Identification of errors-in-variables ARX models using modified dynamic iterative PCA |
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| Institution: | 1. Department of Computer Science, Indian Institute of Technology Madras, India;2. Department of Chemical Engineering, Indian Institute of Technology Madras, India;1. U.S. Pakistan Center for Advanced Studies in Energy (USPCASE), National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan;2. School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan;1. School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China;2. CASIC Research Institute of Intelligent Decision Engineering, Beijing, 100074, China;1. Electronic Information Engineering Key Laboratory of Electronic Information of State Ethnic Affairs Commission, College of Electrical Engineering, Southwest Minzu University, Chengdu, Sichuan, 610041, China;2. School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China;1. School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China;2. Institute of Complexity Science, Qingdao University, Qingdao 266071, China |
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| Abstract: | Identification of autoregressive models with exogenous input (ARX) is a classical problem in system identification. This article considers the errors-in-variables (EIV) ARX model identification problem, where input measurements are also corrupted with noise. The recently proposed Dynamic Iterative Principal Components Analysis (DIPCA) technique solves the EIV identification problem but is only applicable to white measurement errors. We propose a novel identification algorithm based on a modified DIPCA approach for identifying the EIV-ARX model for single-input, single-output (SISO) systems where the output measurements are corrupted with coloured noise consistent with the ARX model. Most of the existing methods assume important parameters like input-output orders, delay, or noise-variances to be known. This work’s novelty lies in the joint estimation of error variances, process order, delay, and model parameters. The central idea used to obtain all these parameters in a theoretically rigorous manner is based on transforming the lagged measurements using the appropriate error covariance matrix, which is obtained using estimated error variances and model parameters. Simulation studies on two systems are presented to demonstrate the efficacy of the proposed algorithm. |
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