Near-Optimal MAP Estimation for Markov Jump Linear Systems Using Relaxed Dynamic Programming

Computing the optimal joint maximum a posteriori probability (JMAP) estimate of the state and mode of a Markov jump linear system (MJLS) is known to be a computationally intractable problem. This letter provides a novel approximate method for such a problem that guarantees to be within a pre-specified bound of the optimal estimate. The proposed method builds upon relaxed dynamic programming. Through numerical examples, we show that this method can lead to better estimates with less computations than previous suboptimal methods proposed in the literature.