Multi-Frequency Direction of Arrival Estimation by Low-Rank Approximation
Abstract: We consider the problem of estimating the location of a number of wave-emitting sources, known as the direction of arrival problem. We consider both the two- and three-dimensional case. The method we use works for equally as well as unequally spaced sensors, that are located in (possibly) non-square regions. In the case of wideband signals we show how measurements from multiple frequencies can be used to improve the estimation. To make the direction of arrival estimation we formulate a low-rank optimization problem over so called Hankel matrices. The low-rank optimization problem is solved by a recent fixed-point algorithm, which is based on convex optimization. We also show how a function that is a sum of plane waves can be reconstructed from sparse measurements, once the directions of the waves have been estimated. We test the methods by numerical simulations. The improved performance when using multiple frequencies is clearly demonstrated in one of the examples.
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