Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation. (2009)

• Record Type: Journal Article
• Authors: Lui Lui, Kenneth W. K. Kenneth W. K.; So So, H. C. H. C.
• Other Names: Li Li T.-H. T.-H. Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2009(2009)
• Publication Date: 2009
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2009/178785
• Languages: English
• ISSNs: 1687-6172

Abstract

Abstract : We study the convex optimization approach for parameter estimation of several sinusoidal models, namely, single complex/real tone, multiple complex sinusoids, and single two-dimensional complex tone, in the presence of additive Gaussian noise. The major difficulty for optimally determining the parameters is that the corresponding maximum likelihood (ML) estimators involve finding the global minimum or maximum of multimodal cost functions because the frequencies are nonlinear in the observed signals. By relaxing the nonconvex ML formulations using semidefinite programs, high-fidelity approximate solutions are obtained in a globally optimum fashion. Computer simulations are included to contrast the estimation performance of the proposed semi-definite relaxation methods with the iterative quadratic maximum likelihood technique as well as Cramér-Rao lower bound.