Statistical model and estimation method for ranging a moving ship using a single acoustic receiver in shallow water

Passive acoustics is a versatile tool for maritime situational awareness, enabling applications such as source detection and localization, marine mammal tracking, and geoacoustic inversion. This study focuses on estimating the range between an acoustic receiver and a transiting ship in an acoustically range-independent shallow water environment. Here, acoustic propagation can be modeled by a set of modes that are determined by the shallow water waveguide and seabed characteristics. These modes are dispersive, with phase and group velocities varying with frequency, and their interference produces striation patterns that depend on range and frequency in single-hydrophone spectrograms. These striation patterns can often be characterized by the waveguide invariant (WI), a single parameter describing the waveguide's properties. This paper presents a statistical model and corresponding WI-based range estimation approach using a single hydrophone, leveraging broadband and tonal sounds from a transiting ship. Using data from the Seabed Characterization Experiment 2017 (SBCEX17), the method was evaluated on two commercial ships under different environmental conditions and frequency bands. Range estimation errors remained below ±4% up to 62 km in the best case, with robust performance demonstrated in the 40-60 Hz band.