Distributed Estimation with Quantized Measurements and Communication over Markovian Switching Topologies

TL;DR

This paper develops a distributed estimation algorithm for stochastic systems with quantized measurements over Markovian switching networks, ensuring convergence and analyzing the effects of communication uncertainties.

Contribution

It introduces a novel encoding and estimation method that guarantees convergence in quantized, switching topologies with communication noise.

Findings

Mean-square convergence under specified conditions

Convergence rate matching step size order

Impact of communication noise and switching rate analyzed

Abstract

This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original signal from quantized communication signal, a persistent excitation-compliant linear compression encoding method is introduced. Leveraging this encoding, this paper proposes an estimation-fusion type quantized distributed identification algorithm under a stochastic approximation framework. The algorithm operates in two phases: first, it estimates neighboring estimates using quantized communication information, then it creates a fusion estimate by combining these estimates through a consensus-based distributed stochastic approximation approach. To tackle the difficulty caused by the coupling between these two estimates, two combined Lyapunov functions are constructed to analyze the convergence performance. Specifically, the mean-square convergence of the estimates is established under a conditional expectation-type cooperative excitation condition and the union topology containing a spanning tree. Besides, the convergence rate is derived to match the step size's order under suitable step-size coefficients. Furthermore, the impact of communication uncertainties including stochastic communication noise and Markov-switching rate is analyzed on the convergence rate. A numerical example illustrates the theoretical findings and highlights the joint effect of sensors under quantized communication.