NDLI: Strong consistency of the over- and under-determined LSE of 2-D exponentials in white noise

Content Provider	IEEE Xplore Digital Library
Author	Francos, J.M. Kliger, M.
Copyright Year	2005
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Ben-Gurion Univ., Beer Sheva, Israel (Francos, J.M.; Kliger, M.)
Abstract	We consider the problem of least squares estimation of the parameters of 2D exponential signals observed in the presence of an additive noise field, when the assumed number of exponentials is incorrect. We consider both the case where the number of exponential signals is under-estimated, and the case where the number of exponential signals is over-estimated. In the case where the number of exponential signals is under-estimated we prove the almost sure convergence of the least squares estimates to the parameters of the dominant exponentials. In the case where the number of exponential 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 exponentials.
Sponsorship	IEEE Signal Processing Soc
File Size	297019
File Format	PDF
ISBN	0780388747
ISSN	15206149
DOI	10.1109/ICASSP.2005.1416097
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-03-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	White noise Least squares approximation Parameter estimation Additive noise Convergence Maximum likelihood estimation Gaussian noise Error analysis Performance analysis Algorithm design and analysis
Content Type	Text
Resource Type	Article

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