辨识方法的计算效率(2):迭代算法

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辨识方法的计算效率(2):迭代算法
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                        丁锋丁锋
江南大学 物联网工程学院,无锡,21412;江南大学 控制科学与工程研究中心,无锡,214122;江南大学 教育部轻工过程先进控制重点实验室,无锡,214122
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基金项目:国家自然科学基金(61273194);江苏省自然科学基金(BK2012549);高等学校学科创新引智计划(B12018)

Computational efficiency of the identification methods.Part B: Iterative algorithms

Author:

DING Feng
DING Feng
School of Internet of Things Engineering,Jiangnan University,Wuxi 21412;Control Science and Engineering Research Center,Jiangnan University,Wuxi 214122;Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),Jiangnan University,Wuxi 214122
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摘要:

讨论了最小二乘迭代辨识算法及其计算效率问题.最小二乘迭代算法由于涉及矩阵求逆运算,为减小计算量,提出了基于块矩阵求逆的最小二乘迭代辨识算法.基于块矩阵求逆的最小二乘迭代辨识算法不是一种新算法,只是从辨识算法的实现方式上降低计算负担,它与最小二乘迭代算法产生相同的参数估计,但计算量小.文中研究了伪线性回归系统、多元伪线性回归系统、多变量伪线性回归系统的最小二乘迭代辨识算法及其基于块矩阵求逆的最小二乘迭代算法.

关键词:递推辨识;迭代辨识;参数估计;FIR模型;方程误差模型;CAR模型;CARMA模型;CARAR模型;CARARMA模型;输出误差模型;OEMA模型;OEAR模型;辅助模型辨识;多新息辨识;递阶辨识;耦合辨识

Abstract:

This paper focuses on the computational efficiency of the least squares based iterative algorithms.The computational burdens of the least squares based iterative (LSI) algorithms are heavy due to computing large-size matrix inversion.In order to reduce the computational burdens,the block matrix inversion based LSI algorithms are presented.The proposed methods can reduce the computational cost through simplifying the implementation of the least squares based iterative algorithms,thus the estimation accuracies remain unchanged.The least squares based iterative algorithms and the block matrix inversion based LSI methods are studied for pseudo-linear regression systems,multivariate pseudo-linear regression systems and multivariable pseudo-linear systems.

Key words:recursive identification;iterative identification;parameter estimation;FIR model;equation error model;CAR model;CARMA model;CARAR model;CARARMA model;output error model;OEMA model;OEAR model;auxiliary model identification;multi-innovation identification;hierarchical identification;coupled identification

参考文献

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丁锋.辨识方法的计算效率(2):迭代算法[J].南京信息工程大学学报(自然科学版),2012,4(5):385-401
DING Feng. Computational efficiency of the identification methods. Part B: Iterative algorithms[J]. Journal of Nanjing University of Information Science & Technology, 2012,4(5):385-401

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收稿日期:2012-10-09
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