Bayesian source localization with uncertain Green’s function in an uncertain shallow water oceana
Résumé
Matched-field acoustic source localization is a challenging task when environmental properties of the
oceanic waveguide are not precisely known. Errors in the assumed environment (mismatch) can cause
severe degradations in localization performance. This paper develops a Bayesian approach to improve
robustness to environmental mismatch by considering the waveguide Green’s function to be an
uncertain random vector whose probability density accounts for environmental uncertainty. The
posterior probability density is integrated over the Green’s function probability density to obtain a
joint marginal probability distribution for source range and depth, accounting for environmental
uncertainty and quantifying localization uncertainty. Because brute-force integration in high dimensions
can be costly, an efficient method is developed in which the multi-dimensional Green’s function
integration is approximated by one-dimensional integration over a suitably defined correlation
measure. An approach to approximate the Green’s function covariance matrix, which represents the
environmental mismatch, is developed based on modal analysis. Examples are presented to illustrate
the method and Monte-Carlo simulations are carried out to evaluate its performance relative to other
methods. The proposed method gives efficient, reliable source localization and uncertainties with
improved robustness toward environmental mismatch