Through the sensor estimation of sound speed profiles.

A through-the-sensor method to sense the local sound speed profile (SSP) using measured acoustic wave numbers via an array of hydrophones is proposed. Ocean sounds can be treated as acoustic energy trapped as discrete modes within the water column. A Fredholm integral equation of the first kind relates the linearized (perturbative) sound speed corrections to the wave number differences between the measured values and those calculated from an acoustic kernel. Thus, a method to exploit environmental information deduced from different in situ sonar systems is proposed. Though this inversion can be unstable and non-unique, recent improvements in sparse inversions can lead to robust estimates even without an accurate starting SSP. An iterative algorithm using multiple acoustic frequencies is beneficial to achieve convergence and stability for larger sound speed corrections. This paper will compare broadband incoherent L2- and coherent L1-inversion results. Careful consideration must be made of the acoustic frequency, number of modes, a priori environmental information (e.g., water depth), and array length. The method will be first demonstrated on simulations and recordings from the Littoral Depth Discrimination Experiment 2012 (LIDDEX12) data set.

Moving source ocean acoustic tomography with uncertainty quantification using controlled source-tow observations.

Ocean sound speed and its uncertainty are estimated using travel-time tomography at ranges up to 2 km using a moving source in ∼600 m water depth. The experiment included two 32-element vertical line arrays deployed about 1 km apart and a towed source at ∼10 m depth transmitting a linear frequency modulated waveform. The inversion accounts for uncertainties in the positions and velocities of the source and receivers in addition to the background sound speed state. At these short ranges, the sound speed effects are small and the representational error of the candidate forward models must be carefully evaluated and minimized. This is tested stringently by a separate position parameter inversion and by cross-validating the estimates of sound speed and arrival time, including uncertainties. In addition, simulations are used to explore the effects of adding additional constraints to the inversion and to compare the performance of moving to fixed source tomography. The results suggest that the ray diversity available from the moving source reduces the posterior sound speed uncertainty compared to the fixed source case.

Probabilistic focalization for shallow water localization.

Localizing and tracking an underwater acoustic source is a key task for maritime situational awareness. This paper presents a sequential Bayesian estimation method for passive acoustic source localization in shallow water. The proposed probabilistic focalization approach associates detected directions of arrival (DOAs) to modeled DOAs and jointly estimates the time-varying source location. Embedded ray tracing makes it possible to incorporate environmental parameters that characterize the acoustic waveguide. Due to its statistical model, the proposed method can provide robustness in scenarios with severe environmental uncertainty. We demonstrate performance advantages compared to matched field processing using data collected during the SWellEx-96 experiment.

A performance comparison between m-sequences and linear frequency-modulated sweeps for the estimation of travel-time with a moving source.

This manuscript discusses the utility of maximal period linear binary pseudorandom sequences [also referred to as m-sequences or maximum length sequences (MLSs)] and linear frequency-modulated (LFM) sweeps for the purpose of measuring travel-time in ocean-acoustic experiments involving moving sources. Signal design and waveform response to unknown Doppler (waveform dilation or scale factor) are reviewed. For this two-parameter estimation problem, the well-known wide-band ambiguity function indicates, and moving-source observations corroborate, a significant performance benefit from using MLS over LFM waveforms of similar time duration and bandwidth. The comparison is illustrated with a typical experimental setup of a source suspended aft of the R/V Sally Ride to a depth of∼10 m and towed at∼1 m/s speed. Accounting for constant source motion, the root mean square travel-time variability over a 30 min observation interval is 53 µs (MLS) and 141 µs (LFM). For these high signal-to-noise ratio channel impulse response data, LFM arrival-time fluctuations mostly appear random while MLS results exhibit structure believed to be consistent with source (i.e., towed transducer) dynamics. We conclude with a discussion on signal coherence with integration times up to 11 MLS waveform periods corresponding to ∼27 s.

Multiple constraint matched field processing tolerant to array tilt mismatch.

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

Sparse Bayesian learning for beamforming using sparse linear arrays.

Sparse linear arrays such as co-prime and nested arrays can resolve more sources than the number of sensors. In contrast, uniform linear arrays (ULA) cannot resolve more sources than the number of sensors. This paper demonstrates this using Sparse Bayesian learning (SBL) and co-array MUSIC for single frequency beamforming. For approximately the same number of sensors, co-prime and nested arrays are shown to outperform ULA in root mean squared error. This paper shows that multi-frequency SBL can significantly reduce spatial aliasing. The effects of different sparse sub-arrays on SBL performance are compared qualitatively using the Noise Correlation 2009 experimental data set.

Estimating relative channel impulse responses from ships of opportunity in a shallow water environment.

The uncertainty of estimating relative channel impulse responses (CIRs) obtained using the radiated signature from a ship of opportunity is investigated. The ship observations were taken during a 1.4 km (11 min) transect in a shallow water environment during the Noise Correlation 2009 (NC09) experiment. Beamforming on the angle associated with the direct ray-path yields an estimate of the ship signature, subsequently used in a matched filter. Relative CIRs are estimated every 2.5 s independently at three vertical line arrays (VLAs). The relative arrival-time uncertainty is inversely proportional to source bandwidth and CIR signal-to-noise ratio, and reached a minimum standard deviation of 5 µs (equivalent to approximately 1 cm spatial displacement). Time-series of direct-path relative arrival-times are constructed for each VLA element across the 11 min observation interval. The overall structure of these time-series compares favorably with that predicted from an array element localization model. The short-term standard deviations calculated on the direct-path (7 µs) and bottom-reflected-path (17 µs) time-series are in agreement with the predicted arrival-time accuracies. The implications of these observed arrival-time accuracies in the context of estimating sound speed perturbations and bottom-depth are discussed.

Estimating and removing colorations from the deconvolved impulse response of an underwater acoustic channel.

The impulse response (IR) of an acoustic channel can be obtained by cross-correlating the received signal with the broadband excitation signal in unfavorable noise conditions. However, the deconvolved IR is colored by the IRs of the combined electrical equipment. This letter presents a time domain approach using pre-computed filters to whiten the unknown coloration in order to obtain the channel's time domain waveform. The method is validated with an image-source model and the IR of the channel is recovered with spectral root mean square error of -27 dB. Data results obtained from a pool experiment with non-calibrated equipment yield a whitened IR with standard deviation of 0.9 dB (30-68 kHz band).

Adaptive and compressive matched field processing.

Matched field processing is a generalized beamforming method that matches received array data to a dictionary of replica vectors in order to locate one or more sources. Its solution set is sparse since there are considerably fewer sources than replicas. Using compressive sensing (CS) implemented using basis pursuit, the matched field problem is reformulated as an underdetermined, convex optimization problem. CS estimates the unknown source amplitudes using the replica dictionary to best explain the data, subject to a row-sparsity constraint. This constraint selects the best matching replicas within the dictionary when using multiple observations and/or frequencies. For a single source, theory and simulations show that the performance of CS and the Bartlett processor are equivalent for any number of snapshots. Contrary to most adaptive processors, CS also can accommodate coherent sources. For a single and multiple incoherent sources, simulations indicate that CS offers modest localization performance improvement over the adaptive white noise constraint processor. SWellEx-96 experiment data results show comparable performance for both processors when localizing a weaker source in the presence of a stronger source. Moreover, CS often displays less ambiguity, demonstrating it is robust to data-replica mismatch.

Multi-frequency sparse Bayesian learning for robust matched field processing.

The multi-snapshot, multi-frequency sparse Bayesian learning (SBL) processor is derived and its performance compared to the Bartlett, minimum variance distortionless response, and white noise constraint processors for the matched field processing application. The two-source model and data scenario of interest includes realistic mismatch implemented in the form of array tilt and data snapshots not exactly corresponding to the range-depth grid of the replica vectors. Results demonstrate that SBL behaves similar to an adaptive processor when localizing a weaker source in the presence of a stronger source, is robust to mismatch, and exhibits improved localization performance when compared to the other processors. Unlike the basis or matching pursuit methods, SBL automatically determines sparsity and its solution can be interpreted as an ambiguity surface. Because of its computational efficiency and performance, SBL is practical for applications requiring adaptive and robust processing.

Partial dereverberation used to characterize open circuit scuba diver signatures.

The use of passive acoustics to detect self-contained underwater breathing apparatus (SCUBA) divers is useful for nearshore and port security applications. While the performance of a detector can be optimized by understanding the signal's spectral characteristics, anechoic recording environments are generally not available or are cost prohibitive. A practical solution is to obtain the source spectra by equalizing the recording with the inverse of the channel's impulse response. This paper presents a dereverberation method for signal characterization that is subsequently applied to four recorded SCUBA configurations. The inverse impulse response is computed in the least-square sense, and partial dereverberation of SCUBA is performed over the 6-18 kHz band. Results indicate that early reflections and late reverberation added as much as 6.8 dB of energy. Mean unadjusted sound pressure levels computed over the 0.3-80 kHz band were 130 ± 5.9 dB re 1 µPa at 1 m. Bubble noise carries a significant amount of the total energy and masks the regulator signatures from 1.3 to 6 kHz, depending on the regulator configuration. While the dereverberation method is applied here to SCUBA signals, it is generally applicable to other sources if the impulse response of the recording environment can be obtained separately.

Basin scale coherence of Kauai-Beacon m-sequence transmissions received at Wake Island and Monterey, CA.

The 75 Hz Kauai-Beacon source is well-situated for observing the North Pacific Ocean acoustically, and ongoing efforts enable transmissions and analysis of broadband signals in 2023 and beyond. This is the first demonstration of acoustic receiving along paths to Wake Island (∼3500 km) and Monterey Bay (∼4000 km). The 44 received m-sequence waveforms exhibit excellent phase stability with processing gain approaching the maximum theoretical gain evaluated over the 20 min signal transmission duration. The article concludes with a discussion on the future source utility and highlights research topics of interest, including observed Doppler (waveform dilation), thermometry, and tomography.

Overcoming snapshot-deficient measurements with knowledge-aided approaches.

The use of knowledge-aided covariance is considered for processing underwater acoustic array data in snapshot-deficient scenarios. The knowledge-aided formalism is a technique that combines array data with a known covariance to produce an invertible estimate. For underwater acoustics, simulations of ambient noise provide the a priori covariance allowing degraded signals to be processed adaptively in situations where the sample covariance matrix is rank-deficient. The method is demonstrated for matched field processing using the 21 element array event S5 from the SWellEx-96 experiment. With five snapshots, the knowledge-aided approach significantly reduces localization ambiguity compared to the adaptive white noise gain constraint processor.

Data driven source localization using a library of nearby shipping sources of opportunity.

A library of broadband (100-1000 Hz) channel impulse responses (CIRs) estimated between a short bottom-mounted vertical line array (VLA) in the Santa Barbara channel and selected locations along the tracks of 27 isolated transiting ships, cumulated over nine days, is constructed using the ray-based blind deconvolution algorithm. Treating this CIR library either as data-derived replica for broadband matched-field processing (MFP) or training data for machine learning yields comparable ranging accuracy (∼50 m) for nearby vessels up to 3.2 km for both methods. Using model-based replica of the direct path only computed for an average sound-speed profile comparatively yields∼110 m ranging accuracy.