Observability measure for stochastic systems

In this study, the mutual information between the state sequence and the measurements is proposed as an observability measure and this measure is analyzed in detail for linear time invariant discrete-time Gaussian systems. The following results are found as the two basic properties of the measure from the analyses; the unobservable states of the deterministic system have no effect on it. So the measure proposed here is an observability measure of observable states. Secondly, any observable part with no measurement uncertainty makes the measure infinite.