The paper investigates the distributed estimation problem under low data rate communications. Based on the signal-comparison (SC) consensus protocol under binary-valued communications, a new consensus+innovations type distributed estimation algorithm is proposed. First, the high-dimensional estimates are compressed into binary-valued messages by using a periodic compressive strategy, dithering noises, and a sign function. Next, based on the dithering 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, and a polynomial almost sure convergence rate is also obtained. For the communication cost, the local and global average data rates 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 a lower communication cost can be achieved by increasing event-triggered coefficients. A simulation example is given to demonstrate the theoretical results.

Publication:

SIAM JOURNAL ON CONTROL AND OPTIMIZATION

http://dx.doi.org/10.1137/24M1631328

Author:

JIEMING KE

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 People's Republic of China,

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China

kejieming@amss.ac.cn

XIAODONG LU

School of Automation and Electrical Engineering University of Science and Technology Beijing, Beijing 100083, People's Republic of China, and Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, People's Republic of China

lxd1025744209@163.com

YANLONG ZHAO

Corresponding author

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100149,People's Republic of China

ylzhao@amss.ac.cn

JI-FENG ZHANG

School of Automation and Electrical Engineering, Zhongyuan University of Technology, Zhengzhou 450007, Henan Province, People's Republic of China

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

jif@iss.ac.cn