Asymptotic Variance Expressions for Identified Black-Box Transfer Function Models
1984 (English)In: Proceedings of the 23rd IEEE Conference on Decision and Control, 1984, 951-958 p.Conference paper (Refereed)
Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-typemodels. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due tovariance for a number of typical model uses. Some consequences for input design are also drawn.
Place, publisher, year, edition, pages
1984. 951-958 p.
Identification, Black-box, Transfer function models, Asymptotic, Covariance matrix
IdentifiersURN: urn:nbn:se:liu:diva-103952DOI: 10.1109/CDC.1984.272156OAI: oai:DiVA.org:liu-103952DiVA: diva2:693296
23rd IEEE Conference on Decision and Control, Las Vegas, NV, USA, December, 1984