The uncertainty behavior of an enhanced three-dimensional (3D) localization scheme for pulsed sources based on relative travel times at a large-aperture three-hydrophone array is studied. The localization scheme is an extension of a two-hydrophone localization approach based on time differences between direct and surface-reflected arrivals, an approach with significant advantages, but also drawbacks, such as left-right ambiguity, high range/depth uncertainties for broadside sources, and high bearing uncertainties for endfire sources. These drawbacks can be removed by adding a third hydrophone. The 3D localization problem is separated into two, a range/depth estimation problem, for which only the hydrophone depths are needed, and a bearing estimation problem, if the hydrophone geometry in the horizontal is known as well. The refraction of acoustic paths is taken into account using ray theory. The condition for existence of surface-reflected arrivals can be relaxed by considering arrivals with an upper turning point, allowing for localization at longer ranges. A Bayesian framework is adopted, allowing for the estimation of localization uncertainties. Uncertainty estimates are obtained through analytic predictions and simulations and they are compared against two-hydrophone localization uncertainties as well as against two-dimensional localization that is based on direct arrivals.

中文翻译：

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具有3个水听器的增强型脉冲源定位：不确定性估计

研究了基于相对孔径在大口径三水听器阵列上的脉冲源的增强型三维（3D）定位方案的不确定性行为。定位方案是基于直接和表面反射的到达之间的时间差的两水听器定位方法的扩展，该方法具有明显的优点，但也有缺点，例如左右歧义，宽边声源的高范围/深度不确定性以及端火源的高度不确定性。这些缺点可以通过添加第三个水听器来消除。如果还知道水平方向的水听器几何形状，则3D定位问题分为两个部分：范围/深度估计问题（仅需要水听器深度）和方位估计问题。使用射线理论考虑了声径的折射。通过考虑具有较高转折点的到达位置，可以放宽存在表面反射到达位置的条件，从而可以将其定位在更长的范围内。采用贝叶斯框架，可以估计本地化的不确定性。不确定性估计是通过分析预测和模拟获得的，并将它们与两水听器定位不确定性以及基于直接到达的二维定位进行比较。可以估计本地化的不确定性。不确定性估计是通过分析预测和模拟获得的，并将它们与两水听器定位不确定性以及基于直接到达的二维定位进行比较。可以估计本地化的不确定性。不确定性估计是通过分析预测和模拟获得的，并将它们与两水听器定位不确定性以及基于直接到达的二维定位进行比较。