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

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.