Estimation of Acoustic Propagation Uncertainty Through Polynomial Chaos Expansions

The estimation of sonar system performance in uncertain environments requires the transfer of sound speed, bathymetric and sea surface uncertainty to propagation uncertainty. Currently, methods of estimating the transfer of environmental uncertainty have been based on Monte Carlo simulation of acoustic propagation through an ensemble of environments, or on simplifying assumptions about the physics of propagation either through inhomogeneous media or in the presence of non-separable boundary conditions. In this paper we introduce the polynomial chaos expansion method, which allows the integration of the differential equations of acoustic propagation over a basis expansion that is orthogonal with respect to the probability distribution function describing the environmental variability. The resulting solution converges in a relatively small number of expansion coefficients and may be used to estimate any statistical property of the acoustic field, such as its mean value and its variance