基于矩阵对角化变换的高阶容积卡尔曼滤波

High-degree cubature Kalman filter based on diagonalization of matrix

为了提高高阶容积卡尔曼滤波器(CKF)的滤波性能,提出一种基于矩阵对角化变换的高阶CKF算法.该算法基于高阶容积准则,利用矩阵对角化变换代替标准高阶CKF中的Cholesky分解,使得协方差矩阵分解后的平方根矩阵保留了原有的特征空间信息,状态统计量计算更加准确,从而提高了滤波精度;同时,矩阵对角化变换不要求协方差矩阵正定,增强了算法滤波稳定性.仿真结果表明,所提出的算法是可行而有效的,明显改善了标准高阶CKF的滤波效果.

In order to improve the filtering performance of the high-degree cubature Kalman filter（CKF）, a high-degree cubature Kalman filter based on the diagonalization of the matrix is proposed. Based on the high-degree cubature rule,the diagonalization of the matrix is used to take place of the Cholesky decomposition and the square-rooting matrix of the covariance can preserve the information of the original feature space, so that the state statistics can be calcuated accurately and the filtering accuracy is improved. At the same time, the diagonalization of the matrix does not require the condition that the covariance matrix must be the positive definite matrix and the stability of filtering algorithm is enhanced. The simulation results show that the proposed algorithm is feasible and effective, and it can obviously improve the fltering effect of the standard high-degree CKF algorithm.