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Acoustic vector sensor (AVS) measures acoustic pressure as well as particle velocity, and therefore AVS signal contains 2-D (azimuth and elevation) DOA information of an acoustic source. Existing DOA estimation techniques assume that the source is static and extensively rely on the localization methods. In this paper, a particle filtering (PF) tracking approach is developed to estimate the 2-D DOA from signals collected by an AVS. A constant velocity model is employed to model the source dynamics and the likelihood function is derived based on a maximum likelihood estimation of the source amplitude and the noise variance. The posterior Cramér-Rao bound (PCRB) is also derived to provide a lower performance bound for AVS signal based tracking problem. Since PCRB incorporates the information from the source dynamics and measurement models, it is usually lower than traditional Cramér-Rao bound which only employs measurement model information. Experiments show that the proposed PF tracking algorithm significantly outperforms Capon beamforming based localization method and is much closer to the PCRB even in a challenging environment (e.g., SNR = -10 dB).