基于偏差消除最小二乘估计和Durbin方法的两阶段ARMAX参数辨识

辛斌; 白永强; 陈杰

doi:10.3724/SP.J.1004.2012.00491

基于偏差消除最小二乘估计和Durbin方法的两阶段ARMAX参数辨识

doi: 10.3724/SP.J.1004.2012.00491

辛斌^1,2,3,
白永强^1,2, ,,
陈杰^1,2

1.
北京理工大学自动化学院北京 100081;
2.
复杂系统智能控制与决策教育部重点实验室北京 100081;
3.
曼彻斯特大学商学院决策与认知科学研究中心曼彻斯特 M15 6PB 英国

详细信息

通讯作者:
白永强, 博士, 北京理工大学自动化学院讲师.主要研究方向为智能控制与智能系统. E-mail:byfengyun@bit.edu.cn

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出版历程
- 收稿日期: 2010-05-20
- 修回日期: 2011-11-09
- 刊出日期: 2012-03-20

Two-stage ARMAX Parameter Identification Based on Bias-eliminated Least Squares Estimation and Durbin0s Method

XIN Bin^1,2,3,
BAI Yong-Qiang^{1,2
, ,},
CHEN Jie^1,2

1.
School of Automation, Beijing Institute of Technology, Beijing 100081, P.,R.,China;
2.
Key Laboratory of Complex System Intelligent Control and Decision, Ministry of Education, Beijing 100081, P.,R.,China;
3.
Decision and Cognitive Sciences Research Centre, Manchester Business School, The University of Manchester, Manchester M15 6PB, U.K.

摘要

摘要: 针对带有外生变量的自回归移动平均模型(Autoregressive moving average with exogenous variable, ARMAX)的参数辨识问题提出一种两阶段辨识方法. 首先通过偏差消除最小二乘方法辨识带有外生变量的自回归部分(Autoregressive part with exogenous variable, ARX),然后采用Durbin方法将移动平均部分(Moving average, MA)的参数辨识问题转换成一个长自回归模型(Long autoregressive, LAR)的参数辨识问题, 并利用MA与等价LAR的参数对应关系直接得到MA参数, 最后利用辨识出的MA参数计算出噪声方差. 与扩展最小二乘法的数值仿真比较验证了这种两阶段辨识方法的有效性.
- 自回归移动平均模型 /
- 参数辨识 /
- Durbin方法 /
- 偏差消除最小二乘法
Abstract: This paper proposes a two-stage identification approach for the parameter identification of autoregressive moving average with exogenous variable (ARMAX) model. First, a bias-eliminated least squares method is employed to identify the autoregressive part with exogenous variable (ARX). Then, the Durbin's method is employed to transform the parameter identification of the moving average (MA) part into that of a long autoregressive (AR) model. The MA parameters are derived directly from the parameter relationship between the MA part and its equivalent long AR model. Finally, the noise variance can be computed by using the identified MA parameters. The performance comparison against the extended least-squares method in numerical simulations validates the effectiveness of the two-stage identification approach.
- Autoregressive moving average with exogenous variable (ARMAX) model /
- parameter identification /
- Durbin0s method /
- bias-eliminated least squares method

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参考文献(1)

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