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The robust tracking of abrupt motion is a challenging task in computer vision due to its large motion uncertainty. While various particle filters and conventional Markov-chain Monte Carlo (MCMC) methods have been proposed for visual tracking, these methods often suffer from the well-known local-trap problem or from poor convergence rate. In this paper, we propose a novel sampling-based tracking scheme for the abrupt motion problem in the Bayesian filtering framework. To effectively handle the local-trap problem, we first introduce the stochastic approximation Monte Carlo (SAMC) sampling method into the Bayesian filter tracking framework, in which the filtering distribution is adaptively estimated as the sampling proceeds, and thus, a good approximation to the target distribution is achieved. In addition, we propose a new MCMC sampler with intensive adaptation to further improve the sampling efficiency, which combines a density-grid-based predictive model with the SAMC sampling, to give a proposal adaptation scheme. The proposed method is effective and computationally efficient in addressing the abrupt motion problem. We compare our approach with several alternative tracking algorithms, and extensive experimental results are presented to demonstrate the effectiveness and the efficiency of the proposed method in dealing with various types of abrupt motions.