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  • Research Article
  • Open Access

Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation

EURASIP Journal on Advances in Signal Processing20092009:178785

  • Received: 19 February 2009
  • Accepted: 20 November 2009
  • Published:


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.


  • Convex Optimization
  • Estimation Performance
  • Relaxation Method
  • Semidefinite Program
  • Publisher Note

Publisher note

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Authors’ Affiliations

Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong


© K.W.K. Lui and H.C. So. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.