Joint microphones and sources localization can be achieved by using both time of arrival (TOA) and time difference of arrival (TDOA) measurements, even in scenarios where both microphones and sources are asynchronous due to unknown emission time of human voices or sources and unknown recording start time of independent microphones. However, TOA measurements require both microphone signals and the waveform of source signals while TDOA measurements can be obtained using microphone signals alone. In this letter, we explore the sufficiency of using only microphone signals for joint microphones and sources localization by presenting two mapping functions for both TOA and TDOA formulas. Our proposed mapping functions demonstrate that the transformations of TOA and TDOA formulas can be the same, indicating that microphone signals alone are sufficient for joint microphones and sources localization without knowledge of the waveform of source signals. We have validated our proposed mapping functions through both mathematical proof and experimental results.

翻译：联合麦克风和声源定位可以通过同时使用到达时间（TOA）和到达时间差（TDOA）测量来实现，即使在麦克风和声源因人体语音或声源未知发射时间以及独立麦克风未知录音起始时间而导致异步的场景下也是如此。然而，TOA测量需要麦克风信号和声源信号的波形，而TDOA测量仅凭麦克风信号即可获得。本文通过提出针对TOA和TDOA公式的两种映射函数，探讨了仅使用麦克风信号进行联合麦克风和声源定位的充分性。我们提出的映射函数表明，TOA和TDOA公式的变换可以相同，这意味着仅凭麦克风信号足以实现联合麦克风和声源定位，而无需了解声源信号的波形。我们通过数学证明和实验验证了所提出的映射函数。