SYSTEMS WITH FINITE COMMUNICATION BANDWIDTH CONSTRAINTS .1. STATE ESTIMATION PROBLEMS

In this paper, we investigate a state estimation problem involving fin ite communication capacity constraints. Unlike classical estimation pr oblems where the observation is a continuous process corrupted by addi tive noises, there is a constraint that the observations must be coded and transmitted over a digital communication channel with finite capa city. This problem is formulated mathematically, and some convergence properties are defined, Moreover, the concept of a finitely recursive coder-estimator sequence is introduced, A new upper bound for the aver age estimation error is derived for a large class of random variables, Convergence properties of some coder-estimator algorithms are analyze d. Various conditions connecting the communication data rate with the rate of change of the underlying dynamics are established for the exis tence of stable and asymptotically convergent coder-estimator schemes.