Design of robust two-dimensional polynomial beamformers as a convex optimization problem with application to robot audition
This work addresses robust beamforming for robot audition, specifically for humanoid robots with microphone arrays, but it is incremental as it extends a previously proposed data-independent beamformer to two dimensions.
The authors tackled the problem of designing robust two-dimensional polynomial beamformers for flexible steering in azimuth and elevation by formulating it as a convex optimization problem, and the results showed that the proposed design approximates the original fixed beamformer very accurately, making it suitable for real-time applications.
We propose a robust two-dimensional polynomial beamformer design method, formulated as a convex optimization problem, which allows for flexible steering of a previously proposed data-independent robust beamformer in both azimuth and elevation direction.~As an exemplary application, the proposed two-dimensional polynomial beamformer design is applied to a twelve-element microphone array, integrated into the head of a humanoid robot. To account for the effects of the robot's head on the sound field, measured head-related transfer functions are integrated into the optimization problem as steering vectors. The two-dimensional polynomial beamformer design is evaluated using signal-independent and signal-dependent measures. The results confirm that the proposed polynomial beamformer design approximates the original fixed beamformer design very accurately, which makes it an attractive approach for robust real-time data-independent beamforming.