Asymptotic variance expressions for estimated frequency functions

	Asymptotic variance expressions for estimated frequency functions
	Xie, LL ; Ljung, L
刊名	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
	2001-12-01
卷号	46 期号:12 页码:1887-1899
关键词	accuracy asymptotic variance FIR models system identification
ISSN号	0018-9286
英文摘要	Expressions for the variance of an estimated frequency function are necessary for many issues In model validation and experiment design. A general result is that a simple expression for this variance can be obtained asymptotically as the model order tends to infinity. This expression shows that the variance is inversely proportional to the signal-to-noise ratio frequency by frequency. Still, for low order models the actual variance may be quite different. This has also been pointed out in several recent publications. In this contribution we derive an exact expression for the variance, which is not asymptotic in the model order. This expression applies to a restricted class of models: AR-models, as well as fixed pole models with a polynomial noise model. It brings out the character of the simple approximation and the convergence rate to the limit as the model order increases. It also provides nonasymptotic lower bounds for the general case. The calculations are illustrated by numerical examples.
WOS研究方向	Automation & Control Systems ; Engineering
语种	英语
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号	WOS:000173370600004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/16018]
专题	中国科学院数学与系统科学研究院
通讯作者	Xie, LL
作者单位	1.Linkoping Univ, Dept Elect Engn, S-58183 Linkoping, Sweden 2.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xie, LL,Ljung, L. Asymptotic variance expressions for estimated frequency functions[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2001,46(12):1887-1899.
APA	Xie, LL,&Ljung, L.(2001).Asymptotic variance expressions for estimated frequency functions.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,46(12),1887-1899.
MLA	Xie, LL,et al."Asymptotic variance expressions for estimated frequency functions".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 46.12(2001):1887-1899.