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Likelihood Analysis of Power Spectra and Generalized Moment Problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-2681-8383
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 9, p. 4580-4592Article in journal (Refereed) Published
Abstract [en]

We develop an approach to the spectral estimation that has been advocated by [ A. Ferrante et al., "Time and spectral domain relative entropy: A new approach to multivariate spectral estimation,"IEEE Trans. Autom. Control, vol. 57, no. 10, pp. 2561-2575, Oct. 2012.] and, in the context of the scalar-valued covariance extension problem, by [P. Enqvist and J. Karlsson, "Minimal itakurasaito distance and covariance interpolation," in Proc. 47th IEEE Conf. Decision Control, 2008, pp. 137-142]. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou, and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In this paper, we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017. Vol. 62, no 9, p. 4580-4592
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-214494DOI: 10.1109/TAC.2017.2672862ISI: 000408569300020Scopus ID: 2-s2.0-85029838609OAI: oai:DiVA.org:kth-214494DiVA, id: diva2:1147925
Note

QC 20171009

Available from: 2017-10-09 Created: 2017-10-09 Last updated: 2017-10-09Bibliographically approved

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