Multiple target tracking using maximum likelihood principle

Proposes a method (tracking algorithm (TAL)) based on the maximum likelihood (ML) principle for multiple target tracking in near-field using outputs from a large uniform linear array of passive sensors. The targets are assumed to be narrowband signals and modeled as sample functions of a Gaussian stochastic process. The phase delays of these signals are expressed as functions of both range and bearing angle (“track parameters”) of respective targets. A new simplified likelihood function for ML estimation of these parameters is derived from a second-order approximation on the inverse of the data covariance matrix. Maximization of this likelihood function does not involve inversion of the M×M data covariance matrix, where M denotes number of sensors in the array. Instead, inversion of only a D×D matrix is required, where D denotes number of targets. In practice, D≪M and, hence, TAL is computationally efficient. Tracking is achieved by estimating track parameters at regular time intervals wherein targets move to new positions in the neighborhood of their previous positions. TAL preserves ordering of track parameter estimates of the D targets over different time intervals. Performance results of TAL are presented, and it is also compared with methods by Sword and by Swindlehurst and Kailath (1988). Almost exact asymptotic expressions for the Cramer-Rao bound (CRB) on the variance of angle and range estimates are derived, and their utility is discussed