自适应平方根球型无迹卡尔曼滤波算法

Adaptive Square Root Spherical Unscented Kalman Filtering Algorithm

针对传统无迹卡尔曼滤波器存在跟踪精度低、数值稳定性差、鲁棒性弱等缺点,提出了一种基于球型无迹变换的自适应平方根UKF滤波算法(Adaptive Square Root UKF Filtering Algorithm Based on Spherical Unscented Transform,ASRS-UKF)。该算法在标准的平方根UKF算法上,首先改用了球型无迹变换对权系数以及sigma点进行计算选取;其次改进了平方根UKF中平方根矩阵的分解方法;同时在预测误差协方差矩阵中引入了自适应衰减因子。最后,通过将该算法同平方根UKF以及强跟踪UKF算法进行仿真对比,结果表明,ASRS-UKF算法在减少计算量、加快计算速度的同时还提高了滤波精度和稳定性,而且对于系统模型匹配不佳的情况下,仍具有良好的跟踪性能。

The traditional unscented Kalman filter has such shortcomings as low tracking accuracy,poor numerical stability,and weak robustness.In this paper,an adaptive square root UKF filtering algorithm based on spherical unscented transform(ASRS-UKF)is presented.Based on the standard square root UKF algorithm,firstly,we use the spherical unscented transform to calculate and choose the weight coefficient and sigma points.Secondly,we improve the decomposition method of the square root matrix in square root UKF.And at the same time,adaptive attenuation factor is introduced into the prediction error covariance matrix.Finally,a comparison is made between the proposed algorithm,the square root UKF algorithm,and the strong tracking UKF algorithm.The results show that the ASRS-UKF algorithm can improve the filtering accuracy and stability while reducing the computational load and speeding up the calculation.Moreover,the ASRS-UKF algorithm still has good tracking performance when the system model is not matched well.