Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers
(2013) 21st European Signal Processing Conference (EUSIPCO 2013) In 2013 Proceedings of the 21st European Signal Processing Conference (Eusipco) Abstract
 We develop a parametric highresolution 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 coneigenvectors 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 highresolution 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 coneigenvectors 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 CramerRao bound. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4709833
 author
 Andersson, Fredrik ^{LU} ; Carlsson, Marcus ^{LU} ; Tourneret, JeanYves 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
 in
 2013 Proceedings of the 21st European Signal Processing Conference (Eusipco)
 publisher
 IEEEInstitute 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
 8815338a2aab4cc1b856ded22600f0ee (old id 4709833)
 alternative location
 http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6811555
 date added to LUP
 20141106 11:20:55
 date last changed
 20161013 04:38:57
@misc{8815338a2aab4cc1b856ded22600f0ee, abstract = {We develop a parametric highresolution 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 coneigenvectors 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 CramerRao bound.}, author = {Andersson, Fredrik and Carlsson, Marcus and Tourneret, JeanYves and Wendt, Herwig}, keyword = {frequency estimation,nonlinear least squares,Hankel matrices,Kronecker's theorem,missing data,alternating direction method of,multipliers}, language = {eng}, publisher = {ARRAY(0x9ec2b48)}, series = {2013 Proceedings of the 21st European Signal Processing Conference (Eusipco)}, title = {Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers}, year = {2013}, }