Bayesian localization of an unknown number of ocean acoustic sources

Abstract

This paper considers localizing an unknown number of ocean acoustic sources when properties of the environment are poorly known. A Bayesian formulation is developed in which environmental parameters, noise statistics, and the number, locations, and complex spectra (amplitudes and phases) of multiple sources are considered unknown random variables constrained by acoustic data and prior information. The number of sources is determined during a burn-in stage by minimizing the Bayesian information criterion using hybrid optimization with an efficient source birth/death scheme. Optimal estimates and marginal posterior probability distributions for source locations are computed employing a variety of sampling approaches. Environmental properties and source locations and are treated as explicit parameters and marginalized using Markov-chain Monte Carlo sampling methods. In particular, environmental parameters are treated using Metropolis-Hastings sampling applied efficiently in a principal-component space, and source locations are treated using Gibbs sampling since the corresponding conditional probability distributions can be computed efficiently using normal-mode methods. Source and noise spectra are sampled implicitly by applying analytic maximum-likelihood solutions expressed in terms of the explicit parameters. This represents an empirical Bayesian approximation within a hierarchical formulation, and significantly reduces the dimensionality and improves sampling efficiency in the inversion. © 2013 Acoustical Society of America.