  We introduce a new method for robust beamforming, where the goal is to
estimate a signal from array samples when there is uncertainty in the angle of
arrival. Our method offers state-of-the-art performance on narrowband signals
and is naturally applied to broadband signals. Our beamformer operates by
treating the forward model for the array samples as unknown. We show that the
"true" forward model lies in the linear span of a small number of fixed linear
systems. As a result, we can estimate the forward operator and the signal
simultaneously by solving a bilinear inverse problem using least squares. Our
numerical experiments show that if the angle of arrival is known to only be
within an interval of reasonable size, there is very little loss in estimation
performance compared to the case where the angle is known exactly.
