控制理论与应用2024，Vol.41Issue(7)：1197-1206,10.DOI:10.7641/CTA.2024.30538
二值量测误差FIR系统参数迭代辨识
Iterative parameter identification of binary output FIR systems with measurement errors
摘要
Abstract
In this paper,we consider the problem of parameter identification for a class of finite impulse response(FIR)systems with binary outputs and measurement errors,where the measurement errors result in a certain probability of obtaining opposite values for the binary measurements.Firstly,for the considered FIR system,a maximum likelihood estimator(MLE)of the parameter is given,and the strong convergence and asymptotic normality of the MLE are proved under certain regularity conditions of the noise.In addition,by analysing the properties of the likelihood function,an iterative algorithm for solving the MLE is given based on the expectation-maximum(EM)method.In order to adapt to more general measurement error situations,an iterative solution algorithm with projection is given,and the boundedness of the iterative estimation sequence is theoretically proved.Further,a necessary and sufficient condition for the likelihood function to have a unique maximum point is obtained for a given number of observations,and the iterative estimation error is shown to converge to zero with an exponential rate under persistent excitation input conditions.Finally,the effectiveness of the proposed algorithm is verified based on numerical simulation results.关键词
二值观测/极大似然估计/系统辨识/强收敛性/渐近正态性/指数收敛速度Key words
binary-valued observation/maximum likelihood estimate/system identification/strong convergence/asymptotic normality/exponential rate引用本文复制引用
郭健,薛文超,王婷,张纪峰..二值量测误差FIR系统参数迭代辨识[J].控制理论与应用,2024,41(7):1197-1206,10.基金项目
国家重点研发计划项目(2018YFA0703800),国家自然科学基金项目(T2293770,12226305,12288201),中国科学院青年创新促进会项目资助.Supported by the National Key R&D Program of China(2018YFA0703800),the National Natural Science Foundation of China(T2293770,12226305,12288201)and the Youth Innovation Promotion Association CAS. （2018YFA0703800）
