Objective Functions for Ocean Acoustic Inversion Derived by Likelihood Methods

Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.