Time delay estimation (TDE) plays an important role in localizing and tracking radiating acoustic sources. Although many efforts have been devoted to this problem in the literature, the robustness of TDE with respect to noise and reverberation remains a great challenge for practical systems. In this paper, we investigate the TDE problem in acoustic single-input/multiple-output (SIMO) systems in reverberant and noisy environments. We first define a Cauchy estimator in the frequency domain, which is robust in dealing with speech as the SIMO system's excitation. This robust estimator is then used to construct a cost function, from which a robust multichannel frequency-domain adaptive filter is deduced. This adaptive algorithm is subsequently employed to blindly identify the acoustic impulse responses between the source and the microphones. Finally, the time difference of arrival is determined from the identified channel responses.