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The problem of estimating the direction of arrivals (DOA) of narrowband sources impinging on a uniform circular array is considered. We present a method that uses as input the values of a small number of uniformly spaced beams and apply a model-fitting approach taking into account the statistical properties of the beams. The approach, which is called the "global matched filter" fits simultaneously to the observations all the elements needed to explain them. It chooses, among all the representations satisfying a constraint with a sensible physical interpretation, the one with minimal energy. The method drastically improves upon the conventional beamformer and has a performance comparable with the best high-resolution (HR) techniques. It further applies when the number of sources exceeds the number of sensors: a situation that cannot be handled by standard HR techniques.