Multiple source localization using Bayesian theory in an uncertain environment

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 problem, 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 observation 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 dimensionality and difficulty of the inversion. Genetic algorithms are used for the optimization and all the samples of the parameter 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 localization of two sources in an uncertain shallow water environment, and a Monte Carlo performance evaluation study is carried out.