Iterative parameter estimate with batched binary-valued observations  

作　　者：Yanlong ZHAO Wenjian BI Ting WANG 

机构地区：[1]Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China(Information Sciences)》2016年第5期154-171,共18页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 61174042, 11171333);National Basic Research Program of China (973 Program) (Grant No. 2014CB845301)

摘　　要：In 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.In 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.

关 键 词：Binary-valued observation maximum likelihood estimate strongly convex system identification exponential rate 

分 类 号：O212.1[理学—概率论与数理统计]