Spatial domain decomposition-based physics-informed neural networks for practical acoustic propagation estimation under ocean dynamics.

Practical acoustic propagation modeling is significantly affected by ocean dynamics, and then can be exploited in numerous oceanic applications, where "practical" refers to modeling acoustic propagation in simulations that mimic real-world ocean environments. Physics-based numerical models provide approximate solutions of wave equation and rely on accurate prior environmental knowledge while the environment of practical scenarios is largely unknown. In contrast, data-driven machine learning offers a promising avenue to estimate practical acoustic propagation by learning from dataset. However, collecting such a high-quality, noise-free, and dense dataset remains challenging. Under the practical hurdle posed by the above approaches, the emergence of physics-informed neural network (PINN) presents an alternative to integrate physics and data but with limited representation capacity. In this work, a framework, termed spatial domain decomposition-based physics-informed neural networks (SPINNs), is proposed to enhance the representation capacity in spatially dependent oceanic scenarios and effectively learn from incomplete and biased prior physics and noisy dataset. Experiments demonstrate SPINNs' advantages over PINN in practical acoustic propagation estimation. The learning capacity of SPINNs toward physics and dataset during training is further analyzed. This work holds promise for practical applications and future expansion.

Snapshot-deficient active target localization in beam-time domain using multi-frequency expectation-maximization algorithm.

The two-dimensional (2D) active target localization is generally hindered by the high temporal and spatial sidelobe levels in snapshot-deficient scenarios, where the adaptive approaches undergo performance degeneration since they require many snapshots to build the sample covariance matrix. Aiming at working robustly in snapshot-deficient active scenarios, a 2D expectation-maximization-based vertical-time-record (EMVTR) approach is proposed to compensate for the snapshot deficiency and achieve the high-resolution active localization by reconstructing the covariance matrix using estimated hyperparameters, i.e., signal powers and noise variance. With the short-time Fourier transform, the proposed approach could reduce echoes' temporal correlation and attain robust beam-time localization in mild reverberation. The multi-frequency EMVTR is derived from the single-frequency case to improve the weak echo localization. The performance is evaluated by considering single and multiple target echoes in simulation and a single moving target with tank experimental data. The results manifest the proposed EMVTR's robustness and effectiveness for the 2D active localization in snapshot-deficient scenarios.

Graph-guided Bayesian matrix completion for ocean sound speed field reconstruction.

Reconstructing ocean sound speed field (SSF) from limited and noisy measurements/estimates is crucial for many ocean acoustic applications, including underwater tomography, target localization/tracking, and communications. Classical reconstruction methods include deterministic approaches (e.g., spline interpolation) and geostatistical methods (e.g., kriging). They exhibit a strong link to linear regression and Gaussian process regression in machine learning (ML) literature, by uniformly viewing them as supervised regression models that learn the mapping from the geographical locations to the sound speed outputs. From a unified ML perspective, theoretical analysis indicates that classical reconstruction methods have several drawbacks, such as the sensitivity to noises and high computational cost. To overcome these drawbacks, inspired by the recent thriving development of graph machine learning, we introduce graph-guided Bayesian low-rank matrix completions (LRMCs) for fine-scale and accurate ocean SSF reconstruction. In particular, a more general graph-guided LRMC model is proposed that encompasses the state-of-the-art one as a special case. The proposed model and the associated inference algorithm simultaneously exploit the global (low-rankness) and local (graph structure) information of ocean sound speed data, thus striking an outstanding balance of reconstruction accuracy and computational complexity. Numerical results using real-life ocean SSF data have demonstrated the encouraging performances of the proposed approaches.

Striking the right balance: Three-dimensional ocean sound speed field reconstruction using tensor neural networks.

Accurately reconstructing a three-dimensional (3D) ocean sound speed field (SSF) is essential for various ocean acoustic applications, but the sparsity and uncertainty of sound speed samples across a vast ocean region make it a challenging task. To tackle this challenge, a large body of reconstruction methods has been developed, including spline interpolation, matrix/tensor-based completion, and deep neural networks (DNNs)-based reconstruction. However, a principled analysis of their effectiveness in 3D SSF reconstruction is still lacking. This paper performs a thorough analysis of the reconstruction error and highlights the need for a balanced representation model that integrates expressiveness and conciseness. To meet this requirement, a 3D SSF-tailored tensor DNN is proposed, which uses tensor computations and DNN architectures to achieve remarkable 3D SSF reconstruction. The proposed model not only includes the previous tensor-based SSF representation model as a special case but also has a natural ability to reject noise. The numerical results using the South China Sea 3D SSF data demonstrate that the proposed method outperforms state-of-the-art methods. The code is available at https://github.com/OceanSTARLab/Tensor-Neural-Network.

Robust sparse reconstruction of attenuated acoustic field with unknown range of source.

In this paper, we present a gridless algorithm to recover an attenuated acoustic field without knowing the range information of the source. This algorithm provides the joint estimation of horizontal wavenumbers, mode amplitudes, and acoustic attenuation. The key idea is to approximate the acoustic field in range as a finite sum of damped sinusoids, for which the sinusoidal parameters convey the ocean information of interest (e.g., wavenumber, attenuation, etc.). Using an efficient finite rate of innovation algorithm, an accurate recovery of the attenuated acoustic field can be achieved, even if the measurement noise is correlated and the range of the source is unknown. Moreover, the proposed method is able to perform joint recovery of multiple sensor data, which leads to a more robust field reconstruction. The data used here are acquired from a vertical line array at different depths measuring a moving source at several ranges. We demonstrate the performance of the proposed algorithm both in synthetic simulations and real shallow water evaluation cell experiment 1996 data.

Tensor-based basis function learning for three-dimensional sound speed fields.

Basis function learning is the stepping stone towards effective three-dimensional (3D) sound speed field (SSF) inversion for various acoustic signal processing tasks, including ocean acoustic tomography, underwater target localization/tracking, and underwater communications. Classical basis functions include the empirical orthogonal functions (EOFs), Fourier basis functions, and their combinations. The unsupervised machine learning method, e.g., the K-singular value decomposition (K-SVD) algorithm, has recently tapped into the basis function design, showing better representation performance than the EOFs. However, existing methods do not consider basis function learning approaches that treat 3D SSF data as a third-order tensor, and, thus, cannot fully utilize the 3D interactions/correlations therein. To circumvent such a drawback, basis function learning is linked to tensor decomposition in this paper, which is the primary drive for recent multi-dimensional data mining. In particular, a tensor-based basis function learning framework is proposed, which can include the classical basis functions (using EOFs and/or Fourier basis functions) as its special cases. This provides a unified tensor perspective for understanding and representing 3D SSFs. Numerical results using the South China Sea 3D SSF data have demonstrated the excellent performance of the tensor-based basis functions.

Tensor dictionary learning for representing three-dimensional sound speed fields.

Ocean sound speed field (SSF) representation is often plagued with low resolution (i.e., the capability of explaining fine-scale fluctuations). This drawback, however, is inherent in a number of classical SSF basis functions, e.g., empirical orthogonal functions, Fourier basis functions, and more recent tensor-based basis functions learned via the higher-order orthogonal iterative algorithm. For two-dimensional depth-time SSF representation, recent attempts relying on dictionary learning have shown that fine-scale sound speed information can be well preserved by a large number of basis functions. They are learned from the historical data without imposing rigid constraints on their shapes, e.g., the orthogonal constraints. However, generalizing the dictionary learning idea to represent three-dimensional (3D) spatial ocean SSF is non-trivial, in terms of both problem formulation and algorithm development. It calls for integrating the dictionary learning framework and the tensor-based basis function learning framework, a recently proposed one that captures the 3D sound speed correlations well. To achieve this goal, we develop a 3D SSF-tailored tensor dictionary learning algorithm that learns a large number of tensor-based basis functions with flexible shapes in a data-driven fashion. Numerical results based on the South China Sea 3D SSF data have showcased the superiority of the proposed approach over the prior method.

An Iterative Deconvolution-Time Reversal Method with Noise Reduction, a High Resolution and Sidelobe Suppression for Active Sonar in Shallow Water Environments.

Matched filtering is widely used in active sonar because of its simplicity and ease of implementation. However, the resolution performance generally depends on the transmitted waveform. Moreover, its detection performance is limited by the high-level sidelobes and seriously degraded in a shallow water environment due to time spread induced by multipath propagation. This paper proposed a method named iterative deconvolution-time reversal (ID-TR), on which the energy of the cross-ambiguity function is modeled, as a convolution of the energy of the auto-ambiguity function of the transmitted signal with the generalized target reflectivity density. Similarly, the generalized target reflectivity density is a convolution of the spread function of channel with the reflectivity density of target as well. The ambiguity caused by the transmitted signal and the spread function of channel are removed by Richardson-Lucy iterative deconvolution and the time reversal processing, respectively. Moreover, this is a special case of the Richardson-Lucy algorithm that the blur function is one-dimensional and time-invariant. Therefore, the iteration deconvolution is actually implemented by the iterative temporal time reversal processing. Due to the iterative time reversal method can focus more and more energy on the strongest target with the iterative number increasing and then the peak-signal power increases, the simulated result shows that the noise reduction can achieve 250 dB in the "ideal" free field environment and 100 dB in a strong multipaths waveguide environment if a 1-ms linear frequency modulation with a 4-kHz frequency bandwidth is transmitted and the number of iteration is 10. Moreover, the range resolution is approximately a delta function. The results of the experiment in a tank show that the noise level is suppressed by more than 70 dB and the reverberation level is suppressed by 3 dB in the case of a single target and the iteration number being 8.

Passive Source Localization Using Compressive Sensing.

This paper presents an underwater passive source localization method by forming an underdetermined linear inversion problem. The signal strength on a specified grid is evaluated using sparse reconstruction algorithms by exploiting the spatial sparsity of the source signals. Our strategy leads to a high ratio of measurements to sparsity (RMS), an increase in the peak sharpness with a low side lobe level, and minimization of the dimensionality of the problem due to the formulation of the system equation of the multiple snapshots based on the data correlation matrix. Furthermore, to reduce the computational burden, pre-locating with Bartlett is presented. Our proposed technique can perform close to Bartlet and white noise gain constraint processes in the single-source scenario, but it can give slightly better results while localizing multiple sources. It exhibits the respective characteristics of traditionally used Bartlett and white noise gain constraint methods, such as robustness to environmental/system mismatch and high resolution. Both the simulated and experimental data are processed to demonstrate the effectiveness of the method for underwater source localization.

Improved snapshot-deficient active target localization using the knowledge-aided covariance of reverberation.

Underwater reverberation often hinders the effectiveness of adaptive methods in active target localization with snapshot-deficient conditions. To overcome this challenge, a knowledge-aided reverberation covariance-based approach is proposed to maintain high resolution while reducing sidelobe levels. Using the aided reverberation covariance computed from the reverberation model, the knowledge-aided sample covariance matrix is constructed and used to decrease reverberation and compensate for snapshot deficiency. Simulations show that the proposed approach can localize targets with improved resolution and reduce reverberation levels in low signal-to-reverberation ratio situations, manifesting its potential to enhance adaptive processing reliability for active target localization.