Source depth estimation with feature matching using convolutional neural networks in shallow water.

A feature matching method based on the convolutional neural network (named FM-CNN), inspired from matched-field processing (MFP), is proposed to estimate source depth in shallow water. The FM-CNN, trained on the acoustic field replicas of a single source generated by an acoustic propagation model in a range-independent environment, is used to estimate single and multiple source depths in range-independent and mildly range-dependent environments. The performance of the FM-CNN is compared to the conventional MFP method. Sensitivity analysis for the two methods is performed to study the impact of different environmental mismatches (i.e., bottom parameters, water column sound speed profile, and topography) on depth estimation performance in the East China Sea environment. Simulation results demonstrate that the FM-CNN is more robust to the environmental mismatch in both single and multiple source depth estimation than the conventional MFP. The proposed FM-CNN is validated by real data collected from four tracks in the East China Sea experiment. Experimental results demonstrate that the FM-CNN is capable of reliably estimating single and multiple source depths in complex environments, while MFP has a large failure probability due to the presence of strong sidelobes and wide mainlobes.

Passive synthetic aperture for direction-of-arrival estimation using sparse Bayesian learning.

Passive synthetic aperture (PSA) extension for a moving array has the ability to enhance the accuracy of direction-of-arrival (DOA) estimation by constructing a larger virtual aperture. The array element overlap in array continuous measurements is required for the traditional extended towed array measurement (ETAM) methods. Otherwise, the phase factor estimation is biased, and the aperture extension fails when multiple sources exist. To solve this problem, passive aperture extension with sparse Bayesian learning (SBL) is proposed. In this method, SBL is used to simultaneously estimate the phase correction factors of different targets, followed by phase compensation applied to the extended aperture manifold vectors for DOA estimation. Simulation and experimental data results demonstrate that this proposed method successfully extends the aperture and provides higher azimuth resolution and accuracy compared to conventional beamforming (CBF) and SBL without extension. Compared with the traditional ETAM methods, the proposed method still performs well even when the array elements are not overlapped during the motion.

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.

Implementation of Bartlett matched-field processing using interpretable complex convolutional neural network.

Neural networks have been applied to underwater source localization and achieved better performance than the conventional matched-field processing (MFP). However, compared with MFP, the neural networks lack physical interpretability. In this work, an interpretable complex convolutional neural network based on Bartlett processor (BC-CNN) for underwater source localization is designed, the output and structure of which have clear physical meanings. The relationship between the convolution weights of BC-CNN and replica pressure of MFP is discussed, which effectively presents the interpretability of the BC-CNN. Simulation experiments using two kinds of labels demonstrate the equivalence between the Bartlett MFP and BC-CNN.

Deep-learning geoacoustic inversion using multi-range vertical array data in shallow water.

A multi-range vertical array data processing (MRP) method based on a convolutional neural network (CNN) is proposed to estimate geoacoustic parameters in shallow water. The network input is the normalized sample covariance matrices of the broadband multi-range data received by a vertical line array. Since the geoacoustic parameters (e.g., bottom sound speed, density, and attenuation) have different scales, the multi-task learning is used to estimate these parameters simultaneously. To reduce the influence of the uncertainty of the source position, the training and validation data are composed of the simulation data of different source depths. Simulation results demonstrate that compared with the conventional matched-field inversion (MFI), the CNN with MRP alleviates the coupling between the geoacoustic parameters and is more robust to different source depths in the shallow water environment. Based on the inversion results, better localization performance is achieved when the range-dependent environment is assumed to be a range-independent model. Real data from the East China Sea experiment are used to validate the MRP method. The results show that, compared with the MFI and the CNN with single-range vertical array data processing, the use of geoacoustic parameters from MRP achieves better localization performance.

Multiple source localization using learning-based sparse estimation in deep ocean.

This paper proposes the use of gated feedback gated recurrent unit network (GFGRU), a learning-based sparse estimation algorithm, for multiple source localization in the direct arrival zone of the deep ocean. The GFGRU, trained on sound field replicas of a single source generated by an acoustic propagation model, is used to estimate the ranges and depths of multiple sources without knowing the number of sources. The performance of GFGRU is compared to the Bartlett processor, feedforward neural network (FNN), and sparse Bayesian Learning (SBL) algorithm. Simulations indicate that GFGRU behaves similarly to SBL and offers modest localization performance improvement over the Bartlett and FNN in the presence of array tilt mismatch. The results of real data from the South China Sea also verify the robustness of the proposed GFGRU using a 105 m-aperture vertical array in the deep ocean.

Mode separation with one hydrophone in shallow water: A sparse Bayesian learning approach based on phase speed.

An approach of broadband mode separation in shallow water is proposed using phase speed extracted from one hydrophone and solved with sparse Bayesian learning (SBL). The approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, is used to build the dictionary matrix for SBL. Given a multi-frequency pressure vector on one hydrophone, SBL estimates a set of sparse coefficients for a large number of atoms in the dictionary. With the estimated coefficients and corresponding atoms, the separated normal modes are retrieved. The presented method can be used for impulsive or known-form signals in a shallow-water environment while no bottom information is required. The simulation results demonstrate that the proposed approach is adapted to the environment where both the reflected and refracted modes coexist, whereas the performance of the time warping transformation degrades significantly in this scenario.

Deep-learning source localization using autocorrelation functions from a single hydrophone in deep ocean.

In the direct arrival zone of the deep ocean, the multi-path time delays have been used for acoustic source localization. One of the challenges in conventional localization methods is to artificially determine which paths the extracted delays belong to. A convolutional neural network, taking the autocorrelation functions as the input feature directly, is proposed for source localization to avoid the path determination procedure. Since some multi-path arrivals may not be visible due to absorption in the bottom of the ocean, a data augmentation method based on a ray propagation model is proposed. Tests on simulated and real data validate the method.

A multi-task learning convolutional neural network for source localization in deep ocean.

A multi-task learning (MTL) method with adaptively weighted losses applied to a convolutional neural network (CNN) is proposed to estimate the range and depth of an acoustic source in deep ocean. The network input is the normalized sample covariance matrices of the broadband data received by a vertical line array. To handle the environmental uncertainty, both the training and validation data are generated by an acoustic propagation model based on multiple possible sets of environmental parameters. The sensitivity analysis is investigated to examine the effect of mismatched environmental parameters on the localization performance in the South China Sea environment. Among the environmental parameters, the array tilt is found to be the most important factor on the localization. Simulation results demonstrate that, compared with the conventional matched field processing (MFP), the CNN with MTL performs better and is more robust to array tilt in the deep-ocean environment. Tests on real data from the South China Sea also validate the method. In the specific ranges where the MFP fails, the method reliably estimates the ranges and depths of the underwater acoustic source.

Block sparse Bayesian learning for broadband mode extraction in shallow water from a vertical array.

The horizontal wavenumbers and modal depth functions are estimated by block sparse Bayesian learning (BSBL) for broadband signals received by a vertical line array in shallow-water waveguides. The dictionary matrix consists of multi-frequency modal depth functions derived from shooting methods given a large set of hypothetical horizontal wavenumbers. The dispersion relation for multi-frequency horizontal wavenumbers is also taken into account to generate the dictionary. In this dictionary, only a few of the entries are used to describe the pressure field. These entries represent the modal depth functions and associated wavenumbers. With the constraint of block sparsity, the BSBL approach is shown to retrieve the horizontal wavenumbers and corresponding modal depth functions with high precision, while a priori knowledge of sea bottom, moving source, and source locations is not needed. The performance is demonstrated by simulations and experimental data.

A feedforward neural network for direction-of-arrival estimation.

This paper examines the relationship between conventional beamforming and linear supervised learning, then develops a nonlinear deep feed-forward neural network (FNN) for direction-of-arrival (DOA) estimation. First, conventional beamforming is reformulated as a real-valued, linear inverse problem in the weight space, which is compared to a support vector machine and a linear FNN model. In the linear formulation, DOA is quickly and accurately estimated for a realistic array calibration example. Then, a nonlinear FNN is developed for two-source DOA and for K-source DOA, where K is unknown. Two training methodologies are used: exhaustive training for controlled accuracy and random training for flexibility. The number of FNN model hidden layers, hidden nodes, and activation functions are selected using a hyperparameter search. In plane wave simulations, the 2-source FNN resolved incoherent sources with 1° resolution using a single snapshot, similar to Sparse Bayesian Learning (SBL). With multiple snapshots, K-source FNN achieved resolution and accuracy similar to Multiple Signal Classification and SBL for an unknown number of sources. The practicality of the deep FNN model is demonstrated on Swellex96 experimental data for multiple source DOA on a horizontal acoustic array.

Geoacoustic inversion using ray-based blind deconvolution of shipping sources.

The ray-based blind deconvolution algorithm can provide an estimate of the channel impulse responses (CIRs) between a shipping source of opportunity and the elements of a receiving array by estimating the unknown phase of this random source through wideband beamforming along a well-resolved ray path. However, due to the shallow effective depth (typically <10 m) and low frequency content (typically less than a few kHz) associated with shipping sources, the interfering direct and surface arriving pair and subsequent bottom and surface-bottom arrival pair cannot always be resolved in the CIR arrival-time structure. Nevertheless, this study demonstrates that the bottom reflection loss can be inferred from the ratio of the magnitude spectra of these two arrival pairs if a frequency-dependent correction (which can be purely data based) is applied to correct for the dipole source effect. The feasibility of the proposed approach is demonstrated to invert for the geoacoustic parameters of a soft-layer covering the ocean floor using a nonlinear least-square algorithm.

Deep-learning source localization using multi-frequency magnitude-only data.

A deep learning approach based on big data is proposed to locate broadband acoustic sources using a single hydrophone in ocean waveguides with uncertain bottom parameters. Several 50-layer residual neural networks, trained on a huge number of sound field replicas generated by an acoustic propagation model, are used to handle the bottom uncertainty in source localization. A two-step training strategy is presented to improve the training of the deep models. First, the range is discretized in a coarse (5 km) grid. Subsequently, the source range within the selected interval and source depth are discretized on a finer (0.1 km and 2 m) grid. The deep learning methods were demonstrated for simulated magnitude-only multi-frequency data in uncertain environments. Experimental data from the China Yellow Sea also validated the approach.

Ship localization in Santa Barbara Channel using machine learning classifiers.

Machine learning classifiers are shown to outperform conventional matched field processing for a deep water (600 m depth) ocean acoustic-based ship range estimation problem in the Santa Barbara Channel Experiment when limited environmental information is known. Recordings of three different ships of opportunity on a vertical array were used as training and test data for the feed-forward neural network and support vector machine classifiers, demonstrating the feasibility of machine learning methods to locate unseen sources. The classifiers perform well up to 10 km range whereas the conventional matched field processing fails at about 4 km range without accurate environmental information.

Source localization in an ocean waveguide using supervised machine learning.

Source localization in ocean acoustics is posed as a machine learning problem in which data-driven methods learn source ranges directly from observed acoustic data. The pressure received by a vertical linear array is preprocessed by constructing a normalized sample covariance matrix and used as the input for three machine learning methods: feed-forward neural networks (FNN), support vector machines (SVM), and random forests (RF). The range estimation problem is solved both as a classification problem and as a regression problem by these three machine learning algorithms. The results of range estimation for the Noise09 experiment are compared for FNN, SVM, RF, and conventional matched-field processing and demonstrate the potential of machine learning for underwater source localization.

Theoretical analysis of warping operators for non-ideal shallow water waveguides.

Signals propagating in waveguides can be decomposed into normal modes that exhibit dispersive characteristics. Based on the dispersion analysis, the warping transformation can be used to improve the modal separability. Different from the warping transformation defined using an ideal waveguide model, an improved warping operator is presented in this paper based on the beam-displacement ray-mode (BDRM) theory, which can be adapted to low-frequency signals in a general shallow water waveguide. For the sake of obtaining the warping operators for the general waveguides, the dispersion formula is first derived. The approximate dispersion relation can be achieved with adequate degree of accuracy for the waveguides with depth-dependent sound speed profiles (SSPs) and acoustic bottoms. Performance and accuracy of the derived formulas for the dispersion curves are evaluated by comparing with the numerical results. The derived warping operators are applied to simulations, which show that the non-linear dispersion structures can be well compensated by the proposed warping operators.