Environmentally and statistically robust matched-field source localization based on information geometry principles.

Matched field processing (MFP) is generalized beamforming method which utilizes the physics of wave propagation in the ocean waveguide to estimate the range, depth and azimuth of the sources or inversion the waveguide. Traditional MFP only uses the pressure information of the sound field. The vector sensor measures the pressure and three orthogonal components of the particle velocity simultaneously. A novel MFP method based on vertical vector-sensor array for location is proposed. Three Bartlett processors are put forward based on matching acoustic intensity flux. The performance of this algorithm is examined in simulation example. They can suppress side-lobes effectively with high resolution. And the fusion algorithm for the newly Bartlett processors is introduced in to take full advantage of the vector field. Furthermore, the combine processors have a more promising performance. Hence, the method base on matching acoustic intensity flux brings a new way for MFP.

A set of non-Euclidean cross-spectral density matrix (CSDM) estimators based on the Frechet mean and median is applied to spatially localize an acoustic source in a stochastic shallow water environment driven by internal gravity waves. The resulting geometric-based matrix estimates are incorporated into matched-field processors defined through steering matrices using intrinsic distance measures between pairs of CSDMs on a Riemannian manifold for each replica source location. Their performance is evaluated using the probability of correct localization to determine any improvement in source localization over the conventional (maximum likelihood) statistical approach for CSDM estimation.

It has been proposed that source localization in passive sonar be accomplished via some form of matched field processing (MFP). Fully coherent, minimum variance distortionless response (MVDR) MFP assumes complete and perfect characterization of the underwater multipath propagation channel and is known to be extremely sensitive to mismatch between model parameters and actual environmental parameters. A minimax, multirank signal variation of MVDR MFP, semicoherent MVDR MFP, is presented. Simulation results show semicoherent MVDR MFP to be both relatively robust to mismatch, with respect to relative amplitudes and phases among multipath arrivals, and comparable in performance to fully coherent MVDR MFP under no mismatch conditions. >

Matched field processing (MFP) is an established technique for source localization in known multipath acoustic environments. Unfortunately, in many situations, particularly those involving high frequency signals, imperfect knowledge of the actual propagation environment prevents accurate propagation modeling and source localization via MFP fails. For beamforming applications, this actual-to-model mismatch problem was mitigated through a frequency downshift, made possible by a nonlinear array-signal-processing technique called frequency difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029]. Here, this technique is extended to conventional (Bartlett) MFP using simulations and measurements from the 2011 Kauai Acoustic Communications MURI experiment (KAM11) to produce ambiguity surfaces at frequencies well below the signal bandwidth where the detrimental effects of mismatch are reduced. Both the simulation and experimental results suggest that frequency difference MFP can be more robust against environmental mismatch than conventional MFP. In particular, signals of frequency 11.2 kHz-32.8 kHz were broadcast 3 km through a 106-m-deep shallow ocean sound channel to a sparse 16-element vertical receiving array. Frequency difference MFP unambiguously localized the source in several experimental data sets with average peak-to-side-lobe ratio of 0.9 dB, average absolute-value range error of 170 m, and average absolute-value depth error of 10 m.

Underwater source localization using receiver arrays is often achieved with a purely model-based approached, i.e., matched-field processing using simulated replica-field. However, these approaches only yield reasonable predictions if the complicated ocean environment can be precisely described, which is often a daunting task. Alternatively, by turning to a data-driven approach, source localization can be achieved without the strong dependence on model-parameters. Recently, source localization in the Santa Barbara Channel (∼580 m depth, downward refracting profile) has been achieved via measurements of ships of opportunity, and machine learning classifiers. In this presentation, relative channel impulse responses, estimated via the ray-based blind deconvolution, are used to train a neural network to predict the latitude and longitude of a surface ship within the Santa Barbara Channel. Localization results for simulated and experiment data are presented and implications for future work are discussed.Underwater source localization using receiver arrays is often achieved with a purely model-based approached, i.e., matched-field processing using simulated replica-field. However, these approaches only yield reasonable predictions if the complicated ocean environment can be precisely described, which is often a daunting task. Alternatively, by turning to a data-driven approach, source localization can be achieved without the strong dependence on model-parameters. Recently, source localization in the Santa Barbara Channel (∼580 m depth, downward refracting profile) has been achieved via measurements of ships of opportunity, and machine learning classifiers. In this presentation, relative channel impulse responses, estimated via the ray-based blind deconvolution, are used to train a neural network to predict the latitude and longitude of a surface ship within the Santa Barbara Channel. Localization results for simulated and experiment data are presented and implications for future work are discussed.

The authors present an approach for reducing the threshold observation time required to achieve high-resolution localization of multiple broadband sources. The proposed techniques are based on a space-time statistic called the steered covariance matrix (STCM). The STCM, like the well-known cross-spectral density matrix (CSDM), has asymptotic properties which facilitate high-resolution source localization. In broadband settings, however, the STCM has the advantage that it can be estimated with much greater statistical stability than the CSDM. The STCM is used in conjunction with minimum variance and linear predictive spectral estimation to obtain the steered minimum variance (STMV) and steered linear prediction (STLP) methods. Analytical and simulation results are presented that indicate that the STMV and STLP methods exhibit lower threshold observation times than their CSDM-based counterparts. >

A technique is developed for range-dependent matched field processing (MFP) where the field is computed using a parabolic equation (PE) approximation to the acoustic wave equation. The two-dimensional PE field is computed at each sensor in the array for a set of possible source ranges, depths, and bearings to form an N*2-dimensional model for the acoustic field. Discrete estimates of the position of the source are obtained by applying MFP, in which the match is optimized as a function of source position. Using simulated data, source localization in a noisy range-dependent environment is illustrated for several types of array. For the cases studied in this report, a lower level of ambiguity in localization was observed for range-dependent MFP than for a related range-independent problem. >

Acoustic waves are well-suited for remote sensing applications and structural health monitoring purposes because they convey information about their source and can be measured using non-contacting methods. Source localization is an important structural health monitoring task; however, traditional time-of-flight array signal processing techniques used to localize acoustic sources are ill-suited for many structural engineering applications due to the potential for complicated propagation paths, the dispersive propagation of acoustic waves in structures, and the coupling of the vibrating structure and the surrounding medium. Thus, source localization experiments were conducted using matched field processing (MFP) for a 0.9-m diameter round aluminum plate excited by the impact of a 1.3-cm stainless-steel ball bearing dropped from 7.6-cm. A 14-sensor linear remote acoustic array placed 8.9-cm above the plate measured the sound radiated by the 0.64-cm thick plate. MFP array signal processing localization techniques were used along with a physics-based finite element acoustic model to localize the excitation on the structure. Source localization results in both a quiet environment and environment with additive white Gaussian noise are discussed, and these results are compared to those from an acoustic model where plate edge reflections are neglected. [Work was sponsored by a SMART Scholarship and the NEEC.]

Source localization is an important structural health monitoring task, yet traditional localization techniques struggle due to complex geometries, dispersive wave propagation, and structure-medium coupling. This study applied matched field processing (MFP), a source localization technique developed for underwater acoustics, to localize impact sources on metal plates using remote acoustic measurements of airborne sound in conjunction with a physics-based acoustic-wave propagation model. A linear array of 14 microphones recorded radiated sound from a stainless-steel ball bearing dropped onto a 0.64 cm-thick, 91.4 cm-diameter aluminum plate in the nominal 5-20 kHz bandwidth. Physics-based finite element models were developed for both infinite and finite plates. The infinite plate model emphasized generic sound radiation with proper time-windowing, while the finite plate model included edge reflections specific to the plate studied. Both models achieved localization errors within 0.5 cm when data were temporally trimmed to accommodate model constraints. In environments with additive Gaussian noise, the finite plate model maintained greater than 80% localization accuracy down to a signal-to-noise ratio of -7.5 dB. Results further showed that MFP is robust to moderate mismatches in source characterization, but deviations in sensor location approaching a half-wavelength and deviations in plate thickness approaching 10% can reduce localization accuracy.

Incomplete environmental knowledge is a factor that can adversely affect the prediction capability of physics-based signal processors to localize acoustic sources in ocean waveguides. Environmental uncertainty effectively introduces unwanted additional degrees of freedom into the signal processing scheme. Including a quantitative measure of this incomplete information into the processor can be accomplished by considering the influence of alternative environments, each weighted by their probability of occurrence. An approach is outlined to account for environmental uncertainty in matched field processing by the use of polynomial chaos basis expansions to represent the replica vectors in terms of stochastic Green’s functions. These bases are interpreted as representing the effect of introducing additional degrees of freedom due to environmental uncertainty, because the pressure field replicas are specified as random processes. In this manner, a processor correlates the measured pressure field with a set of statistically weighted propagators between a replica source location and a sensor array. [Work sponsored by ONR through NRL base funding.]

Compressive sensing based techniques have recently been applied successfully to underwater acoustics problems such as beamforming and matched field processing. Sparse Bayesian Learning (SBL) is one of the fast compressive sensing methods and is formulated using Bayesian statistics. In the SBL framework, source amplitudes are modeled as complex Gaussian random variables with unknown variance. Evidence maximization is performed to estimate the unknown source amplitude variance and source position. A major advantage of SBL over more commonly used methods such as basis pursuit is that it is computationally faster. In this work, we develop a robust sparse Bayesian learning algorithm that can account for model mismatch leading to errors in the replica vector dictionary. Specifically, the likelihood function is modified so that it takes into account the covariance matrix of error in replica vectors. We also extend the SBL algorithm to process observations from multiple frequencies. The derived update rule combines observations from all the frequencies in a holistic manner. We demonstrate the robust SBL algorithm with simulations. A comparison is done with other compressed sensing methods including basis pursuit and orthogonal matching pursuit.

Matched field processing (MFP) has been widely used in source localization in shallow waters, whose performance is strongly correlated with the knowledge of environmental properties and proper selection of sound propagation model. This paper presents a neural network based approach for source ranging of moving target, which does not need heavy sound field calculation and no requirement of environmental information as a known prior. This neural network is designed to determine source range by observing multiple-frequency sound fields as excited by the source and recorded on a single vector receiver. In synthetic tests, this neural network is first trained on training data set as to adaptively select the optimal features through error back propagation, and then its localization performance is validated on testing data set. This approach is then tested on ship noise data as collected by a single vector sensor, and the relative error is smaller than 0.1 through comparing to GPS calculations. The promising results suggest the proposed approach can be further developed for source ranging applications with light system.

The domain of Matched-field processing (MFP) has been comprehensively studied in temperate oceans. But MFP source localization in under-ice shallow water environment has rarely conducted and is a topic of great novelty. The frequent interactions of sound and ice will lead dramatic reflection, attenuation and modal dispersion which will pose additional difficulties and uncertainties to localization due to the intense environmental sensitivity of the MFP method. This paper constructs the basic MFP source localization scheme in under-ice environment. Firstly, a hybrid acoustic propagation model called OASR-KRAKENC that considers the effects of ice reflection and attenuation are constructed to generate the replicas in under-ice waveguide. Then the incoherent broadband MFP approach of conventional linear correlation (Bartlett) and minimum variance (MV) algorithm are verified by the real data collected from the northern Yellow Sea in winter. The localization performance of real data validates the feasibility of MFP in under-ice environment.

In 1955, Jean-Louis Koszul has written a seminal paper entitled “Sur la forme hermitienne canonique des espaces homogenes complexes“. Let G be a Lie group and let B be a closed subgroup of G, Koszul introduced a hermitian form that he called canonical hermitian form of the complex homogeneous space G/B with an invariant volume form. In this seminal paper, Koszul has investigated homogeneous spaces and necessary conditions to carry a nondegenerate 2-form derived from the invariant volume element. The advantage of this form for the determination of homogeneous bounded domains was underlined by Elie Cartan in last sentence of his 1932 paper “Sur les domaines bornes de l’espace de n variables complexes”, observing that a necessary condition for G/B to be a bounded domain is that this form is positive definite. Hirohiko Shima has first observed that this geometry of Koszul Hessian structures is linked with Information Geometry. Jean-Louis Koszul also developed these structures in a Lecture “Exposes sur les Espaces Homogenes Symetriques” given at Sao-Paulo in 1958. We will synthetize these Jean-Louis Koszul works of 1955 and 1958 on this invariant form. We will put these elements in the context of more recent researches as a recent work of Della Vedova on covering spaces of symplectic manifolds (co-adjoint orbits, endowed with their canonical Kirillov-Kostant-Souriau symplectic structure) admitting homogeneous non Chern-Ricci flat special compatible almost complex structures, or Biquard extension of Kostant-Sekiguchi-Vergne correspondance. In last part, we develop the role of homogeneous bounded domains and invariant Koszul form in the framework of Information Geometry with use-case of Gaussian laws.

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.