引用本文: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.[点击复制]
GUO Jian,XUE Wen-chao,WANG Ting,ZHANG Ji-Feng.Iterative parameter identification of binary output FIR systems with measurement errors[J].Control Theory and Technology,2024,41(7):1197~1206.[点击复制]
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
摘要点击 87  全文点击 35  投稿时间：2023-08-09  修订日期：2024-06-02
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DOI编号  DOI: 10.7641/CTA.2024.30538
  2024,41(7):1197-1206
中文关键词  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
英文关键词  binary-valued observation  maximum likelihood estimate  system identification  strong convergence  asymptotic normality  exponential rate
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.
作者单位E-mail
郭健 中国科学院数学与系统科学研究院 j.guo@amss.ac.cn 
薛文超* 中国科学院数学与系统科学研究院 wenchaoxue@amss.ac.cn 
王婷 北京科技大学智能科学与技术学院  
张纪峰 中国科学院数学与系统科学研究院  
中文摘要
      本文考虑了量测数据为二值输出且含量测误差的一类有限脉冲响应(FIR)系统的参数辨识问题, 其中, 量测误差使得二值型量测值有一定概率得到相反的取值. 首先, 对所考虑的 FIR 系统, 给出了参数的极大似然估计(MLE), 证明了在噪声满足一定正则条件下MLE的强收敛性和渐近正态性. 此外, 通过分析似然函数的性质, 给出了一种基于期望最大化(EM)方法的MLE迭代求解算法. 为适应更一般的量测误差情形, 给出了带投影的迭代求解算法, 并从理论上证明了迭代估计序列的有界性. 进一步, 在给定数量的观测下, 得到了似然函数具有唯一最大值点的必要和充分条件, 并在持续激励输入条件下, 证明了迭代估计误差以指数速度收敛到零. 最后, 利用数值模拟结果验证了所提出算法的有效性.
英文摘要
      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.