Structure estimation accuracy in discrete layered media

We consider the problem of estimating structure (interface reflection coefficient values) from noisy reflection observations of a discrete, layered, lossless waveguide; this is a special case of the general acoustic reflection inverse problem. Our approach is to develop a statistical lower bound, the Cramer-Rao bound, on estimator performance. We demonstrate, by computing the bound for the one- and two-reflector cases, that the bound is not merely theoretical but also provides, through its parametric behavior, physical insight into the estimation problem. In addition, we present two estimator structures for this problem, a statistically optimal estimator, (maximum-likelihood), and a suboptimal estimator (based on the special character of the medium's response), and compare their performance. We perform Monte Carlo tests to verify that, for high signal-to-noise ratios, estimator performance is predicted by the Cramer-Rao bound. Moreover, we find that in these regions the ad hoc estimator performs comparably to the maximum likelihood.