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A posteriori probability source localization in an uncertain sound speed, deep ocean environment
Abstract
The a posteriorisource position probability density function for a narrow-band source in an uncertain acoustic environment is derived. The implementation of this probability density function (pdf) is termed the optimum uncertain field processor (OUFP). It is shown that the OUFP is a generalization of matched-field processing to situations in which there is uncertainty about the environment. The robustness of the OUFP is illustrated through performance comparisons to a matched-field algorithm.
... Thus, the geoacoustic parameters are often included as unknown parameters to account for environmental uncertainty. [16][17][18][19][20][21][22][23] To solve the source positions, focalization [16][17][18][19][20] involves maximizing the posterior probability density over all parameters to seek the globally optimal solution, while marginalization [21][22][23] integrates the posterior probability density over environmental parameters to obtain the joint marginal probability distributions for source parameters. The advantage of marginalization is that the joint marginal distribution provides a quantitative measure of localization uncertainty. ...
... Thus, the geoacoustic parameters are often included as unknown parameters to account for environmental uncertainty. [16][17][18][19][20][21][22][23] To solve the source positions, focalization [16][17][18][19][20] involves maximizing the posterior probability density over all parameters to seek the globally optimal solution, while marginalization [21][22][23] integrates the posterior probability density over environmental parameters to obtain the joint marginal probability distributions for source parameters. The advantage of marginalization is that the joint marginal distribution provides a quantitative measure of localization uncertainty. ...
... In the MFP approaches, [16][17][18][19][20][21][22][23][26][27][28] a large number of field replicas generated by acoustic propagation models were used to reflect the environmental uncertainty. Similarly, in this study, we solve source localization using one sensor by exploiting a large number of replicas, as in MFP, for deep learning, 32-34 a state-of-the-art method in machine learning. ...
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.
... Thus the geoacoustic parameters are often included as unknown parameters to account for environmental uncertainty. [13][14][15][16][17][18][19][20] To solve the source positions, focalization [13][14][15][16][17] involves maximizing the posterior probability density over all parameters to seek the globally opa) Electronic mail: nhq@mail.ioa.ac.cn timal solution, while marginalization [18][19][20] integrates the posterior probability density over environmental parameters to obtain the joint marginal probability distributions for source parameters. The advantage of marginalization is that the joint marginal distribution provides a quantitative measure of localization uncertainty. ...
... Thus the geoacoustic parameters are often included as unknown parameters to account for environmental uncertainty. [13][14][15][16][17][18][19][20] To solve the source positions, focalization [13][14][15][16][17] involves maximizing the posterior probability density over all parameters to seek the globally opa) Electronic mail: nhq@mail.ioa.ac.cn timal solution, while marginalization [18][19][20] integrates the posterior probability density over environmental parameters to obtain the joint marginal probability distributions for source parameters. The advantage of marginalization is that the joint marginal distribution provides a quantitative measure of localization uncertainty. ...
... In the MFP approaches [13][14][15][16][17][18][19][20][23][24][25] , a large number of field replicas generated by acoustic propagation models were used to reflect the environmental uncertainty. In this study, we solve source localization using one sensor by exploiting a large number of replicas, as in MFP, for deep learning, 29-31 a state-of-the-art method in machine learning. ...
A deep learning approach based on big data is proposed to locate broadband acoustic sources with one hydrophone in ocean waveguides. 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 environmental 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 tested for simulated data in uncertain environments and on experimental data. In both tests, the deep learning methods successfully estimated source ranges and depths in uncertain environments.
... Other approaches incorporate uncertain environmental parameters as additional unknowns constrained by a priori information in the localization problem, [16][17][18][19][20][21][22][23][24] which makes the localization robust to mismatch with respect to these parameters. Two general approaches, namely, focalization and marginalization, have been considered. ...
... [16][17][18] The marginalization approach formulates the problem within a Bayesian framework. [19][20][21][22][23][24] Bayes' rule relates the a priori probability density and the likelihood to the posterior probability density (PPD) which quantifies the probability of the unknown parameters given the measured data and prior information. The analysis is carried out for the extended PPD involving the localization parameters as well as the environmental parameters. ...
... In the original development of Bayesian MFP by Richardson and Nolte, 19 the source signal was regarded as an unknown quantity sðf m Þ ¼ s l ðf m Þ with a Rayleigh distributed amplitude and a uniform phase. However, a deterministic model which considers the source term s l ðf m Þ as a deterministic quantity is more flexible and has been used in many recent applications (e.g., Refs. ...
The localization of an acoustic source in the oceanic waveguide is a difficult task because the oceanic environment is often poorly known. Uncertainty in the environment results in uncertainty in the source position and poor localization results. Hence, localization methods dealing with environmental uncertainty are required. In this paper, a Bayesian approach to source localization is introduced in order to improve robustness and obtain quantitative measures of localization uncertainty. The Green's function of the waveguide is considered as an uncertain random variable whose probability density accounts for environmental uncertainty. The uncertain distribution over range and depth is then obtained through the integration of the posterior probability density (PPD) over the Green's function probability density. An efficient integration technique makes the whole localization process computationally efficient. Some results are presented for a simple uncertain Green's function model to show the ability of the proposed method to give reliable PPDs.
... This suggests that opening up the search window in one or more of these parameters would make the beamformer more tolerant of uncertainty in the other parameters [6,9,10]. Another well-known approach is based on solving the problem of localization by incorporating environmental variability a priori [11][12][13]. The current state of research related to the use of MFP in ocean acoustics is presented in the review [14]. ...
... Equations (9) - (11) suggest that the distribution of the squared coherent state amplitude |a µ | 2 in the phase plane is localized mainly in the region, formed by points located at distances ...
The paper describes the beamforming procedures in an acoustic waveguide based on representing the field on the antenna as a superposition of several stable components formed by narrow beams of rays [A.L. Virovlyansky, J. Acoust. Soc. Am. ${\bf 141}$, 1180-1189 (2017)]. A modification of the matched field processing method is proposed, based on the transition from comparing the measured and calculated fields on the antenna to comparing their stable components. The modified approach becomes less sensitive to the inevitable inaccuracies of the environmental model. In the case of a pulsed source, the stable components carry signals whose arrival times can be taken as input parameters in solving the inverse problems. The use of the stable components as the initial fields on the aperture of the emitting antenna makes it possible to excite narrow continuous wave beams propagating along given ray paths.
... While a number of approaches have been proposed to correct unsynchronized time bases across different sources and receivers for geoacoustic inversions [5], [6], [24], [36], [37], it is shown in this paper that inversions with ABSTT yield reduced uncertainty, especially when the signal-to-noise ratio (SNR) is low. The investigation based on probabilistic matched-field inversions [14], [16], [19], [33], and a numerical example of an idealized shallow water waveguide with a mud layer overlaying a sand basement is utilized to demonstrate the analysis. In addition, field work data collected during the Seabed Characterization Experiment 2017 (SBCEX17) on the New England Mud Patch in the Middle Atlantic Bight is analyzed to show a real-world example. ...
... The investigation is within the frame work of probabilistic matched-field inversions [14], [16], [19], [33] based on Bayes' theorem P (m |d ) ∝ P (m)P (d |m ) ...
Numerical and experimental studies were conducted to investigate the advantage of utilizing absolute travel time information in Bayesian geoacoustic inversions of broadband acoustic data. It is shown that inversions using absolute travel time can yield smaller uncertainties compared to inversions using relative arrival time and maximum-likelihood estimates for clock time synchronization. Experimental data collected in the Seabed Characterization Experiment on the New England Mud Patch in the Middle Atlantic Bight were used for real data demonstration, and it is shown that inversions using relative arrival times have greater uncertainty in estimating source distance, which consequently affects the overall posterior probability distribution of inverted parameters. Numerical study enables investigation of performance dependence on the signal-to-noise ratio, and it is found that absolute travel time information may have more profound advantages when the signal-to-noise ratio is low.
... Вместе с тем, в реальных условиях не только геометрия АР, но и истинные параметры среды априори неизвестны, а следовательно, рассчи-танная реплика сигнала всегда отличается от принятой на величину некоторой ошибки, обусловленной неточным знанием характеристик канала (профиля скорости звука, глубины волновода, параметров грунта). Для частичной компенсации эффекта рассогласования в акустике океана предложен ряд адаптивных методов (см., например, [9][10][11][12][13]), применение которых позволяет несколько повысить качество восстановления источника. Однако подавляющее большинство этих алгоритмов использует трудоемкую процедуру одновременного поиска как искомых координат, так и неизвестных параметров волновода. ...
... Для сравнения на рис. 6б показано поведение выходной мощности (15) строенной с привлечением робастной матрицы (9), позволяющей повысить устойчивость процедуры оценивания и частично скомпенсировать эффект детерминированного несоответствия. При расчетах поиск источника по дальности осуществлялся в диапазоне 0-300 м с шагом 1 м, а по глубине -в интервале 0-18 м с шагом 0.5 м; параметр регуляризации ε, используемый в адаптивном методе, задавался равным где Из приведенных графиков видно, что во всех случаях положение абсолютного максимума выходного эффекта наблюдается при м и м, что довольно близко к истинным значениям координат источника. ...
... From the probabilistic standpoint, the network model learns the nonlinear relationship between µ and p l ( f ), in other words, the distribution of P(µ|p l ( f )) [32]. In Equation (1), η can influence the distribution; therefore, training the network model in various η cases of input features is an effective way to improve the robustness. ...
Shallow water passive source localization is an essential problem in underwater detection and localization. Traditional matched-field processing (MFP) methods are sensitive to environment mismatches. Many neural network localization methods still have room for improvement in accuracy if they are further adjusted to underwater acoustic characteristics. To address these problems, we propose a deep learning localization method via improved input features and network structure, which can effectively estimate the depth and the closest point of approach (CPA) range of the acoustic source. Firstly, we put forward a feature preprocessing scheme to enhance the localization accuracy and robustness. Secondly, we design a deep learning network structure to improve the localization accuracy further. Finally, we propose a method of visualizing the network to optimize the estimated localization results. Simulations show that the accuracy of the proposed method is better than other compared features and network structures, and the robustness is significantly better than that of the MFP methods. Experimental results further prove the effectiveness of the proposed method.
... MFP is a powerful technique because it explores the full-field complexity of waveguide propagation [2], but its greatest limitation derives from this very fact: if the model of the environment is not an accurate representation of it, a situation called model mismatch, MFP degrades and the inversion results will not be meaningful. Several robust processors that tolerate incomplete knowledge of the environment have been developed [3][4][5]. One particular technique introduced by Collins and Kuperman, termed focalization, includes environmental parameters in the search space along with source coordinates and simultaneously adjusts (focuses) the environment and localizes the source [6]. ...
Matched field processing (MFP) is an inversion method that combines signal processing techniques with predictions of the acoustic field computed by numerical models and has been applied extensively to source localization. MFP's performance is dependent on accurate environment knowledge and degrades as the uncertainties about environmental parameters accumulate, resulting in model mismatch. To reduce model mismatch, the focalization technique can be used, by including environmental parameters in the search space in addition to source position, thus allowing the environment to be handled as a lens that can be focused. To this effect, a genetic algorithm is employed to efficiently optimize for multiple parameters simultaneously. This paper considers the inversion of experimental data from a shallow-water, mildly range-dependent track from the CALCOM'10 sea trial, which was not designed for source localization inversion and has multiple uncertainties for the accurate modelling of the channel. The experiment was run off the southern coast of Portugal, with an acoustic source being towed along various tracks and the signals acquired by a 16-element vertical line array deployed on a drifting buoy. Particularly, sound speed data is limited to low-resolution temperature measurements at receiver position. The results show that when a focalization step is included prior to MFP and the sound speed profile is incorporated into the optimization successful inversion for source range and depth is achieved.
... Other signal processing algorithms attempt to increase the robustness of MFP using Bayesian signal processing [Richardson & Nolte (1991), Spiesberger (2005)], but are again found to fail when the measure field is too high in frequency or is transmitted from a source that is far from the array. ...
This thesis focuses on understanding the way that acoustic and electromagnetic waves propagate through an inhomogeneous or turbulent environment, and analyzes the effect that this uncertainty has on signal processing algorithms. These methods are applied to determining the effectiveness of matched-field style source localization algorithms in uncertain ocean environments, and to analyzing the effect that random media composed of electrically large scatterers has on propagating waves. The first half of this dissertation introduces the frequency-difference autoproduct, a surrogate field quantity, and applies this quantity to passive acoustic remote sensing in waveguiding ocean environments. The frequency-difference autoproduct, a quadratic product of frequency-domain complex measured field values, is demonstrated to retain phase stability in the face of significant environmental uncertainty even when the related pressure field’s phase is as unstable as noise. This result demonstrates that a measured autoproduct (at difference frequencies less than 5 Hz) that is associated with a pressure field (measured in the hundreds of Hz) and which has propagated hundreds of kilometers in a deep ocean sound channel can be consistently cross-correlated with a calculated autoproduct. This cross-correlation is shown to give a cross-correlation coefficient that is more than 10 dB greater than the equivalent cross-correlation coefficient of the measured pressure field, demonstrating that the autoproduct is a stable alternative to the pressure field for array signal processing algorithms. The next major result demonstrates that the frequency-difference autoproduct can be used to passively localize remote unknown sound sources that broadcast sound hundreds of kilometers to a measuring device at hundreds of Hz frequencies. Because of the high frequency content of the measured pressure field, an equivalent conventional localization result is not possible using frequency-domain methods. These two primary contributions, recovery of frequency-domain phase stability and robust source localization, represent unique contributions to existing signal processing techniques. The second half of this thesis focuses on understanding electromagnetic wave propagation in a random medium composed of metallic scatterers placed within a background medium. This thesis focuses on developing new methods to compute the extinction and phase matrices, quantities related to Radiative Transfer theory, of a random medium composed of electrically large, interacting scatterers. A new method is proposed, based on using Monte Carlo simulation and full-wave computational electromagnetics methods simultaneously, to calculate the extinction coefficient and phase function of such a random medium. Another major result of this thesis demonstrates that the coherent portion of the field scattered by a configuration of the random medium is equivalent to the field scattered by a homogeneous dielectric that occupies the same volume as the configuration. This thesis also demonstrates that the incoherent portion of the field scattered by a configuration of the random medium, related to the phase function of the medium, can be calculated using buffer zone averaging. These methods are applied to model field propagation in a random medium, and propose an extension of single scattering theory that can be used to understand mean field propagation in relatively dense (tens of particles per cubic wavelength) random media composed of electrically large (up to 3 wavelengths long) conductors and incoherent field propagation in relatively dense (up to 5 particles per cubic wavelength) media composed of electrically large (up to two wavelengths) conductors. These results represent an important contribution to the field of incoherent, polarimetric remote sensing of the environment.
... Matched-field processing (MFP) is a method for localizing sources transmitting sound in the ocean. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] The method relies on the calculation of replica fields with a sound propagation model for a combination of candidate source ranges and depths. These replicas are then correlated (via an inner product computation, for example) with the sound received at a number of hydrophones. ...
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.
... A series of methods have been developed to solve the problem of model mismatch. Richardson [7] used the maximum a posterior estimation and realized narrow-band ASL in the deep-sea uncertain sound velocity field, the result of which was more stable than that of MFP. Krolik [8] used the minimum variance beamforming to realize ASL in a random ocean channel, which had high stability to the random change of the sound speed profile (SSP) between the acoustic source and the receiver. ...
In order to analyze the frequency periodicity characteristics of acoustic field interference and realize acoustic source ranging (ASR), the normal mode model is used to analyze the interference characteristics of the broadband acoustic field under the condition of horizontally layered medium; the broadband received signal field when the broadband pulse signal passes through the acoustic field is also simulated. The variation of interference patterns with frequency is analyzed, and their spatial interference characteristics and mechanisms are analyzed. Based on the interference theory, the relation between the acoustic source range and the frequency periodicity of the broadband acoustic intensity interference is derived. Simulation and experimental results show that this relation can accurately estimate the far-field acoustic source range, and the estimation accuracy and real-time performance are greatly improved compared with previous methods. Besides, simulation shows that the method combined with multiple-receiver ranging obtains high-precision direction of arrival (DOA) estimation as well as ASR. The relation between acoustic source position and broadband acoustic field interference frequency periodicity can be used to improve far-field ASR and DOA estimation, which is of great value for oceanography, marine engineering, and marine military. In addition, this relation can also be extended to that between the modal interference frequency periodicity and other related parameters in other physical fields for parameter inversion.
... 1 Matched-field processing (MFP) 2 has been proposed and applied for years to estimate source depth, and they normally determine the source location from a two-dimensional (2D) ambiguity surface of distance vs depth. [3][4][5][6] However, these MFP methods may perform poorly when the environmental model (as sound-speed profile, SSP, or ocean bottom) used to generate the replica field deviates from real environment. 7,8 In a deep-ocean environment, the acoustical signal from sources close to the ocean surface and recorded by bottommoored hydrophones have low propagation losses over a moderate distance (the range is determined through direct transmission path). ...
Multiple approaches for depth estimation in deep-ocean environments are discussed. First, a multispectral transformation for depth estimation (MSTDE) method based on the low-spatial-frequency interference in a constant sound speed is derived to estimate the source depth directly. To overcome the limitation of real sound-speed profiles and source bandwidths on the accuracy of MSTDE, a method based on a convolution neural network (CNN) and conventional beamforming (CBF) preprocessing is proposed. Further, transfer learning is adapted to tackle the effect of noise on the estimation result. At-sea data are used to test the performance of these methods, and results suggest that (1) the MSTDE can estimate the depth; however, the error increases with distance; (2) MSTDE error can be moderately compensated through a calculated factor; (3) the performance of deep-learning approach using CBF preprocessing is much better than those of MSTDE and traditional CNN.
... Guiding by the above-mentioned, our interest in this paper is proposing an improved PF tracking scheme to achieve real-time source localization and SSF inversion simultaneously. PF as a Bayesian method estimates the optimum source and environmental parameters based on the PPDs [25]. Here, two kinds of PFs are used to track the parameters of both moving source (depth, range, and speed) and SSF (three EOFs) including their underlying uncertainties in the form of time-evolving PPDs. ...
Both source localization and environmental inversions are practical problems for long-standing applications in underwater acoustics. This paper presents an approach of the moving source localization and sound speed field (SSF) inversion in shallow water. The approach is formulated in a state-space model with a state equation for both the source parameters (e.g., source depth, range, and speed) and SSF parameters (first three empirical orthogonal function coefficients, EOFs) and a measurement equation that incorporates underwater acoustic information via a vertical line array (VLA). As a sequential processing algorithm that operates on nonlinear systems with non-Gaussian probability densities, an improved sequential importance resampling type particle filtering (SIR PF) is proposed to counter degeneracy. The improved PF performs tracking of source and SSF parameters simultaneously, and evaluates their uncertainties in the form of time-evolving posterior probability densities (PPDs). The performance of improved PF is illustrated with well-tracked simulations of real-time source localization and time-varying SSF inversion. Moreover, the influence of different particle numbers on PF tracking accuracy and computational cost is also demonstrated. Simulation results show that the high-particle-number PF has an outperform performance. For a given hardware system, the reasonable compromise between accuracy and computational cost is a matter of tradeoff.
... Range estimation, which we refer to commonly as "ranging," is part of the more general location or localization problem, and important as a component of positioning, navigation, and timing (PNT) of underwater platforms, especially when surfacing for position fixes is impractical or undesired (e.g., Dosso, 2003;Richardson and Nolte, 1991;Skarsoulis and Piperakis, 2009;Tan et al., 2011;Tolstoy, 1993;Van Uffelen et al., 2016;Van Uffelen et al., 2013). Various international scientific and governmental organizations deploy undersea vehicles or gliders in sustained monitoring missions for collection of data from the regional and near-shore to the global and deep-ocean environments. ...
This study identifies general characteristics of methods to estimate the absolute range between an acoustic transmitter and a receiver in the deep ocean. The data are from three days of the PhilSea10 experiment with a single fixed transmitter depth (∼998 m) and 150 receiver depths (∼210–5388 m) of known location, and a great-circle transmitter-receiver distance of ∼510 km. The proposed ranging methods compare observed acoustic records with synthetic records computed through the HYCOM (hybrid coordinate ocean model) model. More than 8900 transmissions over 3 days characterize the statistical variation of range errors. Reliable ranging methods de-emphasize the parts of the data records least likely to be reproduced by the synthetics, which include arrival amplitudes, the later parts of the acoustic records composed of nearly horizontally launched rays (i.e., the finale), and waves that sample a narrow span of ocean depths. The ranging methods proposed normalize amplitudes, measure travel times, or reject parts of the waveforms beyond a critical time. All deliver reliable range estimates based on the time and path-averaged HYCOM model, although the final method performs best. The principles behind these methods are transportable and expected to provide reliable range estimates in different deep water settings.
... Matched-field processing 165 (MFP) has been applied to ocean source localization for decades with reasonable success. 166,167 Recent MFP modifications incorporate compressive sensing since there are only a few source locations. 4,33,168,169 However, MFP is prone to model mismatch. ...
Acoustic data provide scientific and engineering insights in fields ranging from biology and communications to ocean and Earth science. We survey the recent advances and transformative potential of machine learning (ML), including deep learning, in the field of acoustics. ML is a broad family of techniques, which are often based in statistics, for automatically detecting and utilizing patterns in data. Relative to conventional acoustics and signal processing, ML is data-driven. Given sufficient training data, ML can discover complex relationships between features and desired labels or actions, or between features themselves. With large volumes of training data, ML can discover models describing complex acoustic phenomena such as human speech and reverberation. ML in acoustics is rapidly developing with compelling results and significant future promise. We first introduce ML, then highlight ML developments in four acoustics research areas: source localization in speech processing, source localization in ocean acoustics, bioacoustics, and environmental sounds in everyday scenes.
... The combination of MFP with MCMC has been used in ocean acoustics to ensure convergence when extracting the medium parameters and to estimate source position in uncertain media (Richardson & Nolte 1991;Tollefsen & Dosso 2014). In the present paper, we use this combination on seismic data to solve a complex optimization problem where classical grid searches are too time-consuming and gradient-descent like methods fail due to many local minima. ...
We introduce a methodology based on array processing to detect and locate weak seismic events in a complex fault zone environment. The method is illustrated using data recorded by a dense array of 1108 vertical component geophones in a 600 m × 600 m area on the Clark branch of the San Jacinto Fault. Because surface and atmospheric sources affect weak ground motion, it is necessary to discriminate them from weak seismic sources at depth. Source epicentral positions and associated apparent velocities are extracted from continuous seismic waveforms using Match Field Processing (MFP). We implement MFP at specific frequencies targeting surface and subsurface sources, using for computational efficiency a forward model of acoustic source in a homogenous medium and Markov Chain Monte Carlo sampling. Surface sources such as Betsy gun shots and a moving vehicle are successfully located. Weak seismic events are also detected outside of the array, and their backazimuth angle is retrieved and found to be consistent with the fault geometry. We also show that the homogeneous acoustic model does not yield satisfying results when extracting microseismic event depth, because of the ambiguity between depth and the apparent velocity based on surface data.
... Matched-field processing 152 (MFP) has been applied to ocean source localization for decades with reasonable success. 153,154 Recent MFP modifications incorporate compressive sensing since there are only a few source locations. 3,31,155 However, MFP is prone to model mismatch. ...
Acoustic data provide scientific and engineering insights in fields ranging from biology and communications to ocean and Earth science. We survey the recent advances and transformative potential of machine learning (ML), including deep learning, in the field of acoustics. ML is a broad family of statistical techniques for automatically detecting and utilizing patterns in data. Relative to conventional acoustics and signal processing, ML is data-driven. Given sufficient training data, ML can discover complex relationships between features. With large volumes of training data, ML can discover models describing complex acoustic phenomena such as human speech and reverberation. ML in acoustics is rapidly developing with compelling results and significant future promise. We first introduce ML, then highlight ML developments in five acoustics research areas: source localization in speech processing, source localization in ocean acoustics, bioacoustics, seismic exploration, and environmental sounds in everyday scenes.
... To all others SSPs the use of beamforming came with a reduction in performance from around 30% in range compared with spatial diversity. 113 ...
This thesis addresses an acoustic underwater source localization with application to an at-sea experiment. We propose a new matching method based on a fit-metric called as Hausdorff distance (HD) as a cost-function to be minimized, in order to perform the localization inversion. The 2-D localization, in range and depth, is performed by matching the patterns of time difference of arrival (TDOA) when using only one hydrophone at the reception and by matching the TDOA and the Angle of Arrival (AOA) when using an array of hydrophones at the reception, between respectively measured and modeled sequences. The modelled TDOA was obtained based on the Ray-path acoustic propagation model. The data sets analyzed here were collected during two experiments in a context of passive localization considering a motionless target: The tank of GIPSA-LAB using cooperative and non-cooperative systems which were verified by simulations with respect to the signal-to-noise ratio and the ALMA 2015, collected by the Direction générale de l’armement (DGA) using a cooperative system which took place in a shallow water environment of the southern coast of France. During the ALMA experiment the acoustic data were measured over a 10m-high vertical linear array (VLA), composed of 64 hydrophones, allowing not only matching the TDOA but also the Angle of Arrival (AOA). Several variants of the Hausdorff Distance are applied in two different processes: First, separately in each single hydrophone, and then combined in order to improve the localization accuracy (spatial diversity), and the second, the information from the different hydrophones are combined (beamforming) and the HD variants are applied to find the target location. The results of both processes are compared and proved to reduce the ambiguity either is depth and in range, thus improving the final accuracy. The Cramer Rao Bound showing the minimal variance performed based on deterministic equations is presented with the best result of each process. Very satisfactory performance and accuracy are obtained. The conclusions and perspectives of this work are discussed at the end.
... Par conséquent, beaucoup d'améliorations ont été proposées afin d'augmenter la robustesse de ces algorithmes face à ces incertitudes sur les paramètres océaniques. [Richardson91] ont proposé l'utilisation de l'inférence bayésienne dans leur travaux pour la localisation de source. Le principe consiste à inclure les incertitudes des paramètres océaniques et la position à priori de la source pour inférer la probabilité à posteriori de la position de la source. ...
La connaissance de l'environnement marin est nécessaire pour un grand nombre d'applications dans le domaine de l'acoustique sous-marine comme la communication, la localisation et détection sonar et la surveillance des mammifères marins. Il constitue le moyen principal pour éviter les interférences néfastes entre le milieu naturel et les actions industriels et militaires conduites en zones côtières.Notre travail de thèse se place dans un contexte de sonar actif avec des fréquences allant de 1 kHz à 10 kHz pour des distances de propagations allant de 1 km à plusieurs dizaines de kilomètres. Nous nous intéressons particulièrement aux environnements de propagation grands fonds, à l'utilisation des antennes industrielles comme les antennes de flancs, les antennes cylindriques et les antennes linéaires remorquées, et à l'utilisation de signaux large bande afin de travailler avec des résolutions en distance et en vitesse très élevées. Le travail de recherche présenté dans ce mémoire est dédié à la recherche de nouveaux paramètres discriminants pour la classification de cible sous-marine en sonar actif et notamment à l'estimation de l'immersion instantanée.Cette étude présente : (1) les calculs de nouvelles bornes de Cramer-Rao pour la position d'une cible en distance en et en profondeur, (2) l'estimation conjointe de la distance et de l'immersion d'une cible à partir de la mesure des temps d'arrivées et des angles d'élévations sur une antenne surfacique et (3) l'estimation conjointe de la distance, de l'immersion et du gisement d'une cible à partir de la mesure des temps d'arrivées et des pseudo-gisements sur une antenne linéaire remorquée.Les méthodes développées lors de cette étude ont été validées sur des simulations, des données expérimentales à petite échelle et des données réelles en mer.
... Uncertainty of the ocean environment motivates the use of stochastic models to capture the random nature of the phenomena ranging from ambient noise and scattering to distant shipping and the nonstationary nature of this hostile medium. Therefore, processors that do not take these effects into account are doomed to large errors [10][14] . When contemplating the broadband problem it is quite natural to develop temporal techniques especially if the underlying model is the full wave equation; however, if we assume a normal-mode propagation model then it is more natural to: (1) filter the broadband receiver outputs into narrow bands; (2) process each band with a devoted processor; and then (3) combine the narrowband results to create a broadband solution. ...
When sound propagates in the shallow ocean, source characteristics complicate the analysis of received acoustic data considerably especially when they are broadband and spatially complex. Noise whether ambient, distant shipping, wind blown surface generated complicates this already chaotic environment even further primarily because these disturbances propagate through the same inherent oceanic medium. The broadband problem can be decomposed into a set of narrowband problems by decomposing the source spectrum into its set of narrowband lines. A generic Bayesian solution to the broadband pressure-field enhancement and modal function extraction problem is developed that leads to a so-called nonparametric estimate of the desired posterior distribution enabling statistical inference.
Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.
Geoacoustic inversions using broadband acoustic data acquired during the Seabed Characterization Experiment 2017 conducted in the New England Mud Patch area in March 2017 are presented in this article. The primary goal of the data inversions is to estimate the compressional wave speed and density profiles of the sediment layers. Both linear perturbative and nonlinear Bayesian inversion methods are utilized. These two inversion methods share the same principle of solution schemes, i.e., to minimize the difference between the signal acquired (or derived quantities) at the receiver and the prediction by the optimized bottom model. The differences between the two approaches are in the type of data utilized for inversion and on the inversion procedure used to determine the bottom geoacoustic properties. The linear inversion method uses the time difference of modal arrival, while the Bayesian inversion uses the bandpass-filtered sound pressure waveform. One of the study objectives is for the Bayesian inversion to provide a reference solution to the inverse problem and determine the ability of the linear inversion method to provide comparable results as compared with a more exhaustive search used in the Bayesian method. Another objective is to use the verified linear inversion method that is computationally faster to explore different models of sediment layering structure and to estimate the most appropriate bottom model for the experimental area.
Underwater source localization by deep neural networks (DNNs) is challenging since training these DNNs generally requires a large amount of experimental data and is computationally expensive. In this paper, label distribution-guided transfer learning (LD-TL) for underwater source localization is proposed, where a one-dimensional convolutional neural network (1D-CNN) is pre-trained with the simulation data generated by an underwater acoustic propagation model and then fine-tuned with a very limited amount of experimental data. In particular, the experimental data for fine-tuning the pre-trained 1D-CNN are labeled with label distribution vectors instead of one-hot encoded vectors. Experimental results show that the performance of underwater source localization with a very limited amount of experimental data is significantly improved by the proposed LD-TL.
The paper discusses representation of the wave field on a vertical array in an underwater sound channel as the superposition of components stable with respect to large-scale perturbations of the sound velocity field. Each such component is formed by a narrow beam of rays incident on the array aperture. This representation makes it possible to modify traditional matched field processing by switching from comparison of the measured and calculated fields at the array to comparison of the stable components of these fields. It is shown that the modified approach in solving the problem of source localization makes it possible to weaken the requirements on the accuracy of the mathematical model of the medium.
Multipath arrivals are identified and extracted from midfrequency impulse responses at a vertical line array produced by a broadband source transmitting linearly frequency modulated pulses in the SBCEX 17 experiment. Arrival times are extracted from received data using particle filtering and smoothing. Specifically, sequential filtering is applied to the received time series at sixteen phones for the estimation of three paths generated by sound interacting with the propagation medium. This is followed up with a smoother that provides “crisp” arrival time probability densities. A peak-finding method is used to identify a fourth path. The estimated arrival times obtained by the process above are linked with a sound propagation model based on ray tracing and linearization for estimation of source location and water column depth and sound speed. An exhaustive search follows for inversion for sediment sound speed and thickness. Because the source is moving, receptions are available on a track and arrival time estimation and corresponding inversion are performed at every source location within the track. The unknown parameters are estimated sequentially with two approaches. Approach one is linearization using prior information from one location propagated to the next. Approach two relies on a second particle filter, capturing the dynamic evolution of parameters along the track. Both techniques lead to sediment property estimation. Results from the two methods agree, pointing to robustness in inversion when impulse responses and arrival times estimated from those are employed as input to the inverse problem.
Existing detection methods have mismatch problem when applyed to the real uncertain ocean, which will lead to the detection performance degradation. However, there has been little work on defining the practical quantitative measures of environmental sensitivity. In this article we define a measure of environmental sensitivity for target detection performance loss in an uncertain ocean for realistic uncertainties in various environmental parameters (water-column sound speed profile and seabed geoacoustic properties). The Monte Carlo approach is used to transfer the environment uncertainty through the forward problem and quantify the resulting variability in the detection performance loss. The computer simulation is based on the Malta Plateau, a well-studied shallow-water region of the Mediterranean Sea. The simulation result shows that 1) the sensitivity is range and depth dependent and in the sound channel the sensitivity is much smaller than in other regions of the ocean; 2) the sound speed profile and the upper seabed layer are most sensitive parameters for the detection performance loss; 3) the sensitivity is frequency dependent. The seabed layer properties such as sediment thickness, density and attenuation coefficient have less influence on the detection as the frequency increases.
The paper describes the beamforming procedures in an acoustic waveguide based on representing the field on the antenna as a superposition of several stable components formed by narrow beams of rays [A. L. Virovlyansky, J. Acoust. Soc. Am. 141, 1180–1189 (2017)]. A modification of the matched field processing method is proposed, based on the transition from comparing the measured and calculated fields on the antenna to comparing their stable components. The modified approach becomes less sensitive to the inevitable inaccuracies of the environmental model. In the case of a pulsed source, the stable components carry signals whose arrival times can be taken as input parameters in solving the inverse problems. The use of the stable components as the initial fields on the aperture of the emitting antenna makes it possible to excite narrow continuous wave beams propagating along given ray paths.
In a range-dependent and time-varying environment, such as at the Shallow Water 2006 (SW06) experimental site, matched field processing often has difficulty localizing a moving source emitting a narrowband signal when signal mismatch is difficult to mitigate given only the nominal sound speed profile and bottom properties along the source track. Based on the range-averaged mode wavenumbers and depth functions estimated from data received on a vertical line array by synthetic beamforming (without any environmental information) using Doppler shift as a reference, a method is proposed in this paper to search for the source depth first and then the source range. Source localization is demonstrated with the SW06 data for two source runs along and oblique to the shelf. Robustness is achieved by minimizing/breaking the coupling between range and depth, when one of them can be estimated using non-environment-related input.
Matched-field processing is applied to source localization and detection of sound sources in the ocean. The source spectrum is included in the set of unknown parameters and is estimated in the localization/detection process. Bayesian broadband (multi-tonal) incoherent and coherent processors are developed, integrating the source spectrum estimation using a Gibbs sampler and are first evaluated in source localization via point estimates and probability density functions obtained from synthetic signals. The coherent performance is superior to the incoherent one both in terms of source location estimates and density spread. The two processors are also applied to real data from the Hudson Canyon experiment. Subsequently, using Receiver Operating Characteristic (ROC) curves, the two processors are evaluated and compared in the task of joint detection and localization. The coherent detector/localization processor is superior to the incoherent one, especially as the number of frequencies increases. Joint detection and localization performance is evaluated with Localization-ROC curves.
Matched field processing (MFP) refers to a variety of source localization schemes for known complicated environments and involves matching measured and calculated (replica) fields to identify source locations. MFP may fail for several reasons, most notably when the calculated fields are insufficiently accurate. This error commonly prevents MFP-based long-range (>100 km) source localization in the deep ocean (from 5 to 6 km depth) for signal frequencies of hundreds of Hz, even when extensive high-signal-to-noise ratio field measurements are available. Recently, below-band MFP utilizing the frequency-difference autoproduct [Worthmann, Song, and Dowling (2015). J. Acoust. Soc. Am, 138(6), 3549–3562] achieved some shallow-ocean localization success at a 3 km source-to-array range with signal frequencies in the tens of kHz. The performance of this technique, when extended to matching the measured frequency-difference autoproduct with a composite mode-ray replica, is described here for deep ocean source localization. The ocean propagation data come from the PhilSea10 experiment and involve source-to-array ranges from 129 to 379 km and nominal 100-Hz-bandwidth signals having center frequencies from 250 to 275 Hz. Based on an incoherent average of five signal samples, the frequency-difference technique was 90%–100% successful at four different source-to-array ranges using single-digit-Hz difference frequencies.
The traditional method of matched field processing is based on comparing the complex amplitudes of the measured and calculated sound fields in an underwater waveguide. Because of the high sensitivity of the wave field to variations in environmental parameters, the use of this approach requires accurate knowledge of the ocean-acoustic environment. In this paper, it is shown that under conditions of uncertain environment, instead of comparing the depth dependencies of complex field amplitudes, it is advisable to compare their field amplitude distributions in the phase plane “grazing angle–depth.” Such distributions are calculated using the coherent state expansion borrowed from quantum mechanics. Due to the absence of multipath in the phase space, the amplitudes of the coherent states are less sensitive to variations in the environmental parameters than the total wave field. This makes it possible to construct the similarity coefficients of measured and calculated fields that almost “do not notice” the differences of the compared fields caused by weak sound-speed variations, and “react” only to differences caused by strong changes in the sound-speed field and/or source position.
An adaptive modal MUSIC algorithm is constructed to localize an acoustic source by a vertical array operating under conditions of incomplete information on a waveguide propagation channel . The results of statistical modeling are presented, which demonstrate the probabilities of correct source localization versus the input signal-to-noise ratio and the sample size. The method is validated by its application to the experimental data observed in the Ladoga Lake. It is shown that this method ensures greater stability of the estimation procedure to mismatch between the true and expected signal replica compared to the conventional element-space MUSIC.
The actual ocean is an uncertain acoustic propagation environment. For the localization algorithms that rely on the precise ocean environmental parameters, the environmental mismatch problems will exist and performance degradation may be very serious. In the uncertain ocean environment, the uncertainties of sound field will have different effects on different normal modes propagating in the sound field, thus analysis of the mismatch characteristics of normal modes affected by uncertain environmental parameters can provide technical guidance for practical engineering applications. Based on the shallow-water acoustic propagation model, this paper simulates and analyzes the mismatch results of the modal depth eigenfunction and the horizontal wave number of each normal mode under conditions of environmental mismatch. Research indicates that the influence of different environmental parameters on normal modes in the sound field is not exactly the same. It was found that the sound-speed profile and seawater depth affect significantly, followed by sediment sound speed, the other parameters appear to be relatively minor importance.
A robust Capon-type algorithm is constructed for source localization by a partially calibrated array operating in an uncertain environment. Results of statistical modeling are presented to determine the accuracy of source localization and the probability of correct source detection. Experimental testing of the proposed method is carried out to demonstrate its performance in Ladoga Lake.
A robust algorithm designed to localize a source in an acoustic waveguide without perfect knowledge of array calibration is constructed, that is a generalization of the known RARE (RAnk REduction) method in application to signal reception under the condition of incomplete information on a propagation medium. It has been established by means of statistical modeling that the proposed method gives a significant advantage in the accuracy of the source position estimation as well as in the achieved probability of its correct localization in comparison with the traditional RARE algorithm that assumes a priori knowledge of channel characteristics. The restriction on the permissible norm of mismatch between presumed and actual replica fields, for which a correct solution of the inverse problem is possible, has been found. The proposed algorithm is validated by its application to the experimental data observed in the Ladoga Lake. It has been shown that under real conditions the presented approach is rather efficient and ensures an acceptable source reconstruction quality without the need for a computationally intensive joint estimation of both the source and waveguide parameters.
Acoustic and elastic wave propagation is being investigated in media such as the ocean, the earth, biological tissues and solid materials. In these different areas, many specific imaging techniques have been developed which differ in the wavelength of the sound, its polarisation and the instrumentation used. In this interdisciplinary book, leading experts in underwater acoustics, seismology, acoustic medical imaging and non-destructive testing present basic concepts as well as the recent advances in imaging. The different subjects tackled show significant similarities. This volume gives an up-to-date-overwiew of the field and is intended for scientists and graduates alike.
The statistics of the mode space detector (MSD) whose modes are characterized by some degree of mismatch to truth [that is, the mismatched mode space detector (MMSD)] are derived. As a measure of the “containing relation” between the mode spaces derived from different environmental realizations we propose the relative projection error metric, through which the performance of the MMSD can be further investigated and compared to the MSD using accurate environmental knowledge. From this performance analysis, we suggest that by simply using the greatest dimensional physically supported mode space, we can obtain a robust MSD. It can achieve the same performance robustness as the energy detector—the performance is only determined by the array signal energy and is insensitive to the specific source position and environmental conditions. It can also avoid the potentially-significant performance degradation of the Bayesian detector when applied to certain deterministic scenarios at a cost of small average performance degradation. Numerical simulations in a typical uncertain shallow-water environment support our assertions.
The shallow ocean is an ever changing environment primarily due to temperature variations in its upper layers (< 100 m) directly affecting sound propagation throughout. The need to develop processors capable of tracking these changes implies a stochastic as well as an environmentally adaptive design. The stochastic requirement follows directly from the multitude of variations created by uncertain parameters and noise. Some work has been accomplished in this area, but the stochastic nature was constrained to Gaussian uncertainties. It has been clear for a long time that this constraint was not particularly realistic leading to a Bayesian approach that enables the representation of any uncertainty distribution. Sequential Bayesian techniques enable a class of processors capable of performing in an uncertain, nonstationary (varying statistics), non-Gaussian, variable shallow ocean environment. A solution to this problem is addressed by developing a sequential Bayesian processor capable of providing a joint solution to the modal function tracking (estimation) and environmental adaptivity problem. The posterior distribution required is multi-modal (multiple peaks) requiring a sequential (nonstationary) Bayesian approach. Here the focus is on the development of a particle filter (PF) capable of providing reasonable performance for this problem. In our previous effort on this problem nonlinear/non-Gaussian processors were developed to operate on synthesized data based on the Hudson Canyon experiment using normal-mode representations. Here we extend the processors by applying them to the actual hydrophone measurements obtained from the 23-element vertical array. The adaptivity problem is attacked by allowing the modal coefficients to be estimated from the measurement data jointly along with tracking of the modal functions—the main objective.
When under uncertain ocean environment, the environmental model of matched field processing (MFP) is different from the real world. The performance of MFP decreases largely beacuse of the environmental mismatch. In order to improve its robustness to the environmental mismatch, a MFP with posterior probability constraints (MFP-PPC) is proposed. The algorithm derives the posterior probability density function (PDF) of the source locations from Bayesian Criterion, then the main lobe of AMFP is protected by posterior PDF, so the MFP-PPC has not only the merit of high resolution as AMFP, but also the advantage of robustness. We use experimental data to evaluate the algorithm, the results shown that in the uncertain ocean environment the MFP-PPC is robust not only to the moored source, but also to the moving source. Meanwhile, the localization and tracking is consistent with the trajectory of the moving source.
This paper considers concurrent matched-field processing of data from multiple, spatially-separated acoustic arrays with application to towed-source data received on two bottom-moored horizontal line arrays from the SWellEx-96 shallow water experiment. Matched-field processors are derived for multiple arrays and multiple-snapshot data using maximum-likelihood estimates for unknown complex-valued source strengths and unknown error variances. Starting from a coherent processor where phase and amplitude is known between all arrays, likelihood expressions are derived for various assumptions on relative source spectral information (amplitude and phase at different frequencies) between arrays and from snapshot to snapshot. Processing the two arrays with a coherent-array processor (with inter-array amplitude and phase known) or with an incoherent-array processor (no inter-array spectral information) both yield improvements in localization over processing the arrays individually. The best results with this data set were obtained with a processor that exploits relative amplitude information but not relative phase between arrays. The localization performance improvement is retained when the multiple-array processors are applied to short arrays that individually yield poor performance.
This paper considers approaches to combining information from multiple arrays in matched-field processing (MFP) for underwater acoustic source localization. The standard approach is to apply conventional MFP for each array independently, and sum the resulting Bartlett ambiguity surfaces computed for each array; this approach assumes that individual arrays comprise calibrated sensors which are synchronized in time. However, if the relative calibration and/or time synchronization is known between some or all arrays, more informative multiple-array processors can be derived using maximum-likelihood methods. If the relative calibration between arrays is known, the observed variation in received signal amplitude between arrays provides additional information for matched-field localization which is absent in the standard processor. If synchronization is known between arrays, phase variations provide additional localization information. Multiple-array processors accounting for different levels of interarray information 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 the number of frequencies for simulated shallow-water scenarios with multiple horizontal and/or vertical arrays. The analysis indicates that, dependent on array configurations, significant 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 and array (calibration and synchronization) mismatch; however, this degradation can be partially mitigated by including additional frequencies in the processing.
This paper develops a localization method to estimate the depth of a target in the context of active sonar, at long ranges. The target depth is tactical information for both strategy and classification purposes. The Cramer–Rao lower bounds for the target position as range and depth are derived for a bilinear profile. The influence of sonar parameters on the standard deviations of the target range and depth are studied. A localization method based on ray back-propagation with a probabilistic approach is then investigated. Monte-Carlo simulations applied to a summer Mediterranean sound-speed profile are performed to evaluate the efficiency of the estimator. This method is finally validated on data in an experimental tank.
In shallow water ocean, the multi-path structure information of acoustic signals received by a vertical array is useful for target localization. Matched field processing (MFP) is a perfect method for localization using this multi-path structure information when the environment knowledge is known completely. But the environment knowledge usually cannot be known exactly in real ocean - especially as regards the geoacoustic parameters, such as the density, sound speed and attenuation coefficient of the seabed, which are all difficult to acquire. The environment knowledge mismatch restricts matched field processing localization performance. This paper presents a method of matched field localization for a short vertical array in shallow water which can be used for target localization when knowledge of the geoacoustic parameters of the seabed is unknown. This is based on geoacoustic parameters inversion with short-range co-operative source data. The presented localization method combines a geoacoustic parameters inversion method and a broadband matched field localization method. On one hand, a geoacoustic parameters inversion method based on plane wave reflection theory is studied, using low frequency impulsive data from a short-range co-operative point source recorded on a vertical array. On the other hand, a robust broadband coherent matched field localization method in beam domain is also studied. Through real experimental data analysis it can be shown that the presented method has a good localization performance. The range estimation error of the presented method is 5% and the depth estimation error is 2 meters using the data recorded by a 7-meter vertical received array - when the signal-to-noise ratio (SNR) of array element output is 2 dB, and the target distance is 2.2 kilometers away from the received array.
Under ideal known environmental conditions, matched field processing has been shown in a series of papers to be a promising signal processing technique for localizing acoustic sources (see [1] and the references therein). The standard adaptive approaches which have been considered require accurate replica fields finely gridded over the search parameter space for both localization and sidelobe control. Moreover, it is unlikely that detailed knowledge of the ocean environment would be available since it is expensive to obtain highly accurate knowledge of the three dimensional ocean environment (including bottom structure). Finally, it is impractical to generate replica fields incorporating the increasing complexity of a range dependent environment which still remains imperfectly known because of inadequate sampling. To counter these latter issues, we have introduced multiple constraints to the maximum likelihood method (MLM) to construct a beamformer (MCM) more tolerant to environmental mismatch of a deterministic nature. The result is a plane wave or matched field beamformer which accommodates some mismatch in the environment with only a small reduction in resolution while still suppressing sidelobes. In this paper, we briefly present the underlying principles used to derive this beamforming method and follow this with an application to a matched field processing example for a shallow water ocean environment.
This article discusses the impact of incorrect estimates of the water column depth on matched-field source localization in a shallow-water environment. Computer calculations were performed for the case of a nominal 100-m depth water column subject to water-depth variations of up to 3.5 m, which would be caused by long-period ocean swell or by tidal changes. The environment was assumed to be range independent (by proper choice of the geometry); thus the question of rough surface scattering was not an issue. The calculations incorporated source depths of 25, 50, and 75 m, a propagation distance of 4 km, an acoustic frequency of 150 Hz, and a linear vertical receiving array. The array consisted of 21 hydrophones with an interelement spacing of 2.5 m, and it spanned the center one-half of the water column (25- to 75-m depth). The matched-field algorithm utilized in this study is the high-resolution maximum-likelihood estimator. A primary result of the work is that, as the output of the matched-field processor degrades due to water-depth mismatch, the apparent source location varies in a systematic way; i.e., the source appears closer and deeper for increasing water depth and, conversely, the source appears farther and shallower for decreasing water depths. Another significant observation is that, as acoustic modes are stripped from the waveguide due to reduced channel depth, instabilities in the solution of the processor cause random variations in localization estimates.
For many acoustic environments a target's acoustic field incident on a hydrophone array segment is not representable by a plane wave, but is a function, generally, of three coordinates: range, depth, and bearing. In these cases a conventional beamformer, which is designed to detect plane waves, cannot localize the target accurately. Techniques have been developed recently to exploit the complexity of the field to estimate the source location coordinates by correlating the received field on the array with accurate replicas of the acoustic field, derived from knowledge of the environment. The potential utility of such techniques has been demonstrated in determining range and depth for simulated high‐SNR signals. In this paper, however, they are shown to exhibit excessive sidelobes for low SNR. To alleviate this problem, two high‐resolution techniques, the Maximum Likelihood Method (MLM I and “Alternate Orthogonal Projection” (AOP), or linear predictor, are applied to the simulated case of one target in white noise in a Pekeris environment. MLM is seen to produce stable main peaks which localize targets precisely with low sidelobes, while AOP is shown to be unstable in the presence of random noise and to produce false peaks even when the noise fields are stable.
The calculated complex sound field cj for sensor j at depth zj and range rj from a sound source of frequency ω and depth z0 can be written in the normal-mode form as cj= (2π/rj)1/2 ΣmUm(z0) Um(zj) exp[i (kmrj−ωt)]. Here, km is the horizontal wavenumber of mode m and Um is the depth function of the mth mode. It is proposed that the detection factor DF=ΣJj=1 cjc*k〈 (c0jc0k*) *〉 is a reasonable measure for determination of whether a set of sound pressure measurements {c0j} for j=1,2,⋅⋅⋅,J is a good fit to calculated values of {cj} for an assumed location of the sound source. Here 〈 〉 denotes a time average and * denotes complex conjugate. Several examples are shown where a set of {c0j} are calculated for a given source location in a typical shallow water channel and values of DF are then calculated for a grid of range depth or range azimuth locations.
Subject Classification: [43]60.20; [43]30.82.
In this paper, the sensitivity of matched field processing to sound‐speed profile mismatch will be examined (based upon archival profiles resulting in various degrees of mismatch). A 10‐Hz source is considered whose field is generated by a normal mode model and only the water‐borne energy is used, thereby eliminating issues relating to the estimation of bottom parameters. This paper will examine how array parameters, i.e., number of phones and array depth, affect range and depth localization for various degrees of mismatch. In particular, it will be seen where an array is most and least sensitive to sound‐speed mismatch as a function of depth from the surface and range from the source, and the degree to which range and depth resolution are possible under ideal, as well as under likely, mismatch conditions.
For much of the World's oceans, the stability of the water column beneath the thermocline is quite well represented by N 2 (z) = gρ −1 ∂ z ρ′ = N O 2 e −2z/B , where ∂ z ρ′ is the vertical gradient in potential density, N O ≈ 3 cycles/h is the surface‐extrapolated “Brunt‐Väisälä” frequency, and B ≈ 1.3 km is the stratification scale. This leads to an idealized sound channel C(z) = C 1 [1 + ε(η + e −η − 1)] = C[1 + ε(1/2)η 2 − (1/6)η 3 + …] with a minimum velocity at the axis z = z 1 , η = (z − z 1 )/ 1 2 B being dimensionless depth relative to z 1. The parameters ε, z 1 are explicitly expressed in terms of the five coefficients α, β, γ, a, b (temperature, salinity, pressure coefficients of C; temperature and salinity coefficients of ρ′), given only the form of N(z) and a representative T, S relation. The up‐down asymmetry of the channel, a consequence of the fundamental structure of the oceans, plays a first‐order role in the propagation characteristics. As an application, the ray arrivals for an axial source and receiver are computed.
For many acoustic environments, the power in a target's acoustic field incident on a linear array segment is concentrated in horizontal angle but distributed over a significant vertical angle. For these environments, both signal-to-noise ratio (S/N) gains and range, bearing, and depth estimates may be possible from an ambiguity surface processor obtained as a spatial correlation using a replica of the signal field in the three unknown source location parameters. This report presents an initial evaluation of an ambiguity surface processor for the Pekeris acoustic environment. Results for a vertical array segment indicate high-quality estimates of both range and depth. For a segment with horizontal extent and for known source depth, the sharp main peak of the ambiguity surface also supports the high quality estimates of source range and bearing, although for small array tilt angles, the quality of the range estimate is limited by the prevailing S/N because of the presence of extraneous sidelobe peaks. Increasing the tilt angle significantly reduces the level of the sidelobe peaks. Furthermore, the ambiguity surface processor achieves gain enhancements up to 2 dB using a purely horizontal array, and in excess of 20 dB using the vertical array.
In this paper, a method for determining the position of an underwater
acoustic source from observations of the associated acoustic field and
information about the acoustic environment is presented. This algorithm,
unlike matched field processing algorithms, does not require complete
knowledge of the acoustic environment, but can determine source position
even with uncertain or imprecise information about the environment. The
algorithm is termed the optimum uncertain field processing algorithm.
Parameter estimation theory is utilized to derive the new algorithm.
This provides a systematic, optimal approach to the problem, and allows
environmental uncertainty to be easily incorporated into the algorithm.
In addition to estimating source position, estimates of parameters of
the acoustic environment can also be calculated. This makes simultaneous
source localization and acoustic tomographic estimation of ocean
parameters possible. A detailed discussion of the acoustic propagation
models used in the research is presented. The defining equation for the
optimum uncertain field processor is then derived. It is shown that the
algorithm reduces to a popular matched field processing technique for
the special case in which the environment is completely known. A series
of studies that illustrate the robust performance of the uncertain field
processor, relative to the performance of matched field processing
methods, is made. Estimation of ocean acoustic parameters is also
illustrated. The affects of environmental uncertainty, source position,
and frequency on localization performance are examined.
Conventional bearing estimation procedures employ planewave steering vectors as replicas of the true field and seek to resolve in angle by maximizing a power function representing the agreement between actual and replica fields. For vertical arrays in oceanic waveguides the received field depends on range and depth, and it is natural to replace the "look-direction" ( theta ) by a "look-position" ( r, z ). Thus an environmental model is constructed by specifying ocean depth, sound speed profile, bottom properties, etc., and a propagation model is employed to construct a replica of the field that would be received on the array for a particular source position. The usual estimators (e.g., Bartlett or maximum likelihood) are then used to gauge the agreement between actual and replica fields and the true source position is identified as that position where the agreement is best. The performance of this kind of matched-field processing is strongly affected by the environment. In particular, we demonstrate through simulations that for a deep-water Pacific environment dominated by waterborne paths, ambiguities or sidelobes are associated with convergence zones. In the absence of mismatch between replica and actual fields we find that a 16-element array performs extremely well in low-frequency regimes. Mismatch caused by uncertainties in phone positions, bottom parameters, ocean sound speed, surface and bottom roughness, etc., causes degradation in localization performance. The impact of some of these effects on conventional and maximum likelihood estimators is examined through simulation.