A finite-dimensional coder-estimator for rate-constrained state estimation

Abstract

This paper considers the problem of estimating the state of a linear system via a digital link with a finite bit-rate R. Classical estimation theory does not apply here since the estimator only observes the transmitted sequence of finite-valued symbols. A new coder-estimator for linear systems with process and measurement noise is given. Provided that a certain inequality linking the bit-rate to the dynamical parameters is satisfied, and under very mild assumptions on the noise distributions, the expected absolute estimation error remains of the same order as in the classical situation with infinite bit-rate. In particular, if the classical estimation error approaches zero, then the finite b..