Abstract: The performance of the Unscented Kalman filter would be degraded in accuracy or divergences when the system states are uncertain and strong nonlinear, an improved strong tracking SVD-UKF algorithm is proposed. The iteration of covariance matrix in UKF is improved by Singular Value Decomposition（SVD） of covariance matrix, ensured the stability of the iteration of covariance matrix and restrained the negative definiteness of system state covariance matrix. Multiple fading factors matrices are introduced in improved SVD-UKF, in order to automatic improve system state covariance matrix based on Strong Tracking Filter（STF） theory framework, and realize the strong tracking of the real state while system status are mutating. The proposed strong tracking SVD-UKF is applied to the BDS/INS integrated system for simulation, simulation results show the effectiveness of the presented algorithm.

Key words: Unscented Kalman Filter（UKF）, Singular Value Decomposition（SVD）, strong tracking, fading factor, integrated navigation

摘要： 针对无迹卡尔曼滤波（Unscented Kalman Filter，UKF）在系统强非线性或状态模型不精确的情况下，存在滤波精度降低甚至发散的问题，提出一种改进的强跟踪SVD-UKF算法。该算法采用奇异值分解（Singular Value Decomposition，SVD）的方法改进UKF中状态协方差矩阵的迭代，保证协方差矩阵的非负定性及迭代的稳定性；算法基于强跟踪滤波（Strong Tracking filter，STF）理论框架，对改进的SVD-UKF引入多重渐消因子自适应调整状态协方差矩阵，在系统状态发生突变的情况下，实现系统真实状态的强跟踪。将该算法在BDS/INS组合导航中仿真验证，结果表明了该算法的有效性。

关键词: 无迹卡尔曼滤波（UKF）, 奇异值分解（SVD）, 强跟踪, 渐消因子, 组合导航