# Numerically robust transfer function modeling from noisy frequency domain data

@article{Bultheel2005NumericallyRT, title={Numerically robust transfer function modeling from noisy frequency domain data}, author={Adhemar Bultheel and Marc Van Barel and Yves Rolain and Rik Pintelon}, journal={IEEE Transactions on Automatic Control}, year={2005}, volume={50}, pages={1835-1839} }

Using vector orthogonal polynomials as basis functions for the representation of the rational form of a linear time invariant system, in frequency domain identification problems, it is shown that the notorious numerical ill conditioning of these maximum likelihood problems can be overcome completely. For the identification of high-order (100/100) systems operating over a wide frequency band, or even in the situation of over- or undermodeling, condition numbers less than ten are reported for…

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## References

SHOWING 1-10 OF 25 REFERENCES

Best Conditioned Parametric Identification of Transfer Function Models in the Frequency Domain

- Mathematics
- 1995

In this paper, it is shown that rational transfer function models based on orthogonal Forsythe polynomials minimize the condition number of the Jacobian of estimators in a least-squares framework. As…

On the use of orthogonal polynomials in high order frequency domain system identification and its application to modal parameter estimation

- MathematicsProceedings of 1994 33rd IEEE Conference on Decision and Control
- 1994

In this paper a maximum likelihood frequency domain identification technique is presented for the parametric transfer function of very high order linear time invariant systems. Through the use of…

Generating robust starting values for frequency-domain transfer function estimation

- MathematicsAutom.
- 1999

Parametric identification of transfer functions in the frequency domain-a survey

- MathematicsIEEE Trans. Autom. Control.
- 1994

This paper gives a survey of frequency domain identification methods for rational transfer functions in the Laplace (s) or z-domain through a study of the (equivalent) cost functions.

Frequency-domain system identification using non-parametric noise models estimated from a small number of data sets

- MathematicsAutom.
- 1997

Parametric and nonparametric identification of linear systems in the presence of nonlinear distortions-a frequency domain approach

- MathematicsIEEE Trans. Autom. Control.
- 1998

A related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties.

Analyses, development and applications of TLS algorithms in frequency domain system identification

- Mathematics
- 1997

An overview of frequency domain total least squares (TLS) estimators for rational transfer function models of linear time-invariant multivariable systems is given and the asymptotic behavior of the GTLS and BTLS estimators is studied.

On the frequency scaling in continuous-time modeling

- MathematicsIEEE Transactions on Instrumentation and Measurement
- 2005

It is shown that the optimal frequency scaling also strongly depends on the estimation algorithm and that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean.

Transfer function synthesis as a ratio of two complex polynomials

- Mathematics
- 1963

Experimental frequency response data obtained from a linear dynamic system is processed to obtain the transfer function as a ratio of two frequency-dependent polynomials. The difference between the…