An important aspect of a humanoid robot is audition. Previous work has presented robot systems capable of sound localization and source segregation based on microphone arrays with various configurations. However, no theoretical framework for the design of these arrays has been presented. In the current paper, a design framework is proposed based on a novel array quality measure. The measure is based on the effective rank of a matrix composed of the generalized head related transfer functions (GHRTFs) that account for microphone positions other than the ears. The measure is shown to be theoretically related to standard array performance measures such as beamforming robustness and DOA estimation accuracy. Then, the measure is applied to produce sample designs of microphone arrays. Their performance is investigated numerically, verifying the advantages of array design based on the proposed theoretical framework.

翻译：人形机器人的一个重要方面是听觉。以往的研究已提出了基于不同构型麦克风阵列、能够实现声源定位和声源分离的机器人系统，但尚未建立用于设计这些阵列的理论框架。本文提出了一种基于新型阵列质量度量的设计框架。该度量基于广义头相关传递函数矩阵的有效秩，该函数可解释除耳朵位置外的麦克风位置分布。研究表明，该度量在理论上与波束形成鲁棒性、波达方向估计精度等标准阵列性能指标相关。随后，将该度量应用于生成麦克风阵列的示例设计方案，并通过数值仿真验证其性能，证实了基于该理论框架进行阵列设计的优越性。