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

Summary, in English

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: Fredrik Andersson; Marcus Carlsson; Jean-Yves Tourneret; Herwig Wendt
• Department/s: Mathematics (Faculty of Engineering); Centre for Mathematical Sciences; ELLIIT: the Linköping-Lund initiative on IT and mobile communication; eSSENCE: The e-Science Collaboration
• Publishing year: 2013
• Language: English
• Publication/Series: 2013 Proceedings of the 21st European Signal Processing Conference (Eusipco)
• Links: http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6811555
• Document type: Conference paper
• Publisher: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Topic: Computer Vision and Robotics (Autonomous Systems); Mathematics
• Keywords: frequency estimation; nonlinear least squares; Hankel matrices; Kronecker's theorem; missing data; alternating direction method of; multipliers
• Conference name: 21st European Signal Processing Conference (EUSIPCO 2013)
• Conference date: 2013-09-09 - 2013-09-13
• Conference place: Marrakech, Morocco
• Status: Published