一种引入U-D矩阵分解的加速度模型卡尔曼滤波算法

One Kalman Filtering Algorithm of the Accelerating Model Using the U-D Factorization

在机动目标加速度模型的标准卡尔曼滤波算法中,由于在量测更新的协方差阵计算中有个矩阵与一个半正定矩阵相减的运算,当它在小型机和微机上实现时,有可能导致协方差阵P出现不对称或负定的情况。所以在机动目标加速度模型的标准卡尔曼滤波算法的基础上,引入U-D矩阵分解,构造出一种协方差平方根自适应滤波算法,用来解决卡尔曼滤波的数值稳定性问题。它从原理上保证协方差阵在递推计算过程中始终保持正定性,具有速度快,精度高,计算量少的特点,有一定的应用价值。

In the standard kalman filter of an accelerating target, the covariance matrix P may become dissymmetry or minus because of a subtracting between two matrixes when it is counted with a minitype computer or a PC. So a covariance square root filter algorithm by using U-D factorization is given in the paper to solve the problem of the kalman filter’s stability. The filter is based on a standard kalman filter of the accelerating target. It can ensure that the covariance matrix P keep positive in the calculation...