Near- optimal range and depth estimation using a vertical array in a correlated multipath environment

This paper proposes a near-optimal procedure to localize a single stationar y source in a two-path underwater acoustic environment. The investigation i s for an M-element vertical array with omnidirectional sensors. The range a nd depth estimators are developed using a linear least-squares technique wh en a set of auto- and cross-correlators is used for time difference of arri val (TDOA) estimates. A weighting matrix is derived to achieve the approxim ate maximum likelihood (ML) performance of the weighted least-squares range and depth estimators. The expressions for error variances and covariances of the range and depth estimates are derived with a small error analysis te chnique. It is verified analytically that the error covariance matrix of th e weighted least-squares solutions reaches the Cramer-Rao lower bound in th e small error region. The correlation of the range and depth estimation err ors is investigated. Results show that the range and depth estimation error s are highly correlated in a multipath environment. The accuracy properties of the proposed multipath localization procedure are analyzed using differ ent array configurations. The results show that the performances of the ran ge and depth estimators are significantly improved if the linear-dependent TDOA estimates are included for localizing and that the unweighted range an d depth estimators, using the entire set of TDOA's, are approximately optim al for most of the applications. The theoretical development of error varia nce and covariance expressions of the range and depth estimates, which inco rporates the correlation in the TDOA estimates, is corroborated with Monte Carlo simulations.