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

We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. The system is assumed to follow either a nominal or an anomalous model, where the nominal model may stand for, e.g., the non-maneuvering motion regime of a target or the fault-free operation mode of a sensor, and the anomalous model may stand for, e.g., the abrupt evasive maneuvers of a target or the faulty operation of a sensor. As is well known, the optimal algorithm requires implementation of an exponentially growing number of primitive Kalman filters. On the other hand, the system's switching dynamics is not Markov because of the a priori bounded number of model switches, thus ruling out the use of popular estimation schemes such as the interacting multiple model (IMM) and generalized pseudo-Bayesian (GPB) filters. We derive an efficient scheme that uses a number of primitive Kalman filters that is linear in the number of possible maneuvers. The scheme resembles the IMM algorithm in that it uses interaction between some of the primitive filters before every estimation cycle, thus reducing the number of such filters. The algorithm's performance is evaluated via a simulation study, and shown to outperform the state-of-the-art IMM filter in a typical example.