Observability criteria and estimator design for stochastic linear hybrid systems

A stochastic linear hybrid system is said to be observable if the hybrid state of the system can be uniquely determined from its output. In this paper, we derive conditions for the observability of stochastic linear hybrid systems by exploiting the information obtained from system noise characteristics. Having established the necessary criteria for observability, we study the effect of these conditions on estimator design, and also find bounds on the switching times of the system to achieve guaranteed estimator performance. We then apply these results to the estimation of a two-mode aircraft trajectory.