扩展卡尔曼粒子滤波算法的一种修正方法

Novel Modified Method for Extension Kalman Particle Filter

针对扩展卡尔曼粒子滤波(EKF-PF)算法滤波精度较低的缺点,提出对其建议分布进行高阶修正的新算法.该算法针对非线性系统方程,基于二阶泰勒级数展开,利用高阶项对一阶扩展卡尔曼滤波(EKF)的状态估计向量及协方差阵做出适当修正,同时考虑到协方差阵计算中存在矩阵相减运算、计算误差以及参数不匹配等因素的影响,采用矩阵QR分解技术保证了协方差阵的正定性.新算法在一定程度上减小了局部线形化的截断误差,提高了建议分布的逼近程度.仿真实验表明,新算法在计算量增加不多的情况下,滤波精度有明显的提高.

In order to overcome the flaw that the extended Kalman particle filter （EKF-PF） has poorer filtering precision, an appropriate modified principle which adjusting the proposal distribution with second order extended terms is presented. Based on the Taylor series extension theory, the state estimation and it＇s covariance matrix of the first order extended Kalman filter（EKF） are modified using the second order Taylor series expansion terms derived from the nonlinear dynamic system, while taking account of the negative influence of the matrix subtraction operation of covariance matrix calculation, computation error and mismatching of parameters, etc. The two powerful linear algebra techniques, QR factorization and Cholesky factorization are employed to ensure the positive definite of the covariance matrix. Hence, the truncated error of the local linearization is reduced in certain degree and the approachability of proposal distribution is enhanced. Simulation results show that the filtering precision of the proposed algorithm is improved notablely with appropriately increasing computing load.