Model order selection rule for estimating the parameters of 2-D sinusoids in colored noise

Mark Kliger, Joseph M. Francos

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the problem of jointly estimating the number as well as the parameters of two-dimensional sinusoidal signals, observed in the presence of an additive colored noise field. In this framework we consider the problem of least squares estimation of the parameters of 2-D sinusoidal signals observed in the presence of an additive noise field, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is under-estimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where the number of sinusoidal signals is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a large family of model order selection rules.

Original languageEnglish
Title of host publication2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
PagesIII85-III88
StatePublished - 1 Dec 2006
Event2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France
Duration: 14 May 200619 May 2006

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
ISSN (Print)1520-6149

Conference

Conference2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
Country/TerritoryFrance
CityToulouse
Period14/05/0619/05/06

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