基于奇异值分解的Unscented粒子滤波及其应用研究

摘要

Aiming at the problems in particle filter that the importance density function is difficult to select and the system state covariance matrix may appear negative definiteness, this paper puts forward a new kind of Singular Value Decomposition Unscented Particle Filter (SVDUPF) algorithm.The algorithm adopts adaptive factor to regulate the dynamic model error, uses the singular value decomposition to restrain the negative definiteness of the matrix, and uses the improved UKF algorithm to generate the importance density function, which can make up for the defects of the particle filter.The proposed algorithm is used in the single- variable, non-static state growth model for simulations.The results show that the proposed algorithm has a filtering precision obviously better than that of EKF and UPF algorithm, which can improve the calculating precision of the model.%针对粒子滤波存在重要性密度函数难以选取和系统状态协方差阵可能出现负定性的问题,提出一种新的奇异值分解Unscented粒子滤波 (SVDUPF)算法.该算法采用自适应因子调节动力学模型误差,通过奇异值分解抑制系统状态协方差矩阵的负定性,并以改进的UKF算法产生重要性密度函数,以弥补粒子滤波重要性密度函数难以选取的缺陷.将提出的算法应用到单变量非静态状态增长模型中并进行仿真验证,结果表明,提出算法的滤波精度明显优于EKF和UPF算法,能提高模型的解算精度.