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We propose a robust two-dimensional polynomial beamformer design method,formulated as a convex optimization problem, which allows for flexible steeringof a previously proposed data-independent robust beamformer in both azimuth andelevation direction.~As an exemplary application, the proposed two-dimensionalpolynomial beamformer design is applied to a twelve-element microphone array,integrated into the head of a humanoid robot. To account for the effects of therobot's head on the sound field, measured head-related transfer functions areintegrated into the optimization problem as steering vectors. Thetwo-dimensional polynomial beamformer design is evaluated usingsignal-independent and signal-dependent measures. The results confirm that theproposed polynomial beamformer design approximates the original fixedbeamformer design very accurately, which makes it an attractive approach forrobust real-time data-independent beamforming.

Design of robust two-dimensional polynomial beamformers as a convex optimization problem with application to robot audition