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Quantized Distributed Estimation with Event-triggered Communication and Packet Loss

Ying Wang, Yanlong Zhao, Ji-Feng Zhang, Karl Henrik Johansson

TL;DR

This paper tackles distributed parameter estimation in wireless sensor networks where both measurements and communications are quantized and subject to packet loss. It proposes an event-triggered, one-bit encoding scheme with a Laplace-dithered triggering rule and a one-bit reconstruction method to cope with losses, achieving decaying transmission rates. The authors establish almost sure convergence and derive the convergence rate near $O\left(\sqrt{\frac{(\ln k)^{1+\tau}}{k^{1-\nu}}}\right)$ together with a decaying bit-rate of $O\left(\frac{1}{k^{\nu}}\right)$, and they reveal a trade-off between speed and communication. A numerical example with six sensors demonstrates the method's benefits over non-cooperative approaches. These results provide guidance for designing energy-efficient distributed estimation in WSNs under unreliable channels.

Abstract

This paper focuses on the problem of quantized distributed estimation with event-triggered communication and packet loss, aiming to reduce the number of transmitted bits. The main challenge lies in the inability to differentiate between an untriggered event and a packet loss occurrence. This paper proposes an event-triggered distributed estimation algorithm with quantized communication and quantized measurement, in which it introduces a one-bit information reconstruction method to deal with packet loss. The almost sure convergence and convergence rate of the proposed algorithm are established. Besides, it is demonstrated that the global average communication bit-rate decreases to zero over time. Moreover, the trade-off between communication rate and convergence rate is revealed, providing guidance for designing the communication rate required to achieve the algorithm's convergence rate. A numerical example is supplied to validate the findings.

Quantized Distributed Estimation with Event-triggered Communication and Packet Loss

TL;DR

This paper tackles distributed parameter estimation in wireless sensor networks where both measurements and communications are quantized and subject to packet loss. It proposes an event-triggered, one-bit encoding scheme with a Laplace-dithered triggering rule and a one-bit reconstruction method to cope with losses, achieving decaying transmission rates. The authors establish almost sure convergence and derive the convergence rate near together with a decaying bit-rate of , and they reveal a trade-off between speed and communication. A numerical example with six sensors demonstrates the method's benefits over non-cooperative approaches. These results provide guidance for designing energy-efficient distributed estimation in WSNs under unreliable channels.

Abstract

This paper focuses on the problem of quantized distributed estimation with event-triggered communication and packet loss, aiming to reduce the number of transmitted bits. The main challenge lies in the inability to differentiate between an untriggered event and a packet loss occurrence. This paper proposes an event-triggered distributed estimation algorithm with quantized communication and quantized measurement, in which it introduces a one-bit information reconstruction method to deal with packet loss. The almost sure convergence and convergence rate of the proposed algorithm are established. Besides, it is demonstrated that the global average communication bit-rate decreases to zero over time. Moreover, the trade-off between communication rate and convergence rate is revealed, providing guidance for designing the communication rate required to achieve the algorithm's convergence rate. A numerical example is supplied to validate the findings.

Paper Structure

This paper contains 9 sections, 2 theorems, 25 equations, 4 figures.

Table of Contents

  1. INTRODUCTION
  2. Problem formulation
  3. Graph theory
  4. System description
  5. Assumptions
  6. Algorithm Design
  7. Main results
  8. Numerical example
  9. CONCLUSIONS

Key Result

Theorem 1

If Assumptions AG-ADP hold, then the proposed algorithm is almost surely convergent. Moreover, for any $\tau>0$, its almost sure convergence rate is if $2\sigma\geq 1-\nu$, where $\tilde{\theta}_{k,i}=\hat{\theta}_{k,i}-\theta$ is the estimation error, $\sigma=\frac{\alpha\beta h\lambda_2\underline{f}\underline{g}\delta_{\psi}^2 \delta_{\phi}^2}{2\beta\bar{\phi}^2\underline{f} +\alpha \underline{

Figures (4)

  • Figure 1: Communication graph.
  • Figure 2: Convergence of Algorithm \ref{['Algorithm']} with $\nu=0.1$.
  • Figure 3: Comparison between Algorithm \ref{['Algorithm']} and non-cooperative algorithm.
  • Figure 4: Convergence rates and average communication bitrates with different $\nu=0,0.1,0.2,0.4,0.6$.

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 3