GPS动态数据处理中的快速Kalman滤波算法

Fast Kalman Filtering Algorithm for GPS Kinematic Data Processing

根据GPS数据处理中的Kalman滤波状态转移矩阵和设计矩阵大量存在零元素的特点,将其构造成特定稀疏矩阵。再利用稀疏矩阵乘法,同时结合矩阵对称性、矩阵求逆降维等方法,可大大减少Kalman滤波的乘法次数。在非差C/A伪距情况下,该算法乘法总次数不到传统算法的1/3;在双差伪距P1,P2+双差载波情况下,该算法乘法总次数甚至不到1/6;其耗时也只有传统算法的1/3左右,因而大大提高了Kalman滤波的计算效率。

Sparse matrix is constructed owing to the presence of quantities of zero elements in state transformation matrix and designed matrix in this paper. Then a fast Kalman filtering algorithm is given in the paper based on sparse matrix multiplication, matrix symmetry and dimension reduction of the matrix inversion. It is shown, by theoretical analysis and numerical results, that the number of multiplication of the new method is less than one-third of the traditional method in the case of non-difference C/A pseudoranges, and it is even less than one-sixth in the case of double-difference pseudoranges P1, P2 q- double-difference carrier phases L1, L2. The computation time is one-third or so. So the fast Kalman filtering algorithm has better performance in GPS kinematic positioning.