Tracking a moving vessel from bearing measurements

This paper presents a method for tracking a distant moving target using only bearing measurements obtained from a tracking platform. The method is an improvement of the Hinich-Bloom passive tracking approach presented in [1]. The target is assumed to be moving at constant speed on a fixed heading, whereas the platform maneuvers during the measurement period. The direction cosines of the bearings are computed with respect to a rotation of the coordinate system that places 0° at the mean estimated target bearing. This is done to minimize the approximation bias due to the linearization of sine bearing as a function of inverse range and time. The coordinate system is rotated back to estimate the target coordinates. When the noise is Gaussian, the estimates of target range and heading are approximately maximum likelihood when the target's relative range is slowly varying during the observation period. In this case the mean square errors of the target parameter estimates are the smallest achievable within the order of the approximation.     

N-port analysis of a projector consisting of a coaxial array of ferroelectric shells

The coupling between a coaxial array of six ferroelectric shells and its fluid environment is computed by an application of N-port theory. Properties of the lowest ("breathing") mode of the shells are determined by using three-dimensional finite elements, and this knowledge is utilized in defining an N-port representation of the array. An N-port representation of the external fluid is obtained by solving the Helmholtz integral equation that relates fluid velocities and pressure on the exterior of the array. The two N-ports are coupled together in a standard circuit-theoretic manner to produce an equation for the electrical driving-point impedance of the loaded projector. Several frequency responses, which illustrate the effects of varying certain parameters are presented.     

Acoustic Detection and Localization of a Turboprop Aircraft by an Array of Hydrophones Towed Below the Sea Surface

The acoustic spectrum of a propeller-driven aircraft is dominated by a series of spectral lines that are harmonically related to the blade rate (which is equal to the product of the propeller rotation rate and the number of blades on the propeller). We show that an array of acoustic sensors towed below the sea surface can be used for the passive detection and localization of such an aircraft. The acoustic energy from an aircraft is found to reach the subsurface sensors via two propagation paths: a bottom reflection path that enables the aircraft to be detected at long ranges, and a direct path that is present only when the aircraft passes overhead. For each of these paths, the observed variation with horizontal range of the Doppler shift in the blade rate closely matches the variation predicted by the simple model presented in this paper. Good agreement between theory and experiment is also obtained for the variation with horizontal range of the aircraft's apparent bearing. Thus, by using the observed Doppler shift and apparent bearing information, we were able to estimate the aircraft's horizontal range, speed, direction, and altitude.      

On the ability to estimate narrow-band signal parameters usingtowed arrays

Using the Cramer-Rao lower bound (CRLB) as an indicator of potential performance, the limits on the estimation and resolution capabilities of a towed line array of uniformly spaced hydrophones to provide frequency and bearing information about narrowband signals are examined. It is assumed that a monochromatic plane wave arrives at the array for each source. Several versions of the bounds are computed using different assumptions about which parameters have known values and about the way in which the samples are taken in space and in time. It is shown that the CRLB values for different situations can be compared to provide information about the effective use of a moving aperture for estimation of the parameters of narrowband signals arriving at the array. It is also shown that adding at least one hydrophone occupying a fixed position in space can improve the bearing estimates of a towed array by supplying additional frequency information if both the bearings and frequencies of the sources are unknown     

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.     

A nearly unbiased inherently stable bearings-only tracker

A pseudolinear estimator for bearings only tracking is presented. It is demonstrated through calculations and simulations that it has a performance close to the computationally far more complex maximum-likelihood estimator, in contrast to the earlier well-known pseudolinear estimator in Cartesian coordinates. Using the mean time point as the time reference of this estimator is necessary in order to avoid bias     

Use of the kurtosis statistic in the frequency domain as an aid in detecting random signals

Power spectral density estimation is often employed as a method for signal detection. For signals which occur randomly, a frequency domain kurtosis estimate supplements the power spectral density estimate and, in some cases, can be employed to detect their presence. This has been verified from experiments with real data of randomly occurring signals. In order to better understand the detection of randomly occurring signals, sinusoidal and narrow-band Gaussian signals are considered, which when modeled to represent a fading or multipath environment, are received as non-Ganssian in terms of a frequency domain kurtosis estimate. Several fading and muitipath propagation probability density distributions of practical interest are considered, including Rayleigh and log-normal. The model is generalized to handle transient and frequency modulated signals by taking into account the probability of the signal being in a specific frequency range over the total data interval. It is shown that this model produces kurtosis values consistent with real data measurements. The ability of the power spectral density estimate and the frequency domain kurtosis estimate to detect randomly occurring signals, generated from the model, is compared using the deflection criterion. It is shown, for the cases considered, that over a large range of conditions, the power spectral density estimate is a better statistic based on the deflection criterion. However, there is a small range of conditions over which it appears that the frequency domain kurtosis estimate has an advantage. The real data that initiated this analytical investigation are also presented.     

Appraisal of gas-hydrate/free-gas from VP/VS ratio in the Makran accretionary prism

Existence of gas-hydrate in the marine sediments elevates both the P- and S-wave seismic velocities, whereas even a small amount of underlying free-gas decreases the P-wave velocity considerably and the S-wave velocity remains almost unaffected. Study of both P- and S-wave seismic velocities or their ratio (V_P/V_S) for the hydrate-bearing sediment provides more information than that obtained by the P- or S-wave velocity alone for the quantitative assessment of gas-hydrate. We estimate the P- and S-wave seismic velocities across a BSR (interface between gas-hydrate and free-gas bearing sediments) using the travel time inversion followed by a constrained AVA modeling of multi channel seismic (MCS) data at two locations in the Makran accretionary prism. Using this V_P/V_S ratio, we then quantify the amount of gas-hydrate and free-gas based on two rock-physics models. The result shows an estimate of 12–14.5% gas-hydrate and 4.5–5.5% free-gas of the pore volume based on first model, and 13–20% gas-hydrate and 3–3.5% free-gas of the pore volume based on the second model, respectively.     

Localization of a broadband source using a matched-mode procedurein the time-frequency domain

In this paper, we present a nonconventional matched-mode procedure for localizing a broadband source in the time-frequency domain. This hybrid coherent and incoherent approach exploits both the temporal and spatial characteristics of the multimode arrival structure at a receiving sensor array. In the previous work, a time-domain technique was developed to deal with narrowband signals coherently. It consists of the following three steps. The first step employs a receiving sensor array to separate the modes by the conventional modal filtering approach. The second step is to estimate the energy and relative arrival times of the various modes which arrive at the receiver. The last step uses the differences of modal travel times to estimate the source range, and uses the ratios of modal energies to estimate the source depth. Here, we employ bandpass filters to divide the received broadband signal into several subfrequency bands, and apply the first and second steps of the previously developed coherent narrowband technique to the subfrequency bands in the time domain. The results obtained from subfrequency bands are then combined incoherently in the frequency domain to produce an estimate of the source position. Numerical simulation of an experiment with explosive sources at the shallow water site of the Yellow Sea is presented     

Source localization using subspace estimation and spatial filtering

Subspace-tracking algorithms have traditionally been unable to deal with a large number of sources and at the same timepreserve their computationally efficiency, since, typically, efficiency goes down as the cube of the signal subspace dimension. One solution to this problem, which is presented in this paper, is to use a newly developed algorithm for the design of spatial filters in matrix form, in order to spatially filter the incoming data snapshots. The result is that the signal subspaces are confined to small angular sectors and, thus, the effective number of signals present is reduced. A method is developed for designing spatial filters in an efficient manner by formulating the design procedure as a rank-deficient linear least-squares problem. The source-bearing estimation is done using the signal-covariance matrix, which is updated using a recently developed fast algorithm, which is necessary in situations where one or more sources are nonstationary. The combination of the subspace-based bearing-estimation and spatial filter algorithms is shown to give good performance in cases of medium signal-to-noise ratio and is capable of resolving sources that are below the resolution limit of both conventional and adaptive beamforming. In addition, the use of spatial filtering makes it possible to estimate bearings for more than N narrow-band sources, using an N-element array. An example illustrating this capability is given.     

Onboard correction of mispointing errors in satellite altimeterreturns [oceanographic measurement]

An investigation to determine whether useful onboard mispointing corrections to satellite altimeter measurements for errors in antenna mispointing can be made with the European Research Satellite (ERS-1) altimeter is reported. An analytic model of the nonlinear mispointing control loop is developed and the step response and signal-to-noise ratio (SNR) behavior of the loop in isolation are derived. The ERS-1 altimeter is expected to have a maximum static mispointing error of 0.2° and a maximum harmonic error of 0.1°. Taking these values as typical, it is concluded that with a loop time response of about one minute, it is not possible to correct the biased estimate of backscattering coefficient without decreasing its SNR. However, it is possible to achieve an unbiased estimate with a noise level significantly less than the uncorrected bias, but a successful implementation would require very accurately calibrated range gate samplers     

Indirect estimation of the clay content of clay-rocks using acoustic measurements: New insights from the Montiers-sur-Saulx deep borehole (Meuse,France)

This work benefited from a comprehensive set of logging and mineralogical data that was acquired from the 2-km-deep EST433 borehole of Montiers-sur-Saulx (Meuse, France). A multiple linear regression analysis was performed on three sets of data: (a) sonic data (P- and S-wave velocities), (b) total combinable magnetic resonance (TCMR) porosity data, and (c) X-ray diffraction (XRD) data. The analysis was performed to estimate the clay content in the Callovo-Oxfordian (COx) claystone and other clay-rocks of the stratigraphic column. The inferred statistical relationships were compared to results obtained from a conventional spectral gamma ray (GR) approach.The results indicate that simple linear regressions using only elastic wave velocities (a) accounted for more than 81% of the vertical variability of the clay content in the COx formation (i.e., coefficient regression R² values greater than 81%) and (b) enable the estimation of clay content with the same accuracy as the spectral GR approach. Both approaches, our acoustic regressions and spectral GR methodology, provide estimate errors that are within the range of uncertainties associated with the XRD analysis applied. Moreover, using the whole set of XRD data showed that the elastic wave velocities and the TCMR porosity as explanatory variables are better predictors of total clay content than swelling clay mineral content.Blind estimations of clay content were performed using data acquired in clay-rocks from the same stratigraphic column and in the COx formation located a few kilometers distant in the EST423 borehole. The results demonstrated that the established regressions must be used with caution when vertically and horizontally extrapolating the estimated clay content. This difficulty is partly explained by the influence of the microstructure of the studied clay-rocks, which was insufficiently taken into account via the petrophysical variables considered in this work.     

Experimental measurement of the array bearing error caused bybathymetric refraction

Experimental measurements have been carried out to identify the effects of a realistic bottom bathymetry on detecting a source with a horizontal line array. The measurements have been conducted over a 1:10000 scale model of the Santa Lucia Escarpment. The experiments measured the bearing error obtained in locating a CW source with a horizontal line array using plane-wave beamforming. The error in the detected bearing is caused by the bending of sound rays in the horizontal plane, commonly referred to as horizontal or bathymetric refraction. The results of the experiment demonstrate large bearing errors which vary rapidly and do not increase monotonically with range. The rapid variation of the bearing errors was unexpected and was a result which has not been previously identified. The magnitude of the errors was also a function of the across slope look direction and frequency, with bearing errors as large as 26° for low frequencies. At higher frequencies, the bearing error is reduced. An analytical solution for the acoustic field over a shear supporting sloping bottom has been used to approximate the results of the experiment. The simulation confirmed the trends in the experimental results by showing bearing errors of the same order of magnitude with the same dependence on across slope direction and frequency. Most importantly, the theoretical results also showed a rapidly varying bearing error as a function of across slope range     

Passive sonar detection and localization by matched velocityfiltering

This paper presents a new bearings-only method of detecting and tracking low signal-to-noise ratio (SNR) wideband targets on a constant course and velocity trajectory. A track-before-detect strategy based on matched velocity filtering is adopted using spatial images constructed from a sequence of power bearing map (PBM) estimates accumulated during a track. To lower the threshold SNR for detection, a discrete bank of matched velocity filters integrates the PBM images over a range of hypothesized trajectories, such an approach eliminates the need to estimate the number of targets since signal detection is determined by comparing the output of each matched filter (MF) to a decision threshold. The distribution of the MF output is derived based on a single point target in diffuse noise assumption. Receiver operating characteristic curves show a definite detection gain under low SNR conditions for matched velocity filtering (track-before-detect) over detection from a single PBM     

Waves and diffusion on the sea surface

The frequency spectrum of surface elevations in the presence of wind waves is well known. On this basis, one can estimate the frequency spectrum of vertical velocities in sea-surface waves. Owing to liquid incompressibility, the spectrum of horizontal velocities should have the same frequency dependence. The use of the dispersion equation for waves on the surface of a heavy liquid allows one to obtain to the spatial spectrum of velocities. Therefore, one can estimate the spatial structure function of the velocity field. For short waves and large depths, the structure function increases as r ^1/2, where r is the distance between the points of observations. For long waves and shallow depths h, this increase is proportional to r. The coefficient of turbulent mixing K(r) of pollution spots of size r on the sea surface is now estimated as the product of the spot size and the rms difference of velocities. As a result, depending on r and h, the exponent in the r ⁿ dependence of K(r) may vary between 1.25 and 1.5. This outcome provides an explanation for a scatter in the values of the exponent n, a phenomenon that has been observed by many experimentalists.     

Bearing capacity of offshore umbrella suction anchor foundation in silty soil under varying loading modes

Considering the current disadvantages of present offshore wind turbine foundations, a novel anchor foundation with skirt and branches is proposed, called offshore umbrella suction anchor foundation (USAF). A series of experiments and numerical simulations were performed to explore the bearing capacity of the USAF under various kinds of loading modes. The bearing characteristics and the anchor–soil interactions are described in detail for horizontal static loading, horizontal cyclic loading, and an antidrawing (pullout) test in silty soil. In the static loading test, the load–deflection of the anchor under step loading was analyzed and the normalized curve of the load–deflection was obtained to determine the ultimate horizontal bearing capacity of the anchor under normal working conditions. Under horizontal cyclic loading, the relationship between the plastic cumulative deformation and cyclic number was determined. In addition, the responses of USAF were investigated for a low wave frequency and storm surges. In the drawing test, it was found that a “segmentation phenomenon” occurred during the test. Moreover, a method to identify the maximum antidrawing load of USAF was provided based on dynamic mechanics. The numerical results show that the use of anchor branches and skirt can enhance the bearing performance of USAF to a certain degree. However, the anchor branch has a slight positive influence on the bearing performance improvement. The USAF is not only similar to a stiff short pile, but a rotation occurs. The failure envelope under composite loading (V-M) was obtained and the changes associated with changes in the aspect ratio of the internal compartment were clarified.     

CRB approximations for a horizontal array observing a narrow-bandtarget with partial coherence

It is demonstrated that simple approximations are available for the Cramer-Rao lower bounds on estimates of range, bearing and frequency using a moving line array. The results are extended to include the effects of the partial coherence of the source     

Water-temperature effect on the spectral density of wind gravity waves and on sea-surface roughness

The results of hourly measurements of sea roughness and hydrometeorological parameters, which were automatically taken from special buoys over a long period of time, were used. These buoys were located in the open regions of both the Atlantic and Pacific oceans in different climatic zones; the mean water-surface temperature around the buoys varies from 1–3°C to 26–28°C. In addition to measurement results, the tables contain data on the spectral density of sea roughness for a wide range of frequencies. An analysis of these data, which was made for a short-wave region of the wind-wave spectrum, for the first time revealed a noticeable watertemperature dependence of the spectral density of wind waves within the frequency range 0.30–0.40 Hz, which corresponds to wave lengths of 9-4 m. The presence of such dependence is explained by a rapid temperature change in kinematic sea-water viscosity. Earlier, we indicated the temperature dependence of only very short spectral components that relate to a centimetric wavelength range. The statistical significance of the watertemperature effect on the spectral density of waves of the indicated frequency is supported by the results of a variance analysis. Temperature variations in the parameter of sea-surface roughness, which is determined, first of all, by the energy of the spectral shortwave region, are estimated. Altimetry is the basic method which is used in remotely determining the velocity of near-water wind. This method allows one to obtain records of deviations of the sea surface from the geoid surface and to calculate (on the basis of these records) the spectral density of wave components of almost any frequency. It is known that the wave-spectrum components in the region of low frequencies are almost always affected by ripple. Consequently, the energy of these components is determined not only by wind forcing, and only the components in the range of frequencies exceeding approximately 0.3 Hz are purely windy. Therefore, using the results of sea-surface altimetry in order to determine the velocity of near-water wind, one should use the spectral densities of wave components in this frequency region. The water-temperature dependence of the spectral density of short wind waves is manifested only in a certain frequency interval, which supports this recommendation.     

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     

First Calibration Results for the SARAL/AltiKa Altimetric Mission Using the Gavdos Permanent Facilities

This work presents the first calibration results for the SARAL/AltiKa altimetric mission using the Gavdos permanent calibration facilities. The results cover one year of altimetric observations from April 2013 to March 2014 and include 11 calibration values for the altimeter bias. The reference ascending orbit No. 571 of SARAL/AltiKa has been used for this altimeter assessment. This satellite pass is coming from south and nears Gavdos, where it finally passes through its west coastal tip, only 6 km off the main calibration location. The selected calibration regions in the south sea of Gavdos range from about 8 km to 20 km south off the point of closest approach. Several reference surfaces have been chosen for this altimeter evaluation based on gravimetric, but detailed regional geoid, as well as combination of it with other altimetric models.

Based on these observations and the gravimetric geoid model, the altimeter bias for the SARAL/AltiKa is determined as mean value of ?46mm ±10mm, and a median of ?42 mm ±10 mm, using GDR-T data at 40 Hz rate. A preliminary cross-over analysis of the sea surface heights at a location south of Gavdos showed that SARAL/AltiKa measure less than Jason-2 by 4.6 cm. These bias values are consistent with those provided by Corsica, Harvest, and Karavatti Cal/Val sites. The wet troposphere and the ionosphere delay values of satellite altimetric measurements are also compared against in-situ observations (?5 mm difference in wet troposphere and almost the same for the ionosphere) determined by a local array of permanent GNSS receivers, and meteorological sensors.