We present a fully distributed estimation method to estimate an unknown parameter matrix for autoregressive-moving average with exogenous input (ARMAX) models over directed sensor networks, based on the extended least squares (ELS) algorithm and diffusion strategies. Each sensor in the network is only allowed to communicate with its neighbors in the proposed diffusion-based ELS algorithm in order to make communication over the network possible and to increase the robustness, scalability, and privacy of the system. Without resorting to independence, stationarity, or persistent excitation (PE) conditions for the regressors and the Gaussian property for the system noises, the convergence of the proposed distributed ELS algorithm is established over directed networks in this paper. The cooperative decaying excitation condition for the convergence results also shows that even if any individual sensor cannot estimate the unknown parameter matrix accurately by using the traditional non-cooperative ELS algorithm, the whole network can still fulfill the estimation task by using the distributed ELS algorithm, which is called the cooperative property of the distributed algorithms. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Publication:

AUTOMATICA

http://dx.doi.org/10.1016/j.automatica.2026.112914

Author:

Siyu Xie

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China

E-mail addresses: syxie@uestc.edu.cn

Rongjiang Li

State Key Laboratory of Mathematica Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

E-mail addresses: lirongjiang@amss.ac.cn

Die Gan

College of Artificial Intelligence, Nankai University, Tianjin 300350, China

The State Key Laboratory of Autonomous Intelligent Unmanned Systems, Beijing, China

Corresponding author at: College of Artificial Intelligence, Nankai University, Tianjin 300350, China

E-mail addresses: gandie@amss.ac.cn