Paper Info
Title
Frequency estimation based on Hankel matrices and the alternating direction method of multipliers
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 Cramér-Rao bound.
Year
Venue
Keywords
2013
Signal Processing Conference
Hankel matrices,eigenvalues and eigenfunctions,frequency estimation,least squares approximations,optimisation,spectral analysis,Cramér-Rao bound,Hankel matrices,Kroneckers theorem,alternating direction method of multipliers,approximation weights,complex exponentials,con-eigenvectors,exponential damping,frequency estimation,linear combinations,nonlinear least squares problem,numerical simulations,optimization problem,parametric high-resolution method,Hankel matrices,Kronecker's theorem,alternating direction method of multipliers,frequency estimation,missing data,nonlinear least squares
Field
DocType
Citations 
Linear combination,Kronecker delta,Kronecker's theorem,Mathematical analysis,Matrix (mathematics),Parametric statistics,Non-linear least squares,Hankel matrix,Optimization problem,Mathematics
Conference
2
PageRank 
References 
Authors
0.40
4
4
Name
Order
Citations
PageRank
Fredrik Andersson1124.44
Marcus Carlsson283.64
Jean-Yves Tourneret383564.32
Herwig Wendt417033.82