A 1-D search solution for localization from frequency measurements

A source that emits a constant frequency tone and moves at a constant course and speed can be localized through measurements of the Doppler shifted frequencies (DSF). With five unknowns, namely, the rest frequency and the positions and speeds in the x-y directions, five separate sensors would normally be necessary to give five DSP measurements for instantaneous localization. The equations are nonlinear, and the standard solution is by grid search or iteration. The high dimensionality leads to a large computational requirement. By incorporating DSF rates, a quantity available from frequency line trackers, a one-dimensional grid search solution is possible which requires only three sensors and reduces the computational load. The derivation of the grid search technique is given, together with simulation results. The conclusion is that at high signal-to-noise ratios (SNR), the scheme reaches the three-sensor Cramer-Rao lower bound; at lower SNR's or with increased sensors, the grid search answer is a good initializer for a nonlinear optimization algorithm that gives a maximum likelihood estimate     

Track Parameter Estimation from Multipath Delay Information

It is desired to track the location of an underwater acoustic source with range difference measurements from a stationary passive array. Many times, the array has only one or two sensors, and the multipath and intersensor range difference measurements are insufficient to localize and track a source moving along an arbitrary path [1]. Here, we propose to track sources with one- or two-sensur stationary passive arrays by making the simplifying assumption that the source's path can be described by a small set of so-called track parameters. Range difference information can then be used to estimate the track parameter set rather than the source location as a function of time. In this paper, we choose the track parameters to specify a straight-line constant-velocity constant-depth path. Cramer-Rao bounds are presented for estimating these track parameters from the time history of multipath and intersensor range difference measurements. It is shown that this track parameter set cannot be accurately estimated from the time history of a single multipath range difference without side information (an independent velocity estimate, for instance), although multipath and intersensor range difference measurements from a two-sensor array are generally sufficient to estimate the track parameter set. Computationally efficient techniques are presented which estimate track parameters from range difference measurements taken from one- and two-sensor arrays. Monte-Carlo simulations are presented which show that these techniques have sample mean-square error approximately equal to the Cramer-Rao bound when a single multipath range difference and an independent velocity estimate are available. The sample mean-square error is shown to be in the range of two to ten times the corresponding Cramer-Rao bounds when these techniques are applied to two-sensor range difference data.     

Acoustic tracking of a freely drifting sonobuoy field: experimental results

This paper describes a regularized acoustic inversion algorithm for tracking individual elements of a freely drifting sonobuoy field using measured acoustic arrival times from a series of impulsive sources. The acoustic experiment involved 11 sonobuoys distributed over an 8/spl times/6-km field, with a total of six sources deployed over 72 min. The inversion solves for an independent track for each sonobuoy (parameterized by the sonobuoy positions at the time of each source transmission), as well as for the source positions and transmission instants. Although this is a strongly under-determined problem, meaningful solutions are obtained by incorporating a priori information consisting of prior estimates (with uncertainties) for the source positions and initial sonobuoy positions and a physical model for sonobuoy motion along preferentially smooth tracks. The inversion results indicate that the sonobuoys move approximately 260-700 m during the source-deployment period. Closely spaced sonobuoys move along similar tracks; however, there is considerable variability in track directions over the entire field. Positioning uncertainties in horizontal coordinates are estimated using a Monte Carlo appraisal procedure to be approximately 100 m in an absolute sense and 65 m in a relative sense. A sensitivity study indicates that the uncertainties of the a priori position estimates are the limiting factor for track accuracy, rather than data uncertainties or source configuration.     

First measurements from a deep-tow transient electromagnetic sounding system

An electromagnetic sounding system has been developed to map the shallow electrical conductivity structure of the deep sea floor. The instrument consists of a magnetic source and several colinear magnetic receivers forming an array which is towed along the seafloor. The source generates a time varying magnetic field; the shape of the resulting magnetic field waveform at the receivers depends on the electrical conductivity below the seafloor between the receivers and the source. The instrument can be towed systematically over a study area under acoustic transponder or GPS navigation to construct a map of the electrical conductivity. Towing speeds of greater than 1 m s^–1 (2 knots) can be achieved without adversely effecting data quality. The instrument is sufficiently robust to survive continual contact with thinly sedimented, abrasive basalt. We present the first results from a deployment in August, 1990 near the Cleft Segment of the Juan de Fuca Ridge along an 8 km track to the west of the spreading center. Unforeseen problems with the instrument restricted the utility of the measurements for constructing detailed vertical conductivity profiles, but the measurements were adequate to determine an average conductivity in the upper 25 m, at more than 70 stations. The conductivity was found to vary from 0.1 to 0.4 S/m along the track.     

A piecewise matched-field tracking algorithm

Matched-field tracking (MFT) algorithms have been successfully applied to both simulated and measured data to determine the most likely positions of a sound source that is localized ambiguously by a matched-field processing (MFP) system. They have been used to track sources moving linearly or on a circular path at constant speed and heading. The input to the trackers is a set of ambiguity surfaces, contiguous in time, generated by MFP. These algorithms assume that the track start and end times are known a priori; this restriction is removed in the piecewise MFT algorithm (PTA). The PTA was applied to narrow-band measured data collected during the PACIFIC SHELF 93 trial to successfully identify the significant source track segments     

Portable acoustic tracking system for divers (PATS)

A portable acoustic tracking system (PATS) has been developed for the Navy to track underwater construction teams in water depths to 200 ft. The tracking system can be deployed and operated by the divers and is intended for use in remote areas and for nearshore survey, maintenance, and construction work. A self-calibrating system provides a geographically justified track for up to eight divers. Diver position coordinates are computed from acoustic measurements at periodic intervals and displayed for control purposes. The positions are also recorded for future reference.     

阿拉伯海热带气旋生成特征分析

利用印度气象局（India Meteorological Department,IMD）、国际气候管理最佳路径档案库（International Best Track Archive for Climate Stewardship,IBTrACS）提供的1982—2020年阿拉伯海热带气旋路径资料,美国国家环境预报中心（National Centers for Environmental Prediction,NCEP）再分析资料,对近39 a阿拉伯海热带气旋源地和路径特征、活跃区域、频数及气旋累积能量（accumulated cyclone energy,ACE）指数的季节特征和年际变化特征进行分析,并结合环境因素,说明其物理成因。结果表明：阿拉伯海热带气旋多发于10°~25°N,65°~75°E海域,5—6月、9—12月发生频数较高且强度较强,1—4月、7—8月发生频数较低且气旋近中心最大风速均小于35 kn;频数的季节变化主要受控于垂直风切变要素;阿拉伯海热带气旋发生频数和ACE近年有上升趋势,年际变化主要受控于海面温度（sea surface temperature,SST）和850 hPa相对湿度要素。     

Inversion of Lloyd Mirror Field for Determining a Source's Track

This paper describes a simple approach for inferring the depth and track of a sound source at short ranges by inversion of acoustic field data at a set of sea bottom hydrophones. At short ranges, the acoustic field consists of a dominant Lloyd mirror (LM) signal from the direct and surface-reflected ray paths and a series of bottom-reflected paths that modulate the LM signal. A computationally efficient propagation model based on the method of images is developed to calculate replica fields for the inversion. The matched field inversion method for inferring the source depth and track is demonstrated using data from an experiment carried out in shallow water off the east coast of Canada. The estimated values were in very good agreement with independent measurements taken during the experiment.     

Passive acoustic synthetic aperture processing techniques

Various parameters associated with the track of a stable CW source moving with constant velocity are estimated using synthetic aperture and Doppler processing techniques. These include the source frequency before Doppler distortion by its motion, the relative speed between the source and a constant velocity receiver, the range at closest approach to the source track, and the relative bearing to the source. Different processing techniques are suggested for a range of signal stabilities and observation times. Frequency analysis, or Doppler processing, supplements conventional synthetic aperture processing, and for relatively unstable signals a synthetic Doppler method is recommended. This method makes use of a rapid scan of signals from a succession of sensors in a horizontal line array to stimulate a higher speed motion of the array     

A neural approach to the assignment algorithm for multiple-targettracking

A neural network is presented for performing data association for multiple-target tracking on an optimal assignment basis, i.e., the sum of likelihood functions of measurement-to-track file associations is optimized. The likelihoods are shown to be derivable from a Kalman filter, which updates and maintains the track files from the measurements assigned by the neural network. Not only are measurements assigned to track files on an optimal basis, but undetected targets and unassigned measurements are identified also. A multiple-target tracking system utilizing the neural network, in conjunction with Kalman filtering, can also automatically delete and initiate track files. The solution to the data association problem, and therefore the design of the neural network, is based on the minimization of a properly defined energy function. Computer simulations indicate the ability of the neural network to converge quickly to the optimal hypothesis under various conditions, provided that the ambiguity in the scenario is not extreme. The computational complexity involved is moderate     

双浮板液舱晃荡特性的数值研究

基于黏性流理论,采用动网格技术和6自由度模型,以及动量源方法,建立了双浮板液舱晃荡的数值模型。分别采用3种不同空间步长的网格离散计算区域,进行了网格收敛性验证。通过光滑液舱晃荡的模型试验和解析得到的爬高最大值,验证了数值模型的精确性。在载液率为50%,激励幅值为2 mm条件下,对双浮板液舱晃荡进行了数值计算,与光滑液舱相比,双浮板液舱晃荡的最大爬高明显减小。通过一个激励周期内双浮板液舱晃荡的波面显示发现,液舱晃荡模式由光滑液舱的驻波模式变为U管模式,晃荡模式的改变起到了明显地抑制液舱晃荡的效果。     

A Review of: “Numerical Modeling of Water Waves,Second Edition”

Optimal interpolation in the spatial domain is limited by computer storage requirements and the computational effort to invert the autocovariance matrix. The procedure can be simplified by use of the fast Fourier transform (FFT), where matrix inversion is replaced by a quotient of power spectral density (PSD) functions in the spectral domain. Such a methodology is developed and utilized to estimate an altimetric mean sea surface from a single 35‐day cycle of ERS‐1. ERS‐1 radial orbit error is first reduced by minimizing dual crossover residuals with TOPEXIPoseidon through solution for a sinusoidal correction for each ascending and descending arc along with the relative altimeter bias. A regular grid for ascending (descending) arcs is then formed by use of the equator‐crossing longitudes and the along‐track displacement. Gaps in the altimeter data set are filled by use of a reference model. PSDs derived from the data and reference surface enable computation of the least‐Squares estimator in the spectral domain, from which the optimally interpolated surface heights for ascending (descending) arcs are derived by the inverse Fourier operator. The resolution is bounded across track by the Nyquist frequencies, which for the 35‐day repeat period correspond to 1.44° longitudinal spacings or 160 km. For consistency, the along‐track resolution is reduced to a comparable level. The combination of the ascending and descending sea surface heights yields a surface up to the isotropic frequency that corresponds to surface spherical harmonics of degree and order 250. Comparisons show that the model performs almost as well as the Ohio State University model present on the TOPEXIPoseidon CD‐ROMs.     

海洋二号卫星微波散射计后向散射系数业务化面元匹配算法

本文提出了一种可业务化运行的海洋二号卫星散射计面元匹配方法,该算法主要用于将按时序排列的后向散射系数及相关参数投影到相应风矢量单元。面元匹配方法主要包括地面网格划分和后向散射系数观测结果重采样两个关键步骤。为简化计算,本文采用了以星下点轨迹为中心,以顺轨向及交轨向为坐标轴的地面网格划分方式。在重采样过程中,本文提出了一种“三点标定”重采样方法,利用观测脉冲的地面足印中心,星下点轨迹的起点,以及过地面足印中心做星下点轨迹垂线的交点,三点形成的直角三角形来计算每个后向散射系数观测结果在地面网格中对应的坐标。该直角三角形的两直角边分别对应观测脉冲在顺轨向和交轨向的坐标。同时,为减少由于星下点数据空间分布不连续引起的面元匹配误差,在采用三点标定法进行重采样之前,首先对星下点时空分布不连续的区域对时间插值,然后以时间为坐标,对星下点经度、纬度分别进行内插。对风矢量面元位置分布和风矢量反演精度等分析表明,本文提出的面元匹配算法,可在满足高质量海面风场反演的要求。     

Sensor position estimation and source ranging in a shallow water environment

Underwater acoustic transient signals are generated mechanically at known positions along a wharf. These signals are received by a wide aperture planar array of four underwater acoustic sensors, whose positions relative to the wharf are unknown. A method is described that enables the positions of the sensors to be estimated from accurate differential time-of-arrival measurements (with 0.1 /spl mu/s precision) as the signal wavefronts traverse the array. A comparison of the estimated positions with the nominal positions of the first three sensors, which form a 20-m-wide aperture horizontal line array, reveals a 2-cm displacement of the middle sensor from the line array axis. This slight bowing of the line array results in overranging (bias error of 3%) when the wavefront curvature method is used with the nominal collinear sensor positions to locate a static source of active sonar transmissions at a range of 59.2 m. The use of the spherical intersection method coupled with the estimated sensor positions of the line array provides an order of magnitude improvement in the range estimate (within 0.3% of the actual value). However, systematic ranging errors are observed when the sound propagation medium becomes nonstationary. Next, the differences in the arrival times of the direct path and boundary-reflected path signals at the middle sensor of the wide aperture line array are estimated using the differential phase residue of the analytic signal at the sensor output. These multipath delays are used to estimate the range and depth of the source. Although the average value of the multipath range estimates is within 0.5% of the actual value, the variance of the range estimates is 50 times larger when compared with the results of the spherical intersection and wavefront curvature methods. The multipath delay data are also processed to provide a reliable estimate of the temporal variation in the water depth enabling the tidal variation to be observed.     

Geoacoustic model parameter estimation using a bottom-moored hydrophone array

This paper describes results from an experiment carried out to investigate geoacoustic inversion with a bottom-moored hydrophone array located in the shallow waters of the Timor Sea off the northern coast of Australia. The array consisted of two arms in a V shape, horizontally moored at a site that was essentially flat over a large area. Hydrophone positions were estimated using an array element localization (AEL) technique that established relative uncertainties of less than 1 m on the seafloor. The data used for geoacoustic inversion were from experiments with continuous wave (CW) tones in the 80- to 195-Hz band transmitted from a towed projector. A hybrid search algorithm determined the set of geoacoustic model parameters that maximized the Bartlett fit (averaged coherently spatially at each tone and incoherently over frequency) between the measured and modeled data at the array. Due to the long range experimental geometry, the inversion was sensitive to attenuation in the sediment. The inverted geoacoustic profile performed well in a simple test for localizing the sound source at other sites in the vicinity of the array. Range-depth localization performance for the horizontal array was comparable to that for an equivalent vertical array.     

Geoacoustic Inversions of Horizontal and Vertical Line Array Acoustic Data From a Surface Ship Source of Opportunity

The application of an inversion methodology produces the first demonstration of a simultaneous solution for geoacoustic and source track parameters from acoustic data collected in a shallow-water, sandy sediment environment. Inversion solutions from data collected in the 2006 Shallow Water Experiment (SW06) are extracted from noise measurements of a surface ship source on an L-array. The methodology includes a screening algorithm to determine a set of frequencies for the inversion data. In addition, the methodology assesses the accuracy of the inversion solution and incorporates an estimation of parameter value uncertainties. The solution from the inversion of the horizontal component of the L-array data from the surface ship source before its closest point of approach (CPA) is used to construct modeled propagation loss for comparison with observed received level (RL) structure as the source departs from CPA. Inversion of the data from a single element in the vertical component of the L-array produces a solution that agrees with the solution obtained from the inversion of horizontal subaperture data. Also, modeled transmission loss (TL) structure obtained from the single-element inversion solution reproduces the depth dependence of the RL structure observed at other elements of the vertical component of the L-array.      

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     

Seafloor Roughness Measured by a Laser Line Scanner and a Conductivity Probe

To support modeling acoustic backscatter from the seafloor, a conductivity probe and a laser line scanner were deployed jointly to measure bottom roughness during an experiment off the New Jersey coast in summer 2006. The conductivity probe in situ measurement of porosity (IMP2) is impervious to water turbidity and yields a 1-D profile with 10-mm horizontal spacing and 1-mm resolution in the vertical direction. The laser line scanner is limited by water visibility but it provides 2-D grid points with resolutions 0.3 mm across track, 0.5 mm along track, and 0.3 mm in the vertical direction. Two sets of data, suitable to model mid- to high-frequency acoustic backscatter, were collected from two sites 900 m apart on August 14 and 17, 2006. The roughness spectra obtained from the laser scanning were compared to those measured by the IMP2. The spectra from the two methods are consistent over wave number range 0.0188–3 rad/cm, which are the wave number range common to both methods. The efficacy of the laser scanner is also confirmed by showing the spectral line created by the IMP2's periodic probing marks. The 2-D spectra generated from the laser scan data show that the bottom roughness at these sites is azimuthally isotropic, but significant spatial heterogeneity is observed.      

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability, the convective derivatives in the free-surface boundary conditions are treated using an upwind-biased stencil. Instead of solving for the radiation impulse response functions, a pseudo-impulsive Gaussian type displacement is employed in order to tailor the frequency-content to the discrete spatial resolution. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth-order convergence of the calculations on simple geometries is demonstrated, along with a nearly linear scaling of the solution effort with increasing grid resolution. The code is validated by comparison with analytical and semi-analytical solutions using submerged and floating closed-form geometries. Calculations are also made for a modern bulk carrier, and good agreement is found with experimental measurements.     

Frequency dependence of sediment attenuation in two low-frequencyshallow-water acoustic experimental data sets

Shallow-water transmission loss measurements taken in 1988 and 1993 along the same cross slope track on the New Jersey shelf are examined for the frequency interval 50-1000 Hz. Computed results, using a geoacoustic model based on a linear frequency dependence of the sediment volume attenuation, showed less loss than the measured data at the higher frequencies. A two stage, least squares procedure, is developed as a means of quantitatively examining the differences between the measured and computed results. The procedure focuses on the frequency dependence of the sediment volume attenuation and allows the comparison between measurements and computations to be formulated as a statistical test of hypothesis. A geoacoustic model, using a nonlinear frequency dependency and reasonable uncertainty for the sediment volume attenuation, provides a good fit to the data