Filtering Over Non-Gaussian Channels: The Role of Anytime Capacity

Filtering over noisy channels is of interest in many network applications, in which a node infers a time-varying state by using messages received from another node that can observe such a state. This letter explores filtering with general models for state disturbance and communication channels by deriving a sufficient condition for which the estimation error is bounded. Specifically, the sufficient condition is expressed in terms of anytime capacity, a notion that characterizes the maximum sequential communication rate. The joint design of encoder and estimator with bounded estimation error is also presented.