The optimal Bayesian filter for a single target is known to provide the best tracking performance in a cluttered environment. However, its main drawback is the increase of memory size and computation quantity with time. In this paper, the inevitable problem of the optimal Bayesian filter is resolved in a suboptimal fashion by using a receding horizon strategy. As a result, the problem of memory and computational requirements is diminished. As a priori information, the horizon initial state is estimated from the validated measurements on the receding horizon. Consequently, the suboptimal algorithm proposed allows the real time implementation.