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IMA Journal of Mathematical Control and Information 1984 1(4):323-338; doi:10.1093/imamci/1.4.323
© 1984 by Institute of Mathematics and its Applications
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Black-box Identification of Transfer Functions: Asymptotic Results for Increasing Model Order and Data Records

LENNART LJUNG and ZHEN-DONG YUAN{dagger}

Department of Electrical Engineering, Linköping University S-581 83 Linköping, Sweden
{dagger} On leave from East China Normal University Shanghai, P.R.C.

The problem of estimating the transfer function of a linear stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model order may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer-function estimates are investigated. In an earlier paper results were given for models, parametrized as finite impulse responses. In this article these results are extended to more general parametrizations and to general noise models. A main result is that the variance of the transfer-function estimate at a certain frequency is asymptotically given by the noise-to-signal ratio at that frequency, multiplied by the ratio of the model order to the number of data points.


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