This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the estimation of ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay.
In this paper, we propose a novel automated framework which recovers orders, delay, output noise distribution along with parameter estimates. The primary tool utilized in the proposed framework is generalized spectral decomposition. The proposed algorithm systematically estimates all the parameters in two steps. The first step utilizes estimates of the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the efficacy of the proposed method and are observed to deliver consistent estimates even at low signal to noise ratio (SNR).
CKKS Cryptosystem-Based Secure Parameter Identification for Multi-Participant ARX Systems
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Zhongyuan University of Technology（中原工学院）；University of Science and Technology Beijing（北京科技大学）
Data-Driven Tensor Decomposition Identification of Homogeneous Polynomial Dynamical Systems
School of Data Science and Society, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校数据科学与社会学院）；Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard（麻省理工学院和哈佛大学博德研究所埃里克和温迪·施密特中心）；Department of Mathematics, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校数学系）；Department of Biostatistics, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校生物统计学系）
Identification of Successive "Unobservable" Cyber Data Attacks in Power Systems Through Matrix Decomposition
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Exponent；New York Power Authority（纽约电力局）；New York State Energy Research and Development Authority（纽约州能源研究与开发局）
Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods
Department of Automation；Systems Engineering, Federal University of Santa Catarina, Florianópolis, 88040-900, Santa Catarina, Brazil；Harold Vance Department of Petroleum Engineering, Texas A\&M University, College Station, 77843-3116, Texas, USA
