This paper considers simultaneous localization of multiple acoustic sources when properties of the ocean environment (water column and seabed) are poorly known [1, 2]. A Bayesian formulation is applied in which the environmental parameters, noise statistics, and locations and complex strengths (amplitudes and phases) of multiple sources are considered unknown random variables constrained by acoustic data and prior information. The posterior probability density (PPD) over all parameters is defined and integrated using efficient Markov-chain Monte Carlo methods to produce joint marginal probability densities for source ranges and depth. This approach also provides quantitative uncertainty analysis for all parameters, which can aid in understanding the inverse problem and may be of practical interest (e.g., source-strength probability distributions). Closed-form maximum-likelihood expressions for source strengths and noise variance at each frequency (developed in the following section) allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. An example is presented of multiple-source localization in an uncertain shallow-water environment.
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