We introduce a Bayesian estimation approach for the passive localization of an acoustic source in shallow water using a single mobile receiver. The proposed probabilistic focalization method estimates the time-varying source location in the presence of measurement-origin uncertainty. In particular, probabilistic data association is performed to match time-differences-of-arrival (TDOA) observations extracted from the acoustic signal to TDOAs predictions provided by the statistical model. The performance of our approach is evaluated using real acoustic data recorded by a single mobile receiver.