Cramer–Rao lower bounds applied to shallow water geoacoustic parameter estimation using the distribution of the interference invariant

Abstract

One can exploit the broadband acoustic striation patterns produced by loud merchant ships in shallow water to obtain geoacoustic parameters. One measures these patterns as a function of range and frequency, calculates their two dimensional Fourier transform to produce intensity as a function of wavenumber and delay, then performs an inverse Radon transform to obtain the distribution of the interference invariant. With this observable, one can perform a global inversion for parameters of interest, such as sediment and bottom sound speed, density, and attenuation. If the parameter estimate is unbiased and the observable vector Gaussian has high signal-to-noise ratio, then one can obtain the theoretical minimum variance and covariance associated with the parameters by solving for the Cramer–Rao lower bound (CRLB). In this presentation, the parameters of interest are assumed to be deterministic and observed ‘‘noise’’ is a function not only of additive Gaussian noise at the hydrophone, but also due to uncertainty in other model parameters, such as hydrophone depth and range bias. This talk will present numerically calculated CRLB as a method for determining the performance of this inversion method.