State estimation via a capacity-limited communication channel

This paper considers the problem of estimating the state of a remote system via a digital communication channel with finite capacity. Classical estimation theory does not apply since the estimator only observes the transmitted sequence of finite-valued symbols. Assuming no process or observation noise, a coding and estimation scheme is presented that generates an asymptotic mean-square error of zero, provided that the data rate and system parameters satisfy a certain condition. This scheme works for D-dimensional, time-varying, nonlinear systems that satisfy a Lipschitz-type condition, under very mild restrictions on the initial condition distribution. In the one-dimensional, linear time invariant case, the convergence condition reduces to an inequality that improves on previous results.