AR模型辨识的稀疏结构迭代算法  

Sparse Structure Based Iterative Algorithm for AR Model Identification

作　　者：段晓君[1] 杜小勇[2] 

机构地区：[1]国防科技大学理学院数学与系统科学系,湖南长沙410073 [2]国防科技大学电子科学与工程学院ATR实验室,湖南长沙410073

出　　处：《数学的实践与认识》2009年第22期148-153,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(60604020);航天支撑技术基金

摘　　要：模型估计是机器学习领域一个重要的研究内容,动态数据的模型估计是系统辨识和系统控制的基础.针对AR时间序列模型辨识问题,证明了在给定阶数下AR模型参数的最小二乘估计本质上也是一种矩估计.根据结构风险最小化原理,通过对模型拟合度和模型复杂度的折衷,提出了基于稀疏结构迭代的AR序列模型估计算法,并讨论了基于广义岭估计的最优正则化参数选取规则.数值结果表明,方法能以节省参数的方式有效地实现AR模型的辨识,比矩估计法结果有明显改善.Model estimation is an important issue in machine learning field. Especially, the correlation estimation of dynamic data is the foundation of system identification and system control. Aiming at Autoregressive（AR） time series, it is firstly pointed out that the parameters estimated by the Least Square method given model order equals to those estimated by moment method in this paper. Secondly, a new algorithm for AR time series estimation based on sparse structure learning is put forward by synthetically considering the model fidelity and parameter sparsity. And a principle of selecting an optimal regularization parameter is discussed. Simulation results show that this algorithm can realize AR model identification with parsimonious parameters with enough precision, and its effect is much better than that of moment method.

关 键 词：稀疏结构 AR模型估计 节省参数 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] TP391[自动化与计算机技术—控制科学与工程]