On an Iterative Method for Direction of Arrival Estimation using Multiple Frequencies

Abstract

We develop a method for the estimation of the location of sources from measurements at multiple frequencies, including wideband measurements, recorded by a linear array of sensors. We employ interpolation matrices to address unequal sampling at different frequencies and make use of the Kronecker theorem to cast the nonlinear least squares problem associated with direction of arrival estimation into an optimization problem in the space of sequences generating Hankel matrices of fixed rank.We then obtain approximate solutions to this problem using the alternating direction method of multipliers. The resulting algorithm is simple and easy to implement. We provide numerical simulations that illustrate its excellent practical performance, significantly outperforming subspace-based methods both at low and high signal-to-noise ratio.