Skip to main content

Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation

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.

Publisher note

To access the full article, please see PDF.

Author information

Affiliations

Authors

Corresponding author

Correspondence to H. C. So.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Lui, K.W.K., So, H.C. Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation. EURASIP J. Adv. Signal Process. 2009, 178785 (2009). https://doi.org/10.1155/2009/178785

Download citation

Keywords

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