High frequency source localization in a shallow ocean sound channel using frequency difference matched field processing

Coherence of the frequency-difference autoproduct deduced from high-frequency acoustic fields scattered from a rough sea surfacea)

The prevalence of random scattering from a rough ocean surface increases with increasing χ=kh cos θ, where k is the acoustic wavenumber, h is the root-mean-square surface height, and θ is the incidence angle. Generally, when χ≫1, coherence between incident and surface-scattered fields is lost. However, such coherence may be recovered when χ≫1 by considering the frequency-difference autoproduct of the surface-scattered field, a quadratic product of complex fields at nearby frequencies. Herein, the autoproduct's coherent reflection coefficient for χ> 20 is determined from surface-scattered sound fields obtained from 50 independent realizations of the rough ocean surface measured in pelagic waters off the coast of California in January 1992. The recordings were made with a source at a depth of 147 m that broadcasted 30 and 40 kHz signals to a single receiver 576 m away at depth of 66 m. An analytic formula for the coherent reflection coefficient of the frequency-difference autoproduct, based on the Kirchhoff approximation and a Gaussian surface autocorrelation function, compares favorably with measurements. Improved agreement with the single-receiver measurements is possible via a minor adjustment to the surface autocorrelation length. The adjustment identified here matches that determined previously from horizontal spatial coherence estimates utilizing the experiment's eight-element receiving array.

Coherent reflection recovery in scattering from the ocean surface using the frequency-difference autoproducta)

The coherence of rough sea-surface-scattered acoustic fields decreases with increasing frequency. The frequency-difference autoproduct, a quadratic product of acoustic fields at nearby frequencies, mimics a genuine field at the difference frequency. In rough-surface scattering, the autoproduct's lower effective frequency decreases the apparent surface roughness, restoring coherent reflection. Herein, the recovery of coherent reflection in sea surface scattering via the frequency-difference autoproduct is examined for data collected off the coast of New Jersey during the Shallow Water '06 (SW06) experiment. An acoustic source at depth 40 m and receiver at depth 24.3 m and range 200 m interrogated 160 independent realizations of the ocean surface. The root mean square surface height h was 0.167 m, and broadcast frequencies were 14-20 kHz, so that 2.5 ≤kh cos θ≤ 3.7 for acoustic wavenumber k and incidence angle θ. Measured autoproducts, constructed from scattered constituent fields, show significant coherent reflection at sufficiently low difference frequencies. Theoretical results, using the Kirchhoff approximation and a non-analytic surface autocorrelation function, agree with experimental findings. The match is improved using a numerical strategy, exploiting the relationship between autoproduct-based coherence recovery, the ocean-surface autocorrelation function, and the ocean-surface height spectrum. Error bars computed from Monte Carlo scattering simulations support the validity of the measured coherence recovery.

Multifrequency matched-field source localization based on Wasserstein metric for probability measures

Matched-field processing (MFP) for underwater source localization serves as a generalized beamforming approach that assesses the correlation between the received array data and a dictionary of replica vectors. In this study, the processing scheme of MFP is reformulated by computing a statistical metric between two Gaussian probability measures with the cross-spectral density matrices (CSDMs). To achieve this, the Wasserstein metric, a widely used notion of metric in the space of probability measures, is employed for developing the processor to attach the intrinsic properties of CSDMs, expressing the underlying optimal value of the statistic. The Wasserstein processor uses the embedded metric structure to suppress ambiguities, resulting in the ability to distinguish between multiple sources. In this foundation, a multifrequency processor that combines the information at different frequencies is derived, providing improved localization statistics with deficient snapshots. The effectiveness and robustness of the Wasserstein processor are demonstrated using acoustic simulation and the event S5 of the SWellEx-96 experiment data, exhibiting correct localization statistics and a notable reduction in ambiguity. Additionally, this paper presents an approach to derive the averaged Bartlett processor by evaluating the Wasserstein metric between two Dirac measures, providing an innovative perspective for MFP.

High-resolution frequency-difference beamforming for a short linear array

Conventional beamforming (CBF) is a commonly employed approach for detecting and estimating the direction-of-arrival (DOA) of acoustic signals in underwater environments. However, CBF becomes ambiguous due to spatial aliasing when the received signal's half wavelength is smaller than the array spacing. Frequency-difference beamforming (FDB) allows for processing data in the lower frequency Δf without encountering spatial aliasing by utilizing the product of array data at frequency f with its complex conjugate at frequency f+Δf. However, lower frequency results in a wider mainlobe, which can lead to poorer DOA performance for short arrays. In this paper, a fourth-order cumulants FDB method and a conjugate augmented FDB method are proposed to extend an M-element uniform linear array to 2M-1 and 4M-3 elements. The proposed methods generate narrower beams and lower sidelobe levels than the original FDB for short arrays with large spacing. And by setting the signal subspace dimension reasonably, the proposed methods can improve the weak target detection ability under strong interference compared with FDB. Last, we verify the excellent performance of the proposed methods through simulations and experimental data.

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.

Localization of a remote source in a noisy deep ocean sound channel using phase-only matched autoproduct processing

Long-range passive source localization is possible in the deep ocean using phase-only matched autoproduct processing (POMAP) [Geroski and Dowling (2021). J. Acoust. Soc. Am. 150, 171-182], an algorithm based on matched field processing that is more robust to environmental mismatch. This paper extends these prior POMAP results by analyzing the localization performance of this algorithm in the presence of environmental noise. The noise rejection performance of POMAP is assessed using both simulated and measured signal data, with noise data based on environmental noise measurements. Herein, signal and noise measurements are from the nominally one-year-long PhilSea10 ocean acoustic propagation experiment. All signals were recorded from a single moored source, placed near the ocean sound channel 129.4 km away from a nearly water-column-spanning distributed vertical line array. The source transmitted linear frequency modulated chirps with nominal bandwidth from 200 to 300 Hz. The noise measurements used in this study were collected in the months after this source stopped transmitting, and synthetic samples of noise are calculated based on the characteristics of this measured noise. The effect that noise rejection algorithms have on the source localization performance of POMAP is also evaluated, but only 1 dB of performance improvement is achieved using these.

Difference frequency coherent matched autoproduct processing for source localization in deep ocean

Matched autoproduct processing (MAP) refers to a matched field processing (MFP) style array signal processing technique for passive source localization, which interrogates frequency-difference autoproduct instead of genuine acoustic pressure. Due to frequency downshifting, MAP is less sensitive to environmental mismatch, but it suffers from low spatial resolution and a low peak-to-sidelobe ratio of ambiguity surface. These source localization metrics are herein improved with coherent approaches. Specifically, the coherent normalized MFP is extended to coherent matched autoproduct processing (CMAP), a difference frequency coherent algorithm that exploits correlations among the autoproducts at various difference frequencies and eliminates the phase factor of the source spectrum for passive source localization. Phase-only coherent matched autoproduct processing is a CMAP derivation technique that only uses phase information. Through simulations in a Munk sound-speed profile environment, sensitivity analysis in the South China Sea environment, and high signal-to-noise ratio experimental measurements, these two algorithms are validated as compared to the conventional MFP and incoherent MAP. Simulation investigations demonstrate that difference frequency coherent algorithms can suppress sidelobes while simultaneously enhancing the localization resolution and robustness. The experimental results generally support the findings of the simulations.

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.

Coarse-to-Fine Localization of Underwater Acoustic Communication Receivers

For underwater acoustic (UWA) communication in sensor networks, the sensing information can only be interpreted meaningfully when the location of the sensor node is known. However, node localization is a challenging problem. Global Navigation Satellite Systems (GNSS) used in terrestrial applications do not work underwater. In this paper, we propose and investigate techniques based on matched field processing for localization of a single-antenna UWA communication receiver relative to one or more transmit antennas. Firstly, we demonstrate that a non-coherent ambiguity function (AF) allows significant improvement in the localization performance compared to the coherent AF previously used for this purpose, especially at high frequencies typically used in communication systems. Secondly, we propose a two-step (coarse-to-fine) localization technique. The second step provides a refined spatial sampling of the AF in the vicinity of its maximum found on the coarse space grid covering an area of interest (in range and depth), computed at the first step. This technique allows high localization accuracy and reduction in complexity and memory storage, compared to single step localization. Thirdly, we propose a joint refinement of the AF around several maxima to reduce outliers. Numerical experiments are run for validation of the proposed techniques.

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 β. 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 β. 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 β, comparison between MFP and AI, self-calibration of the array tilt, and recent developments such as adaptive AI, which can handle the dependence of β on the propagation angle, including steep-angle arrivals.

Sim-to-real localization: Environment resilient deep ensemble learning for guided wave damage localization

Guided ultrasonic wave localization systems use spatially distributed sensor arrays and wave propagation models to detect and locate damage across a structure. Environmental and operational conditions, such as temperature or stress variations, introduce uncertainty into guided wave data and reduce the effectiveness of these localization systems. These uncertainties cause the models used by each localization algorithm to fail to match with reality. This paper addresses this challenge with an ensemble deep neural network that is trained solely with simulated data. Relative to delay-and-sum and matched field processing strategies, this approach is demonstrated to be more robust to temperature variations in experimental data. As a result, this approach demonstrates superior accuracy with small numbers of sensors and greater resilience to spatially nonhomogeneous temperature variations over time.

Recovery of coherent reflection from rough-surface scattered acoustic fields via the frequency-difference autoproduct

The acoustic field reflected from a random rough surface loses coherence with the incident field in the Kirchhoff approximation as kh cos θ increases, where k is the incident field wavenumber, h is the root mean square roughness height, and θ is the incidence angle. Thus, for fixed rough-surface properties and incidence angle, a reflected field at lower wavenumber should retain more coherence. Recent results suggest that the frequency-difference autoproduct formed from complex acoustic field amplitudes at two nearby frequencies can recover acoustic information at the difference of those frequencies even when the difference frequency is below the recorded field's bandwidth. Herein analytical, computational, and experimental results are presented for the extent to which the frequency-difference autoproduct recovers coherence from randomly rough-surface-scattered constituent fields that have lost coherence. The analytical results, developed from the Kirchhoff approximation and formal ensemble averaging over randomly rough surfaces with Gaussian height distributions and Gaussian correlation functions, indicate that the coherence of the rough-surface-reflected frequency-difference autoproduct depends on the surface correlation length and Δkh cos θ, where Δk is the difference of the autoproduct's constituent field wavenumbers. These results compare favorably with Monte Carlo simulations of rough surface scattering, and with laboratory experiments involving long surface correlation lengths where 1  ≤kh cos θ≤ 3.

Robust long-range source localization in the deep ocean using phase-only matched autoproduct processing

Passive source localization in the deep ocean using array signal processing techniques is possible using an algorithm similar to matched field processing (MFP) that interrogates a measured frequency-difference autoproduct instead of a measured pressure field [Geroski and Dowling, J. Acoust. Soc. Am. 146, 4727-4739 (2019)]. These results are extended herein to a new MFP-style algorithm, phase-only matched autoproduct processing, that is more robust at source-array ranges as large as 225 km. This new algorithm is herein described and compared to three existing approaches. The performance of all four techniques is evaluated using measured ocean propagation data from the PhilSea10 experiment. These data nominally span a 12-month period; include six source-array ranges from 129 to 450 km; and involve signals with center frequencies between 172.5 and 275 Hz, and bandwidths of 60 to 100 Hz. In all cases, weight vectors are calculated assuming a range-independent environment using a single sound-speed profile measured near the receiving array. The frequency-differencing techniques considered here are capable of localizing all six sources, with varying levels of consistency, using single-digit-Hz difference frequencies. At source-array ranges up to and including 225 km, the new algorithm requires fewer signal samples for success and is more robust to the choice of difference frequencies.

Passive Source Localization Using Acoustic Intensity in Multipath-Dominant Shallow-Water Waveguide

The array invariant technique has been recently proposed for passive source localization in the ocean. It has successfully estimated the source–receiver horizontal range in multipath-dominant shallow-water waveguides. However, it requires a relatively large-scale hydrophone array. This study proposes an array invariant method that uses acoustic intensity, which is a vector quantity that has the same direction as the sound wave propagating through a water medium. This method can be used to estimate not only the source–receiver horizontal range, but also the azimuth to an acoustic source. The feasibility of using a vector quantity for the array invariant method is examined through a simulation and an acoustic experiment in which particle velocity signals are obtained using a finite difference approximation of the pressure signals at two adjacent points. The source localization results estimated using acoustic intensity are compared with those obtained from beamforming of the acoustic signals acquired by the vertical line array.

Deep learning-based high-frequency source depth estimation using a single sensor

The sensitivity of underwater propagation models to acoustic and environmental variability increases with the signal frequency; therefore, realizing accurate acoustic propagation predictions is difficult. Owing to this mismatch between the model and actual scenarios, achieving high-frequency source localization using model-based methods is generally difficult. To address this issue, we propose a deep learning approach trained on real data. In this study, we focused on depth estimation. Several 18-layer residual neural networks were trained on a normalized log-scaled spectrogram that was measured using a single hydrophone. The algorithm was evaluated using measured data transmitted from the linear frequency modulation chirp probe (11-31 kHz) in the shallow-water acoustic variability experiment 2015. The signal was received through two vertical line arrays (VLAs). The proposed method was applied to all 16 sensors of the VLA to determine the estimation performance with respect to the receiver depth. Furthermore, frequency-difference matched field processing was applied to the experimental data for comparison. The results indicate that ResNet can determine complicated features of high-frequency signals and predict depths, regardless of the receiver depth, while exhibiting robust environmental and positional variability.

Measurements of the correlation of the frequency-difference autoproduct with acoustic and predicted-autoproduct fields in the deep ocean

Frequency-domain spatial-correlation analysis of recorded acoustic fields is typically limited to the bandwidth of the recordings. A previous study [Lipa, Worthmann, and Dowling (2018) J. Acoust. Soc. Am. 143(4), 2419-2427] suggests that limiting such analysis to in-band frequencies is not strictly necessary in a Lloyd's mirror environment. In particular, below-band field information can be retrieved from the frequency-difference autoproduct, a quadratic product of measured complex pressure-field amplitudes from two nearby frequencies. The frequency-difference autoproduct is a surrogate field that mimics a genuine acoustic field at the difference frequency. Here, spatial-correlation analysis is extended to deep-ocean acoustic fields measured during the PhilSea10 experiment. The frequency-difference autoproduct, at difference frequencies from 0.0625 to 15 Hz, is determined from hundreds of Philippine Sea recordings of 60 or 100 Hz bandwidth signals with center frequencies from 172.5 to 275 Hz broadcast to a vertical receiving array 129-450 km away. The measured autoproducts are cross correlated along the array with predicted acoustic fields and with predicted autoproduct fields at corresponding below-band frequencies. Stable measured cross correlations as high as 80%-90% are found at the low end of the investigated difference-frequency range, with consistent correlation loss due to mismatch at the higher below-band frequencies.

Frequency-difference autoproduct cross-term analysis and cancellation for improved ambiguity surface robustness

Frequency-differencing, or autoproduct processing, techniques are one area of research that has been found to increase the robustness of acoustic array signal processing algorithms to environmental uncertainty. Previous studies have shown that frequency differencing techniques are able to mitigate problems associated with environmental mismatch in source localization techniques. While this method has demonstrated increased robustness compared to conventional methods, many of the metrics, such as ambiguity surface peak values and dynamic range, are lower than would typically be expected for the observed level of robustness. These previous studies have suggested that such metrics are reduced by the inherent nonlinearity of the frequency-differencing method. In this study, simulations of simple multi-path environments are used to analyze this nonlinearity and signal processing techniques are proposed to mitigate the effects of this problem. These methods are used to improve source localization metrics, particularly ambiguity surface peak value and dynamic range, in two experimental environments: a small laboratory water tank and in a deep ocean (Philippine Sea) environment. The performance of these techniques demonstrates that many source localization metrics can be improved for frequency-differencing methods, which suggests that frequency-differencing methods may be as robust as previous studies have shown.

The effects of refraction and caustics on autoproducts

Quadratic products of complex amplitudes from acoustic fields with nonzero bandwidth, denoted "autoproducts," can mimic acoustic fields at frequencies lower or higher than the bandwidth of the original field. While this mimicry has been found to be very promising for a variety of signal processing applications, its theoretical extent has, thus far, only been considered under the most elementary ray approximation. In this study, the combined effects of refraction and diffraction are considered in environments where refraction causes neighboring rays to cross and form caustics. Acoustic fields on and near caustics are not well-predicted by elementary ray-acoustic theory. Furthermore, caustics introduce frequency dependence to the nearby acoustic field and a phase shift on the acoustic waves that passes through them. The effects these caustics have on autoproducts is assessed here using two simple, range-independent waveguides with index of refraction (n) profiles that are n²-quadratic and n²-linear. It is found that in multipath regions where rays have passed through differing numbers of caustics, the ability of autoproducts to mimic out-of-band fields is substantially hindered.

Autoproducts in and near acoustic shadow zones created by barriers

The autoproducts are nonlinear mathematical constructs developed from acoustic fields with non-zero bandwidth. When averaged through the field's bandwidth, the autoproducts may mimic a genuine acoustic field at frequencies that are lower or higher than the original field's bandwidth. The resulting opportunity to extend signal processing to user-selectable below- or above-band frequencies is intriguing for many signal processing algorithms. Based on prior work, the limitations of the autoproducts' mimicry of out-of-band fields are understood when the in-band acoustic field is well-represented by ray acoustics. Thus, the focus in this study is on autoproducts in acoustic shadow zones behind barriers containing only diffracted acoustic fields where a sum of ray-path contributions is not an adequate field description. Diffraction is expected to be a detriment to autoproduct techniques due to its sensitivity to frequency. Two ideal shadow-zone environments with exact analytic Helmholtz-equation solutions are considered: Sommerfeld's half-plane problem, also known as knife-edge diffraction, and Mie scattering from a sphere with ka = 40, where k is the wavenumber and a is the sphere's radius. With the exception of the shadow regions, autoproducts experience only mild degradation in field-mimicry performance when compared to what the ray-based theory would predict.

Long-range frequency-difference source localization in the Philippine Sea

Matched field processing (MFP) refers to a variety of source localization schemes for known complicated environments and involves matching measured and calculated (replica) fields to identify source locations. MFP may fail for several reasons, most notably when the calculated fields are insufficiently accurate. This error commonly prevents MFP-based long-range (>100 km) source localization in the deep ocean (from 5 to 6 km depth) for signal frequencies of hundreds of Hz, even when extensive high-signal-to-noise ratio field measurements are available. Recently, below-band MFP utilizing the frequency-difference autoproduct [Worthmann, Song, and Dowling (2015). J. Acoust. Soc. Am, 138(6), 3549-3562] achieved some shallow-ocean localization success at a 3 km source-to-array range with signal frequencies in the tens of kHz. The performance of this technique, when extended to matching the measured frequency-difference autoproduct with a composite mode-ray replica, is described here for deep ocean source localization. The ocean propagation data come from the PhilSea10 experiment and involve source-to-array ranges from 129 to 379 km and nominal 100-Hz-bandwidth signals having center frequencies from 250 to 275 Hz. Based on an incoherent average of five signal samples, the frequency-difference technique was 90%-100% successful at four different source-to-array ranges using single-digit-Hz difference frequencies.

A simple method for depth estimation of a sound source at known range in the deep sea

Based on the distribution of acoustic intensity at different depths at a fixed distance, a simple method is proposed to estimate the sound source depth at known range in the deep sea. First, the method calculates the acoustic intensity distribution of all the depths at a receiving distance. Second, the depths with the strongest acoustic intensity are selected. Sound sources are set at the selected depths to calculate the transmission loss (TL) at the same distance through the acoustic model, and the depth of the minimum superimposed TL is considered as the depth of the original sound source. The simulation and experiment verify the feasibility and reliability of the method.

Frequency-difference beamforming in the presence of strong random scattering

Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029] is a nonlinear, out-of-band signal processing technique used to beamform non-zero bandwidth signals at below-band frequencies. This is accomplished with the frequency-difference autoproduct AP(Δω)=P(ω₂)P^*(ω₁), a quadratic product of complex field amplitudes that mimics a genuine field at the difference frequency, Δω=ω₂-ω₁. For frequency-difference beamforming, AP(Δω) replaces the in-band complex field in the conventional beamforming algorithm. Here, the near-field performance of frequency-difference beamforming is evaluated in the presence of 1 to 30 high-contrast spherical scatterers with radius a placed between, and in the plane defined by the source and a 12-element linear receiving array with element spacing d. Based on the center frequency wave number, k, of the 150-200 kHz frequency sweep source signal, the scatterers are large, ka ≈ 15; the array is sparse, kd = 37; and the average source-to-receiver distance is up to 4.3 mean-free-path lengths. Beamforming results from simulations and experiments show that in-band beamforming loses peak-to-sidelobe ratio and fails to reliably locate the source as the scatterer count increases. Using the same signals, frequency-difference beamforming with difference frequencies from 5 to 25 kHz localizes sources reliably with higher peak-to-side-lobe ratios, though with reduced resolution.

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.

Application and Extension of Vertical Intensity Lower-Mode in Methods for Target Depth-Resolution with a Single-Vector Sensor

In this paper, based on the reactive component of the vertical intensity, the method for target depth resolution has been improved. In the previous existing research results, using the reactive component of vertical intensity, the research objects for target depth resolution in shallow water, can only be the targets whose frequencies can only excite the first two normal modes, and the depth of targets whose frequencies excite more than two normal modes cannot be correctly identified. The basic idea of the improved method is to classify targets on the foundation of the lower-mode correlation quantity of the vertical intensity. Based on the improved method, we can realize depth resolution of the targets whose frequency can excite the first three normal modes so as to effectively expand the working band useful for target depth resolution. Finally, we can realize the three-dimensional target depth resolution so as to distinguish the aerial, surface and underwater targets. The feasibility of the algorithm is verified by simulation and experimental data processing.

A Three-Dimensional Target Depth-Resolution Method with a Single-Vector Sensor

This paper mainly studies and verifies the target number category-resolution method in multi-target cases and the target depth-resolution method of aerial targets. Firstly, target depth resolution is performed by using the sign distribution of the reactive component of the vertical complex acoustic intensity; the target category and the number resolution in multi-target cases is realized with a combination of the bearing-time recording information; and the corresponding simulation verification is carried out. The algorithm proposed in this paper can distinguish between the single-target multi-line spectrum case and the multi-target multi-line spectrum case. This paper presents an improved azimuth-estimation method for multi-target cases, which makes the estimation results more accurate. Using the Monte Carlo simulation, the feasibility of the proposed target number and category-resolution algorithm in multi-target cases is verified. In addition, by studying the field characteristics of the aerial and surface targets, the simulation results verify that there is only amplitude difference between the aerial target field and the surface target field under the same environmental parameters, and an aerial target can be treated as a special case of a surface target; the aerial target category resolution can then be realized based on the sign distribution of the reactive component of the vertical acoustic intensity so as to realize three-dimensional target depth resolution. By processing data from a sea experiment, the feasibility of the proposed aerial target three-dimensional depth-resolution algorithm is verified.

Measurement of autoproduct fields in a Lloyd's mirror environment

Conventional frequency-domain acoustic-field analysis techniques are typically limited to the bandwidth of the field under study. However, this limitation may be too restrictive, as prior work suggests that field analyses may be shifted to lower or higher frequencies that are outside the field's original bandwidth [Worthmann and Dowling (2017). J. Acoust. Soc. Am. 141(6), 4579-4590]. This possibility exists because below- and above-band acoustic fields can be mimicked by the frequency-difference and frequency-sum autoproducts, which are quadratic products of frequency-domain complex field amplitudes at a pair of in-band frequencies. For a point source in a homogeneous acoustic half-space with a flat, pressure-release surface (a Lloyd's mirror environment), the prior work predicted high correlations between the autoproducts and genuine out-of-band fields at locations away from the source and the surface. Here, measurements collected in a laboratory water tank validate predictions from the prior theory using 40- to 110-kHz acoustic pulses measured at ranges between 175 and 475 mm, and depths to 400 mm. Autoproduct fields are computed, and cross-correlations between measured autoproduct fields and genuine out-of-band acoustic fields are above 90% for difference frequencies between 0 and 60 kHz, and for sum frequencies between 110 and 190 kHz.

Performance comparisons of frequency-difference and conventional beamforming

Frequency-difference beamforming [Abadi, Song, and Dowling (2012b). J. Acoust. Soc. Am. 132, 3018-3029] is an unconventional beamforming method for use with sparse receiver arrays. It involves beamforming a quadratic product of complex field amplitudes, P(ω₂)P^*(ω₁), at the difference frequency, ω₂-ω₁, instead of beamforming the complex field amplitude P(ω) at frequencies ω within the signal bandwidth. Frequency-difference beamforming is readily implemented with ordinary transducer array recordings of non-zero bandwidth signals. Results for, and comparisons of, frequency-difference beamforming from simulations and experiments are reported herein. In particular, spherical-wave beamforming is investigated using 15 and 165 kHz pulse signals in a 1.07-m-diameter water tank with a linear array having 14 elements spaced 5.08 cm apart. Here, frequency-difference beamforming using the high-frequency pulses provides comparable results to conventional beamforming at 15 kHz. Plane-wave beamforming is investigated using 11.2-32.8 kHz frequency-sweep signals broadcast 3 km through a 106-m-deep ocean sound channel to a vertical array having 16 elements spaced 3.75 m apart. Here, frequency difference beamforming in the 1.7-2.3 kHz difference frequency band provides results comparable to conventional beamforming in this band.

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.

The frequency-difference and frequency-sum acoustic-field autoproducts

The frequency-difference and frequency-sum autoproducts are quadratic products of solutions of the Helmholtz equation at two different frequencies (ω₊ and ω_-), and may be constructed from the Fourier transform of any time-domain acoustic field. Interestingly, the autoproducts may carry wave-field information at the difference (ω₊ - ω_-) and sum (ω₊ + ω_-) frequencies even though these frequencies may not be present in the original acoustic field. This paper provides analytical and simulation results that justify and illustrate this possibility, and indicate its limitations. The analysis is based on the inhomogeneous Helmholtz equation and its solutions while the simulations are for a point source in a homogeneous half-space bounded by a perfectly reflecting surface. The analysis suggests that the autoproducts have a spatial phase structure similar to that of a true acoustic field at the difference and sum frequencies if the in-band acoustic field is a plane or spherical wave. For multi-ray-path environments, this phase structure similarity persists in portions of the autoproduct fields that are not suppressed by bandwidth averaging. Discrepancies between the bandwidth-averaged autoproducts and true out-of-band acoustic fields (with potentially modified boundary conditions) scale inversely with the product of the bandwidth and ray-path arrival time differences.

Impact of array tilt on source-range estimation in shallow water using the array invariant

The array invariant proposed for robust source-range estimation in shallow water is based on the dispersion characteristics in ideal waveguides for broadband signals. With minimal knowledge of the environment, the approach involves plane-wave beamforming using a vertical array, utilizing multiple arrivals (i.e., eigenrays) separated in beam angle and travel time. In the presence of array tilt, however, the beam angle estimates are shifted, which potentially affects the range estimation based on the array invariant. Conversely, the array tilt could be estimated for a known source range. In this paper, the sensitivity to array tilt is analyzed theoretically and examined using simulations and data. It is found that even a small tilt angle (e.g., <2°) of a 1.2 -m long vertical array near the surface, if not compensated for, can result in a relative range error of 20% or more, for a high-frequency source (7-19 kHz) at 3-km range in approximately 100 -m deep shallow water. Moreover, the power spectrum of the time-evolving array tilt estimated for 9 min shows a dominant period of 5.6 s, which is consistent with the surface wave period concurrently measured from a waverider buoy.

Adaptive frequency-difference matched field processing for high frequency source localization in a noisy shallow ocean

Remote source localization in the shallow ocean at frequencies significantly above 1 kHz is virtually impossible for conventional array signal processing techniques due to environmental mismatch. A recently proposed technique called frequency-difference matched field processing (Δf-MFP) [Worthmann, Song, and Dowling (2015). J. Acoust. Soc. Am. 138(6), 3549-3562] overcomes imperfect environmental knowledge by shifting the signal processing to frequencies below the signal's band through the use of a quadratic product of frequency-domain signal amplitudes called the autoproduct. This paper extends these prior Δf-MFP results to various adaptive MFP processors found in the literature, with particular emphasis on minimum variance distortionless response, multiple constraint method, multiple signal classification, and matched mode processing at signal-to-noise ratios (SNRs) from -20 to +20 dB. Using measurements from the 2011 Kauai Acoustic Communications Multiple University Research Initiative experiment, the localization performance of these techniques is analyzed and compared to Bartlett Δf-MFP. The results show that a source broadcasting a frequency sweep from 11.2 to 26.2 kHz through a 106 -m-deep sound channel over a distance of 3 km and recorded on a 16 element sparse vertical array can be localized using Δf-MFP techniques within average range and depth errors of 200 and 10 m, respectively, at SNRs down to 0 dB.

Array invariant-based source localization in shallow water using a sparse vertical array

The array invariant proposed for robust source localization in shallow water exploits the beam-time migration of broadband signals. The approach requires minimal knowledge of the environment, but involves plane wave beamforming using a short-aperture vertical array in stratified acoustic waveguides. In this paper, the array invariant approach is extended to a large-aperture vertical array that is sparse with significant variation of the sound speed across the aperture for conventional beamforming. The extension is feasible because the array invariant in shallow water utilizes surface/bottom-reflected arrivals that behave like those in ideal waveguides. Robust source-range estimation is demonstrated using data from a 16-element, 56-m long vertical array at various ranges (1.5-3.5 km) from a broadband source (0.5-2 kHz) in approximately 100-m deep shallow water.