Swath bathymetry using phase difference: theoretical analysis ofacoustical measurement precision

The phase difference principle is widely applied nowadays to sonar systems used for sea floor bathymetry. The apparent angle of a target point is obtained from the phase difference measured between two close receiving arrays. Here we study the influence of the phase difference estimation errors caused by the physical structure of the backscattered signals. It is shown that, under certain current conditions, beyond the commonly considered effects of additive external noise and baseline decorrelation, the processing may be affected by the shifting footprint effect: this is due to the fact that the two interferometer receivers get simultaneous echo contributions coming from slightly shifted seabed parts, which results in a degradation of the signal coherence and, hence, of the phase difference measurement. This geometrical effect is described analytically and checked with numerical simulations, both for square- and sine-shaped signal envelopes, its relative influence depends on the geometrical configuration and receiver spacing; it may be prevalent in practical cases associated with bathymetric sonars. The cases of square and smooth signal envelopes are both considered. The measurements close to nadir, which are known to be especially difficult with interferometry systems, are addressed in particular     

两种基于贝叶斯点估计理论的多声源定位方法研究

海洋环境参数失配是制约匹配场定位性能的主要因素之一。为了克服环境失配,本文基于贝叶斯理论,将环境参数与声源的距离和深度一起作为未知量进行反演。然而在进行多声源定位时,反演参数的维数几何增长,极大地增加了反演问题的复杂性和计算量。为此本文将声源强度和噪声方差表示成其极大似然估计值,从而将这些参数进行隐式采样,大大降低了反演的维数和难度。文章比较了两种贝叶斯点估计方法,最大后验概率密度方法和最大边缘后验概率密度方法。最大后验概率密度方法的解是令后验概率密度取得最大值的参数组合,可以利用优化算法快速获得。最大边缘后验概率密度法将其他参数积分,得到目标参数的一维边缘概率分布,分布的最大值为反演结果。该方法得到最优估计值的同时可以获取参数估计的不确定信息。在环境参数和声源参数都未知的情况下,利用蒙特卡洛法在不同信噪比情况下对两种声源定位方法进行分析,实验结果表明：(1)对于敏感参数,如声源距离、水深和海水声速,最大边缘后验概率密度法比最大边缘后验概率密度方法的性能好。(2)对于较不敏感的参数,如海底声速、海底密度和海底声衰减,当信噪比较低时,最大边缘后验概率密度方法能较好地平滑噪声,从而比最大边缘后验概率密度法具有更好的性能。由于声源距离和深度是敏感参数,研究表明最大边缘后验概率密度法提供了一种在不确知环境下更可靠的多声源定位方法。     

Matched field inversion for geoacoustic model parameters usingadaptive simulated annealing

A method is described for the estimation of geoacoustic model parameters by the inversion of acoustic field data using a nonlinear optimization procedure based on simulated annealing. The cost function used by the algorithm is the Bartlett matched-field processor (MFP), which related the measured acoustic field with replica fields calculated by the SAFARI fast field program. Model parameters are perturbed randomly, and the algorithm searches the multidimensional parameter space of geoacoustic models to determine the parameter set that optimizes the output of the MFP. Convergence is driven by adaptively guiding the search to regions of the parameter space associated with above-average values of the MFP. The performance of the algorithm is demonstrated for a vertical line array in a shallow water enviornment where the bottom consists of homogeneous elastic solid layers. Simulated data are used to determine the limits on estimation performance due to error in experimental geometry and to noise contamination. The results indicate that reasonable estimates are obtained for moderate conditions of noise and uncertainty in experimental geometry     

Meter-Scale Seafloor Geodetic Measurements Obtained from Repeated Multibeam Sidescan Surveys

Abstract

We calibrate a technique to use repeated multibeam sidescan surveys in the deep ocean to recover seafloor displacements greater than a few meters. Displacement measurements from seafloor patches (3?km by 20?km) on the port and starboard side of the ship are used to estimate vertical and across-track displacement. We present displacement measurements from a survey of the Ayu Trough southwest of the Marianas Trench using a 12?kHz multibeam. Vertical and across-track displacement errors for the 12?kHz multibeam sonar are typically 0–2?m with RMS uncertainties of 0.25–0.67 m in the across-track and 0.37–0.75 m in the vertical as determined by 3-way closure tests. The uncertainty of the range-averaged sound velocity is a major error source. We estimate that variations in the sound velocity profile, as quantified using expendable bathythermographs (XBTs) during data collection, contribute up to 0.3?m RMS uncertainty in the across-track direction and 1.6?m RMS uncertainty in the vertical direction.     

Integrating Uncertainty Theories with GIS for Modeling Coastal Hazards of Climate Change

Prediction of coastal hazards due to climate change is fraught with uncertainty that stems from complexity of coastal systems, estimation of sea level rise, and limitation of available data. In-depth research on coastal modeling is hampered by lack of techniques for handling uncertainty, and the available commercial geographical information systems (GIS) packages have only limited capability of handling uncertain information. Therefore, integrating uncertainty theory with GIS is of practical and theoretical significance. This article presents a GIS-based model that integrates an existing predictive model using a differential approach, random simulation, and fuzzy set theory for predicting geomorphic hazards subject to uncertainty. Coastal hazard is modeled as the combined effects of sea-level induced recession and storm erosion, using grid modeling techniques. The method is described with a case study of Fingal Bay Beach, SE Australia, for which predicted responses to an IPCC standard sea-level rise of 0.86 m and superimposed storm erosion averaged 12 m and 90 m, respectively, with analysis of uncertainty yielding maximum of 52 m and 120 m, respectively. Paradoxically, output uncertainty reduces slightly with simulated increase in random error in the digital elevation model (DEM). This trend implies that the magnitude of modeled uncertainty is not necessarily increased with the uncertainties in the input parameters. Built as a generic tool, the model can be used not only to predict different scenarios of coastal hazard under uncertainties for coastal management, but is also applicable to other fields that involve predictive modeling under uncertainty.     

Integrating Uncertainty Theories with GIS for Modeling Coastal Hazards of Climate Change

Prediction of coastal hazards due to climate change is fraught with uncertainty that stems from complexity of coastal systems, estimation of sea level rise, and limitation of available data. In-depth research on coastal modeling is hampered by lack of techniques for handling uncertainty, and the available commercial geographical information systems (GIS) packages have only limited capability of handling uncertain information. Therefore, integrating uncertainty theory with GIS is of practical and theoretical significance. This article presents a GIS-based model that integrates an existing predictive model using a differential approach, random simulation, and fuzzy set theory for predicting geomorphic hazards subject to uncertainty. Coastal hazard is modeled as the combined effects of sea-level induced recession and storm erosion, using grid modeling techniques. The method is described with a case study of Fingal Bay Beach, SE Australia, for which predicted responses to an IPCC standard sea-level rise of 0.86 m and superimposed storm erosion averaged 12 m and 90 m, respectively, with analysis of uncertainty yielding maximum of 52 m and 120 m, respectively. Paradoxically, output uncertainty reduces slightly with simulated increase in random error in the digital elevation model (DEM). This trend implies that the magnitude of modeled uncertainty is not necessarily increased with the uncertainties in the input parameters. Built as a generic tool, the model can be used not only to predict different scenarios of coastal hazard under uncertainties for coastal management, but is also applicable to other fields that involve predictive modeling under uncertainty.     

Analysis of swath bathymetry sonar accuracy

The practical limitations of many bottom mapping sonars lie in their ability to accurately estimate the angle of arrival. This paper addresses the accuracy of angle estimation when employed to determine the location of an extended target such as the bottom. A Gaussian model is assumed for the bottom backscatter and the corresponding Cramer-Rao lower bound for the variance of the angle estimate is determined for multi-element linear arrays. The paper focuses on determining the performance of high-resolution swath bathymetry sonars and, therefore, concentrates on the ability to determine bottom location with short pulses. Two error mechanisms, footprint shift and uncorrelated noise, are identified as important contributors to measurement errors. The two-element interferometric sonar configuration is investigated in detail. It is shown through the use of probability distributions, the Cramer-Rao bound, and simulation that it is difficult to get a good estimate of performance through simulation alone. Performance enhancement through pre-estimation and post-estimation averaging of multiple snapshots and changes in performance with pulse length and pulse rise time are also considered. Bottom estimation performance employing multi-element arrays is compared and contrasted with that of the two-element interferometric array. It is determined that there is little benefit associated with the multi-element array in terms of angle estimation performance alone. However, when other considerations such as angle ambiguities, multiple angles of arrival, and physical shortcomings associated with practical arrays are taken into account, the multi-element array is favored.     

Robust regression-based EKF for tracking underwater targets

In underwater target tracking applications, measurement uncertainty and inaccuracies are usually modeled as additive Gaussian noise. The Gaussian model of noise may not be appropriate in many practical systems. The non-Gaussian noise and the model non-linearity arising in a tracking system will seriously affect the tracking performance. This paper discusses one way to create a robust version of the extended Kalman filter for enhanced underwater target tracking. State estimation in the filter is done through the robust regression approach and Welsch's proposal is used in the regression process. Monte Carlo simulation results with heavy-tailed contaminated observation noise demonstrate the robustness of the proposed estimation procedure     

多波束测深误差源对测点位置归算影响研究

针对Rob Hare提出的多波束测点位置归算精度估计模型的不足,建立了顾及各项改正数之间相关性的改进模型.在多波束测点位置归算模型的基础上,分析了影响测点位置归算的各项误差来源,推导了各误差源对测点位置归算精度估计的影响量,结合算例,分别利用两种模型计算了各误差源对测点位置归算精度的影响量级,绘制了各误差源的误差曲线图与总位置误差曲线图,通过对计算结果的分析比较,得出了两种模型在评估多波束测点位置归算精度时存在的差异,由于顾及到改正数间的相关性,认为改进模型更加科学合理.     

Estimating ocean transports with dynamic height moorings: An application in the Atlantic Deep Western Boundary Current at 26°N

Efficient monitoring of large-scale current systems for climate research requires the development of new techniques to estimate ocean transports. Here, a methodology for continuous estimation of dynamic height profiles and geostrophic currents from moored temperature sensors is presented. The technique is applied to moorings deployed in the Atlantic Deep Western Boundary Current at 26.5°N, off Abaco, the Bahamas (WOCE ACM-1 array). Relative geostrophic currents are referenced using bottom pressure sensors and available shipboard direct velocity (lowered-ADCP) sections over the period of the deployment, to obtain a time series of absolute volume transport. Comparison with direct velocity measurements from a complete array of current meters shows good agreement for the mean transport and its variablity on time scales longer than 10 days, but larger variability in the current meter derived transport at time scales shorter than 10 days. A rigorous error analysis assesses the contributions of various error sources in the geostrophic as well as direct transport estimates. Low-frequency drift of the bottom pressure sensors is found to be the largest error source in the geostrophic transport estimates and recommendations for improvement of the technique and related measurement technologies are made.     

Data Uncertainty Estimation in Matched-Field Geoacoustic Inversion

This paper examines a variety of approaches to treating unknown data uncertainties in matched-field geoacoustic inversion. Both optimal parameter estimation via misfit minimization and parameter uncertainty estimation via Gibbs sampling are considered. The misfit is based on the likelihood function for Gaussian-distributed errors, which requires specification of the data variance at each frequency. Unfortunately, independent knowledge of variance is rarely available due to unknown theory errors. Many applications of matched-field minimization implicitly assume that variance effects are uniform over frequency; however, this can be a poor assumption as theory errors generally vary with frequency. Parameter uncertainty estimation to date has used fixed maximum-likelihood (ML) variance estimates, which does not account for the variance uncertainty in estimating parameter uncertainties. This paper considers two new approaches to treating data uncertainty in matched-field inversion: Including variances explicitly as additional (nuisance) parameters in the inversion, and treating variances as implicit unknowns by constraining the misfit according to an ML variance formulation (this includes variance uncertainty without increasing the number of unknown parameters). All of the above approaches are compared for realistic synthetic test cases and for shallow-water acoustic data measured in the Mediterranean Sea as part of the PROpagation channel SIMulator experiment (PROSIM'97).     

Tidal analysis of an equally or randomly spaced record with small number of data samples

Problems in the analysis of short-period tides from an equally or randomly spaced record with a limited number of data samples have been investigated. In dealing with an equally spaced record, the primary cause of estimation error is the interference between the major short-period tides such as M₂, N₂, K₁ and P₁. A measure of the interference is given by a function which decreases in an oscillatory fashion with observational duration and/or difference of frequencies between paired constituents. The iterative Darwin method (IDM), newly introduced, and the least-squares method (LSM) can reduce the interference effectively to obtain accurate estimates. Another source of error is due to the interference between a major tide and a minor tide such as T₂ andv ₂. To hold an accuracy of 1 cm in amplitude, we must employ a long record of around one year, or we must include the influential minor tides among the major tides a priori. In dealing with randomly spaced data or randomly sampled data from a long record, on the other hand, a major source of error lies in the random noise resulting from the long-period tides such as M_m and S_a. If the number of data samples is greater than 360 and if random noise is within ±10 cm, both IDM and LSM can estimate tidal constants with probable errors of about 1 cm in amplitude and a few degrees in phase.     

Modeling Propagation and Reverberation Sensitivity to Oceanographic and Seabed Variability

The propagation of bottom and oceanographic variability through to the variability of acoustic transmissions and reverberation is evaluated with a simple adiabatic model interacting with Gaussian distributed uncertainty in a narrow frequency band. Results show that there is significant sensitivity of time series and reverberation uncertainty to different types of environmental uncertainty. For propagation over uncertain bottoms, it is shown that it is that later part of the time series, corresponding to the highest angle energy reflecting most often off the surface and bottom, that is most sensitive to bottom uncertainty. This implies that the larger reverberation contributions from the highest grazing angles with the largest scattering strength is also the most uncertain. Conversely, it is the lowest angle arrivals which are most sensitive to uncertainty in the sound-speed profile. These behaviors are predicted analytically by the theory [K.D. LePage, in “Impact of Littoral Environmental Variability on Acoustic Predictions and Sonar Performance,” Kluwer, 2002, pp. 353-360].     

A statistical study of acoustic signals backscattered from the seabottom

Backscattering measurements were performed in shallow water on sand, gravel, and clay bottoms. The equipment included a parametric array that emitted pulses of differential frequencies (8 to 40 kHz) with a 3° directivity. The ranges did not exceed 50 m. The grazing angles varied from 4° to 90°. The bottom backscattering strength does not depend on the emitted pulse type (frequency and length). If one fits a Lambert law to the variations of the backscattering strength versus the grazing angle, the value at the origin fluctuates between-15 and-22 dB without any clear effect from the different bottom types. Statistical tests show that under the experimental measurement conditions: (1) the alternative received signal does not generally follow a normal distribution; (2) among five classical distributions in sonar and radar that have been fitted to the detected-integrated signal (exponential, Weibull, chi-2, log-normal, Rice), the best-fitted law is the log-normal; (3) signals backscattered by separated areas of the same bottom can hardly be regarded as stationary and, even less, homogeneous; and (4) with an anisotropic bottom topography the statistical properties depend on the aspect under which this topography is seen     

System-orthogonal functions for sound speed profile perturbation

Empirical orthogonal functions (EOFs) are typically derived from direct measurements of the sound speed profile (SSP) and they are orthogonal in regard to the statistics of the SSP uncertainty. Viewed from the output end of a particular sonar system, however, the effect of an error in one EOF is usually coupled with the effect of the error in another due to the strongly nonlinear relation between the SSP parameters and the system response. In this paper, a new set of basis functions, orthogonal in regard to sonar performance measure, is developed to characterize SSP perturbations. The performance measure used is the Cramer-Rao bound (CRB) for SSP expansion coefficients derived from a full-field random Gaussian signal model; a closed-form, analytical solution is obtained for both the range-independent and adiabatically range-dependent environments. The derived functions make the CRB matrix diagonal, decoupling the errors in the estimation of the expansion coefficients. Compared to the EOFs, the new set of basis functions depends on both the statistics of the sound speed uncertainty and the sound waveguide propagation property; it incorporates the measurement noise as well. The development makes possible the investigation of the relative significance of the individual basis functions in system response; it also provides a novel framework for optimum acoustic parameterization in adaptive rapid environmental assessment.     

A study on propeller noise source localization in a cavitation tunnel

Localizing noise sources in cavitation experiments is an important research subject along with predicting noise levels. A cavitation tunnel propeller noise localization method is presented. Propeller noise measurement experiments were performed in the MOERI cavitation tunnel. To create cavitating conditions, a wake-generating dummy body was devised. In addition, 10 hydrophones were put inside a wing-shaped casing to minimize the unexpected flow inducing noise around the hydrophones. After measuring both of the noises of the rotating propeller behind the dummy body and acoustic signals transmitted by a virtual source, the data were processed via three objective functions based on the ideas of matched field processing and source strength estimation to localize noises on the propeller plane. In this paper, the measured noise analysis and the localization results are presented. Through the experiments and the analysis, it was found that the source localization methods that have been used in shallow water applications could be successfully adapted to the cavitation tunnel experiments.     

Swath bathymetry: principles of operation and an analysis of errors

The principles of swath bathymetry are described, and the main cause of depth error is identified as acoustic interference, particularly from the sea surface. An error analysis is presented which gives the relationship among depth errors, the signal-to-interference ratio, the grazing angle, receiver spacing, and area resolution. It permits a prediction of when its measurement of depth can meet the accuracies required for nautical charting. Ways of reducing multipath interference and of minimizing its effect when it does occur are discussed. Particularly important are area averaging, the use of widely spaced receivers with ambiguities resolved by the vernier technique, and phase tracking for avoiding bias problems     

Depth dependence of noise resulting from ship traffic and wind

Under conditions of distantly generated noise, the noise level is found to decrease with depth in the mid-northeastern Pacific. These data show a decrease in noise level greater than 25 dB between critical depth and the ocean bottom. A result of this decrease is that locally wind-generated noise can be detected on near-bottom receivers for wind speeds less than 10 kn. It is shown that the noise level generated form local sources such as wind and nearby shipping is almost independent of receiver depth. The differences in spectra shape between the distant shipping noise and wind-generated noise and the low noise levels detected near the ocean bottom allow the measurement in the frequency band at 200-500 Hz of local wind noise level for wind speeds less than 10 kn     

Separation of incident and reflected waves in wave–current flumes

A technique is developed to separate the incident and reflected waves propagating on a known current in a laboratory wave–current flume by analyzing wave records measured at two or more locations using a least squares method. It can be applied to both regular and irregular waves. To examine its performance, numerical tests are made for waves propagating on quiescent or flowing water. In some cases, to represent the signal noise and measurement error, white noise is superimposed on the numerically generated wave signal. For all the cases, good agreement is observed between target and estimation.     

Differential phase estimation with the SeaMARCII bathymetricsidescan sonar system

A maximum-likelihood estimator is used to extract differential phase measurements from noisy seafloor echoes received at pairs of transducers mounted on either side of the SeaMARC II bathymetric sidescan sonar system. Carrier frequencies for each side are about 1 kHz apart, and echoes from a transmitted pulse 2 ms long are analyzed. For each side, phase difference sequences are derived from the full complex data consisting of base-banded and digitized quadrature components of the received echoes. With less bias and a lower variance, this method is shown to be more efficient than a uniform mean estimator. It also does not exhibit the angular or time ambiguities commonly found in the histogram method used in the SeaMARC II system. A figure for the estimation uncertainty of the phase difference is presented, and results are obtained for both real and simulated data. Based on this error estimate and an empirical verification derived through coherent ping stacking, a single filter length of 100 ms is chosen for data processing applications