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

Generalized frequency-sum beamforming for low frequencies

For direction-of-arrival (DOA) estimation in the low-frequency range, we improve spatial resolution using generalized frequency-sum (gFS) beamforming with the Qth order frequency-sum autoproduct. The order Q does not exceed the maximum value, determined by the criteria that the sum of frequencies used to create the autoproduct must be less than the array's spatial Nyquist frequency. Unlike other high-resolution beamformers, gFS maintains stable performance even with a single snapshot and is unaffected by the coherence of steering vectors. Rigorous analysis using the multinomial expansion has shown the inapplicability of gFS to multi-DOA scenarios. Simulation and experimental results support that the method is a practical alternative for low-frequency single-DOA estimation with limited data.

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.

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.

Single Hydrophone Passive Source Range Estimation Using Phase-Matched Filter

Algorithms working in mode space instead of directly matching the received complex sound pressure were developed to improve computational efficiency and robustness, but these algorithms may be inconvenient to apply in practice because manual operations are often inevitable when performing modal filtering. Based on a phase-matched filter, an imperfect matching scheme named the modal phase based matched impulse response (MP-MIR) is proposed to estimate the source range rapidly and conveniently with a single hydrophone. The field to be matched is still the received complex sound pressure. The replica field is a sum of several “phase” modes, which can be efficiently and conveniently synthesized merely with the horizontal wavenumbers of normal modes and the source–receiver range. The effectiveness of the proposed MP-MIR was demonstrated in localizing 84 emissions along a weakly range-dependent track at ranges of 2.54–20 km in the South China Sea. Although it was found, from cross-correlation coefficients, that the received signals showed strong variation even between adjacent emissions, MP-MIR outperformed the classical matched impulse response (MIR) with a lower standard deviation in most cases, demonstrating good robustness and potential for practical applications.

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.

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.

Model-based convolutional neural network approach to underwater source-range estimation

This paper is part of a special issue on machine learning in acoustics. A model-based convolutional neural network (CNN) approach is presented to test the viability of this method as an alternative to conventional matched-field processing (MFP) for underwater source-range estimation. The networks are trained with simulated data generated under a particular model of the environment. When tested with data simulated in environments that deviate slightly from the training environment, this approach shows improved prediction accuracy and lower mean-absolute-error (MAE) compared to MFP. The performance of this model-based approach also transfers to real data, as demonstrated separately with field data collected in the Beaufort Sea and off the coast of Southern California. For the former, the CNN predictions are consistent with expected source range while for the latter, the CNN estimates have lower MAE compared to MFP. Examination of the trained CNNs' intermediate outputs suggests that the approach is more constrained than MFP from outputting very inaccurate predictions when there is a slight environmental mismatch. This improvement appears to be at the expense of decreased certainty in the correct source range prediction when the environment is precisely modeled.

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.

Introduction to the Special Issue on Acoustic Source Localization

Spatial localization based on acoustic observations is a rich field of interest in acoustic signal analysis. This special issue takes a close look at the diverse and growing range of problems in this area and the broad perspectives and methodologies that are presently being developed to solve them. The collection of articles presents recent advances in localization in complex and uncertain environments across a wide range of acoustic disciplines, from animal bioacoustics and acoustic signal processing in underwater environments to in air environments, architectural acoustics, and acoustic transduction.