Necessary conditions for a maximum likelihood estimate to become asymptotically unbiased and attain the Cramer-Rao lower bound. II. Range and depth localization of a sound source in an ocean waveguide.

Analytic expressions for the first order bias and second order covariance of a maximum-likelihood estimate (MLE) are applied to the problem of localizing an acoustic source in range and depth in a shallow water waveguide with a vertical hydrophone array. These expressions are then used to determine necessary conditions on sample size, or equivalently signal-to-noise ratio (SNR), for the localization MLE to become asymptotically unbiased and attain minimum variance as expressed by the Cramer-Rao lower bound (CRLB). These analytic expressions can be applied in a similar fashion to any ocean-acoustic inverse problem involving random data.