Data rate limits for the remote state estimation problem

In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which a system can be regularly observed. The observer here is assumed to receive its state information through a communication channel of a finite bit-rate capacity. In this paper, we provide a new characterization of restoration entropy which does not require to compute any temporal limit, i.e., an asymptotic quantity. Our new formula is based on the idea of finding an adapted Riemannian metric on the state space that allows to 'see' the decisive quantity that determines the restoration entropy - a certain type of Lyapunov exponent - in only one step of time.