The estimation of the shape of an array using a hidden Markov model

A hidden Markov model (HMM) technique for the estimation of the shape of a towed array is presented. It is assumed that there is a far-field source radiating sound containing possibly weak spectral lines. The technique uses either the Fourier coefficients at a given frequency computed from a single time block or the maximal eigenvector of a sample spectral covariance matrix. The technique is illustrated using several simulations. The results of these simulations indicate that the HMM technique yields shape and bearing estimates more accurate than those provided by a maximum-likelihood array shape estimation technique     

Calculation of the shape of a towed underwater acoustic array

An important area of towed underwater acoustic research is the determination of the 3D positions of all hydrophones in the array. Although there are a number of methods available that provide position information at a small number of locations along the array, an interpolation scheme is needed that will permit the estimation of the position of all hydrophones so that further processing of acoustic data may proceed. An interpolation technique based on a twisted quartic spline approximation to a space curve is presented. This technique provides the advantages of numerical stability, necessary smoothness, and satisfaction of physical boundary conditions. Most importantly, it permits the estimation of the positions of all hydrophones in an array     

Temporal domain processing for a synthetic aperture array

A method for the synthesis of an aperture with improved bearing resolution and signal gain is described. The proposed method temporally synthesizes data from an overlap correlator, which is obtained by aperture domain averaging of phase differences. Previous studies, such as extended towed array measurements (ETAM), had a restriction in that the overlapped hydrophones between successive measurements of a towed array were required to have identical positions in space. In this paper, however, it is shown that the phase correction factors can be estimated without restriction on the positions of the overlapped hydrophones. This implies that the proposed method is able to utilize more snapshots to extend the towed array. Simulation results showed that the proposed method resulted in higher estimation accuracy than ETAM. In addition, the effects of coherency and other systematic errors on the proposed method were examined     

A Simplified Subspace Fitting Method for Estimating Shape of a Towed Array

Although the existing array shape estimation methods using reference sources demonstrate good performance, most of the methods require at least two reference sources 2RS in known locations and the reference sources must be in far field. This communication proposes a simplified subspace fitting method that uses only a single reference source 1RS. In the proposed method, the horizontal and vertical positions of each sensor are modeled by applying fixed intersensor spacing and sensor angles, so that the unknown parameters of the cost function are reduced. Furthermore, the Cramer–Rao lower bound (CRLB) is investigated for the proposed method. The results of the numerical experiments indicate that the proposed method is practical for estimating the shape of a towed array.      

Combined Geoacoustic Inversion of Propagation and Reverberation Data

Sonar performance predictions in shallow water are strongly dependent on good knowledge of the geoacoustic and scattering properties of the seabed. One technique to extract information about the bottom is to use a towed source and a towed horizontal array. This towed system has been shown to be applicable for characterizing the bottom properties locally by inversion of the acoustic signals received directly on the towed array at short ranges. The same towed system has also been applied to extract bottom properties from long-range reverberation data providing effective bottom properties over a large area. However, independent geoacoustic inversion of the short-range propagation and long-range reverberation data can introduce low sensitivity and uncertainty in the extracted bottom properties. An attempt to resolve this low sensitivity and ambiguity is made by a simultaneous geoacoustic inversion of short-range propagation and long-range reverberation data with the intention of constraining the possible solutions of the bottom properties.      

Time-domain geoacoustic inversion of high-frequency chirp signal from a simple towed system

An inversion method using a towed system consisting of a source and two receivers is presented. High-frequency chirp signals that have been emitted from the source are received after multiple penetrations and reflections from the shallow water sub-bottom structure and are processed for geoacoustical parameter estimation. The data are processed such that a good resolution and robustness is achieved via matched filtering, which requires information about the source signal. The inversion is formulated as an optimization problem, which maximizes the cost function defined as a normalized correlation between the measured and modeled signals directly in the time domain. The very fast simulated reannealing optimization method is applied to the global search problem. The modeled time signal is obtained using a ray approach. An experiment was carried out in the Mediterranean Sea using a towed source and receiver system. The inversion method is applied to the experimental data and results are found to be consistent with previous frequency-domain analyses using measurements from a towed horizontal array of receivers and measurements on a vertical array.     

The maximum likelihood estimator for acoustic synthetic apertureprocessing

The maximum likelihood estimator of source amplitude, bearing, and frequency for a moving towed line array of equispaced elements is discussed. A two-dimensional search in equivalent phase and frequency variables is found to yield the best estimates of the unknown parameters. Application to a physical experiment and comparison with the Cramer-Rao bound verify the unity of the approach     

Geoacoustic Information Content of Horizontal Line Array Data

This paper examines the effectiveness of horizontal line arrays (HLAs) for matched-field inversion (MFI) by quantifying geoacoustic information content for a variety of experiment and array factors, including array length and number of sensors, source range and bearing, source-frequency content, and signal-to-noise ratio (SNR). Emphasis is on bottom-moored arrays, while towed arrays are also considered, and a comparison with vertical line array (VLA) performance is made. The geoacoustic information content is quantified in terms of marginal posterior probability distributions (PPDs) for model parameters estimated using a fast Gibbs sampler approach to Bayesian inversion. This produces an absolute, quantitative estimate of the geoacoustic parameter uncertainties which can be directly compared for various experiment and array factors.     

Modal Inversion Analysis for Geoacoustic Properties of the New Jersey Continental Shelf in the SWAT Experiments

In this paper, inversion for bottom sediment properties at a site on the New Jersey continental shelf is studied as part of the Shallow Water Acoustic Technology (SWAT) project. A source towed at a constant water depth over a range of some tens of kilometers transmitted low-frequency continuous wave (cw) signals, which were measured on a bottom-moored vertical line array of receivers. For the along-shelf geometry, the zeroth-order asymptotic Hankel transform is then applied to the acoustic field at 50 Hz measured on the resulting synthetic aperture horizontal array created at each receiver depth. The resulting horizontal wave number spectra, which have peaks corresponding to the mode eigenvalues, are observed to have slightly different values at different receiver depths, and therefore, stochastic mode inversion is exploited to utilize all of the observed peak position information. The estimated sound-speed profile (SSP) for the upper 10 m of sediment is then compared with an inversion result obtained using midfrequency (2–16 kHz) chirp sonar pulses reflected at normal incidence from the sediment. Although obtained using totally different inversion techniques, both estimated profiles are shown to be in good agreement in the top 10 m of sediment. The acoustic field simulated using the inverted SSP also agrees well with the measured acoustic field at each receiver depth. Furthermore, simulated sound fields which use this profile as input data are shown to be effective in predicting the measurements obtained at a different frequency (125 Hz) and for a different (cross-shelf) geometry.      

An environmental assessment in the Strait of Sicily: measurementand analysis techniques for determining bottom and oceanographicproperties

In October 1997, the EnVerse 97 shallow-water acoustic experiments were jointly conducted by SACLANT Centre, TNO-FEL, and DERA off the coast of Sicily, Italy. The primary goal of the experiments was to determine the sea-bed properties through inversion of acoustic data. Using a towed source, the inversion method is tested at different source/receiver separations in an area with a range-dependent bottom. The sources transmitted over a broadband of frequencies (90-600 Hz) and the signals were measured on a vertical array of hydrophones. The acoustic data were continuously collected as the range between the source and receiving array varied from 0.5 to 6 km. An extensive seismic survey was conducted along the track providing supporting information about the layered structure of the bottom as well as layer compressional sound speeds. The oceanic conditions were assessed using current meters, satellite remote sensing, wave height measurements, and casts for determining conductivity and temperature as a function of water depth. Geoacoustic inversion results taken at different source/receiver ranges show sea-bed properties consistent with the range-dependent features observed in the seismic survey data. These results indicate that shallow-water bottom properties may be estimated over large areas using a towed source fixed receiver configuration     

Detection of transient signals in multipath environments

This research examines methods for detecting unknown transient waveforms that are contaminated by noise. The sensitivity of the performance levels of the energy detector and the lack of knowledge about the structure of the transient waveform motivate the examination of other moment- or spectra-based detection techniques. We examine the performance of a bispectral energy detector and show that its performance will degrade if the bispectra is smoothed and that signals with no bispectral content can be detected if the bispectra is not smoothed. Further, it is shown that the performance levels of the bispectral detector are slightly better, and slightly less sensitive, than those of the energy detector for the multipath linear frequency modulated signal. Finally, the performance levels of narrowband implementations of the energy and bispectral energy detectors are compared. It is shown that for a large enough sample, the performance levels of the bispectral detector are nearly as good as those of the optimal energy detector for the single narrowband signal case. However, when the received waveform contains multiple narrowband components, the narrowband bispectral detector performs slightly better than the energy detector     

拖曳线列阵声纳中隔振模块研究

介绍了作为隔振模块研究依据的拖缆抖动特性的试验研究结果及隔振模块理论分析方法 ,给出了隔振模块有关参数变化对隔振量影响的理论值 ,提供了隔振模块隔振量试验方法 ,某隔振模块隔振量的测量结果以及装与不装隔振模块情况下 ,声阵的拖曳噪声声压谱级的测量结果     

Towed array shape estimation using Kalman filters-theoreticalmodels

The dynamical behavior of a thin flexible array towed through the water is described by the Paidoussis equation. By discretizing this equation in space and time a finite-dimensional state-space representation is obtained where the states are the transverse displacements of the array from linearity in either the horizontal or vertical plane. The form of the transition matrix in the state-space representation describes the propagation of transverse displacements down the array. The outputs of depth sensors and compasses located along the array are shown to be related in a simple, linear manner to the states. From this state-space representation a Kalman filter which recursively estimates the transverse displacements and hence the array shape is derived. It is shown how the properties of the Kalman filter reflect the physics of the propagation of motion down the array. Solutions of the Riccati equation are used to predict the mean square error of the Kalman filter estimates of the transverse displacements     

A modeling study on steady-state and transverse dynamic motion of a towed array system

A numerical technique for mathematically modeling the steady-state and transverse dynamic motion of an underwater towed sonar array is presented. The transverse vibration response of the array is modeled using the finite difference method; the array itself is assumed to be nonneutrally buoyant and possesses a complex modulus and hence inherent damping. The results obtained from this model should provide useful information for further studying the beamforming and passive-ranging performance degradation and predicting the self-noise level of the towed array system.     

Four-element CODAR beam forming

An HF radar called the Coastal Ocean Dynamics Applications Radar (CODAR) is presently being used in several forms to measure ocean surface parameters. The original version was developed by the National Oceanic and Atmospheric Administration (NOAA) and utilizes a four-element receive array. The array consists of four equally spaced elements arranged on a circle with a radius of 0.2151 wavelengths (at 25.4 MHz). It was designed to measure ocean currents using a direction-finding technique based on an extension to a simple two-element interferometer. The problem of determining the bearing of a radiating source can be readily shown to be equivalent to that incurred in spectral estimation. In an attempt to improve upon the processing of existing data, modern nonlinear spectral estimation techniques are applied in a beam-forming bearing estimation procedure and compared against several direction-finding algorithms. Enhancement of bearing estimators via analysis of the eigenstructure of a spatial correlation matrix is included. Antenna response patterns are calculated and used to investigate properties of direction-finding algorithms. Simulated data are used for a comparison of direction finding and beam forming. The asymmetrical bias of each method is investigated to determine its effect on the error in estimating the angle of arrival of a radar target.     

Cramer-Rao lower bounds for sonar broad-band modulation parameters

A role of passive sonar signal processing is the detection and estimation of the parameters associated with amplitude modulated broad-band signals. An example of such signals is propeller noise. Discrete frequency lines occur at the rotational frequency of the propulsion shaft and at the blade frequency. This correspondence provides expressions for the Cramer-Rao lower bounds for the estimates of broad-band signal power, modulation level, modulation frequency, and modulation phase. It is shown that for low broad-band-signal-to-broad-band-noise ratios, the estimates of power and modulation level are uncoupled from the estimates of modulation frequency and phase     

Simultaneous reception of long-range low-frequency backscattered sound by a vertical and a horizontal array

Simultaneous measurements of low-frequency sound generated by an explosive source and backscattered from the seafloor in the eastern Mediterranean were made with two receiver configurations: a towed horizontal array and a vertical array. Images of the scattering features on the beam-time data of the horizontal array were useful in the interpretation of the scattering process and in estimating areas of scatterers received by the vertical array, and permitted scattering strengths to be estimated for both configurations. Images of the vertical array data provided information about the vertical arrival angles at the array from specific scatterers. At long range, the sound from the scattering features was received at grazing angles less than13deg. The scattering strengths for three features varied from - 47 to - 25 dB. The mean frequency dependence over the band 125 to 700 Hz varied from 0 to 2.5 dB/octave with greater variations occurring within smaller bands.     

Passive systems theory with narrow-band and linear constraints: Part I--Spatial diversity

This paper studies passive problems where the receiver extracts from the source radiated signature information concerning the parameters defining the relative source/receiver geometry. A model encompassing the fundamental global and local characteristics for passive positioning and navigation is presented. It considers narrow-band signals, imposes linear constraints on the geometry, and exhibits explicitly the symmetry between the space and time aspects. The analysis concentrates on questions of global geometry identifiability, emphasizing the passive global range acquisition. The maximum-likelihood processor is analyzed by studying the ambiguity structure associated with inhomogeneous passive narrowband tracking. Bounds on the global and local mean-square error performance are studied and tested via Monte Carlo simulations. By considering two limiting geometries, a distant and a close observer, simple approximate expressions for the mean-square errors are presented and compared to the exact bounds. Herein the study is restricted to stationary geometries where the source is located by an extended array (spatial diversity). Subsequent papers generalize the study to moving sources (temporal diversity) and to coupled geometries.     

Towed array shape estimation using multimodel partitioning filters

The problem of towed array shape estimation is reformulated and shown to be mathematically equivalent to the problem of state estimation with abruptly changing bias of the plant noise process. An algorithm belonging to the family of adaptive multimodel partitioning algorithms is subsequently applied to this problem, and its performance is comparatively evaluated with that of nonadaptive algorithms previously proposed through simulation experiments     

Experimental investigation of the angular dependence of low-frequency seabed reverberation

Linear frequency-modulated (LFM) signals with 600 Hz bandwidth, centered at 1.1 kHz were transmitted from a towed source in a shallow-water environment in the Mediterranean Sea and received at a distant vertical line array (VLA). Arrivals recorded on the VLA were beamformed to give incident intensity as a function of vertical angle. Simultaneous measurements of quasimonostatic reverberation were made on a horizontal line array (HLA), towed close to the source. In this paper, these data are analyzed to study the relation between the angle at which sound arrived at the patch of seabed surrounding the VLA and the intensity of quasimonostatic reverberation returned from that patch. The validity of three candidate relations (Lambert's Law, angle-independent scattering and an intermediate relation) is investigated and scattering strength parameters (Lambert /spl mu/ and equivalents) are also deduced for the patch of seabed surrounding the VLA. Only weak evidence is found to support one of the scattering relations (the intermediate) over the other two and the reasons for this are discussed. The physical processes that may underlie the intermediate relation are also discussed.