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 di?erent maneuvering modes, in addition to the non-maneuvering one). While admitting an unlimited number of mode transitions, the soft bound renders that number ˉnite with probability 1. In addition, 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 algorithms devised for hybrid systems having Markov mode switching mechanisms. The novel solution approach adopted herein is based on transforming the non-Markovian mode switching mechanism to an equivalent Markovian one, at the price of augmenting the mode deˉnition, and increasing the dimension of the state space involved. A standard interacting multiple model (IMM) ˉlter is then applied to the transformed (Markovian) 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 ˉlter for hard-bounded mode transitions, and 2) a standard IMM ˉlter directly applied to the original problem. The study shows that even when working outside its operating envelope (e.g., when the number of mode switches is hard-bounded, or when the mode transition mechanism is truly Markov), the new ˉlter closely approximates the best ˉlter for the scenario.
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