The problem of localizing an unknown number of stationary transient emitters using passive sensors in the presence of missed detections and false alarms is investigated. Each measurement is based on one detection by a passive sensor and consists of a time of arrival and a bearing. It is assumed that measurements within a short time interval have to be associated before estimation. Both a Bernoulli measurement model and a Poisson measurement model are considered for each target. These two measurement models lead to two different proposed problem formulations: one is an S-dimensional (S-D) assignment problem and the other is a cardinality selection problem. The former can be solved by the Lagrangian relaxation algorithm reliably when the number of sensors is small. The sequential m-best 2-D (SEQ[m(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 be-comes large. Simulation results show that the SEQ[m(2-D)] assignment algorithm is efficient for real-time processing with reliable associations and estimates. In the cardinality selection formulation, a list of measurements is modeled as either realizations of a random variable with a uniform–Gaussian mixture (UGM) density or a Poisson point process (PPP). Because of an efficient way of incorporating false alarm rate, the UGM formulation is shown to be a useful alternative to the PPP   formulation. Simulation studies show that both UGM and PPP formulations, which are based on the expectation–maximization algorithm, require the right initial estimates to yield reliable localization results.