Novel Modified Method for Extension Kalman
Particle Filter
Lei Ming, Han Chongzhao, Xiao Mei
(School of Electronics and Information Engineering, Xi'an Jiaotong University, Xi'an
710049, China)
Abstract: 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.
Keywords: particle filter; extended Kalman filter; Taylor series extension