矩阵外积法Kalman滤波器在动态GPS定位中的应用

由于计算机有效字长的限制,滤波算法在计算机上实施时易于产生误差积累,误差协方差失去正定性或对称性,从而出现数值计算中的不稳定现象.一般情况下,当状态变量维数超过10时,滤波过程中出现滤波结果不稳定现象概率增大.为了解决滤波器数值计算不稳定问题,实践中提出并应用了许多方法,如自适应滤波、固定增益滤波、平方根滤波等.这些算法的不足是计算繁琐,效率低下.提出一个基于矩阵外积法所设计的快速、稳定的滤波算法,该卡尔曼滤波算法速度快,效率高,数值稳定性好,运算量少,将其应用于动态GPS定位验证了其有效性.

Kalman Filter based on Matrix Accumulative Algorithm and its Application to Dynamic GPS Positioning

Because of the computer word length,filter algorithm is prone to accelerate error.The error covariance will be out of symmetry,as a result,instability will appear in the value calculation.Generally,when the state variable dimension exceeds ten,the probability of result instability in the process of filtering increases.To deal with filter value calculation instability,people put forward and carry out lots of methods in practice such as self-adaptive filter,fixed amplitude filter and square root filter,etc.The disadvantages of these algorithms are fussy calculation and bad efficiency.This paper puts forward a new Kalman filter based on matrix accumulative algorithm.The Kalman filter algorithm is fast,efficient and stable.It decreases the computing volume.Simulation examples for dynamic GPS positioning shows their effectiveness.