Systems with finite communication bandwidth constraints. I. State estimation problems

TLDR

State estimation must be performed over a digital channel with finite capacity, unlike classical continuous observation models. The paper investigates and mathematically formulates a state estimation problem under finite communication capacity constraints, defining convergence properties. The authors introduce a finitely recursive coder‑estimator sequence to address the finite‑bandwidth estimation problem. They derive an upper bound on average estimation error, analyze convergence of coder‑estimator algorithms, and establish conditions linking communication data rate to system dynamics for stable, asymptotically convergent schemes.

Abstract

In this paper, we investigate a state estimation problem involving finite communication capacity 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 and asymptotically convergent coder-estimator schemes.