Tracking maneuvering targets with a soft bound on the number of maneuvers

We revisit the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. In a previous paper we have addressed a version of the problem where we have assumed the existence of a deterministic, known hard bound on the number of mode transitions. In addition, it was assumed that the system can possess only two modes, e.g., the maneuvering and non-maneuvering regimes of a tracked target. In the present paper we relax both assumptions: we assume a soft, stochastic bound on the number of mode transitions, and altogether remove the restriction on the number of modes of the system (thus, e.g., the target can have multiple different maneuvering modes, in addition to the non-maneuvering one). Similarly to the case where the number of transition was deterministically hard-bounded, the existence of the bound renders the mode switching mechanism non-Markov. Thus, the two formulations address similar, though not identical, problems, that cannot be solved by direct application of standard algorithms for hybrid systems. The novel solution approach is based on transforming the non-Markovian mode switching mechanism to an equivalent Markovian one, at the price of augmenting the mode definition. A standard interacting multiple model (IMM) filter is then applied to the transformed problem in a straightforward manner. The performance of the new method is demonstrated via a simulation study comprising three examples, in which the new method is compared with 1) the filter for hard-bounded mode transitions, and 2) a standard IMM filter directly applied to the original problem. The study shows that even when working outside its operating envelope, the new filter closely approximates the best filter for the scenario.