Dosso Stan E, Wilmut Michael J
School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada.
J Acoust Soc Am. 2009 Feb;125(2):717-22. doi: 10.1121/1.3056555.
This paper compares focalization and marginalization approaches to source tracking when uncertain ocean environmental parameters are included, in addition to source locations, in a Bayesian inversion formulation. Focalization consists of determining the source track that maximizes the posterior probability density (PPD) over all source and environmental parameters. An efficient focalization approach is developed by applying the Viterbi algorithm to compute the optimal track from range-depth conditional probability distributions for each realization of the environmental parameters. This allows source locations to be treated implicitly and the optimization to be applied only to environmental parameters, substantially reducing the dimensionality and complexity of the problem. Marginalization consists of first integrating the PPD over the environmental unknowns to obtain a sequence of joint marginal probability distributions over source range and depth along the track. Applying the Viterbi algorithm to these marginal distributions defines the track estimate, and the distributions themselves quantify the track uncertainty. Monte Carlo analysis of the two approaches for a test case involving both geoacoustic and water-column uncertainties indicates that marginalization provides a significantly more reliable approach to tracking in an unknown environment.
本文比较了在贝叶斯反演公式中，除源位置外还包含不确定海洋环境参数时，源追踪的聚焦法和边缘化法。聚焦法包括确定在所有源和环境参数上使后验概率密度（PPD）最大化的源轨迹。通过应用维特比算法从环境参数每次实现的距离-深度条件概率分布计算最优轨迹，开发了一种有效的聚焦方法。这使得源位置能够被隐式处理，并且优化仅应用于环境参数，从而大幅降低了问题的维度和复杂性。边缘化法首先对环境未知量上的PPD进行积分，以获得沿轨迹的源距离和深度上的联合边际概率分布序列。将维特比算法应用于这些边际分布可定义轨迹估计，并且这些分布本身量化了轨迹不确定性。对一个涉及地声学和水柱不确定性的测试案例的两种方法进行蒙特卡罗分析表明，在未知环境中，边缘化法提供了一种显著更可靠的追踪方法。
