Structural results for finite bit-rate state estimation

Considers the problem of estimating the state of a dynamic system from measurements obtained via a digital link with finite bit-rate R. It is shown that, under a quadratic cost, the problem reduces to coding and estimating the sequence of expected states conditioned on past measurements. The existence of deterministic, optimal coder-estimators for Markovian processes in R^D is then established and their structure derived. These results are then combined to prove that the optimal coder for a Gauss-Markov system consists of a Kalman filter followed by a stage which encodes the latest Kalman estimate according to the symbols previously transmitted