Global convergence of the EM algorithm for ARX models with uncertain communication channels
An expectation maximization (EM) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an output model, both subject to white Gaussian noises. Since the true outputs of the AR...
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| Published in | Systems & control letters Vol. 136; p. 104614 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.02.2020
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| Online Access | Get full text |
| ISSN | 0167-6911 1872-7956 |
| DOI | 10.1016/j.sysconle.2019.104614 |
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| Abstract | An expectation maximization (EM) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an output model, both subject to white Gaussian noises. Since the true outputs of the ARX model are assumed to be unknown, a modified Kalman filter is derived to estimate the output, and then the parameters are estimated by the EM algorithm using the estimated outputs. The Kullback–Leibler divergence and the submartingale are used to prove that the parameter estimates can converge to the true values with the EM algorithm. Furthermore, a simulation example is presented to verify the theoretical results. |
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| AbstractList | An expectation maximization (EM) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an output model, both subject to white Gaussian noises. Since the true outputs of the ARX model are assumed to be unknown, a modified Kalman filter is derived to estimate the output, and then the parameters are estimated by the EM algorithm using the estimated outputs. The Kullback–Leibler divergence and the submartingale are used to prove that the parameter estimates can converge to the true values with the EM algorithm. Furthermore, a simulation example is presented to verify the theoretical results. |
| ArticleNumber | 104614 |
| Author | Liu, Yanjun Huang, Biao Zhu, Quanmin Li, Lun Chen, Jing |
| Author_xml | – sequence: 1 givenname: Jing surname: Chen fullname: Chen, Jing email: chenjing1981929@126.com organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, PR China – sequence: 2 givenname: Biao surname: Huang fullname: Huang, Biao email: bhuang@ualberta.ca organization: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, T6G 2G6, Canada – sequence: 3 givenname: Quanmin surname: Zhu fullname: Zhu, Quanmin email: quan.zhu@uwe.ac.uk organization: Department of Engineering Design and Mathematics, University of the West of England, Bristol BS16 1QY, UK – sequence: 4 givenname: Yanjun surname: Liu fullname: Liu, Yanjun email: yanjunliu_1983@126.com organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, PR China – sequence: 5 givenname: Lun surname: Li fullname: Li, Lun email: lilun0915@163.com organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, PR China |
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