State estimation in hybrid systems with a bounded number of mode transitions

Abstract—We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode transitions in the presence of spurious, or cluttered measurements. The system is assumed to follow, at each time, one of a predefined dynamical models. Two types of uncertainties make the problem challenging. The first is the data uncertainty that follows from the fact that the true measurement of the state is indistinguishable from the clutter measurements that do not carry useful information. The second problem is the intrinsic model uncertainty. Both reasons prevent the computation of the optimal estimator. On the other hand, the mode transitions are not Markov, thus ruling out the direct use of standard approaches for state estimation in cluttered environment. We derive an efficient estimation scheme for systems in cluttered environments capable of performing a bounded number of mode transitions. At the heart of this scheme is a transformation of the non-Markov model set to an equivalent Markovian one and a subsequent utilization of standard approaches matched to the new mode set. The algorithm’s performance is evaluated via a simulation study, and shown to outperform the standard popular approaches. I