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.