辨识方法的计算效率(1):递推算法

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辨识方法的计算效率(1):递推算法
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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(60973043);高等学校学科创新引智计划(B12018)

Computational efficiency of the identification methods. Part A:Recursive 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:

算法的计算量可用其乘法运算次数和加法运算次数表示(除法作为乘法对待,减法作为加法对待).一次乘法运算或一次加法运算称为一个flop,即一次浮点运算.作为"辨识方法的计算效率"系列3篇连载论文的第1篇,主要了讨论递推辨识算法的计算量,包括向量和矩阵基本运算的flop数,以及线性回归系统、多元线性回归系统、多变量系统的随机梯度辨识算法、最小二乘辨识算法、递推最小二乘辨识算法的最经济计算量,即实现算法的最少flop数.

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:

The amount of the calculation of an algorithm may be expressed by the number of multiplication and addition operations (one division is treated as a multiplication,one subtraction treated as an addition).A multiplication or an addition operation is called a flop,i.e.,a floating-point operation.This is the first of three serial papers 'Computational efficiency of the identification methods',which focuses on the computational efficiency of the recursive algorithms,including the flops of the vector and matrix operations,and the minimum flops of the stochastic gradient identification algorithm,the least squares identification algorithm,the recursive least squares identification algorithm for linear regression systems,multivariate linear regression systems and multivariable 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

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丁锋.辨识方法的计算效率(1):递推算法[J].南京信息工程大学学报(自然科学版),2012,4(4):289-300
DING Feng. Computational efficiency of the identification methods. Part A:Recursive algorithms[J]. Journal of Nanjing University of Information Science & Technology, 2012,4(4):289-300

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收稿日期:2012-08-19
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