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 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. 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.