Mode-estimation for jump-linear systems with partial information

In this work the mode estimation problem for special classes of jump systems is investigated in discrete-time. Assuming a non-linear dynamics and full information for the continuous states, a mode estimator is developed based on the conditionally-linear approach, thus extending the scope of application of a previous work. This suboptimal filter is compared with the optimal algorithm (Wonham filter) on a simple numerical example via Monte-Carlo simulations, which confirm the asymptotic optimal behavior of the proposed filter in the case of Gaussian observation noises. A local convergence analysis for the equivalent continuous-time algorithm is proposed for the case of a static mode, which yields an intuitive criterion for observability. In a case of partial information on the continuous states of jump-linear systems, which can not be handled using Wonham filter, a finite dimensional mode estimator is developed in the framework of conditionally-linear filtering. As an numerical example, the problem of gyro failure detection from accurate spacecraft attitude measurements is considered and the filter performance are illustrated via extensive Monte-Carlo simulations.