Reformulation of frequency-difference matched-field processor for high-frequency known-source localization.

Frequency-difference matched-field processing is a high-frequency source localization technique formulated by matching the frequency-difference autoproduct of the measured field and replicas at the difference-frequency. Although it successfully localizes sound sources by sparse vertical array in shallow or deep ocean with an environmental mismatch, there is still some ambiguity in replica modeling and signal processing. Here, the existing conventional processor is modified to match the bandwidth-averaged autoproduct of the measured field with replicas of the bandwidth-averaged autoproduct, or approximately its self-term for the expected source locations. The proposed processor is consistent with the perspective of matched-field processing and can naturally relieve some drawbacks of the existing one, such as low peak or low dynamic range on the ambiguity surface. Numerical tests are carried out in several shallow ocean environments and the source localization using experimental data are performed to confirm the properties of the proposed processor. It is found that the high-frequency diffracted field always leaves traces on its bandwidth-averaged autoproduct field. These high-frequency marks cause a bias in source localization in the presence of a sound speed mismatch even in low difference-frequencies.

3D Off-Grid Localization for Adjacent Cavitation Noise Sources Using Bayesian Inference.

The propeller tip vortex cavitation (TVC) localization problem involves the separation of noise sources in proximity. This work describes a sparse localization method for off-grid cavitations to estimates their precise locations while keeping reasonable computational efficiency. It adopts two different grid (pairwise off-grid) sets with a moderate grid interval and provides redundant representations for adjacent noise sources. To estimate the position of the off-grid cavitations, a block-sparse Bayesian learning-based method is adopted for the pairwise off-grid scheme (pairwise off-grid BSBL), which iteratively updates the grid points using Bayesian inference. Subsequently, simulation and experimental results demonstrate that the proposed method achieves the separation of adjacent off-grid cavitations with reduced computational cost, while the other scheme suffers from a heavy computational burden; for the separation of adjacent off-grid cavitations, the pairwise off-grid BSBL took significantly less time (29 s) compared with the time taken by the conventional off-grid BSBL (2923 s).

Passive Sonar Target Identification Using Multiple-Measurement Sparse Bayesian Learning.

Accurate estimation of the frequency component is an important issue to identify and track marine objects (e.g., surface ship, submarine, etc.). In general, a passive sonar system consists of a sensor array, and each sensor receives data that have common information of the target signal. In this paper, we consider multiple-measurement sparse Bayesian learning (MM-SBL), which reconstructs sparse solutions in a linear system using Bayesian frameworks, to detect the common frequency components received by each sensor. In addition, the direction of arrival estimation was performed on each detected common frequency component using the MM-SBL based on beamforming. The azimuth for each common frequency component was confirmed in the frequency-azimuth plot, through which we identified the target. In addition, we perform target tracking using the target detection results along time, which are derived from the sum of the signal spectrum at the azimuth angle. The performance of the MM-SBL and the conventional target detection method based on energy detection were compared using in-situ data measured near the Korean peninsula, where MM-SBL displays superior detection performance and high-resolution results.

Underwater Acoustic Signal Detection Using Calibrated Hidden Markov Model with Multiple Measurements.

It is important to find signals of interest (SOIs) when operating sonar systems. A threshold-based method is generally used for SOI detection. However, it induces a high false alarm rate at a low signal-to-noise ratio. On the other side, machine-learning-based detection is performed to obtain more reliable detection results using abundant training data, costing intensive time and labor. We propose a method with favorable detection performance by using a hidden Markov model (HMM) for sequential acoustic data, which requires no separate training data. Since the detection results from HMM are significantly affected by the random initial parameters of HMM, the genetic algorithm (GA) is adopted to reduce the sensitivity of the initial parameters. The tuned initial parameters from GA are used as a start point for the subsequent Baum-Welch algorithm updating the HMM parameters. Furthermore, multiple measurements from arrays are exploited both in determining the proper initial parameters with GA and updating the parameters with the Baum-Welch algorithm. In contrast to the standard random selection of the initial point with single measurement, a stable initial point setting by the GA ensures improved SOI detections with the Baum-Welch algorithm using the multiple measurements, which are demonstrated in passive and active acoustic data. Particularly, the proposed method shows the most confidential detection in finding weak elastic surface waves from target, compared to existing methods such as conventional HMM.

Frequency Analysis of Acoustic Data Using Multiple-Measurement Sparse Bayesian Learning.

Passive sonar systems are used to detect the acoustic signals that are radiated from marine objects (e.g., surface ships, submarines, etc.), and an accurate estimation of the frequency components is crucial to the target detection. In this paper, we introduce sparse Bayesian learning (SBL) for the frequency analysis after the corresponding linear system is established. Many algorithms, such as fast Fourier transform (FFT), estimate signal parameters via rotational invariance techniques (ESPRIT), and multiple signal classification (RMUSIC) has been proposed for frequency detection. However, these algorithms have limitations of low estimation resolution by insufficient signal length (FFT), required knowledge of the signal frequency component number, and performance degradation at low signal to noise ratio (ESPRIT and RMUSIC). The SBL, which reconstructs a sparse solution from the linear system using the Bayesian framework, has an advantage in frequency detection owing to high resolution from the solution sparsity. Furthermore, in order to improve the robustness of the SBL-based frequency analysis, we exploit multiple measurements over time and space domains that share common frequency components. We compare the estimation results from FFT, ESPRIT, RMUSIC, and SBL using synthetic data, which displays the superior performance of the SBL that has lower estimation errors with a higher recovery ratio. We also apply the SBL to the in-situ data with other schemes and the frequency components from the SBL are revealed as the most effective. In particular, the SBL estimation is remarkably enhanced by the multiple measurements from both space and time domains owing to remaining consistent signal frequency components while diminishing random noise frequency components.

Detection of Direction-Of-Arrival in Time Domain Using Compressive Time Delay Estimation with Single and Multiple Measurements.

The compressive time delay estimation (TDE) is combined with delay-and-sum beamforming to obtain direction-of-arrival (DOA) estimates in the time domain. Generally, the matched filter that detects the arrivals at the hydrophone is used with beamforming. However, when the ocean noise smears the arrivals, ambiguities appear in the beamforming results, degrading the DOA estimation. In this work, compressive sensing (CS) is applied to accurately evaluate the arrivals by suppressing the noise, which enables the correct detection of arrivals. For this purpose, CS is used in two steps. First, the candidate time delays for the actual arrivals are calculated in the continuous time domain using a grid-free CS. Then, the dominant arrivals constituting the received signal are selected by a conventional CS using the time delays in the discrete time domain. Basically, the compressive TDE is used with a single measurement. To further reduce the noise, common arrivals over multiple measurements, which are obtained using the extended compressive TDE, are exploited. The delay-and-sum beamforming technique using refined arrival estimates provides more pronounced DOAs. The proposed scheme is applied to shallow-water acoustic variability experiment 15 (SAVEX15) measurement data to demonstrate its validity.

Broadband acoustic signal variability induced by internal solitary waves and semidiurnal internal tides in the northeastern East China Sea.

The relation between high-frequency broadband acoustic signal variability and two types of internal waves (short-period internal solitary waves; ISWs, and semidiurnal internal tides; ITs) is investigated using data collected during the shallow-water acoustic variability experiment 2015 in the northeastern East China Sea. In this flat (∼100 m depth) region, an underwater sound channel with sound speed profile (SSP) variability observed during the experiment significantly affects the acoustic variability induced by the ISW, and the arrival structure of the channel impulse response (CIR) modeled by ray tracing. To model the range-dependent SSP due to ISW, the location and characteristics of the mode-1 ISW of wavelength (0.5-1 km) are estimated and verified based on the two-layer Korteweq-de Vries theory and by analyzing the observed temperature fluctuations. It is found from comparison between the measured and modeled CIRs that the ISW scatters the arrival structures of refracted rays. Meanwhile, semidiurnal ITs change the channel size modeled as range-independent considering the wavelengths (15-40 km) longer than the model range (3 km). Higher centroid of acoustic arrival time is found with lower isotherm depressions owing to the multimode ITs, indicative of acoustic energy focusing at the lower channel region.

Acoustic Classification of Surface and Underwater Vessels in the Ocean Using Supervised Machine Learning.

Four data-driven methods-random forest (RF), support vector machine (SVM), feed-forward neural network (FNN), and convolutional neural network (CNN)-are applied to discriminate surface and underwater vessels in the ocean using low-frequency acoustic pressure data. Acoustic data are modeled considering a vertical line array by a Monte Carlo simulation using the underwater acoustic propagation model, KRAKEN, in the ocean environment of East Sea in Korea. The raw data are preprocessed and reorganized into the phone-space cross-spectral density matrix (pCSDM) and mode-space cross-spectral density matrix (mCSDM). Two additional matrices are generated using the absolute values of matrix elements in each CSDM. Each of these four matrices is used as input data for supervised machine learning. Binary classification is performed by using RF, SVM, FNN, and CNN, and the obtained results are compared. All machine-learning algorithms show an accuracy of >95% for three types of input data-the pCSDM, mCSDM, and mCSDM with the absolute matrix elements. The CNN is the best in terms of low percent error. In particular, the result using the complex pCSDM is encouraging because these data-driven methods inherently do not require environmental information. This work demonstrates the potential of machine learning to discriminate between surface and underwater vessels in the ocean.

Multiple snapshot grid free compressive beamforming.

Compressive sensing (CS) based estimation technique utilizes a sparsity promoting constraint and solves the direction-of-arrival (DOA) estimation problem efficiently with high resolution. In this paper a grid free CS based DOA estimation technique is proposed, which uses sequential multiple snapshot data. Conventional CS technique suffers from a basis mismatch issue, while grid free CS technique is relieved of basis mismatch problem. Moreover, when the DOAs are stationary, multiple snapshot processing provides stable estimates over fluctuating single snapshot processing results. For multiple snapshot processing, the generalized version of total variation norm (group total variation norm) is implemented to impose a common sparsity pattern of multiple snapshot solution vectors in a continuous angular domain. Furthermore, an extended version is proposed using the singular value decomposition technique to mitigate computational complexity resulting from a large number of multiple snapshots. Data from SWellEx-96 are used to examine the proposed method. From the experimental data, it was observed that the present method not only offers high resolution even when the sources are coherent, but also the basis mismatch in the conventional CS method can be avoided.

Compressive time delay estimation off the grid.

This paper describes a time delay estimation (TDE) technique using compressive sensing (CS) off the grid, which estimates the channel impulse response in a continuous time domain. The TDE can be formulated into a sparse signal reconstruction problem where the CS technique can be applied. Previous works have used standard finite dimensional CS with evenly discretized grids. However, the actual time delays will not always lie on the discrete grid, and this mismatch between the actual and discretized time delays results in reconstruction degradation. To overcome the basis mismatch, a TDE technique using an off the grid CS framework is proposed by modifying the scheme in the off the grid direction of arrival (DOA) estimation [Xenaki and Gerstoft, J. Acoust. Soc. Am. 137(4), 1923-1935 (2015)]. The effectiveness of the suggested method is demonstrated on real data from a water tank experiment. The off the grid CS TDE is shown to have super-resolution, which enables close arrivals to be distinguished.

Time-domain Helmholtz-Kirchhoff integral for surface scattering in a refractive medium.

The time-domain Helmholtz-Kirchhoff (H-K) integral for surface scattering is derived for a refractive medium, which can handle shadowing effects. The starting point is the H-K integral in the frequency domain. In the high-frequency limit, the Green's function can be calculated by ray theory, while the normal derivative of the incident pressure from a point source is formulated using the ray geometry and ray-based Green's function. For a corrugated pressure-release surface, a stationary phase approximation can be applied to the H-K integral, reducing the surface integral to a line integral. Finally, a computationally-efficient, time-domain H-K integral is derived using an inverse Fourier transform. A broadband signal scattered from a sinusoidal surface in an upwardly refracting medium is evaluated with and without geometric shadow corrections, and compared to the result from a conventional ray model.

Numerical study of three-dimensional sound reflection from corrugated surface waves.

When a sound wave propagates in a water medium bounded by a smooth surface wave, reflection from a wave crest can lead to focusing and result in rapid variation of the received waveform as the surface wave moves [Tindle, Deane, and Preisig, J. Acoust. Soc. Am. 125, 66-72 (2009)]. In prior work, propagation paths have been constrained to be in a plane parallel to the direction of corrugated surface waves, i.e., a two-dimensional (2-D) propagation problem. In this paper, the azimuthal dependence of sound propagation as a three-dimensional (3-D) problem is investigated using an efficient, time-domain Helmholtz-Kirchhoff integral formulation. When the source and receiver are in the plane orthogonal to the surface wave direction, the surface wave curvature vanishes in conventional 2-D treatments and the flat surface simply moves up and down, resulting in minimal temporal variation of the reflected signal intensity. On the other hand, the 3-D propagation analysis reveals that a focusing phenomenon occurs in the reflected signal due to the surface wave curvature formed along the orthogonal plane, i.e., out-of-plane scattering.

Comment on "Reconstructing surface wave profiles from reflected acoustic pulses" [J. Acoust. Soc. Am. 133(5), 2597-2611 (2013)].

A computationally efficient, time-domain Helmholtz-Kirchhoff (H-K) integral was derived and applied to reconstructing surface wave profiles from reflected acoustic pulses [Walstead and Deane, J. Acoust. Soc. Am. 133, 2597-2611 (2013)]. However, the final form of the integral equation incorporating a stationary phase approximation contained a complex phase term exp(iπ/4), which cannot be treated as a simple time delay. In this work, a real time-domain H-K integral is presented that includes an additional Hilbert transform of the time-derivative of the transmitted pulse. Numerical simulation with a sinusoidal surface shows good agreement between the real time-domain formulation and exact H-K integral, while achieving a significant improvement in computational speed (e.g., 2 orders of magnitude).

Compressive spherical beamforming for localization of incipient tip vortex cavitation.

Noises by incipient propeller tip vortex cavitation (TVC) are generally generated at regions near the propeller tip. Localization of these sparse noises is performed using compressive sensing (CS) with measurement data from cavitation tunnel experiments. Since initial TVC sound radiates in all directions as a monopole source, a sensing matrix for CS is formulated by adopting spherical beamforming. CS localization is examined with known source acoustic measurements, where the CS estimated source position coincides with the known source position. Afterwards, CS is applied to initial cavitation noise cases. The result of cavitation localization was detected near the upper downstream area of the propeller and showed less ambiguity compared to Bartlett spherical beamforming. Standard constraint in CS was modified by exploiting the physical features of cavitation to suppress remaining ambiguity. CS localization of TVC using the modified constraint is shown according to cavitation numbers and compared to high-speed camera images.

Range-dependence of acoustic channel with traveling sinusoidal surface wave.

Range-dependence of time-varying acoustic channels caused by a traveling surface wave is investigated through water tank experiments and acoustic propagation analysis schemes. As the surface wave travels, surface reflected signals fluctuate and the fluctuation varies with source-receiver horizontal range. Amplitude fluctuations of surface reflected signals increase with increasing horizontal range whereas the opposite occurs in delay fluctuations. The scattered pressure field at a fixed time shows strong dependence on the receiver position because of caustics and shadow zones formed by the surface. The Doppler shifts of surface reflected signals also depend on the horizontal range. Comparison between measurement data and model results indicates the Doppler shift relies on the delay fluctuation under current experimental conditions.

Emergence of striation patterns in acoustic signals reflected from dynamic surface waves.

A striation pattern can emerge in high-frequency acoustic signals interacting with dynamic surface waves. The striation pattern is analyzed using a ray tracing algorithm for both a sinusoidal and a rough surface. With a source or receiver close to the surface, it is found that part of the surface on either side of the specular reflection point can be illuminated by rays, resulting in time-varying later arrivals in channel impulse response that form the striation pattern. In contrast to wave focusing associated with surface wave crests, the striation occurs due to reflection off convex sections around troughs. Simulations with a sinusoidal surface show both an upward (advancing) and downward (retreating) striation patterns that depend on the surface-wave traveling direction and the location of the illuminated area. In addition, the striation length is determined mainly by the depth of the source or receiver, whichever is closer in range to the illuminated region. Even with a rough surface, the striation emerges in both directions. However, broadband (7-13 kHz) simulations in shallow water indicate that the longer striation in one direction is likely pronounced against a quiet noise background, as observed from at-sea experimental data.