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The standard Capon beamformer (SCB) is known to have better resolution and much better interference rejection capability than the standard data-independent beamformer when the array steering vector is accurately known. However, the major problem of SCB is that it lacks robustness in the presence of array steering vector errors. In this paper, we provide a natural extension of SCB, obtained via covariance matrix fitting, to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector, viz. a constant norm constraint and a spherical uncertainty set constraint, which we refer to as the doubly constrained robust Capon beamformer (DCRCB). DCRCB can be efficiently computed at a comparable cost with that of SCB. Performance comparisons of DCRCB and our previously proposed robust Capon beamformer (RCB) are also presented via a number of numerical examples.