Spectral estimation by least-squares optimization based on rational covariance extension

Fanizza, Giovanna; Nagamune, Ryozo

doi:10.1016/j.automatica.2006.09.003

Cited by 3 publications

(6 citation statements)

References 20 publications

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“…, k. If P is positive definite, all such solutions are parameterized by Theorem 1 in Section III. However, there does not necessarily exist an interpolant of degree at most k − 1 45th IEEE CDC, San Diego, USA, Dec. [13][14][15]2006 ThB12.1 which also satisfies the mirror interpolation conditions. In fact, the following is a simple counterexample.…”

Section: The Antoulas-sorensen Approachmentioning

confidence: 90%

“…However, Antoulas' observation does not come as great surprise to us, since the concept of spectral zeros is a key ingredient in a theory of analytic interpolation developed over the last decades by Byrnes, Georgiou, Lindquist and their coworkers [3]- [12], [14]- [21], [23], [24], [26]. Indeed, given k + 1 interpolation points and corresponding interpolation values, the class of all analytic interpolants of McMillan degree at most k is completely parameterized by the stable spectral zeros.…”

Section: Introductionmentioning

confidence: 95%

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A Global Analysis Approach to Passivity Preserving Model Reduction

Fanizza¹,

Karlsson²,

Lindquist³

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Passivity-preserving model reduction for linear time-invariant systems amounts to approximating a positivereal rational transfer function with one of lower degree. Recently Antoulas and Sorensen have proposed such a modelreduction method based on Krylov projections. The method is based on an observation by Antoulas (in the single-input/singleoutput case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes, Georgiou and Lindquist, namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models.

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Section: The Antoulas-sorensen Approachmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 95%

A Global Analysis Approach to Passivity Preserving Model Reduction

Fanizza¹,

Karlsson²,

Lindquist³

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…, b q from the missing observations sequence y(k) in (4). In this spectral estimation problem, and unlike the conventional parameter estimation method involving missed observations [3,7,10,18,27,34], the system parameters a 1 , . .…”

Section: Problem Descriptionmentioning

confidence: 99%

“…In [5,22], maximum likelihood techniques were also introduced for spectral estimation with missed observations. A new ARMA method, based on the nonlinear optimization of a squared-error criterion, was proposed for the spectral estimation of time series in [10]. This method can accommodate regularly and randomly missed observations.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, in practical situations, there may be a nonzero probability that any measurement consists of noise alone, that is, the measurements are not consecutive, but contain missed observations. The missed measurements are caused by a variety of factors, such as certain failures in the measurement, intermittent sensor failures, accidental loss of some collected data, jamming of some of the data, fading phenomena in propagation channels, and the effect of removing outliers [7,10,18,27].…”

Section: Introductionmentioning

confidence: 99%

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