Performance analysis of integrated polyspectrum based time delay estimators

The problem of estimating the difference in arrival times of a non-Gaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian (or a class of non-Gaussian) noise of unknown cross-correlation. We analyze the asymptotic performance of some recently proposed differential time-delay estimators which exploit the integrated polyspectrum of the measurements. The proposed estimators are asymptotically maximum-likelihood when attention is confined to the integrated polyspectra of the measurements. Therefore, the performance of the estimators approaches the Cramer-Rao (CR) bound asymptotically. Expressions for the relevant CR bound are derived. Computer simulations are presented comparing actual performance with the CR bounds for a simple example