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Iterative parameter estimate with batched binary-valued observations
Zhao, Yanlong; Bi, Wenjian; Wang, Ting
AbstractIn this paper, we consider linear system identification with batched binary-valued observations. We constructed an iterative parameter estimate algorithm to achieve the maximum likelihood (ML) estimate. The first interesting result was that there exists at most one finite ML solution for this specific maximum likelihood problem, which was induced by the fact that the Hessian matrix of the log-likelihood function was negative definite under binary data and Gaussian system noises. The global concave property and local strongly concave property of the log-likelihood function were obtained. Under mild conditions on the system input, we proved that the ML function has a unique maximum point. The second main result was that the ML estimate was consistent under persistent excitation inputs, which infers the effectiveness of ML estimate. Finally, the proposed iterative estimate algorithm converged to a fixed vector with an exponential rate that was proved by constructing a Lyapunov function. A more interesting result was that the limit of the iterative algorithm achieved the maximization of the ML function. Numerical simulations are illustrated to support the theoretical results obtained in this paper well.
KeywordBinary-valued observation maximum likelihood estimate strongly convex system identification exponential rate
Funding ProjectNational Natural Science Foundation of China[61174042] ; National Natural Science Foundation of China[11171333] ; National Basic Research Program of China (973 Program)[2014CB845301]
WOS Research AreaComputer Science
WOS SubjectComputer Science, Information Systems
WOS IDWOS:000375885400019
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Document Type期刊论文
Corresponding AuthorZhao, Yanlong
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhao, Yanlong,Bi, Wenjian,Wang, Ting. Iterative parameter estimate with batched binary-valued observations[J]. SCIENCE CHINA-INFORMATION SCIENCES,2016,59(5):18.
APA Zhao, Yanlong,Bi, Wenjian,&Wang, Ting.(2016).Iterative parameter estimate with batched binary-valued observations.SCIENCE CHINA-INFORMATION SCIENCES,59(5),18.
MLA Zhao, Yanlong,et al."Iterative parameter estimate with batched binary-valued observations".SCIENCE CHINA-INFORMATION SCIENCES 59.5(2016):18.
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