When a broadband source of radiated noise transits past a fixed hydrophone, a Lloyd's mirror constructive/destructive interference pattern can be observed in the output spectrogram. By taking the spectrum of a (log) spectrum, the power cepstrum detects the periodic structure of the Lloyd's mirror fringe pattern by generating a sequence of pulses located at the fundamental quefrency and its multiples. The fundamental quefrency, which is the reciprocal of the frequency difference between adjacent destructive interference fringes, equates to the multipath delay time. An experiment is conducted where a motorboat transits past a hydrophone located about 1 m above the seafloor in very shallow water (20 m deep). The hydrophone has a frequency bandwidth of 90 kHz, and its output is sampled at 250 kHz. A cepstrogram database is compiled from multiple vessel transits, and its cepstrum-based feature vectors (along with ground-truth range data) form the input to train a convolutional neural network (CNN) so that it can predict the source range relative to the hydrophone for other (“unseen”) vessel transits. The CNN provides an accurate prediction of the instantaneous source range even when the range estimate from conventional multipath passive ranging is biased, which occurs at low grazing angles (<).
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