Fastmap: a fast, approximate maximum a posteriori probability parameter estimator with application to robust matched-field processing

Abstract

In many estimation problems, the set of unknown parameters can be divided into a subset of desired parameters and a subset of nuisance parameters. Using a maximum a posteriori (MAP) approach to parameter estimation, these nuisance parameters are integrated out in the estimation process. This can result in an extremely computationally-intensive estimator. This paper proposes a method by which computationally-intensive integrations over the nuisance parameters required in Bayesian estimation may be avoided under certain conditions. The proposed method is an approximate MAP estimator which is much more computationally efficient than direct, or even Monte Carlo, integration of the joint posteriori distribution of the desired and nuisance parameters. As an example of its efficiency, we apply the fast algorithm to matched-field source localization in an uncertain environment.