Matched-field Source Localization Research Articles

Validity of matched-field source localization in under-ice shallow water

Underwater source localization, such as matched-field processing (MFP), triangulation, and waveguide invariant, have been extensively investigated in temperate oceans. Seasonal or yearlong ice floes or ice cover exist in high-latitude sea regions and the polar ocean. In under-ice shallow water, sound interacts frequently with ice and sea bottom, which results in dramatic reflection, attenuation, and modal dispersion. The boundary effects generate more uncertainties in model-based source localization methods, for example, the MFP method. In this work, we develop the preliminary scheme of the under-ice MFP. The performances of the incoherent Bartlett and minimum variance algorithms are verified by real data collected by a 12-element Vertical line array with a space of 1 m for a source (650–750 Hz) at 2.7-km range and 5-m depth in the northern Yellow Sea in winter. The experimental findings demonstrate that the range error is within 2% and the depth error is within 10%. The error primarily originates from the uncertainty of sea bottom parameters.

Tensor‐based matched‐field processing applied to the SWellEx‐96 data

AbstractThis study proposed a matched field source localization method based on tensor decomposition. By considering the advantages of tensors in multidimensional data processing, a three‐dimensional tensor signal model of space‐time‐frequency is constructed, and the signal subspace is estimated using high‐order singular value decomposition. The source position is estimated by matching the measured data tensor signal subspace with the replica field tensor signal subspace. The S5 event data of SWellEx‐96 is processed by the proposed tensor‐based matched‐field processing (TMFP). The comparison with the results of conventional matched field processing shows that TMFP has a better suppression effect on ambient noise under low SNR and better source localization performance.

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.

A graph-based narrowband matched-field source localization method.

Matched field processing (MFP) has been regarded as one of the most successful acoustical methods for positioning underwater sources. In this paper, the narrowband MFP method is combined with a recently developed framework-the graph signal processing (GSP) method. Following the paradigm of GSP, a spatial adjacency matrix is constructed for the arbitrary distributed sensors based on the Green's function, then the source is located by utilizing the graph Fourier transform. The simulation results illustrate that the graph-based MFP outperforms the conventional MFP processors for its better accuracy and fewer requirements for sensor numbers.

Matched field source localization with Gaussian processes.

For a sparsely observed acoustic field, Gaussian processes can predict a densely sampled field on the array. The prediction quality depends on the choice of a kernel and a set of hyperparameters. Gaussian processes are applied to source localization in the ocean in combination with matched-field processing. Compared to conventional processing, the denser sampling of the predicted field across the array reduces the ambiguity function sidelobes. As the noise level increases, the Gaussian process-based processor has a distinctly higher probability of correct localization than conventional processing, due to both denoising and denser field prediction.

Non-linear embedding of acoustic cross-spectral density matrices through diffusion maps.

Based on the notion of similarity or "distance" between cross-spectral density matrices (CSDMs), a recent analysis of matched-field source localization in a stochastic ocean waveguide provided evidence that geodesic distances between CSDMs could be employed to estimate the source location in range and depth. For M acoustic sensors configured as a vertical array, these M×M matrices were estimated from source and replica fields propagated to the array and interpreted as points in a Riemannian manifold whose dimension is M2. Because they serve as fundamental constructs for many source localization algorithms, visualizations of CSDM manifolds are illustrated here in an attempt to gain insight into this geometric approach by using simulated acoustic fields propagated through an ocean waveguide with internal wave-induced variability. The manifold is treated as an undirected, weighted graph whose nodes are CSDMs with edges (weights) describing a measure of similarity between nodes. A non-linear dimensionality reduction technique, diffusion maps, is applied to project these high-dimensional matrices onto a three-dimensional subspace using a spectral decomposition of the graph in an attempt to grasp relationships among such matrices. The mapping is designed to preserve the notion of distance between matrices, allowing for a meaningful visualization of the high-dimensional manifold.

Dimensionality reduction of cross-spectral density matrices using diffusion map projections

Cross-spectral density matrices (CSDMs) constructed for matched-field source localization in an ocean waveguide are both Hermitian and positive semi-definite, allowing them to be interpreted in a non-Euclidean geometric framework as “points” in a Riemannian manifold. This abstract matrix representation can be used to construct distance metrics on the manifold, and distances between pairs of such matrices provide a measure of similarity between the true source CSDM and various replica CSDMs. With this geometric interpretation, the shortest “distance” between pairs of source/replica CSDMs represents an estimate of the source location obtained from acoustic field amplitude and phase acquired on a vertical array [Finette and Mignerey, JASA 143 (2018)]. In this presentation, visualizations of CSDM manifolds obtained from simulated acoustic fields propagating in an ocean waveguide with internal wave-induced variability are illustrated to gain insight into this approach to passive source localization. Since the original manifold resides in a high-dimensional space determined by the number of sensors, manifold learning using diffusion maps is employed to reduce the dimensionality but constrained to retain the relative distance relationships among the CSDMs. The original manifold is projected down to three dimensions for visualization. [Work supported by the Office of Naval Research.]

Improving Statistical Robustness of Matched-Field Source Localization via General-Rank Covariance Matrix Matching

Performance of matched-field source localization is highly dependent on the precision of the model to actual physical processes. Model mismatch, including sound propagation environmental mismatch, statistical mismatch, and system mismatch, causes severe performance degradation. Statistical mismatch occurs when an insufficient snapshot set is used to estimate the data covariance matrix. Diagonal loading can improve the widely used minimum variance distortionless response (MVDR) and minimum power distortionless response (MPDR) processors against statistical mismatch, however, the result relies on selection of the loading level. Previously, a new processor named the matched-covariance estimator (MCE) was shown to have statistically robust estimation capability under white noise conditions by matching the general-rank data covariance matrix with a covariance matrix of the modeled replicas. In this paper, the method is further developed in more realistic application scenarios with discrete point interferences and/or surface-generated noises. Simulations and analyses show that MCE can outperform classical MVDR/MPDR matched-field processors by: 1) exploiting both signal and noise data structure at the same time; 2) being less prone to mistaken nulling of the signal; 3) requiring no rank-1 signal space restriction; and 4) not needing signal-free and long duration training data.

Matched-field source localization with multiple small-aperture arrays

This paper considers combining information from multiple small-aperture arrays in matched-field processing (MFP) for source localization. Assuming individual arrays are comprised of calibrated sensors which are synchronized in time, conventional MFP can be applied for each array and the resulting Bartlett processors summed over arrays. However, if the relative calibration and/or time synchronization is known between some or all arrays, more informative multiple-array processors can be derived by maximum-likelihood methods. For example, if the relative calibration between arrays is known, the observed amplitude variations between arrays provide additional information for source localization; if synchronization is known, phase variations provide localization information. Various multiple-array processors are derived and evaluated in terms of the probability of correct localization from Monte-Carlo analyses for a range of signal-to-noise ratios and number of frequencies for simulated shallow-water scenarios with vertical and horizontal arrays. Effects of environmental mismatch in seabed geoacoustic parameters and water depth are also considered. The analysis indicates that, dependent on array configurations, substantial improvements in source localization performance can be achieved when including relative amplitude and/or phase information in the multiple-array processor. The improvement is reduced by environmental mismatch; this degradation can be partially mitigated by including additional frequencies in the processing.

Matched-field source localization with non-synchronized sensor arrays

This paper considers matched-field ocean acoustic source localization based on acoustic field measurements at an array of sensors which are not synchronized in time or at an array which is comprised of non-synchronized combinations of synchronized sub-arrays. Standard matched-field methods are based on acoustic-field measurements at a time-synchronized array to allow coherent processing over space (the array aperture). For non-synchronized systems, frequency-coherent/space-incoherent processing can be applied if the complex source spectrum (amplitude and phase) is known, but this is rarely the case in practical applications. However, time- and frequency-coherent processing are not the only possibilities. Maximum-likelihood methods can be applied to derive optimal matched-field processors for any state of source/receiver information. Using this method, optimal processors can be developed for broadband matched-field localization with any combination of synchronized and/or non-synchronized components based on the fact that the source amplitude spectrum is the same (although unknown) for all receivers (the phase spectrum is both unknown and variable for non-synchronized components). Bayesian inversion methods are employed to quantify the source-localization information content for various array scenarios.

Matched-field Source Localization with a Mobile Short Horizontal Linear Array in Offshore Shallow Water

Abstract Passive source localization in shallow water has always been an important and challenging problem. Implementing scientific research, surveying, and monitoring using a short, less than ten meter long, horizontal linear array has received considerable attention in the recent years. The short array can be conveniently placed on autonomous underwater vehicles and deployed for adaptive spatial sampling. However, it is usually difficult to obtain a sufficient spatial gain for localizing long-range sources due to its limited physical size. To address this problem, a localization approach is proposed which is based on matched-field processing of the likelihood of the passive source localization in shallow water, as well as inter-position processing for the improved localization performance and the enhanced stability of the estimation process. The ability of the proposed approach is examined through the two-dimensional synthetic test cases which involves ocean environmental mismatch and position errors of the short array. The presented results illustrate the localization performance for various source locations at different signal- to-noise ratios and demonstrate the build up over time of the positional parameters of the estimated source as the short array moves at a low speed along a straight line at a certain depth.

Matched Field Source Localization via Environmental Focalization

In a realistic application of matched field processing for source localization, the ability to localize an acoustic source is strongly affected by the uncertainty of the environment. However, accurate environment measurement is a difficult task in large regions of the ocean. We employ a Bayesian approach, referred to here as focalization, to overcome the mismatch by including the environment in the parameter search space. Focalization maximizes the posterior probability density over the unknown source and environmental parameters. The broadband signals recorded by a vertical line array in a Yellow Sea experiment are presented to demonstrate the feasibility of focalization.

Maximum-likelihood and other processors for incoherent and coherent matched-field localization

This paper develops a series of maximum-likelihood processors for matched-field source localization given various states of information regarding the frequency and time variation of source amplitude and phase, and compares these with existing approaches to coherent processing with incomplete source knowledge. The comparison involves elucidating each processor's approach to source spectral information within a unifying formulation, which provides a conceptual framework for classifying and comparing processors and explaining their relative performance, as quantified in a numerical study. The maximum-likelihood processors represent optimal estimators given the assumption of Gaussian noise, and are based on analytically maximizing the corresponding likelihood function over explicit unknown source spectral parameters. Cases considered include knowledge of the relative variation in source amplitude over time and/or frequency (e.g., a flat spectrum), and tracking the relative phase variation over time, as well as incoherent and coherent processing. Other approaches considered include the conventional (Bartlett) processor, cross-frequency incoherent processor, pair-wise processor, and coherent normalized processor. Processor performance is quantified as the probability of correct localization from Monte Carlo appraisal over a large number of random realizations of noise, source location, and environmental parameters. Processors are compared as a function of signal-to-noise ratio, number of frequencies, and number of sensors.

Performance Analysis of Matched-Field Source Localization Under Spatially Correlated Noise Field

Matched-field processing (MFP) concerns estimation of source locations by exploiting full wave modeling of acoustic waveguide propagation. Typical MFP performance demonstrates a threshold behavior, that is, below some signal-to-noise ratio (SNR), the mean-square error (MSE) increases dramatically. This threshold phenomenon has been intensively investigated previously under spatially white noise field. In this paper, we develop approaches to study MFP performance in the presence of spatially correlated noises. Both the discrete interference and surface-generated noise are considered, and a so-called method of intervals errors (MIE) is derived in the context of the maximum likelihood estimate (MLE). Performance analysis of both narrowband and broadband MFP is implemented for source localization in a realistic shallow water environment. Simulation results suggest that 1) adding either spatially correlated noise increases the MLE threshold SNR compared to the case with white noise only, but effects at high SNR are different, MSE decreasing at the same rate with a point interference while decaying in a slower pace with surface-generated noises; 2) with a strong discrete interference, interference position, rather than strength, matters more in determining the MLE performance, and broadband processing effectively reduces the threshold SNR; 3) effect of the surface-generated noises is highly frequency dependent, and processing using a higher frequency would be preferred; 4) overall the surface-generated noise is more difficult to attack by an adaptive method such as the MLE.

Range-dependent geoacoustic inversion of vertical line array data using matched beam processing

This paper describes the results of range-dependent geoacoustic inversion using vertical line array data obtained from the 4th Matched Acoustic Properties and Localization Experiment conducted in the East Sea of Korea. The narrowband multitone continuous-wave signal from the towed source was analyzed to estimate the range-dependent geoacoustic properties along the radial track. The primary approach is based on the sectorwise inversion scheme. The inversion region up to 7.5 km from the vertical line array was divided into several segments, and the subinversions for each segment were performed sequentially. To reduce the dominance of low-angle arrivals, which bears little information for the bottom segment in question, matched beam processing with beam filtering was used for the cost function. The performance of proposed algorithm was tested using simulated data for an environment representative of the experimental site. The inversion results for the experimental data were consistent with the geophysical database and were validated from matched-field source localization using frequencies different from those used in the inversion.

Applying data nullspace projection method on matched-field source localization in a random internal wave field

In a random internal wave field where temporal varying water-column soundspeed profiles are very difficult to measure, matched-field source localization methods can be greatly degraded due to water-column model mismatch. In this paper, the data nullspace projection is applied to this source localization technique to reduce the effect of unknown water-column soundspeed variations. The basis of this method is to project the acoustic signal onto a data nullspace that is insensitive to water-column soundspeed fluctuations. This method only requires the mean and the second-order statistics of temporal varying water-column soundspeed profiles to calculate soundspeed empirical-orthogonal-functions. It does not require measurements of the exact soundspeed field, i.e., each snapshot, for the matched-field processing. In a simulation test case, a linear wave model is used to generate a random internal wave field, an acoustic source continuously transmits a single frequency tone, and the matched-field processing is implemented with the signal received on both a VLA and a HLA, respectively, for localizing the source position. The simulation results show that applying the data nullspace projection method can dramatically improve the robustness and accuracy of the matched-field source localization, resulting in a random internal wave field.

Performance Analysis for Matched-Field Source Localization: Simulations and Experimental Results

Matched-field methods concern estimation of source locations and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Typical estimation performance demonstrates two fundamental limitations. First, sidelobe ambiguities dominate the estimation at low signal-to-noise ratio (SNR), leading to a threshold performance behavior. Second, most matched-field algorithms show a strong sensitivity to environmental/system mismatch, introducing biased estimates at high SNR. In this paper, some theoretical developments on matched-field performance analysis are summarized, including Bayesian performance bounds and probabilistic ambiguity analysis, both incorporating environmental/system uncertainty/mismatch. Performance analysis is then implemented for source localization in a typical shallow water environment chosen from the Shallow Water Evaluation Cell Experiments (SWellEX). The performance predictions describe the simulations of the maximum-likelihood estimator (MLE) well, including the mean-square error (MSE) in all SNR regions as well as the bias at high SNR. The threshold SNR and bias predictions are also validated through SWellEX experimental data processing. The results suggest the current environmental, acoustic, and statistical modeling has developed to such a level that the optimum theoretical matched-field performance can be achieved in a well-controlled experiment

The effect of source amplitude and phase in matched field source localization

Traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission. The spectral information of the source is estimated via maximum likelihood and is used for localization with the Bartlett processor. Maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance, where the joint posterior probability distribution of all parameters is computed with Gibbs sampling. It is shown that the proposed method has a higher probability of correct localization than the traditional approach.

Broad-band Matched-Field Source Localization in the East China Sea

An incoherent broad-band frequency (100-200 Hz) domain Bartlett processor is applied to the wide-band source (WBS) signals for source localization. The coupled normal mode-parabolic equation theory based on the WKBZ approximation is used to calculate the replica fields in the sloping bottom environment. The experimental analysis shows that the accuracy of the source localization is largely improved with the consideration of the slope of bottom. The range estimates of the majority of signals by localized by matched-field processing in the range from 30.0 to 50.0 km are consistent with the global positioning system measured ranges.

Tabu for matched-field source localization and geoacoustic inversion.

Tabu is a global optimization technique that has been very successful in operations research. In this paper, a Tabu-based method is developed for source localization and geoacoustic inversion with underwater sound data; the method relies on memory to guide the multiparameter search. Tabu is evaluated through a comparison to simulating annealing. Both methods are tested by inverting synthetic data for various numbers of unknown parameters. Tabu is found to be superior to the simulated annealing variant implemented here in terms both of accuracy and efficiency. Inversion results from the SWellEX-96 data set are also presented.