Models for Nonstationary Stochastic Processes with Applications to Underwater Acoustics.

摘要

Some models for nonstationary stochastic processes with time-varying autocorrelation matrices are presented and applied to real data processes. As probability distributions are complete statistical descriptions of a random variable,the fundamental problems are to find conditional distributions for the process x given observations y in a time interval. The Markov condition and the Gaussian distribution are assumed for the process x. Presuming knowledge of the model parameters,the solutions have been stated as the Kalman-Bucy equations. The model parameters consist of the state-transition matrix,the driving noise covariance matrix and the observation noise covariance matrix. A class of linear filters and digital processors,which have simple computer implementation,is presented. The data acquisition consists of simultaneous processing of hydrophone outputs to produce signal power and noise power measurements of underwater acoustic receptions. The study shows that the signal power process is apparently second-order stochastic and that the second-order model is adequate as a smoothing and prediction filter. The noise process has shipping and biological noise which make effective modeling difficult;by selective elimination of such observations a study of ambient ocean noise is possible. The models are useful in studying these nonstationary stochastic processes. (Author)