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Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers

Andersson, Fredrik and Carlsson, Marcus and Tourneret, Jean-Yves and Wendt, Herwig Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers. (2013) In: 21st European Signal and Image Processing Conference (EUSIPCO 2013), 9 September 2013 - 13 September 2013 (Marrakech, Morocco).

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We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker’s theorem to formulate the associated nonlinear least squares problem as an optimization problem in the space of vectors generating Hankel matrices of fixed rank. Approximate solutions to this problem are obtained by using the alternating direction method of multipliers. Finally, we extract the frequency estimates from the con-eigenvectors of the solution Hankel matrix. The resulting algorithm is simple, easy to implement and can be applied to data with equally spaced samples with approximation weights, which for instance allows cases of missing data samples. By means of numerical simulations, we analyze and illustrate the excellent performance of the method, attaining the Craḿer-Rao bound.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org The original PDF of the article can be found at : http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6811555
HAL Id:hal-03669328
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Lund University (SWEDEN)
Laboratory name:
Deposited On:13 Nov 2015 13:11

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