Hellinger versus Kullback-Leibler multivariable spectrum approximation

Augusto Ferrante; Michele Pavon; Federico Ramponi

doi:10.1109/TAC.2008.920238

Hellinger versus Kullback-Leibler multivariable spectrum approximation

Augusto Ferrante, Michele Pavon, Federico Ramponi

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study a matricial version of a generalized moment problem with degree constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors, which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for the dual problem is established in the Byrnes-Lindquist spirit. A matricial Newton-type algorithm is finally provided for the numerical solution of the dual problem. Simulation indicates that the algorithm performs effectively and reliably.

Original language	English (US)
Pages (from-to)	954-967
Number of pages	14
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2008.920238
State	Published - May 2008

Keywords

Approximation of multivariable power spectra
Convex optimization
Hellinger distance
Kullback-Leibler index
Matricial descent method

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2008.920238

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abstract = "In this paper, we study a matricial version of a generalized moment problem with degree constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors, which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for the dual problem is established in the Byrnes-Lindquist spirit. A matricial Newton-type algorithm is finally provided for the numerical solution of the dual problem. Simulation indicates that the algorithm performs effectively and reliably.",

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AU - Pavon, Michele

AU - Ramponi, Federico

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AB - In this paper, we study a matricial version of a generalized moment problem with degree constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors, which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for the dual problem is established in the Byrnes-Lindquist spirit. A matricial Newton-type algorithm is finally provided for the numerical solution of the dual problem. Simulation indicates that the algorithm performs effectively and reliably.

KW - Approximation of multivariable power spectra

KW - Convex optimization

KW - Hellinger distance

KW - Kullback-Leibler index

KW - Matricial descent method

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Hellinger versus Kullback-Leibler multivariable spectrum approximation

Abstract

Keywords

ASJC Scopus subject areas

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