In an era where asynchronous environments pose challenges to traditional self-positioning methods, we propose a new transformation to the existing paradigm. Traditionally, time of arrival (TOA) measurements require both microphone and source signals, limiting their applicability in environments with unknown emission time of human voices or sources and unknown recording start time of independent microphones. To address this issue, our research pioneers a mapping function capable of transforming both TOA and time difference of arrival (TDOA) formulas, demonstrating, for the first time, that they can be identical to one another. This implies that microphone signals alone are sufficient for self-positioning without the need for source signal waveforms, a groundbreaking advancement in the field that carries the potential to revolutionize self-positioning techniques, expanding their applicability in challenging environments. Supported by a robust mathematical proof and compelling experimental results, this research represents a timely and significant contribution to the current discourse in signal, and audio processing.

翻译：在异步环境对传统自定位方法提出挑战的时代，我们提出了一种对现有范式的新转换。传统上，到达时间（TOA）测量需要同时使用麦克风和源信号，这限制了其在人声或声源发射时间未知、独立麦克风录音起始时间不确定的环境中的适用性。为解决这一问题，我们的研究率先提出一种能够同时转换TOA和到达时间差（TDOA）公式的映射函数，首次证明它们可以彼此等价。这意味着仅凭麦克风信号即可实现自定位，而无需源信号波形——这一突破性进展有望彻底革新自定位技术，扩展其在复杂环境中的适用性。该研究得到严谨的数学证明和令人信服的实验结果支撑，为当前信号与音频处理领域的讨论做出了及时且重要的贡献。