Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers
(2013) 21st European Signal Processing Conference (EUSIPCO 2013)- 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4709833
- author
- Andersson, Fredrik LU ; Carlsson, Marcus LU ; Tourneret, Jean-Yves and Wendt, Herwig
- organization
- publishing date
- 2013
- 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
- host publication
- 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)
- conference location
- Marrakech, Morocco
- conference dates
- 2013-09-09 - 2013-09-13
- 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
- 2016-04-04 10:15:43
- date last changed
- 2022-02-21 02:56:21
@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)}}, keywords = {{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}}, url = {{http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6811555}}, year = {{2013}}, }