The array invariant, a robust approach to source-range estimation in shallow water, is based on the dispersion characteristics of broadband signals in ideal waveguides. It involves time-domain plane-wave beamforming using a vertical line array (VLA) to separate multiple coherent arrivals in beam angle and travel time. Typically, a probe signal (i.e., a cooperating source) is required to estimate the Green's function, but the array invariant has been recently extended to a ship of opportunity radiating random signals using a ray-based blind deconvolution [Byun, Kim, Cho, Song, and Byun, J. Acoust. Soc. Am. 142, EL286–EL291 (2017)]. Still, one major drawback is its sensitivity to the array tilt, shifting the beam angles and adversely affecting the array invariant parameter that determines the source range. In this paper, a simple optimization algorithm for simultaneous estimation of the array tilt and the source range is presented. The method is applied to a ship of opportunity (200–900 Hz) circling around a 56-m long VLA at a speed of 3 knots (1.5 m/s) at ranges of 1.8–3.6 km in approximately 100-m deep shallow water. It is found that the standard deviation of the relative range error significantly reduces to about 4%, from 14% with no compensation of the array tilt. The estimated tilt angle displayed as a function of the ship's azimuth angle reveals that the VLA is tilted about 3° towards the northwest, suggesting that the array invariant can serve as a remote sensing technique for calibration of the array tilt using a source of opportunity.

The feasibility of tracking a ship radiating random and anisotropic noise is investigated using ray-based blind deconvolution (RBD) and array invariant (AI) with a vertical array in shallow water. This work is motivated by a recent report [Byun, Verlinden, and Sabra, J. Acoust. Soc. Am. 141, 797–807 (2017)] that RBD can be applied to ships of opportunity to estimate the Green's function. Subsequently, the AI developed for robust source-range estimation in shallow water can be applied to the estimated Green's function via RBD, exploiting multipath arrivals separated in beam angle and travel time. In this letter, a combination of the RBD and AI is demonstrated to localize and track a ship of opportunity (200–900 Hz) to within a 5% standard deviation of the relative range error along a track at ranges of 1.8–3.4 km, using a 16-element, 56-m long vertical array in approximately 100-m deep shallow water.

This paper compares the localization performance of array invariant (AI) and matched field processing (MFP) using a ship of opportunity radiating random noise (200–900 Hz) and a tilted vertical array. AI is a deterministic approach to source-range estimation (i.e., depth-blind), exploiting the dispersion characteristics of broadband signals with minimal/no knowledge of the environment in shallow water. It involves time-domain plane-wave beamforming to separate multiple coherent arrivals (eigenrays) in beam angle and travel time, called “beam-time migration,” from which the source range is directly estimated. In contrast, MFP is a model-based approach that requires accurate knowledge of the environment and array geometry (e.g., array tilt) to generate “replicas” for all possible source locations, finding the best match in the two-dimensional ambiguity surface of range and depth. While AI and MFP are both sensitive to array tilt, AI is equipped with self-calibration capability to estimate the array tilt and source range simultaneously. With the array tilt information from AI incorporated, the performance of MFP for range estimation can be comparable to that of AI to such an extent that the environmental knowledge is accurate.

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.

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When using a sparse array, locating the target signal of a high-frequency component is difficult. Although forecasting the direction in a sparse situation is challenging, the frequency–wavenumber (f–k) spectrum can simultaneously determine the direction and frequency of the analyzed signal. The striation of the f–k spectrum shifts along the wavenumber axis in a sparse situation, which reduces the spatial resolution required to determine the target's direction using the f–k spectrum. In this study, f–k spectra of a high-frequency signal were used for near-field source localization. Snapping shrimp sounds (5–24 kHz) from SAVEX15 (a shallow-water acoustic variability experiment conducted in May 2015) were used as the data source, and a simulation was used to evaluate the proposed method. Beam steering was performed before creating the f–k spectrum to improve spatial resolution. We found that the spatial resolution was improved, and the location of the sound source could be determined when a signal with beam steering was utilized. The shrimp sound from SAVEX15, a near-field broadband signal, was used to determine the shrimp's location (range, 38 m; depth, 100 m) and the tilt of the vertical line array. These results suggest that the proposed analysis helps to accurately estimate the location of sound source.