证集合映射的完全性,但不能体现最优化。通过分析,本文提出了一种新型的区间卡尔曼滤波,将各种误差源归约到先验估计值区间和后验估计值区间中,然后将区间交集运算应用于卡尔曼滤波算法。这种新算法运算量与传统卡尔曼滤波算法相当。通过仿真实验证实,该算法在含时变噪声的高动态导航定位中比传统卡尔曼滤波效果提高2dB。

In traditional Kalman filtering algorithms, optimization estimation cannot be achieved for practical problems because the dynamics system model and noises are unknown. Firstly the impacts of various error sources and interval matrix operations in the traditional Kalman filter are analyzed. The analysis shows that the interval operation can ensure the completeness of set mapping but can not be the optimization. Based on the analysis, a new interval Kalman filtering algorithm is proposed in this paper. In the algorithm, various error sources are reduced to a priori estimation interval and a posterior estimation interval and the interval intersection set operation is adopted to achieve the optimization. This algorithm has comparable computational complexities with the traditional one. Simulations show that the proposed algorithm can achieve a 2dB gain over the traditional Kalman filter in high dynamic navigation and positioning with time-varying noises.