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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Bibliographic Details
Published inSystems & control letters Vol. 136; p. 104614
Main Authors Chen, Jing, Huang, Biao, Zhu, Quanmin, Liu, Yanjun, Li, Lun
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2020
Subjects
ARX model
EM algorithm
Kullback–Leibler divergence
Modified Kalman filter
Parameter estimation
Parameter estimation
Modified Kalman filter
Kullback–Leibler divergence
ARX model
EM algorithm
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Summary: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.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2019.104614