State estimation under bit-rate constraints

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 the 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-estimator yields an expected absolute estimation error of the same order as in the classical situation with no data rate constraint. Hence if the classical estimation error approaches zero, then the rate-constrained error goes to at exactly the same speed.