State Estimation for Hybrid Systems: Applications to Aircraft Tracking ∗

The problem of estimating the discrete and continuous state of a stochastic lin-ear hybrid system, given only the continuous system output data, is studied. Well established techniques for hybrid estimation, known as the Multiple Model Adaptive Estimation algorithm, and the Interacting Multiple Model algorithm, are first reviewed. Conditions that must be satisfied in order to guarantee the convergence of these hybrid estimation algorithms are then presented. These conditions also provide a means to predict, as a function of the system parameters, which transitions in a hybrid system are relatively easy to detect. A new variant of hybrid estimation algorithms, called the Residual-Mean Interacting Multiple Model (RMIMM) algorithm, is then proposed and analyzed. The performance of RMIMM is demonstrated through multi-modal aircraft trajectory tracking examples.