Effects of sensor placement on acoustic vector-sensor arrayperformance

We consider the role played by the sensor locations in the optimal performance of an array of acoustic vector sensors, First we derive an expression for the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous wholespace and show that it has a block diagonal structure, i.e., the source location parameters are uncoupled from the signal and noise strength parameters. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled from each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or “canonical” location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptotic normalization, which are useful measures in three-dimensional bearing estimation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations. We then show that our previously derived geometrical conditions are also sufficient to ensure that this bound is independent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic     

Sparse Cylindrical Sonar Arrays

Sparse arrays offer a means for reducing the cost and complexity of beamforming systems. Most of the work in the literature has focused on sparse linear arrays with isotropic transducer elements, which simplifies analysis greatly. In this paper, we will focus on multibeam cylindrical arrays using highly directive elements for use in fishery applications, which requires a directionally independent imaging performance in the azimuth direction as well as beam steerability in the elevational direction. To populate such an array, we suggest a low periodicity in the azimuth direction of the array, which ensures a (near) directionally independent imaging performance in this direction. At the same time it reduces the complexity of the problem so that a suggested iterative method can find the optimal layout under the given constraints, within reasonable time. The optimality of the constrained solution is verified using a stochastic optimization procedure, with a “loosened” periodicity constraint. Simulations then show that the proposed layout, having low periodicity in the azimuth direction, has a reduced peak sidelobe level compared to the fully sampled array. All of the layouts have been required to support beam steering from $-$30 $^{circ}$ to 0$^{circ}$ in elevation and in all 360$^{circ}$ in azimuth, without deterioration in performance.      

舷侧阵CBF和OBF的阵增益比较

以舷侧阵作为研究对象,首先介绍了常规波束形成器(CBF)和最佳波束形成器(OBF)的波束输出信号模型,然后推导了信号+噪声场合下的阵增益表达式,比较了在不同信号频率和不同信号源方向角下,CBF和OBF的阵增益,最后在增加了有指向性的CW干扰后,分析了此场合下的阵增益,并比较了不同的信号频率下,干扰源方向角的变化对两类波束形成器阵增益的影响。     

Reverberation rejection with a dual-line towed array

Low-frequency bottom reverberation from explosive sources was measured with a dual-line horizontal towed array during a 1991 system engineering trial. The receiver's parallel line arrays were processed coherently in order to unambiguously resolve the reverberation field in azimuth. Initial beamforming that assumed a straight-and-parallel array configuration led to poor or erroneous ambiguity resolution, suggesting the system was deformed significantly from the assumed shape. In the absence of reliable shape measurement data, the array shape was deduced acoustically using tow ship signals and the direct blast of an explosive source. The estimated shape was then used in a shape-compensated beamformer to produce azimuthally unambiguous estimates of the reverberation field. Backlobe rejection of more than 20 dB was attained for both direct blast and distant reverberation energy     

Accuracy of the spatial representation of the seafloor with bathymetric sidescan sonars

When isobath maps of the seafloor are constructed with a bathymetric sidescan sonar system the position of each sounding is derived from estimates of range and elevation. The location of each pixel forming the acoustic backscatter image is calculated from the same estimates. The accuracy of the resulting maps depends on the acoustic array geometry, on the performances of the acoustic signal processing, and on knowledge of other parameters including: the platform's navigation, the sonar transducer's attitude, and the sound rays' trajectory between the sonar and the seafloor. The relative importance of these factors in the estimation of target location is assesed. The effects of the platform motions (e.g. roll, pitch, yaw, sway, surge and heave) and of the uncertainties in the elevation angle measurements are analyzed in detail. The variances associated with the representation (orientation and depth) of a plane, rectangular patch of the seafloor are evaluated, depending on the geometry of the patch. The inverse problem is addressed. Its solution gives the lateral dimensions of the spatial filter that must be applied to the bathymetric data to obtain specified accuracies of the slopes and depths. The uncertainty in the estimate of elevation angle, mostly due to the acoustic noise, is found to bring the main error contribution in across-track slope estimates. It can also be critical for along-track slope estimates, overshadowing error contributions due to the platform's attitude. Numerical examples are presented.On leave at the Naval Research Laboratory, Code 7420, Washington D.C. 20375-5350, U.S.A.     

Effects of random phase changes on the formation of synthetic aperture radar imagery

The effects of Gaussian random and linear phase change on the response of the matched azimuth processor of a synthetic aperture imaging radar is analyzed numerically.     

Directional ocean wave spectra using buoy azimuth, pitch, and rollderived from magnetic field components

Buoy azimuth, pitch, and roll, when used with measurements of buoy vertical acceleration, can provide directional wave spectra. Earlier work, which considered effects of buoy hull magnetism, showed that azimuth can be determined from magnetic field measurements (K.E. Steele and J.C. Lau, 1986). This work is extended to show that buoy pitch and roll, and thus buoy slopes, can also be determined from the same measurements. These slopes can be determined from measurements of the magnetic field components inside the hull along two orthogonal axes parallel to the deck of a buoy. Algorithms are developed for estimation of azimuth, pitch, and roll angles using these measurements. The algorithms account for residual and induced hull magnetism. Azimuth, pitch, roll, and estimates of directional wave spectra are determined both from the magnetic field measurements and from a conventional wave measurement system on the same buoy. Comparisons show that estimates of directional spectra based on magnetometer-derived pitch and roll agree well     

Depth measurement of remote sources using multipath propagation

A submerged acoustic source radiates narrowband Gaussian noise. Its signal propagates to a remote, large aperture vertical array over a multipath channel whose characteristics may or may not be fully known. The primary concern of this study is the accuracy of source depth estimates obtainable from the array output. Cramer-Rao bounds for the depth estimate are calculated. When the velocity profile is known exactly, the value of the bound is quite insensitive to the precise form of the velocity profile. A bound calculated from a constant velocity profile yields an excellent approximation for many situations likely to be encountered in practice. Introduction of an unknown parameter into the velocity profile has little effect on the Cramer-Rao bound for depth. However, a maximum likelihood estimator of depth working with an inaccurate value of the unknown parameter performs poorly. To obtain satisfactory performance, one must estimate the unknown parameters along with the source depth. Simulations demonstrate the success of this approach     

水下爆炸信号的定位研究

被动声纳中,目标定位的测定只能利用目标声源发出的信号或噪声,爆炸声源与常用的电声式脉冲声纳发射器比较起来,具有某些明显的优点,可代替发射换能器来实现距离和方位的测定.针对水下爆炸声源,采用三元标量阵进行研究,通过确定信号到达各个阵元的时延信息来测定其目标方位和距离,并利用内插方法提高定位精度.实验结果表明,不同位置处爆...     

A new approach for predicting the extreme response of structures

In this article a method to estimate the mean upcrossing intensity, μ(u), of a stochastic process is proposed. It is assumed that the stochastic process is a sum of a Gaussian process and a second-order correction term. The method is based on the two-dimensional Saddlepoint approximation. The accuracy of the method is tested on processes having analytical solutions for μ(u). Numerical examples are given where the stochastic process represents (i) the horizontal response of a floating offshore structure in a Gaussian sea, and (ii) the response of a structure subjected to a Gaussian wind velocity process. In addition, the estimates are compared to empirical upcrossing intensities of simulated responses. For case (ii), the obtained μ(u) estimates are compared to estimates obtained by numerical integration.     

The effect of bedform dynamics on computing suspended sediment fluxes using optical backscatter sensors and current meters

The sensitivity of the suspended sediment flux is tested with respect to rapid changes in bed-level across the surf zone of a sandy beach. The suspended flux was computed using a fixed instrument array, but bed-level changes due to ripple migration caused the instrument elevations to be significantly changed during the course of the experiment. The nominal elevations of the instruments were adjusted during data processing (using the MOBS array) to maintain a fixed elevation with respect to bed-level changes. The resultant suspended sediment concentrations and fluxes were significantly different from the unadjusted data, and for the present data set O(35%) less when averaged over the tide. The maximum difference between adjusted and unadjusted fluxes may be O(260%). The results indicate that changes in bed-level, particularly those due to bedform migration, must be accounted for when processing OBS data if reliable estimates of suspended sediment transport are to be obtained in the field.     

Geoacoustic inversion of range-dependent data with added Gaussian noise

A rotated coordinates inversion algorithm is used on subsets of the Inversion Techniques 2001 Geoacoustic Workshop data, to which white Gaussian noise is added. The resulting data sets are equivalent to noisy broad-band signals received on a horizontal line array (HLA) during a single integration time interval. The inversions are performed using a technique called systematic decoupling using rotated coordinates (SDRC), which expands the original idea of rotated coordinates by using multiple sets of rotated coordinates, each corresponding to a different set of bounds, to systematically decouple the unknowns in a series of efficient simulated annealing inversions. The cost function minimized in the inversion is based on the coherent broad-band correlation between data and model cross spectra, which increases the coherence gain of the signal relative to incoherent noise. Using the coherent broad-band cost function with sparse HLA-like data sets, the SDRC inversion method yields good estimates for the sensitive environmental parameters for signal-to-noise ratios as low as -15 dB.     

Directional spectrum of ocean waves from array measurements using phase/time/path difference methods

Wave direction has for the first time been consistently, accurately and unambiguously evaluated from array measurements using the phase/time/path difference (PTPD) methods of Esteva in case of polygonal arrays and Borgman in case of linear arrays. We have used time series measurements of water surface elevation at a 15-gauge polygonal array, in 8 m water depth, operational at the CERC's Field Research Facility at Duck, North Carolina, USA. Two modifications have been made in the methodology. One modification is that we use the true phase instead of the apparent phase, the other modification being that estimates of wave direction are registered only if the relevant gauges in the array are coherent at 0.01 significance level. PTPD methods assume that in a spectral frequency band the waves approach from a single direction, and are simple, expedient and provide redundant estimates of wave direction. Using Esteva's method with the above modifications, we found that at Duck: (i) the directions of swell and surf beat, when energetic swell is present, conform to the schematic diagram of surf beat generation given by Herbers et al., (ii) surf beat of remote origin occurs when the significant wave height, H_mo, falls below 0.41 m, (iii) the surf beat of remote origin is not normally incident at the shore contrary to Herbers et al. In fact we found that the surf beat of remote origin is incident at angles in excess of 45° with respect to the shore normal, and (iv) the surf beat of remote origin is largely trans-oceanic in origin.     

A semi-empirical sea-spectrum model for scattering coefficient estimation

A semi-empirical sea-spectrum model is proposed to be used in a two-scale radar sea scatter model to obtain estimates of radar backscatter over the frequency bandsLtoKu, the incidence angular range20deg-65deg, the azimuth angular range0deg-180degfrom the wind direction and wind speed range 3.5-30 m/s at 19.5 m above the mean sea level. It is shown that the theoretical estimates obtained are consistent with the existing measurements.     

基于全极化SAR的浙江衢山岛DEM信息提取

数字高程模型(digital elevation model, DEM)是重要的地理信息,合成孔径雷达(synthetic aperture radar, SAR)是提取数字高程模型的有效手段之一。本文以浙江衢山岛部分地区为研究区,利用2013年11月27日的Radarsat-2四极化精细工作模式极化SAR数据计算了研究区方位向两相邻分辨单元之间的极化方位角偏移量,从极化方位角偏移量提取了方位向坡度信息,得到了研究区地形的高程数据,并利用实测数据对提取的DEM信息进行了精度检验。结果表明,在海岸带及近海岛礁区域,单景全极化雷达DEM测量是可行的,计算结果的平均相对误差为20%,造成误差的主要原因是海面杂波造成的起算面的改变以及植被的树枝叶层造成方位角的变化导致的高程计算偏差。     

Source-parameter estimation by approximate maximum likelihood and nonlinear regression

Statistical properties of certain parametric methods for array processing in wave fields are investigated. Potential applications are the classic location problem in underwater acoustics and wavenumber-spectrum analysis in geophysical work. Asymptotic normality of Fourier-transformed outputs of an array of sensors is applied to define approximate likelihood functions to be maximized for source-parameter estimation. Usually, the parameters are those of the spectral-density matrix. Liggett's estimates are approximations of maximum likelihood estimates in this sense. Another possibility is to use conditional likelihood functions. As a consequence, the source parameters can be found by solving nonlinear-regression problems. Approximate solutions of the latter, which enhance certain simple estimates by some iterations related to Fisher's scoring method, compare favorably with Liggett's estimates. Key Words-Array processing, beam forming, applications in passive sonar, radar and geophysical work; parametric methods: maximum likelihood and nonlinear regression; theoretical study and numerical experiments.     

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     

Simulating Realistic-Looking Sediment Ripple Fields

Sandy sediment ripples impact sonar performance in coastal waters through Bragg scattering. Observations from data suggest that sandy ripple elevation relative to the mean seafloor as a function of the horizontal coordinates is not Gaussian distributed; specifically, peak amplitude fading over space associated with a random Gaussian process is largely absent. Such a non-Gaussian nature has implications for modeling acoustic scattering from, and penetration into, sediments. An algorithm is developed to generate ripple fields with a given power spectrum; these fields have non-Gaussian statistics and are visually consistent with data. Higher order statistics of these ripple fields and their implications to sonar detection are discussed.      

Field intercomparison of nearshore directional wave sensors

Five measurement strategies (four in situ, one remote) for estimating directional wave spectra were intercompared in a 1980 experiment at the Coastal Engineering Research Center's Field Research Facility in Duck, NC. The systems included two pressure sensor/biaxial current meter combinations (different manufacturers), a triaxial acoustic current meter, an SXY gauge (square array of four pressure sensors), and a shore-based imaging radar. A detailed error analysis suggests sources for differences in estimated wave spectra from the different instruments; in general, they intercompare favorably. The major deviation among in situ gauges was associated with the triaxial acoustic current meter. Reliance on a vertical velocity measurement (instead of a direct pressure or sea-surface elevation measurement) can contribute additional uncertainty in directional spectral estimates. The imaging radar was successful in distinguishing multiple wave trains at the same frequency, which was not possible with the simple spectral estimation analysis applied to in situ data. However, the radar is not useful in providing accurate estimates of spectral density, nor in distinguishing multiple wave trains of different frequencies coming from the same direction. Selection of a measurement strategy for a particular need depends on the precise data requirements for that application. Although the five tested intercompared well, in practice not all are equally suitable for every application.