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Asymptotic variance expressions for estimated frequency functions
Xie, LL; Ljung, L
2001-12-01
Source PublicationIEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN0018-9286
Volume46Issue:12Pages:1887-1899
AbstractExpressions 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.
Keywordaccuracy asymptotic variance FIR models system identification
Language英语
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000173370600004
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation statistics
Cited Times:22[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/16019
Collection中国科学院数学与系统科学研究院
Affiliation1.Linkoping Univ, Dept Elect Engn, S-58183 Linkoping, Sweden
2.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
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.
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