In this paper, we derive a data association algorithm for object tracking in a maximum a posteriori framework: the output of the algorithm is the sequence of measurement-totarget associations with maximum a posteriori probability. We model the object motion as a Markov process, and solve this otherwise combinatorially complex problem efficiently by applying the Viterbi algorithm. A method for combining forward and backward tracking results is also developed, to recover from tracking errors caused by abrupt motion changes of the object. The proposed algorithm is applied to broadcast tennis video to track a tennis ball. Experiments show that its performance is comparable to that of a computationally more expensive particle-filter-based algorithm.