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

Andersson, Fredrik LU ; Carlsson, Marcus LU ; Tourneret, Jean-Yves and Wendt, Herwig (2013) 21st European Signal Processing Conference (EUSIPCO 2013) In 2013 Proceedings of the 21st European Signal Processing Conference (Eusipco)
Abstract
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... (More)
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 Cramer-Rao bound. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
frequency estimation, nonlinear least squares, Hankel matrices, Kronecker's theorem, missing data, alternating direction method of, multipliers
in
2013 Proceedings of the 21st European Signal Processing Conference (Eusipco)
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
21st European Signal Processing Conference (EUSIPCO 2013)
external identifiers
  • WOS:000341754500168
  • Scopus:84901361787
language
English
LU publication?
yes
id
8815338a-2aab-4cc1-b856-ded22600f0ee (old id 4709833)
alternative location
http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6811555
date added to LUP
2014-11-06 11:20:55
date last changed
2017-01-01 07:56:55
@inproceedings{8815338a-2aab-4cc1-b856-ded22600f0ee,
  abstract     = {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 Cramer-Rao bound.},
  author       = {Andersson, Fredrik and Carlsson, Marcus and Tourneret, Jean-Yves and Wendt, Herwig},
  booktitle    = {2013 Proceedings of the 21st European Signal Processing Conference (Eusipco)},
  keyword      = {frequency estimation,nonlinear least squares,Hankel matrices,Kronecker's theorem,missing data,alternating direction method of,multipliers},
  language     = {eng},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers},
  year         = {2013},
}