Internal wave signal processing: a model-based approach

A model-based approach is proposed to solve the oceanic internal wave signal processing problem that is based on state-space representations of the normal-mode vertical velocity and plane wave horizontal velocity propagation models. It is shown that these representations can be utilized to spatially propagate the modal (depth) vertical velocity functions given the basic parameters (wave numbers, Brunt-Vaisala frequency profile, etc.) developed from the solution of the associated boundary value problem as well as the horizontal velocity components. These models are then generalized to the stochastic case where an approximate Gauss-Markov theory applies. The resulting Gauss-Markov representation, in principle, allows the inclusion of stochastic phenomena such as noise and modeling errors in a consistent manner. Based on this framework, investigations are made of model-based solutions to the signal enhancement problem for internal waves. In particular, a processor is designed that allows in situ recursive estimation of the required velocity functions. Finally, it is shown that the associated residual or so-called innovation sequence that ensues from the recursive nature of this formulation can be employed to monitor the model's fit to the data.