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This paper addresses the application of sequential importance sampling (SIS) schemes to tracking directions of arrival (DOAs) of an unknown number of sources, using a passive array of sensors. This proposed technique has significant advantages in this application, including the ability to detect a changing number of signals at arbitrary times throughout the observation period and that the requirement for quasistationarity over a limited interval may be relaxed. We propose the use of a reversible jump Monte Carlo Markov chain (RJMCMC) step to enhance the statistical diversity of the particles. This step also enables us to introduce two novel moves that significantly enhance the performance of the algorithm when the DOA tracks cross. The superior performance of the method is demonstrated by examples of application of the particle filter to sequential tracking of the DOAs of an unknown and nonstationary number of sources and to a scenario where the targets cross. Our results are compared with the PASTd method.