Uncertainty estimation in simultaneous Bayesian tracking and environmental inversion

Abstract

This paper develops a Bayesian approach for two related inverse problems: tracking an acoustic source when ocean environmental parameters are unknown, and determining environmental parameters using acoustic data from an unknown (moving) source. The formulation considers source and environmental parameters as unknown random variables constrained by noisy acoustic data and by prior information on parameter values (e.g., physical limits for environmental properties) and on inter-parameter relationships (limits on radial and vertical source speed). The goal is not simply to estimate parameter values, but to rigorously determine parameter uncertainty distributions, thereby quantifying the information content of the data/prior to resolve source and environmental parameters. Results are presented as marginal posterior probability densities (PPDs) for environmental parameters and joint marginal PPDs for source ranges and depths. Given the numerically intensive inversion, an efficient Markov-chain Monte Carlo importance-sampling approach is developed which combines Metropolis and heat-bath Gibbs' sampling, employs efficient proposal distributions based on a linearized PPD approximation, and considers nonunity sampling temperatures to ensure a complete parameter search. The approach is illustrated with two simulated examples representing tracking a quiet submerged source and geoacoustic inversion using noise from an unknown ship of opportunity. In both cases, source, seabed, and water-column parameters are unknown.

Three-dimensional source tracking in an uncertain environment via Bayesian marginalization

“…Both approaches have been extended to source (rangedepth) tracking in an uncertain environment. [4][5][6] This paper develops a Bayesian marginalization approach to three-dimensional (3D) source tracking in an uncertain shallow-water environment (a previous paper 7 developed 3D focalization-tracking). The approach is applied to experimental data collected with a bottom-moored horizontal line array (HLA) in shallow waters of the Barents Sea, including data due to a continuous-wave towed source and ship noise.…”

“…The PPD sampling applied here follows the development of Dosso and Wilmut, 5 and is carried out via a combination of Metropolis-Hastings sampling of environmental and bearing model parameters and Gibbs sampling of range and depth coordinates. Track constraints are applied as prior information on maximum horizontal and vertical source velocity.…”

“…To increase sampling efficiency, parameter perturbations are drawn from adaptively scaled Cauchy proposal distributions in rotated coordinates, with the initial distribution based on the model covariance matrix for a linearized approximation to the PPD evaluated at the MAP starting model. 5 During a burn-in phase, the model covariance matrix is periodically updated with a nonlinear estimate based on samples collected to that point. PPD sampling then continues until convergence (defined below).…”

“…To ensure complete sampling of the parameter space, sampling at nonunity temperature is employed, with appropriate weighting of the samples in evaluating the integrals. 5 Convergence is evaluated by the Bhattacharyya coefficient…”

Bayesian tracking of multiple acoustic sources in an uncertain ocean environment

“…Matchedfield localization/tracking methods are based on correlating complex acoustic fields observed at a sensor array with replica fields computed numerically for a grid of possible source locations. 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.…”