A model for numerical simulation of nonstationary sonar reverberation using linear spectral prediction

An innovative approach to the numerical generation of nonstationery reverberation time series is presented and demonstrated. The computer simulated reverberation time series are of high quality, in that they are accurate representations of those which would result from an actual sonar system (transmit/receive and horizontal/ vertical beampatterns; pulse type, shape, length, and power; frequency and sampling rate), platform (speed and depth), and environment (wind speed and direction, backscattering strengths, and propagation loss). Volume, surface, and/or bottom reverberation as seen by a multiple beam sonar on a moving platform is generated. The approach utilizes recent developments in linear spectral prediction research in which the spectra of stochastic processes are modeled as rational functions and algorithms are used to efficiently compute optimal estimates of coefficients which specify the spectra. A two-fold sequence is formulated; first, the expected reverberation spectra for all beams are predicted and, second, the stochastic time series are generated from the expected spectra. The expected spectra are predicted using a numerical implementation, referred to as the REVSPEC (reverberation spectrum) model, of a general formulation of Faure, Ol´shevskii, and Middleton. Given the spectra, the Levinson-Durbin method is used to solve the Yule-Walker equations of the autoregressive formulation of linear spectral prediction. The numerical implementation of the approach, referred to as the REVSIM (reverberation simulation) model, produces nonstationary coherent multiple-beam reverberation time series. The formulation of the REVSIM model is presented and typical results given. A comparison is made between the simulation outputs of the REVSIM model and those of the REVGEN (reverberation generator) model, a standard well-accepted time series simulation model, to demonstrate the validity of the new approach.