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Tracking of moving objects, which means determining the positions of the humans in the surrounding, is one of the goals in the field of mobile robots that operate in populated environments. This work is concerned with the special problem of tracking expanded objects in such vicinities. As a solution, a Viterbi based algorithm, which can be useful for real-time systems, is presented. Thus, a maximum-a-posteriori (MAP) filtering technique is applied to perform the tracking process. The mathematical background of the algorithm is proposed. The algorithm is tested and evaluated on real and simulated data. The method uses the robots' sensors in form of a laser range finder and a motion and observation model of the objects being tracked.