Recursive Identification of Errors-in-Variables Systems Based on the Correlation Analysis
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Recursive Identification of Errors-in-Variables Systems Based on the Correlation Analysis Shujun Fan1 · Feng Ding1,2
· Tasawar Hayat3
Received: 22 August 2019 / Revised: 25 April 2020 / Accepted: 28 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper considers a single-input single-output linear dynamic system, whose input and output are corrupted by Gaussian white measurement noises with zero means and unknown variances; the parameter estimation of such a system is a typical errorsin-variables (EIV) system identification problem. This paper proposes the correlation function-based two-step identification methods for the EIV systems. In order to obtain the unbiased parameter estimates of the EIV system, we derive the correlation function equation by using the correlation analysis method and adopt the least squares method and the instrumental variable method to recursively compute the parameter estimates of the model, resulting in the unbiased parameter estimates of the EIV systems. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. Keywords Parameter estimation · EIV system · Correlation analysis · Least squares · Instrumental variable
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Feng Ding [email protected] Shujun Fan [email protected] Tasawar Hayat [email protected]
1
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, People’s Republic of China
2
College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, People’s Republic of China
3
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Circuits, Systems, and Signal Processing
1 Introduction Parameter estimation and system identification are the process of building the mathematical models of dynamical systems based on the observed data from the systems [15–20], which is one traditional research direction in the field of data-driven based mathematical modeling technology [67–70]. Parameter estimation can be applied to many areas such as linear systems, bilinear systems and nonlinear systems [29– 31,81–84]. A lot of parameter and state estimation methods have been presented for system modeling and solving many engineering problems [37–45] such as the multiinnovation identification methods, the maximum likelihood identification methods, the auxiliary model identification methods and the hierarchical identification methods. The errors-in-variables (EIV) system refers to the fact that both the input and output of the system contain measurement noises, which is a model structure that is closer to the practical application of the project [32,46]. For instance, the EIV models can be applied to other dynamical systems related to power systems, which are modeled as delayed differential equations and higher-order descriptors [13,14]. The noise may be introduced to the system input measurement by the sensor itse
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