Automatic estimation of multiple target positions and velocities using passive TDOA measurements of transients

This paper considers the problem of the estimation of the motion parameters of multiple targets moving linearly in a three-dimensional (3-D) observation area contaminated by flutter. The measurements are limited to time differences of arrival (TDOAs) of short-duration acoustic emissions, or transients, generated by the targets. This problem can arise in situations where the level of continuous broadband target-related noise is very low. Owing to the fact that transient emissions are nonstationary and can have low signal-to-noise ratio (SNR), the corresponding TDOA measurement errors are usually non-Gaussian. Therefore, Gaussian mixture distributions are used to appropriately model these errors. An iterative maximum-likelihood optimization technique based on a modified deterministic annealing expectation-maximization (MDAEM) algorithm is applied to this problem. In each iteration, the algorithm uses a nonlinear least-squares (LS) technique in computing the motion parameters for each target. It generalizes the variance deflation method previously used for the initialization of target tracking algorithms and increases the possibility of attaining a globally optimal solution for random initial conditions. Simulation results are presented for several different numbers of targets, clutter densities, and probabilities of gross error of the target related measurements and are found to be comparable to the estimates obtained when the measurement-to-target assignments are exactly known.