不确定海洋环境中基于贝叶斯理论的多声源定位算法

Multiple source localization using Bayesian theory in an uncertain environment

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。

Environmental uncertainty often represents the limiting factor in matched-field localization. Within a Bayesian framework, environmental focalization has been widely applied to solve the augmented localization prob- lem, in which the environmental parameters, source ranges and depths 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. It has to estimate lots of unknown parameters by limited observa- tion information. In the approach, the closed-,form maximum-likelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionali- ty and difficulty of the inversion. Genetic algorithms are used for the optimization and all the samples of the param- eter space are used to estimate the a posteriori probabilities of the model parameters. In order to compensate for the precocious disadvantage of genetic algorithm, the likelihood function is expressed as the empirical exponent relation of the cost function. This method integrates the a posterior probability density over environmental parameters to obtain a sequence of marginal probability distributions over source range and depth, from which the most-probable source location and localization uncertainties can be extracted. Examples are presented for multi-frequency localiza- tion of two sources in an uncertain shallow water environment, and a Monte Carlo performance evaluation study is carried out.