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The general problem of object tracking can be modeled as a Markov process and solved by computing probability distributions of the possible object states, followed by MAP estimation. This paper presents a new framework for the efficient estimation of the probability distribution of the states. In contrast to particle filters, where the possible states are numerous and random, we limit the possible states to a finite candidate set which is guaranteed with high probability to contain the true state of the object. After the problem is reduced to a finite-state Markov process (FSM), forward filtering is used to estimate the distribution of the object state. Moreover, the Viterbi algorithm can also be used to estimate the most likely state sequence. We test the new framework by both these methods and compare the tracking results. Experimental results show the effectiveness and efficacy of the proposed algorithm.