Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation
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 param...
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2009-01-01
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Series: | EURASIP Journal on Advances in Signal Processing |
Online Access: | http://dx.doi.org/10.1155/2009/178785 |
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doaj-da159a2bd318466b94b0ff2d6b5d2fcf2020-11-25T00:23:57ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802009-01-01200910.1155/2009/178785Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter EstimationKenneth W. K. LuiH. C. SoWe 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. http://dx.doi.org/10.1155/2009/178785 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Kenneth W. K. Lui H. C. So |
spellingShingle |
Kenneth W. K. Lui H. C. So Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation EURASIP Journal on Advances in Signal Processing |
author_facet |
Kenneth W. K. Lui H. C. So |
author_sort |
Kenneth W. K. Lui |
title |
Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation |
title_short |
Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation |
title_full |
Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation |
title_fullStr |
Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation |
title_full_unstemmed |
Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation |
title_sort |
semidefinite programming for approximate maximum likelihood sinusoidal parameter estimation |
publisher |
SpringerOpen |
series |
EURASIP Journal on Advances in Signal Processing |
issn |
1687-6172 1687-6180 |
publishDate |
2009-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2009/178785 |
work_keys_str_mv |
AT kennethwklui semidefiniteprogrammingforapproximatemaximumlikelihoodsinusoidalparameterestimation AT hcso semidefiniteprogrammingforapproximatemaximumlikelihoodsinusoidalparameterestimation |
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1725354798212972544 |