平方根UKF算法中奇异值问题的研究

Research on singular value problem in square root UKF algorithm

针对平方根无迹卡尔曼滤波(UKF)算法在求增益时对量测预测协方差矩阵求逆存在易出现奇异值而使滤波失效的问题,根据平方根UKF算法的步骤,以自由落体目标为例,分析了用平方根UKF算法跟踪目标时奇异值产生的原因,并提出在状态估计协方差矩阵更新中引入多重次可靠性因子.最后对各可靠性因子的取值进行了仿真分析.仿真结果表明,本文方法不仅能对平方根UKF中的奇异值问题有抑制作用,增强了算法的可靠性,还能在一定程度提高算法的滤波性能.

To solve the problem that the square root unscented Kalman filter（UKF） algorithm in solving the gain of the measurement prediction covariance matrix inversion is easy to present the singular value which leads to filter failure, and according to the steps of the square root UKF algorithm, this paper uses the free-fall target as an example to analyze the causes of the singular value in using the square root UKF algorithm to track targets, and proposes that multiple reliability factors is introduced into state estimation covariance matrix updating. Finally the paper simulates and analyzes the value of each reliability factor. The results show that the proposed method can not only have the inhibitory effect on the singular value problem of square root in UKF, enhancing the reliability of the algorithm, but also improve the filtering performance of the algorithm to a certain degree.