Simultaneous Bayesian localization of multiple sources in an uncertain ocean environment.

Abstract

This paper considers simultaneous localization of multiple acoustic sources when properties of the ocean environment (water column and seabed) are poorly known. A Bayesian formulation is developed in which the environmental parameters, noise variance, and locations and complex strengths (amplitudes and phases) of multiple sources are considered unknown random variables constrained by acoustic data and prior information. Two approaches are considered for estimating source locations and strengths. The first approach, referred to as focalization, maximizes the posterior probability density (PPD) over all parameters using an adaptive hybrid optimization. The second approach, referred to as marginalization, integrates the PPD to produce marginal probability distributions for source positions and strengths, which quantify localization uncertainties. In this approach, 2‐D Gibbs sampling is applied to source ranges and depths, and Metropolis–Hastings sampling is applied in principal‐component space for environmental parameters. In both approaches, closed‐form maximum‐likelihood expressions for source strengths and noise variance allow these parameters to be sampled implicitly rather than explicitly, reducing the dimensionality of the inversion. Examples are presented of both approaches applied to single‐ and multi‐frequency localization of multiple sources in an uncertain shallow‐water environment.