一种基于奇异值分解的非线性滤波新算法

New Nonlinear Filtering Algorithm Based on SVD

提出一种基于奇异值分解的无导数卡尔曼非线性滤波新算法,对UKF算法进行改进。该算法利用奇异值分解作为工具,将原算法中的协方差矩阵进行奇异值分解,可以在一定程度上避免在递推过程中,由于计算误差和舍入误差而引起的协方差矩阵失去正定性,从而导致算法失效的问题。在不降低滤波精度,不增加算法复杂度的前提下,新算法具有很好的数值稳定性。实例仿真结果验证了本方法的有效性。

A derivative-free Kalman filter method based on the singular value decomposition （SVD） was proposed to improve numerical stability of unscented Kalmanfilter （UKF） algorithm. This method based on UKF framework used SVD technique to decompose the covariance matrix in the original method. The new method succeeds in avoiding the invalidation caused by errors during computation. It has excellent numerical stability without filtering precision degradation and computation complexity increase. A typical numerical example demonstrates the performance of the method. Simulation results demonstrate the validity of the proposed approach further.