On consistency of recursive least squares identification algorithms for controlled auto-regression models |
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Authors: | Yongsong Xiao Feng Ding Yi Zhou Ming Li Jiyang Dai |
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Affiliation: | 1. Control Science and Engineering Research Center, Jiangnan University (Southern Yangtze University), Wuxi 214122, PR China;2. Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang 330063, PR China |
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Abstract: | The recursive least squares (RLS) algorithms is a popular parameter estimation one. Its consistency has received much attention in the identification literature. This paper analyzes convergence of the RLS algorithms for controlled auto-regression models (CAR models), and gives the convergence theorems of the parameter estimation by the RLS algorithms, and derives the conditions that the parameter estimates consistently converge to the true parameters under noise time-varying variance and unbounded condition number. This relaxes the assumptions that the noise variance is constant and that high-order moments are existent. Finally, the proposed algorithms are tested with two example systems, including an experimental water-level system. |
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Keywords: | Modeling Recursive identification Parameter estimation Convergence properties Least squares |
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