State estimation under bit-rate constraints

Abstract

This paper considers the problem of estimating the state of a dynamic system from measurements obtained via a digital link with finite data rate R. The structures of the optimal coder and estimator for Markovian systems are derived. In particular, it is shown that the optimal coder for a Gauss-Markov system consists of a Kalman filter, followed by a stage which encodes thc current Kalman estimate according to the symbols previously transmitted. A new suboptimal coder-estimator for linear systems is then constructed. Provided that a certain inequality linking the data rate to the dynamical parameters is satisfied, and under very mild assumptions on the noise distributions, this coder-estimato..