针对容积卡尔曼滤波器在递推过程中,计算量大、数值不稳定等问题,提出了平方根容积卡尔曼滤波器。该滤波器不仅增强了数值鲁棒性,确保了状态协方差矩阵的正定性,且在一定程度上提高了滤波精度。仿真结果表明,该滤波器的滤波精度与容积卡尔曼滤波相比提高了约10%,且均高于扩展卡尔曼滤波;随着状态维数的增加,该滤波器的估计性能越加优于扩展卡尔曼滤波器。因此对系统维数较高的场合,该滤波器是一种非常有效的非线性滤波算法。

In view of the problems of numerical instability and large amount of computation in recursive process, the modified square root cubature Kalman filter was put forward. The modified filter not only enhances the numerical stability, guarantees positive definiteness of the state covariance, but also increases accuracy. The simulation shows that the accuracy of the filter is higher than that of cubature Kalman filter, and the accuracy of cubature Kalman filter is higher than that of the extended Kalman filter; with the increase of dimension of nonlinear system, the estimation performance of the modified filter is better than that of the extended Kalman filter. The modified filter is an effective nonlinear filtering algorithm for high dimension of nonlinear system.