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。

Comparison of two Bayesian-point-estimation methods in multiple-source localization

Environmental uncertainty represents the limiting factor in matched-field localization. Within a Bayesian framework, both the environmental parameters, and the source parameters are considered to be unknown variables. However, including environmental parameters in multiple-source localization greatly increases the complexity and computational demands of the inverse problem. In the paper, the closed-form maximumlikelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. This paper compares two Bayesian-point-estimation methods: the maximum a posteriori (MAP) approach and the marginal posterior probability density (PPD) approach to source localization. The MAP approach determines the sources locations by maximizing the PPD over all source and environmental parameters. The marginal PPD approach integrates the PPD over the unknowns to obtain a sequence of marginal probability distribution over source range or depth. Monte Carlo analysis of the two approaches for a test case involving both geoacoustic and water-column uncertainties indicates that: (1) For sensitive parameters such as source range, water depth and water sound speed, the MAP solution is better than the marginal PPD solution. (2) For the less sensitive parameters, such as, bottom sound speed, bottom density, bottom attenuation and water sound speed, when the SNR is low, the marginal PPD solution can better smooth the noise, which leads to better performance than the MAP solution. Since the source range and depth are sensitive parameters, the research shows that the MAP approach provides a slightly more reliable method to locate multiple sources in an unknown environment.