NDLI: How to Make Bias and Variance Errors Insensitive to System and Model Complexity in Identification

Content Provider	IEEE Xplore Digital Library
Author	Mårtensson, J. Hjalmarsson, H.
Copyright Year	1963
Abstract	Solutions to optimal input design problems for system identification are sometimes believed to be sensitive to the underlying assumptions. For example, a wide class of problems can be solved with sinusoidal inputs with the same number of excitation frequencies (over the frequency range ) as the number of model parameters. The order of the true system is in many cases unknown and, hence, so is the required number of frequencies in the input. In this contribution we characterize when and how the input spectrum can be chosen so that the (asymptotic) variance error of a scalar function of the model parameters becomes independent of the order of the true system. A connection between these robust designs and the solutions of certain optimal input design problems is also made. Furthermore, we show that there are circumstances when using this type of input allows some model properties to be estimated consistently even when the model order is lower than the order of the true system. The results are derived under the assumptions of causal linear time invariant systems operating in open loop and excited by an input signal having a rational spectral factor with all poles and zeros strictly inside the unit circle.
Sponsorship	IEEE Control Systems Society
Starting Page	100
Ending Page	112
Page Count	13
File Size	482803
File Format	PDF
ISSN	00189286
Volume Number	56
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Robustness System identification Parameter estimation Frequency estimation Time invariant systems Poles and zeros Signal processing Measurement standards Covariance matrix system identification Asymptotic model accuracy low-complexity models optimal input design robust input design
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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