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.Comment: 2 figure