Signal-Comparison-Based Distributed Estimation Under Decaying Average Data Rate Communications

TL;DR

This paper introduces a low bit rate distributed estimation algorithm using a signal-comparison consensus protocol with binary communications, achieving convergence with minimal communication and a controllable trade-off between speed and cost.

Contribution

It proposes a novel SC-based distributed estimation algorithm that combines binary message compression, stochastic event-triggering, and a modified consensus protocol for efficient low-bit communication.

Findings

Estimates converge to true value almost surely and in mean square.

Communication bit rates decay polynomially to zero.

Trade-off between convergence rate and communication cost is established.

Abstract

The paper investigates the distributed estimation problem under low bit rate communications. Based on the signal-comparison (SC) consensus protocol under binary-valued communications, a new consensus+innovations type distributed estimation algorithm is proposed. Firstly, the high-dimensional estimates are compressed into binary-valued messages by using a periodic compressive strategy, dithered noises and a sign function. Next, based on the dithered noises and expanding triggering thresholds, a new stochastic event-triggered mechanism is proposed to reduce the communication frequency. Then, a modified SC consensus protocol is applied to fuse the neighborhood information. Finally, a stochastic approximation estimation algorithm is used to process innovations. The proposed SC-based algorithm has the advantages of high effectiveness and low communication cost. For the effectiveness, the estimates of the SC-based algorithm converge to the true value in the almost sure and mean square sense. A polynomial almost sure convergence rate is also obtained. For the communication cost, the local and global average bit rates for communications decay to zero at a polynomial rate. The trade-off between the convergence rate and the communication cost is established through event-triggered coefficients. A better convergence rate can be achieved by decreasing event-triggered coefficients, while lower communication cost can be achieved by increasing event-triggered coefficients. A simulation example is given to demonstrate the theoretical results.