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Distributed Estimation with Quantized Measurements and Communication over Markovian Switching Topologies

Ying Wang, Jian Guo, Yanlong Zhao, Ji-feng Zhang

TL;DR

This work tackles distributed parameter estimation in stochastic dynamic systems where sensors observe quantized measurements and communicate over quantized, Markov-switching directed topologies. It introduces a persistent-excitation compliant linear compression encoding and an estimation-fusion type quantized distributed identification algorithm, and analyzes their mean-square convergence and rate under a cooperative excitation condition and a union topology containing a spanning tree. Key contributions include a two-Lyapunov framework for coupled estimation errors, convergence-rate results tied to step-size sequences, and an analysis of how stochastic communication noise and switching rates affect performance, all validated via a numerical example showing joint sensor benefits. The proposed EFTQDI approach reduces communication and measurement precision requirements, enabling energy-efficient distributed estimation in wireless sensor networks.

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.

Distributed Estimation with Quantized Measurements and Communication over Markovian Switching Topologies

TL;DR

This work tackles distributed parameter estimation in stochastic dynamic systems where sensors observe quantized measurements and communicate over quantized, Markov-switching directed topologies. It introduces a persistent-excitation compliant linear compression encoding and an estimation-fusion type quantized distributed identification algorithm, and analyzes their mean-square convergence and rate under a cooperative excitation condition and a union topology containing a spanning tree. Key contributions include a two-Lyapunov framework for coupled estimation errors, convergence-rate results tied to step-size sequences, and an analysis of how stochastic communication noise and switching rates affect performance, all validated via a numerical example showing joint sensor benefits. The proposed EFTQDI approach reduces communication and measurement precision requirements, enabling energy-efficient distributed estimation in wireless sensor networks.

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.

Paper Structure

This paper contains 19 sections, 12 theorems, 62 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Motivations
  3. Related literature
  4. Main contribution
  5. Problem formulation
  6. Graph Preliminaries
  7. System Description
  8. Assumptions
  9. Algorithm Design
  10. Main results
  11. Notation
  12. Convergence properties
  13. Proofs of the main results
  14. Proof of Lemma \ref{['lemmaUk']}
  15. Proof of Lemma \ref{['lemmaV_k']}
  16. ...and 4 more sections

Key Result

Lemma 4.1

If Assumptions AG, AP-ADD hold, then the Lyapunov function $U_k$ for fusion estimation error satisfies for all $\alpha_1,\alpha_2 \in(0,\infty)$, where $\bar{N}=\max_{i=1,\ldots,m}N_{i}$ is the biggest size of the neighbor set in the union topology $\mathcal{G}_{\mathcal{C}}$, $\lambda_m\triangleq\max_{u=1,\ldots,s}\|\mathcal{L}^{(u)}\|$, $c_{h}\triangleq\sup_{|p-q|<h}\frac{b_{p}}{b_{q}}$, $\unde

Figures (7)

  • Figure 1: Switching communication topology
  • Figure 2: Convergence of the two estimates with $b_{k}=\frac{1}{k}$.
  • Figure 3: Convergence rate of the two estimates with $b_{k}=\frac{1}{k}$.
  • Figure 4: The comparison between the EFTQDI algorithm and non-cooperative algorithm under $b_{k}=\frac{1}{k}$.
  • Figure 5: Convergence of the two estimates with $b_{k}=\frac{1}{k^{4/5}}$.
  • ...and 2 more figures

Theorems & Definitions (26)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Remark 3.1
  • Remark 3.2
  • Remark 3.3
  • Remark 3.4
  • Lemma 4.1
  • Remark 4.1
  • ...and 16 more