ABSTRACT
This chapter presents a unified approach to the solution of both forced and unforced systems for problems in underwater sound, vibration, signal, and data processing. Prediction of the underwater sound field from solution of the wave equation enables the judicious placement in space of the processing equipment where the received signal is enhanced against the noise. The chapter develops a general solution to a basic canonical problem starting from Abel's formula rather than the Green's function formulation. The solution to a canonical problem in wave propagation is presented first, then applications are carried out to study cases that appear to be at variance with the basic procedure. A versatile approach is presented that systematically reduces to a quadrature problem in prediction and processing of underwater sound and vibration. In estimation, the present approach leads to a Kalman filter formulation with the triangular matrix requiring updates against the latest measurement only, due to its product kernel characteristic.
