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This paper considers the problem of tracking multiple acoustic sources using a single acoustic vector sensor (AVS). Firstly, a particle filtering (PF) approach is developed to track the direction of arrivals of fixed and known number of sources. Secondly, a more realistic tracking scenario which assumes that the number of acoustic sources is unknown and time-varying is considered. A random finite set (RFS) framework is employed to characterize the randomness of the state process, i.e., the dynamics of source motion and the number of active sources, as well as the measurement process. As deriving a closed-form solution for the multi-source probability density is difficult, a particle filtering approach is employed to arrive at a computationally tractable approximation of the RFS densities. The proposed RFS-PF algorithm is able to simultaneously detect and track multiple sources. Simulations under different tracking scenarios demonstrate the ability of the proposed approaches in tracking multiple acoustic sources.