Understanding the characteristics of underwater sound channels is essential for various remote sensing applications. Typically, the time-domain Green’s function or channel impulse response (CIR) is obtained using computationally intensive acoustic propagation models that rely on accurate environmental data, such as sound speed profiles and bathymetry. Ray-based blind deconvolution (RBD) offers a less computationally demanding alternative using plane-wave beamforming to estimate the Green’s function. However, the presence of noise can obscure low coherence ray arrivals, making accurate estimation challenging. This paper introduces a method using the waveguide invariant to improve the signal-to-noise ratio (SNR) of broadband Green’s functions for a moving source without prior knowledge of range. By utilizing RBD and the frequency shifts from the striation slope, we coherently combine individual Green’s functions at adjacent ranges, significantly improving the SNR. In this study, we demonstrated the proposed method via simulation and broadband noise data (200–900 Hz) collected from a moving ship in 100 m deep shallow water.

Frequency–wavenumber (f–k) analysis can estimate the direction of arrival (DOA) of broadband signals received on a vertical array. When the vertical array configuration is sparse, it results in an aliasing error due to spatial sampling; thus, several striation patterns can emerge in the f–k domain. This paper extends the f–k analysis to a sparse receiver-array, wherein a multitude of sidelobes prevent resolving the DOA estimates due to spatial aliasing. The frequency difference-wavenumber ($\Delta f$–k) analysis is developed by adopting the concept of frequency difference, and demonstrated its performance of DOA estimation to a sparse receiver array. Experimental results verify the robustness of the proposed $\Delta f$–k analysis in the estimation of the DOA of cracking sounds generated by the snapping shrimps, which were recorded by a sparse vertical array configuration during the shallow water experiment.

In shallow-water environments, source localization often suffers from reduced performance in conventional array signal processing techniques for frequency bands above 1 kHz due to environmental mismatch. A recently proposed technique, called the steered frequency–wavenumber (SFK) analysis method, overcomes this limitation. By incorporating beam-steering techniques into frequency–wavenumber analysis, this method enables target localization even in sparse conditions where high-frequency signals are received. This study extends the SFK method by applying various adaptive signal processing techniques, with a particular focus on the minimum-variance distortionless response and white noise gain constraint methods. Using snapping shrimp sounds from the SAVEX15 experiment, we analyzed localization performance and compared it with the Bartlett SFK approach. The snapping shrimp signals have frequency components ranging from 5 to 24 kHz and exhibit impulsive characteristics with a duration of 0.2 ms. Signals recorded by a sparse vertical array of 16 sensors, with a 60-m aperture in 100-m shallow water, enabled the localization of a source at a range of 38 m and a depth of 99.8 m.

This study proposes a TDOA-MLP method for estimating the range of snapping shrimp sources from the array-wide time-difference-of-arrival (TDOA) structure measured by a vertical line array. BELLHOP arrival-time replicas were generated for the SAVEX15 environment by varying source range, array tilt, and maximum water depth, and a multilayer perceptron was trained to estimate source range with array tilt as an auxiliary output. To provide a more stringent assessment of range generalization, six continuous source-range intervals were excluded from training, and only their inner portions were used for blocked-holdout evaluation, providing an approximately 2-m separation from the nearest training ranges. The resulting overall range-estimation mean absolute error (MAE) and root mean square error (RMSE) were 0.864 and 1.056 m, respectively, with regional MAEs of 0.762, 0.728, and 1.119 m for the near-, mid-, and far-range regions. Additional analyses showed that the estimation error increased with controlled arrival-time perturbations and varied with the maximum-depth condition. When applied to experimental SAVEX15 snapping shrimp data, the TDOA-MLP produced range distributions and snap-to-snap variations generally consistent with those obtained using template matching, steered frequency-wavenumber analysis, and frequency-difference matched-field processing. Relative to template matching, the mean absolute relative range difference was 4.54%. Because ground-truth source ranges were unavailable for the experimental data, the field results demonstrate consistency among the methods rather than absolute localization accuracy. The proposed method provides a low-dimensional learning-based approach for estimating the range of impulsive snapping shrimp signals from array-wide TDOA structures.