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

## TL;DR

This paper introduces a convex optimization-based method for designing robust two-dimensional polynomial beamformers, enabling flexible steering in azimuth and elevation, with applications in robot audition and integration of head-related transfer functions.

## Contribution

It presents a novel convex optimization framework for 2D polynomial beamformer design that accounts for robot head effects, enhancing robustness and real-time applicability.

## Key findings

- Accurately approximates fixed beamformer design
- Effectively incorporates head-related transfer functions
- Demonstrates robustness in real-time scenarios

## Abstract

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.