Bayesian Sonar Detection Performance Prediction With Source Position Uncertainty Using SWellEx-96 Vertical Array Data

Predicting sonar detection performance is important for the development of sonar systems. The classical sonar equation cannot accurately predict sonar detection performance because it does not incorporate the effect of ocean environmental and source position uncertainty. We propose an analytical receiver operating characteristic (ROC) expression that characterizes the performance of the optimal Bayesian detector in the presence of ocean environmental and source position uncertainty. The approach is based on a statistical model of the environment and a physical model of acoustic propagation, which translates ocean environmental and source position uncertainty to signal wavefront uncertainty. The analytical ROC expression developed in this paper is verified for source position uncertainty due to source motion using both simulated data and real data collected during the Shallow Water Evaluation Cell Experiment (SWellEx-96). The results showed that the primary effect of source position uncertainty on optimal sonar detection performance is captured by the rank that corresponds to the significant eigenvalues of the signal matrix, an ensemble of replica signal wavefronts (normalized acoustic pressure vector) at the receiving array. The results also showed that the proposed ROC expression provides a realistic detection performance prediction for the Bayesian detector for source position uncertainty using real data. The proposed approach to sonar detection performance prediction is much simpler and faster than those using conventional Monte Carlo approaches.     

Performance Analysis for Matched-Field Source Localization: Simulations and Experimental Results

Matched-field methods concern estimation of source locations and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Typical estimation performance demonstrates two fundamental limitations. First, sidelobe ambiguities dominate the estimation at low signal-to-noise ratio (SNR), leading to a threshold performance behavior. Second, most matched-field algorithms show a strong sensitivity to environmental/system mismatch, introducing biased estimates at high SNR. In this paper, some theoretical developments on matched-field performance analysis are summarized, including Bayesian performance bounds and probabilistic ambiguity analysis, both incorporating environmental/system uncertainty/mismatch. Performance analysis is then implemented for source localization in a typical shallow water environment chosen from the Shallow Water Evaluation Cell Experiments (SWellEX). The performance predictions describe the simulations of the maximum-likelihood estimator (MLE) well, including the mean-square error (MSE) in all SNR regions as well as the bias at high SNR. The threshold SNR and bias predictions are also validated through SWellEX experimental data processing. The results suggest the current environmental, acoustic, and statistical modeling has developed to such a level that the optimum theoretical matched-field performance can be achieved in a well-controlled experiment.     

Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables

A key factor for computing environmental contours is the appropriate modeling of the dependence structure among the environmental variables. It is known that all the information on the dependence structure of a set of random variables is contained in the copulas that define their multivariate probability distribution. Provided that copula parameters are estimated by means of statistical inference using observations, recordings, numerical or historical data, uncertainty is unavoidably introduced in their estimates. Parametric uncertainty in the copulas parameters then introduces uncertainty in the environmental contours. This study deals with the assessment of uncertainty in environmental contours due to parametric uncertainty in the copula models that define the dependence structure of the environmental variables. A point estimation approach is adopted to estimate the statistics of the uncertain coordinates of the environmental contours considering they are given in terms of inverse functions of conditional copulas. A case study is reported using copulas models estimated from storm hindcast data for the Gulf of Mexico. Uncertainty in environmental contours of significant wave height, peak period and wind speed is assessed. The accuracy of the point estimation of the mean and variance of the contour coordinates is validated based on Monte Carlo simulations. A parametric study shows the manner in which greater parametric uncertainty induces larger variability in the environmental contours. The influence of parametric uncertainty for different degrees of association is also analyzed. The results indicate that variability between contours considering parametric uncertainty can be meaningful.     

Estimation of Transmission Loss in the Presence of Geoacoustic Inversion Uncertainty

A common problem in sonar system prediction is that the ocean environment is not well known. Utilizing probabilistic based results from geoacoustic inversions we characterize parameters relevant to sonar performance. This paper describes the estimation of transmission loss and its statistical properties based on posterior parameter probabilities obtained from inversion of ocean acoustic array data. This problem is solved by first finding an ensemble of relevant environmental model parameters and the associated posterior probability using a likelihood based inversion of the acoustic array data. In a second step, each realization of these model parameters is weighted with their posterior probability to map into the transmission loss domain. This approach is illustrated using vertical-array data from a recent benchmark data set and from data acquired during the Asian Seas International Acoustics Experiment (ASIAEX) 2001 in the East China Sea. The environmental parameters are first estimated using a probabilistic-based geoacoustic inversion technique. Based on the posterior probability that each of these environmental models fits the ocean acoustic array data, each model is mapped into transmission loss. This enables us to compute a full probability distribution for the transmission loss at selected frequencies, ranges, and depths, which potentially could be used for sonar performance prediction.     

Refraction of Sound in a Horizontally Inhomogeneous, Time-Dependent Ocean

Measurements of the three-dimensional (3-D) structure of a sound-speed field in the ocean with the spatial and temporal resolution required for prediction of acoustic fields are extremely demanding in terms of experimental assets, and they are rarely available in practice. In this study, a simple analytic technique is developed within the ray approximation to quantify the uncertainty in acoustic travel time and propagation direction that results from an incomplete knowledge or purely statistical characterization of sound-speed variability in the horizontal plane. Variation of frequency of an acoustic wave emitted by a narrowband source due to a temporal variation of environmental parameters is considered for deterministic and random media. In a random medium with locally statistically homogeneous, time-dependent 3-D fluctuations of the sound speed, calculation of the signal frequency and bearing angle variances as well as the travel-time bias due to horizontal refraction is approximately reduced to integration of respective statistical parameters of the environmental fluctuations along a ray in a background, range-dependent, deterministic medium. The technique is applied to acoustic transmissions in a coastal ocean, where tidally generated nonlinear internal waves are the prevailing source of sound-speed fluctuations, and in a deep ocean, where the fluctuations are primarily due to spatially diffuse internal waves with the Garrett–Munk spectrum. The significance of 3-D and four-dimensional (4-D) acoustic effects in deep and shallow water is discussed.     

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     

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).     

Study on the uncertainty of the available time under ship fire based on Monte Carlo sampling method

Available safety egress time under ship fire(SFAT) is critical to ship fire safety assessment,design and emergency rescue.Although it is available to determine SFAT by using fire models such as the two-zone fire model CFAST and the field model FDS,none of these models can address the uncertainties involved in the input parameters.To solve this problem,current study presents a framework of uncertainty analysis for SFAT.Firstly,a deterministic model estimating SFAT is built.The uncertainties of the input parameters are regarded as random variables with the given probability distribution functions.Subsequently,the deterministic SFAT model is employed to couple with a Monte Carlo sampling method to investigate the uncertainties of the SFAT.The Spearman’s rank-order correlation coefficient(SRCC) is used to examine the sensitivity of each input uncertainty parameter on SFAT.To illustrate the proposed approach in detail,a case study is performed.Based on the proposed approach,probability density function and cumulative density function of SFAT are obtained.Furthermore,sensitivity analysis with regard to SFAT is also conducted.The results give a high-negative correlation of SFAT and the fire growth coefficient whereas the effect of other parameters is so weak that they can be neglected.     

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.     

Interrelations between matched-field processing and airborne MTIradar

In matched field processing (MFP) the spatial characteristics of a dispersive wave field are exploited to estimate certain parameters of the acoustic field, such as source location or characteristics of the acoustic channel including environmental parameters. In airborne MTI (AMTI) radar, interfering echoes (clutter) are Doppler colored due to the platform motion. Optimum clutter suppression requires space-time or space-frequency processing. Some thoughts concerning cross-fertilization between these two areas are put forward. In particular, the idea of space-time MFP is stressed. A processor for space-time power estimation is proposed     

A hybrid simplex genetic algorithm for estimating geoacousticparameters using matched-field inversion

Matched-fieId inversion (MFI) undertakes to estimate the geometric and geoacoustic parameters in an ocean acoustic scenario by matching acoustic field data recorded at hydrophone array with numerical calculations of the field. The model which provides the best fit to the data is the estimate of the actual experimental scenario. MFI provides a comparatively inexpensive method for estimating ocean bottom parameters over an extensive area. The basic components of the inversion process are a sound propagation model and matching (minimization) algorithm. Since a typical MFI problem requires a large number of computationally intensive sound propagation calculations, both of these components have to be efficient. In this study, a hybrid inversion algorithm which uses a parabolic equation propagation model and combines the downhill simplex algorithm with genetic algorithms is introduced. The algorithm is demonstrated on synthetic range-dependent shallow-water data generated using the parabolic equation propagation model. The performance for estimating the model parameters is compared for realistic signal-to-noise ratios in the synthetic data     

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].     

Wavimeter

A method of extracting wave parameters from surface displacement measured from a moving platform is presented. The article first presents a method for accurately measuring surface displacement using a single beam altimeter and heave sensor. A least squares approach is presented to estimate wave parameters using vessel velocity and perceived wave frequency that eliminates Doppler due to vessel motion. Two techniques for estimating wave frequency are presented: a block data method using MUSIC and a real-time method using demodulation. Sea trial results demonstrate that this method is as effective as a WaveRider buoy for estimating wave parameters.     

Robust broadband matched-field processing: performance in shallowwater

An issue of concern for matched-field processing is the strong dependence between performance and precise knowledge about the environmental parameters. A robust matched-field processor based on minimax robust filtering methods was developed. Here, simulation methods are employed to evaluate the performance of the minimax robust method as well as other robust methods for a range-independent shallow water environment. The performance of the robust methods is compared with that of the nominal processor, that is, the processor based on a single set of environmental parameters thought to be closest to the actual. The matched-field processing performance is evaluated in terms of the peak-to-sidelobe ratio. The simulation results indicate that the robust methods provide significant performance improvements over the nominal processor in the presence of uncertainty in water column sound speed, channel depth, and sound speed in the bottom     

VLF source localization with a freely drifting acoustic sensorarray

The source localization and tracking capability of the freely drifting Swallow float volumetric array is demonstrated with the matched-field processing (MFP) technique using the 14-Hz CW data collected during a 1989 float experiment conducted in the northeast Pacific. Initial MFP of the experimental data revealed difficulties in estimating the source depth and range while the source azimuth estimate was quite successful. The main cause of the MFP performance degradation was incomplete knowledge of the environment. An environment adaptation technique using a global optimization algorithm was developed to alleviate the environmental mismatch problem, allowing the ocean-acoustic environment to be adapted to the acoustic data in a matched-field sense. Using the adapted environment, the 14-Hz source was successfully localized and tracked in azimuth and range within a region of interest using the MFP technique at a later time interval. Two types of environmental parameters were considered, i.e., sound speed and modal wave number. While both approaches yield similar results, the modal wave number adaptation implementation is more computationally efficient     

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。     

A voting-based approach for fast object recognition in underwateracoustic images

This paper describes a voting-based approach for the fast automatic recognition of man-made objects and related attitude estimation in underwater acoustic images generated by forward-looking sonars or acoustic cameras. In general, the continuous analysis of sequences of images is a very heavy task for human operators and this is due to the poor quality of acoustic images. Hence, algorithms able to recognize an object on the basis of a priori knowledge of the model and to estimate its attitude with reference to a global coordinate system are very useful to facilitate underwater operations like object manipulation or vehicle navigation. The proposed method is capable of recognizing objects and estimating their two-dimensional attitude by using information coming from boundary segments and their angular relations. It is based on a simple voting approach directly applied to the edge discontinuities of underwater acoustic images, whose quality is usually affected by some undesired effects such as object blurring, speckle noise, and geometrical distortions degrading the edge detection. The voting approach is robust, with respect to these effects, so that good results are obtained even with images of very poor quality. The sequences of simulated and real acoustic images are presented in order to test the validity of the proposed method in terms of average estimation error and computational load     

基于Sobol法的海底反向散射模型参数敏感度分析

为了对海底声学参数反演中的估计精度做出预估,合理解释反演结果,本文基于Jackson海底声散射模型,利用Sobol算法,对该模型中的耗散系数、速度比等7个参数进行定量的敏感度分析。Sobol算法可以给出参数的一阶敏感度和参数间相互作用的敏感度,适用于分析散射强度的影响因子。仿真结果表明,所选择的声波频率对于参数的敏感度影响不大,模型各参数交互作用较为强烈,速度比的全局敏感度最大,而耗散系数敏感度很小。将参数划分为地声属性参数、粗糙度参数和非均匀性参数,地声属性参数敏感度最大。模型参数敏感度分析结果对于反演有一定的指导作用。     

Rapid geoacoustic characterization: applied to range-dependent environments

The problem of rapid environmental assessment in a range-dependent environment is addressed. For rapid assessment, the exact geoacoustic parameters are not required, nor is it a requirement that the exact structure of the acoustic field (location of peaks and s) be matched by an acoustic prediction model. The parameters that are relevant are the overall transmission loss (incoherent TL), the time spread (/spl tau/), and the slopes of the range/frequency interference patterns (/spl beta/, the waveguide invariant). The rapid geoacoustic characterization algorithm uses a homogeneous single-sediment layer overlying a hard acoustic basement model to optimally match the predicted acoustic observables with those estimated from data. The approach is presented here and is applied to the range-dependent benchmark cases TC1 and TC2 from the Inversion Techniques Workshop held in Gulfport, MS, in May 2001. The technique successfully reproduces the acoustic observables and estimates the sediment sound-speed, density, and attenuation profiles, as well as the sediment thickness.     

不确定海洋环境中基于贝叶斯理论的多声源定位算法

环境参数失配导致定位性能大幅度下降是匹配场定位所面临的难题之一。应用贝叶斯理论对环境聚焦,是当前解决该难题的研究热点。环境聚焦方法的实质是将未知环境参数和声源位置联合优化估计,当出现多个目标时,估计的参数会随着声源个数成倍增加,因此不得不利用有限的观测信息来实现众多参数的估计。本文采用最大似然比方法,获得信号源谱和误差项的最大似然估计,实现这些敏感性较弱参数的间接反演,有效降低了反演参数维数和定位算法复杂度。针对遗传算法的早熟和稳定性差的问题,改进了似然函数的经验表达式。将多维后验概率密度在参数起伏变化范围内积分,得到反演参数的一维边缘概率分布,求解最优值的同时进行反演结果的不确定性分析。本文仿真了位于相同距离、不同深度的两个声源,使用仿真实验验证了提出算法的有效性。