Generalized likelihood ratio test for selecting a geo-acoustic environmental model

A generalized likelihood ratio test is considered for testing acoustic environmental models with application to parameter inversion using an acoustic propagation code. In the following, we use the term “hierarchy of models” to denote a sequence of model structures M₁, M₂, … in which each particular model structure M_m contains all previous ones as special cases. We propose a combined parameter estimation and multiple sequential test for simultaneously determining the model order and its parameters: given the observed data, how many parameters should be included in the model? The last question is important for the order selection problem in hierarchies of models with increasing number of parameters where the observations are corrupted by additive noise. Monte Carlo simulations show the behaviour of the sequential test for selecting a model order as a function of the SNR. Finally, the test is applied to broadband data measured using a vertical array near the island of Elba in the Mediterranean Sea and compared with Akaike´s information criterion