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We develop a parametric high-resolution method for the estimation of thefrequency nodes of linear combinations of complex exponentials with exponentialdamping. We use Kronecker's theorem to formulate the associated nonlinear leastsquares problem as an optimization problem in the space of vectors generatingHankel matrices of fixed rank. Approximate solutions to this problem areobtained by using the alternating direction method of multipliers. Finally, weextract the frequency estimates from the con-eigenvectors of the solutionHankel matrix. The resulting algorithm is simple, easy to implement and can beapplied to data with equally spaced samples with approximation weights, whichfor instance allows cases of missing data samples. By means of numericalsimulations, we analyze and illustrate the excellent performance of the method,attaining the Cram\'er-Rao bound.

Frequency estimation based on Hankel matrices and the alternating direction method of multipliers