A suboptimal algorithm for the optimal Bayesian filter using receding horizon FIR filter

The optimal Bayesian filter (OBF) for a single target is known to provide best tracking performance in a cluttered environment. However, the problem of its memory and computation requirements increases with time. In this paper, the inevitable problem of the OBF of Singer et al. (1974) is resolved by using a suboptimal algorithm. The suboptimal algorithm is derived by using only measurements in the receding horizon interval. With the assumptions that the system and observation transition matrices are observable and the horizon interval length is bounded by the dimension of the system, the unbiased property is satisfied