Assignment and EM approaches for passive localization of multiple transient emitters

This paper investigates the problem of localizing an unknown number of transient emitters using a network of passive sensors measuring angles of arrival in the presence of missed detections and false alarms. It is assumed that measurements within a certain time window of interest have to be associated before they can be fused to estimate the emitter locations. Two measurement models either that any target can generate at most one measurement per sensor or that any target can generate several measurements per sensor are possible within this time window. These two measurement models lead to two different problem formulations: one is an S-D assignment problem and the other is a cardinality selection problem. The S-D assignment problem can be solved by the Lagrangian relaxation algorithm efficiently with a high degree of accuracy when a small number of sensors are used. The sequential m-best 2-D assignment algorithm, which is resistant to the ghosting problem due to the estimation of the emitter signal's emission time, is developed to solve the problem when the number of sensors becomes large. Simulation results show that the sequential m-best 2-D assignment algorithm is suitable for real time processing with reliable associations and estimates. The cardinality selection formulation models a list of measurements as a Poisson point process and is solved by applying the expectation-maximization (EM) algorithm and an information criterion. The convergence of the EM algorithm to the desired global maximum needs an initialization, which is close to the truth. Localization using passive sensors makes it difficult to obtain such an initial estimate. An assignment-based initialization approach is therefore presented. Simulation studies showed that the EM algorithm based on the assignment initialization is able to estimate the number of targets, target locations and directions with a high degree of accuracy.