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NonGaussian impulsive noises distort the source signal and cause problems for direction of arrival (DOA) estimation of an acoustic source. In this paper, a Bayesian framework and its particle filtering (PF) implementation for DOA tracking in the presence of complex symmetric alpha-stable noise process are developed. A constant velocity model is employed to model the source dynamics, and spatial spectra are exploited to formulate a pseudo likelihood of particles. Since the second-order statistics of alpha-stable processes do not exist, the fractional lower order moment matrix of the received data is used to replace the covariance matrix in calculating the spatial spectra. The noise usually spreads and distorts the mainlobe of the likelihood function and the particles cannot be weighted accurately. Hence, the likelihood function is exponentially weighted to emphasize the particles in a high likelihood area and thus enhance the resampling efficiency. The performance of the proposed tracking algorithm is extensively studied under simulated alpha-stable noise environments. The results show that the proposed algorithm significantly outperforms the existing PF tracking approach and the traditional localization approaches in DOA estimation.