An EM algorithm for target tracking with an unknown correlation coefficient of measurement noise

Abstract

In practical applications, the range rate used in a target tracking algorithm will further increase the strong nonlinearity between the measurement and the state, and the unknown correlation coefficient of measurement noise between the range and the range rate will cause suboptimal gain of the filter, which will seriously affect the performance of the filter. In this paper, an expectation maximization (EM)-based sequential modified unbiased converted measurement Kalman filter is proposed for target tracking with an unknown correlation coefficient of measurement noise between the range and the range rate. Firstly, a pseudo measurement is constructed by multiplying the range and the range rate to reduce the strong nonlinearity. The mean and covariance of converted errors are subsequently derived using modified unbiased converted measurement (MUCM) to weaken the error caused by the linearization of the measurement equation, which will effectively improve the dynamic accuracy of target tracking. Then, the converted errors of the position and the pseudo measurement are decorrelated by Cholesky factorization to facilitate the subsequent identification of the correlation coefficient, and the posterior probability distribution of the state is obtained using sequential filtering within the Bayesian framework. Finally, the EM is introduced in the updating procedure of the pseudo measurement to estimate both the target state and the correlation coefficient. The target tracking scenario with an unknown correlation coefficient is built to demonstrate the validity and feasibility of the proposed algorithm. Simultaneously, the results of the normalized error squared validate the consistency of the MUCM.