This paper describes a Bayesian approach to the problem of simultaneous tracking of multiple acoustic sources in a shallow-water environment in which water-column and seabed properties are not well known. The Bayesian formulation is based on treating the environmental parameters, noise statistics, and locations and complex strengths (amplitudes and phases) of multiple sources as unknown random variables constrained by acoustic data and prior information. Markov-chain Monte Carlo methods are applied to numerically sample the posterior probability density to integrate over unknown environmental parameters in a principal-component space. 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 of the inversion. The result is a set of time-ordered joint marginal probability distributions for the range and depth of each source, from which optimal track estimates and uncertainties are obtained.
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