Maximum likelihood propagation-delay estimation in unknown correlated noise using antenna arrays: application to Global Navigation Satellite Systems

The problem of estimating the propagation-delay of a desired signal in the presence of interferences and multipath propagation is addressed. This paper presents the maximum likelihood (ML) propagation-delay estimator for a signal arriving at a sensor array. The novel characteristic herein is that the desired signal impinges on the array with a known steering vector. This fact allows to assume an unknown and arbitrary spatially colored noise.. The Cramér-Rao bound (CRB) for the problem at hand is derived and numerically compared with the variance of the MLE. The MLE is applied to the Global Navigation Satellite Systems, in order to reduce the serious performance deterioration that the interferences and the multipath propagation produce. We show that in presence of coherent reflections of the desired signal the presented estimator is no longer the MLE and becomes biased. However, its bias is much lower than that of other conventional estimators.