Comparison of focalization and marginalization for Bayesian tracking in an uncertain ocean environment

This paper compares focalization and marginalization approaches to source tracking when uncertain ocean environmental parameters are included, in addition to source locations, in a Bayesian inversion formulation. Focalization consists of determining the source track that maximizes the posterior probability density (PPD) over all source and environmental parameters. An efficient focalization approach is developed by applying the Viterbi algorithm to compute the optimal track from range-depth conditional probability distributions for each realization of the environmental parameters. This allows source locations to be treated implicitly and the optimization to be applied only to environmental parameters, substantially reducing the dimensionality and complexity of the problem. Marginalization consists of first integrating the PPD over the environmental unknowns to obtain a sequence of joint marginal probability distributions over source range and depth along the track. Applying the Viterbi algorithm to these marginal distributions defines the track estimate, and the distributions themselves quantify the track uncertainty. Monte Carlo analysis of the two approaches for a test case involving both geoacoustic and water-column uncertainties indicates that marginalization provides a significantly more reliable approach to tracking in an unknown environment.