Adaptive iterative transfer learning for effective snapping shrimp sound detection.

This study aims to detect the bioacoustics signal in the underwater soundscape, specifically those produced by snapping shrimp, using adaptive iterative transfer learning. The proposed network is initially trained with pre-classified snapping shrimp sounds and Gaussian noise, then applied to classify and remove snapping-free noise from field data. This separated ambient noise is subsequently used for transfer learning. This process was iterated to distinguish more effectively between ambient noise and snapping shrimp sounds characteristics, resulting in improved classification. Through iterative transfer learning, significant improvements in precision and recall were observed. The application to field data confirmed that the trained network could detect signals that were difficult to identify using existing threshold classification methods. Furthermore, it was found that the rate of false detection decreased, and detection probability improved with each stage. This research demonstrates that incorporating the noise characteristics of field data into the trained network via iterative transfer learning can generate more realistic training data. The proposed network can successfully detect signals that are challenging to identify using existing threshold classification methods.

Source localization based on steered frequency-wavenumber analysis for sparse array.

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.

An overview of array invariant for source-range estimation in shallow water.

Traditional matched-field processing (MFP) refers to array processing algorithms, which fully exploit the physics of wave propagation to localize underwater acoustic sources. As a generalization of plane wave beamforming, the "steering vectors," or replicas, are solutions of the wave equation descriptive of the ocean environment. Thus, model-based MFP is inherently sensitive to environmental mismatch, motivating the development of robust methods. One such method is the array invariant (AI), which instead exploits the dispersion characteristics of broadband signals in acoustic waveguides, summarized by a single parameter known as the waveguide invariant ß. AI employs conventional plane wave beamforming and utilizes coherent multipath arrivals (eigenrays) separated into beam angle and travel time for source-range estimation. Although originating from the ideal waveguide, it is applicable to many realistic shallow-water environments wherein the dispersion characteristics are similar to those in ideal waveguides. First introduced in 2006 and denoted by χ, the dispersion-based AI has been fully integrated with ß. The remarkable performance and robustness of AI were demonstrated using various experimental data collected in shallow water, including sources of opportunity. Further, it was extended successfully to a range-dependent coastal environment with a sloping bottom, using an iterative approach and a small-aperture array. This paper provides an overview of AI, covering its basic physics and connection with ß, comparison between MFP and AI, self-calibration of the array tilt, and recent developments such as adaptive AI, which can handle the dependence of ß on the propagation angle, including steep-angle arrivals.

The waveguide invariant for a Pekeris waveguide.

A closed-form waveguide invariant ß for a Pekeris waveguide is derived. It is based on the modal Wentzel-Kramers-Brillouin (WKB) dispersion equation and implicit differentiation, in conjunction with the concept of the "effective boundary depth," ΔH(θ), where θ is the propagation angle. First, an explicit formula for ß(m,n) between mode pairs is obtained assuming an ideal waveguide of the effective waveguide depth, H+ΔH(θ), and provides an excellent agreement with the reference value for the Pekeris waveguide of depth H obtained using the normal mode program kraken. Then, a closed-form expression for a group of adjacent modes is derived: ß=(H+ΔH(θ))/(H/ cos2 θ-ΔH(θ)), which can be approximated by ß=cos2 θ as ΔH(θ)/H≪1, the analytical expression for an ideal waveguide.

Direction-of-Arrival Estimation Based on Frequency Difference-Wavenumber Analysis for Sparse Vertical Array Configuration.

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 (Δf-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 Δf-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.

Localization of a distant ship using a guide ship and a vertical array.

A method is presented for estimating the range of a distant ship in shallow water using a vertical array and a guide ship at a known range close to the array. The method involves a combination of four different approaches: blind deconvolution, waveguide invariant, virtual receiver (VR), and array invariant. (1) Blind deconvolution extracts a time-domain Green's function from the broadband acoustic source (guide ship). (2) The Green's function is extrapolated into adjacent ranges using the waveguide invariant, generating a horizontal array of synthetic guide sources. (3) Each guide source then turns into a VR where the output approximates the signal that the distant (objective) ship will produce at the location of the guide source. (4) The horizontal virtual array around the guide ship applies the blind deconvolution again to estimate the Green's function for the objective source, followed by the array invariant to estimate the distance between the two ships. The proposed method is demonstrated using a ship of opportunity radiating broadband noise (100-500 Hz) and a 56.25-m long vertical array in approximately 100-m water.

Adaptive array invariant in range-dependent environments with variable bathymetry.

The adaptive array invariant developed for source-range estimation in shallow water can incorporate the propagation-angle dependence of the waveguide invariant for an ideal waveguide (ß=cos2θ) [Byun and Song, J. Acoust. Soc. Am. 148, 925-933 (2020)]. This paper extends the approach to weakly (adiabatic) range-dependent environments with variable bathymetry, wherein the waveguide invariant is a complex function of the bathymetry between source and receiver as well as the propagation angle in powers of sin2θ. For a given bathymetry, the adaptive array invariant can be implemented in an iterative fashion, and its remarkable performance is demonstrated using a short-aperture vertical array (2.8 m) for a broadband source (0.5-3.5 kHz) towed on a continental slope where the water depth varies from 87.5 to 55 m over a 5-km range.

Extracting Green's functions between ships of opportunity using a vertical array.

A theoretical method for estimating the Green's function between two points in an acoustic waveguide was proposed using a vertical source array that spans sufficient waveguide depth [Roux and Fink, J. Acoust. Soc. Am. 113, 1406-1416 (2003)]. This paper shows that by reversing the role of sources and receivers, the Green's function between two ships (sources) can be extracted using a vertical receiver array with a limited aperture. First, the Green's functions from each ship are estimated along the array via blind deconvolution. Then the Green's function between two ships is obtained by either correlation or convolution of the individual Green's functions summed over the array, depending on the array position with respect to the ships. The feasibility of extracting Green's functions between ships of opportunity radiating random broadband (100-500 Hz) noise is demonstrated using a 56.25-m aperture vertical array in approximately 100-m shallow water.

Adaptive array invariant.

The array invariant (χ) developed for robust source-range estimation in shallow water is based on the broadband dispersion characteristics in ideal waveguides that can be summarized by the waveguide invariant, ß=cos2θ, with propagation angle θ. The standard array invariant relies on the waveguide invariant being constant, e.g., ß = 1, valid for small propagation angles (θ<20°). In this paper, the array invariant is extended to fully incorporate the angle dependence of the waveguide invariant (ß=cos2θ), referred to as adaptive array invariant and denoted by χß=χ/ß, which, in theory, provides a perfect range estimate without constraining the propagation angle. The superior performance of the adaptive array invariant is illustrated via numerical simulations in an ideal waveguide, and then demonstrated using experimental data from a ship of opportunity radiating broadband noise (200-900 Hz) and a vertical array in a shallow-water environment.

Extrapolating Green's functions using the waveguide invariant theory.

The broadband interference structure of sound propagation in a waveguide can be described by the waveguide invariant, ß, that manifests itself as striations in the frequency-range plane. At any given range (r), there is a striation pattern in frequency (ω), which is the Fourier transform of the multipath impulse response (or Green's function). Moving to a different range (r+Δr), the same pattern is retained but is either stretched or shrunken in ω in proportion to Δr, according to Δω/ω=ß(Δr/r). The waveguide invariant property allows a time-domain Green's function observed at one location, g(r,t), to be extrapolated to adjacent ranges with a simple analytic relation: g(r+Δr,t)≃g(r,α(t-Δr/c)), where α=1+ß(Δr/r) and c is the nominal sound speed of 1500 m/s. The relationship is verified in terms of range variation of the eigenray arrival times via simulations and by using real data from a ship of opportunity radiating broadband noise (200-900 Hz) in a shallow-water environment, where the steep-angle arrivals contributing to the acoustic field have ß≈0.92.

Multiple constraint matched field processing tolerant to array tilt mismatch.

A multiple constraint method (MCM) specifically designed to accommodate the uncertainty of array tilt is developed for matched field processing (MFP). Combining the MCM with the white noise gain constraint method results in a processor that is tolerant to both array tilt and environmental mismatch. Experimental results verify the robustness of the proposed MFP to localize and track a surface ship radiating broadband noise (200-500 Hz), using a 56-m long vertical array with tilt in approximately 100-m deep shallow water.

Localization of multiple ships using a vertical array in shallow water.

The blind deconvolution employs conventional plane-wave beamforming using an array, selects a well-resolved angle of arrival for beam steering to estimate the phase component of an unknown source waveform, and then extracts the Green's function between the source and the array. In this letter, the approach is extended to multiple-ship scenarios in which the multipath arrivals from one ship are masked by other ships, adopting the basic concept of successive interference cancellation. Once individual Green's functions are available, the array invariant method based on the beam-time migration can be subsequently applied to estimate each source range. Simultaneous localization of two ships radiating broadband noise (200-900 Hz) is demonstrated using a 16-element, 56-m long vertical array in approximately 100-m deep shallow water.

Remote acoustic illumination using time reversal and a surface ship.

Time-reversal (TR) transmission of the Green's function between a time-reversal mirror (TRM) and a probe source (PS) in an acoustic waveguide produces a spatio-temporal focus at the PS location. The TR focus then behaves as a virtual point source in the outbound direction with respect to the TRM. Further, a collection of adjacent TR focuses may constitute a virtual source array (VSA) that can serve as a remote platform, redirecting the focused field to a selected location beyond the VSA for which the Green's function is not available a priori. The practical limitation to the VSA implementation, however, is the requirement of a PS at multiple adjacent locations to obtain the Green's functions between TRM and VSA. Alternatively, this work proposes the use of a surface ship radiating broadband noise as a PS in conjunction with the waveguide invariant theory, instantly generating a horizontal VSA. The feasibility of remote acoustic illumination using a ship and a TRM is demonstrated using numerical simulations in shallow water.

Real-time tracking of a surface ship using a bottom-mounted horizontal array.

The cascade of blind deconvolution and array invariant has been successful to localize and track a surface ship radiating random waveforms, using a 56-m long vertical array in 100-m deep shallow water. In this paper, it is shown that a 60-m long, bottom-mounted horizontal array can be utilized for blind deconvolution to extract the Green's functions from the same ship (100-800 Hz), in conjunction with the array invariant for source-range estimation. The additional information obtained with a horizontal array is the source bearing (azimuth angle, ϕ) from the well-resolved ray angle identified for blind deconvolution to extract the phase component of the unknown source waveforms. The overall tracking performance shows good agreement with global positioning system (GPS) measurements to less than 11% in terms of standard deviation of relative range error at ranges of 0.3-1.5 km, except when the ship is around the broadside (e.g., | ϕ | < 25 ° ) of the horizontal array. On the other hand, the source bearings are in excellent agreement with the GPS data except near the endfire due to the lower angular resolution. The potential for simultaneous localization of multiple ships is also discussed.

Simultaneous localization of a surface ship and a submerged towed source (L).

The cascade of blind deconvolution and array invariant has been successful for localizing a single source, either a surface ship or a submerged source, using a vertical array without knowledge of the environment or source waveform in shallow water. In this letter, the blind deconvolution is extended to a two-source case where individual Green's functions are separately extracted by exploiting a distinct group of modes strongly excited at different source depths. The subsequent array invariant confirms that a surface ship and a towed source at 50-m depth can be simultaneously localized using a 56-m long vertical array in 100-m deep shallow water.

Array invariant-based calibration of array tilt using a source of opportunity.

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.

Performance comparisons of array invariant and matched field processing using broadband ship noise and a tilted vertical array.

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.

Ray-based blind deconvolution of shipping sources using multiple beams separated by alternating projection.

This article presents a method for improving the performance of the ray-based blind deconvolution (RBD) algorithm, which was first proposed by Sabra, Song, and Dowling [J. Acoust. Soc. Am. 127(2), EL42-EL47 (2010)]. In order to retrieve the channel impulse response (CIR), the original RBD algorithm uses the source signal phase from a selected single beam output. However, when the impinging multipath signals have low coherence, the channel estimate from a selected beam may not show all paths correctly. In this research, the maximum likelihood estimator, which is called the alternating projection, is applied to separate multipath signals. Then the multiple CIRs obtained from those separated signals are coherently combined. This results in more robust detection of existing multipaths. The performance of the proposed method is verified using Noise09 sea experiment data, where the proposed method better resolves the multipath arrival structure.

Array invariant-based ranging of 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.

Cascade of blind deconvolution and array invariant for robust source-range estimation.

The array invariant proposed for robust source localization in shallow water is based on the dispersion characteristics in ideal waveguides. It involves conventional plane-wave beamforming using a vertical array, exploiting multiple arrivals separated in beam angle and travel time, i.e., beam-time migration. The approach typically requires either a short pulse emitted by a source or the Green's function that can be estimated from a probe signal to resolve distinct multipath arrivals. In this letter, the array invariant method is extended to unknown source waveforms by extracting the Green's function via blind deconvolution. The cascade of blind deconvolution and array invariant for robust source-range estimation is demonstrated using a 16-element, 56-m long vertical array at various ranges (1.5-3.5 km) from a towed source broadcasting broadband communication waveforms (0.5-2 kHz) in approximately 100-m deep shallow water.