Empirical and collocation-point methods for estimation of acoustic field and array response probability density functions

Recent research has investigated the representation of acoustic field uncertainties arising from uncertainties of the acoustic environment, with emphasis placed either on the representation of the acoustic field as a random process or on estimation of the acoustic field probability density function (pdf) at a given receiver location. The present work introduces two methods for estimating acoustic field and array response pdfs. The first method is based on the computation of the empirical characteristic function (ECF) of the acoustic field, derived from a random sample in the acoustic parameter space and computation of the corresponding acoustic fields. The acoustic field pdf estimate is obtained as the Fourier transform of the ECF. The second method is based on approximation of the characteristic function using collocation-point methods, which are based on orthogonal-polynomial approximations of the mapping from the parameter space to the acoustic field. Both methods are investigated in two examples: (1) ...