Bayesian multiple-source localization 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 statistics, and locations and complex strengths (amplitudes and phases) of multiple sources are considered to be unknown random variables constrained by acoustic data and prior information. Two approaches are considered for estimating source parameters. Focalization maximizes the posterior probability density (PPD) over all parameters using adaptive hybrid optimization. Marginalization integrates the PPD using efficient Markov-chain Monte Carlo methods to produce joint marginal probability distributions for source ranges and depths, from which source locations are obtained. This approach also provides quantitative uncertainty analysis for all parameters, which can aid in understanding of the inverse problem and may be of practical interest (e.g., source-strength probability distributions). In both approaches, 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. Examples are presented of both approaches applied to single- and multi-frequency localization of multiple sources in an uncertain shallow-water environment, and a Monte Carlo performance evaluation study is carried out.

Bayesian tracking of multiple acoustic sources in an uncertain ocean environment

“…Source strengths and noise variances are treated by applying analytic ML solutions to express these parameters in terms of the explicit parameters, which significantly reduces the dimensionality and difficulty of the inverse problem. This is derived 12 by setting @L/@a t ¼ @L/ @ t ¼ 0 in Eq. (1) to obtain ML solutionŝ…”

“…PASs are evaluated efficiently by marginalizing (sampling) over different types of parameters using different algorithms, as discussed fully in Ref. 12. To summarize briefly here, source locations and environmental properties are treated as explicit parameters and marginalized using Markov-chain Monte Carlo methods 14 (Metropolis-Hastings sampling and Gibbs sampling, respectively).…”

“…Rather than sampling explicitly over source strengths and noise variance, analytic maximum-likelihood (ML) expressions 9,12 were applied that allowed these parameters to be sampled as an implicit function of environmental and source-location parameters, an approach that significantly reduced the dimensionality of the inversion. This paper generalizes the Bayesian approach of multiple-source localization in an uncertain environment 12 to the tracking problem. The parameterization is extended to include the locations and complex strengths of multiple sources at multiple time samples, and constraints on maximum source speed are included as interparameter prior information.…”

“…1,2 Challenging problems in matched-field processing include environmental mismatch, 1,[3][4][5][6][7][8] and localization/tracking of multiple interfering sources. [9][10][11][12] This letter develops and illustrates a Bayesian tracking approach which addresses both of these issues. Environmental mismatch has been addressed for localization/tracking of a single source by including uncertain water-column and/or seabed properties as additional unknown model parameters in an augmented inverse problem.…”

Depth classification of underwater targets based on complex acoustic intensity of normal modes

“…Baggenstoss (2011) carried out localization research of multiple interfering sperm whales using time difference. Dosso and Wilmut (2011) researched multiple underwater targets' localization. Michalopoulou et al (2011) investigated the passive tracking algorithm based on particle * Corresponding author.…”