Localization of a sound source in a noisy environment by hyperbolic curves in quefrency domain

Time Difference of Arrivals (TDOAs) of sound waves between microphones have to do with source localization. How well a sound source can be localized depends on how precisely the TDOAs are estimated. Although many ways to estimate TDOA have been proposed, noise always prevents us from finding exact time differences more or less in practice. Cross correlation has been the most prevalent way to estimate time difference, and various cross correlations robust to noise have also been developed. Nevertheless, much remains to be done for exact TDOA estimation under noisy environments. A novel way to show time delays in quefrency domain by removing noise has been proposed, which is called Minimum Variance Cepstrum (MVC). In particular, it is practically desirable to visualize source position with as few number of sensors as possible. Once TDOAs are obtained precisely, it is enough to show the source position in a 2-D plane using hyperbolic curves with only three sensors. In this work, the MVC is adopted to accurately estimate TDOAs under noise, and a way to localize an acoustic source by intersecting hyperbolic curves using the TDOAs between three microphones is proposed. Numerical simulations on TDOA estimation and source localization with white Gaussian noise demonstrated that the proposed method worked well under the noisy environment, and we compared the results with those of other old but well-established cross correlation estimators. In addition, experiments to detect a leaking point on a pipe successfully showed where the leak sound was generated.