Robust rational approximation for identification

Bultheel, Adhemar; Barel, Marc Van; Rolain, Yves; Schoukens, Johan

doi:10.1109/cdc.2001.980961

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…The theory and computational aspects as well as the use of discrete rational approximation on the unit circle and the real line has been reported on in several papers to which we refer for further details [34][35][36]6]. For an application in system identification see [7]. We just summarize the main results for further reference.…”

Section: First Approach: Vector Orthogonal Polynomialsmentioning

confidence: 99%

Orthogonal basis functions in discrete least-squares rational approximation

Bultheel

Barel

gucht

2004

Journal of Computational and Applied Mathematics

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We consider a problem that arises in the field of frequency domain system identification. If a discrete-time system has an input-output relation Y (z) = G(z)U (z), with transfer function G, then the problem is to find a rational approximationĜ n for G. The data given are measurements of input and output spectra in the frequency points z k : {U (z k), Y (z k)} N k=1 together with some weight. The approximation criterion is to minimize the weighted discrete least squares norm of the vector obtained by evaluating G −Ĝ n in the measurement points. If the poles of the system are fixed, then the problem reduces to a linear least squares problem in two possible ways: by multiplying out the denominators and hide these in the weight, which leads to the construction of orthogonal vector polynomials, or the problem can be solved directly using an orthogonal basis of rational functions. The orthogonality of the basis is important because if the transfer functionĜ n is represented with respect to a non-orthogonal basis, then this least squares problem can be very ill conditioned. Even if an orthogonal basis is used, but with respect to the wrong inner product (e.g., the Lebesgue measure on the unit circle) numerical instability can be fatal in practice. We show that both approaches lead to an inverse eigenvalue problem, which forms the common framework in which fast and numerically stable algorithms can be designed for the computation of the orthonormal basis.

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Section: First Approach: Vector Orthogonal Polynomialsmentioning

confidence: 99%

Orthogonal basis functions in discrete least-squares rational approximation

Bultheel

Barel

gucht

2004

Journal of Computational and Applied Mathematics

Self Cite

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“…Several strategies are proposed in the literature to improve the numerical conditioning of weighted [1,6,13] and unweighted least-squares problems [2]. Optimal conditioning for polynomial models require Forsythe orthogonal polynomials which make J H J equals the identity for the WLLS and the WGTLS [6].…”

Section: Forsythe Orthogonal Polynomial Enable Highorder Modelsmentioning

confidence: 99%

“…Optimal conditioning for rational models can be obtained using vector orthogonal polynomials [1]. These polynomials mix all basis functions of the denominator and all numerators.…”

Section: Forsythe Orthogonal Polynomial Enable Highorder Modelsmentioning

confidence: 99%

Estimating Scalable Common-Denominator Laplace-Domain MIMO Models in an Errors-in-Variables Framework

Vandersteen

Locht

Jenei

et al.

Design, Automation and Test in Europe

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Design of electrical systems demands simulations using models evaluated in different design parameters choices. To enable the simulation of linear systems, one often requires their modeling as ordinary differential equations given tabular data obtained from device simulations or measurements. Existing techniques need to do this for every choice of design parameters since the model representations dont scale smoothly with the external parameter. The paper describes a frequency-domain identification algorithm to extract the poles and zeros of linear MIMO systems. Furthermore, it expresses the poles and zeros as trajectories that are functions of the design parameter(s). The paper describes the used framework, solves the startingvalue problem, presents a solution for high-order systems and provides a model-order selection strategy. The properties of the algorithm are illustrated on microwave measurements of inductors, a variable gain amplifier and a highorder SAW-filter. As shown by these examples, the proposed identification algorithm is very well suited to derive scalable, physically relevant models out of tabular frequencyresponse data.

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