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Systems with finite communication bandwidth constraints. I: State estimation problems. (English) Zbl 0952.93125
Summary: The authors investigate a state estimation problem involving finite communication capability constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, there is a constraint that the observations must be coded and transmitted over a digital communication channel with finite capacity. 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 average estimation error is derived for a large class of random variables. Convergence properties of some coder-estimator algorithms are analyzed. Various conditions connecting the communication data rate with the rate of change of the underlying dynamics are established for the existence of stable asymptotically convergent coder-estimator schemes.

MSC:
93E10Estimation and detection in stochastic control
94A45Prefix, length-variable, comma-free codes (communication theory)