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In the context of control and estimation under information constraints,restoration entropy measures the minimal required data rate above which thestate of a system can be estimated so that the estimation quality does notdegrade over time and, conversely, can be improved. The remote observer here isassumed to receive its data through a communication channel of finite bit-ratecapacity. In this paper, we provide a new characterization of the restorationentropy which does not require to compute any temporal limit, i.e., anasymptotic quantity. Our new formula is based on the idea of finding a specificRiemannian metric on the state space which makes the metric-dependent upperestimate of the restoration entropy as tight as one wishes.

Remote state estimation problem: towards the data-rate limit along the avenue of the second Lyapunov method