Mean square error of the Empirical Transfer Function Estimator for stochastic input signals

Authors:
P. M. T. Broersen
Affiliations:
Department of Multi Scale Physics, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2004

Citing 4
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Quantification of uncertainty in transfer function estimation: a mixed probabilistic—worst-case approach

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System identification (2nd ed.): theory for the user

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On bias in transfer functions estimated with stochastic excitation

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Abstract

The accuracy of the Empirical Transfer Function Estimator (ETFE) with stochastic input has been described with a deterministic and a stochastic approach. The results for bias and variance are different, but the mean square error is infinite in both approaches. In the deterministic approach where the input is considered as a single realization of a stochastic process, a number of frequencies has no finite ETFE estimate. The average number of problematic frequencies will be constant if the number of observations increases.