A unified method for measurement and tracking of contacts from an array of sensors

A multiple target track estimation method that operates directly from array data is presented. The maximum a-posteriori (MAP) estimator for contact states is derived for temporally uncorrelated signals and uncorrelated contact tracks, where the number of contacts is assumed known. This estimator is an iterative algorithm employing a nonlinear programming (NLP) penalty method in conjunction with an expectation–maximization (EM) algorithm. The NLP technique is used to find the MAP track estimate based on the synthetic signal estimates produced by the EM algorithm. This method eliminates the data association step of traditional multitarget tracking approaches by conditioning the measurement process on individual target state distributions. It results in a process similar to the EM algorithm for direction finding, with an additional penalty term imposed by the track distributions. The algorithm is derived as a batch method. An extension to support sequential tracking is also developed. Simulation results for a relevant submarine towed array scenario are presented and discussed.