Least-squares estimation of a class of frequency functions: A finite sample variance expression

Authors:
HåKan Hjalmarsson;Brett Ninness
Affiliations:
Department of Signals, Sensors and Systems, The Royal Institute of Technology, S-100 44 Stockholm, Sweden;School of Electrical Engineering & Computer Science, University of Newcastle, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

A new expression for the variance of scalar frequency functions estimated using the least-squares method is presented. The expression is valid for finite sample size and for a class of model structures, which includes finite impulse response, Laguerre and Kautz models, when the number of estimated parameters coincides with the number of excitation frequencies of the input. The expression gives direct insight into how excitation frequencies and amplitudes affect the accuracy of frequency function estimates. With the help of this expression, a severe sensitivity of the accuracy with respect to the excitation frequencies is exposed. The relevance of the expression when more excitation frequencies are used is also discussed.