Hellinger versus Kullback-Leibler multivariable spectrum approximation

Augusto Ferrante, Michele Pavon, Federico Ramponi

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)954-967
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - May 2008


  • 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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