The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, e.g., by calibration and/or angle- of-arrival errors, which would otherwise seriously deteriorate the performance of an adaptive beamformer. Here, we examine robust Capon beamforming of multi-dimensional arrays, where robustness to angle-of-arrival errors is needed in both azimuth and elevation. It is shown that the commonly used spherical uncertainty sets are unable to control robustness in each of these directions independently. Here, we instead propose the use of flat ellipsoidal sets to control the angle-of-arrival un- certainty. To also allow for other errors, such as calibration errors, we combine these flat ellipsoids with a higher-dimension error ellipsoid. Computationally efficient automatic techniques for estimating the necessary uncertainty sets are derived, and the proposed methods are evaluated using both simulated data and experimental underwater acoustics measurements, clearly showing the benefits of the technique.
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