The problem of estimating the time-delay of the line-of-sight (LOSS) or direct signal received by an antenna array in a multipath scenario is addressed. This problem is essential in many communication, radar, sonar and navigation systems, since the signal that propagates through the direct path may be the only one that bears useful information for the operation of the receiver. In many of these systems, it is possible to have an approximate a priori knowledge about the direction-of-arrival (DOA) of the direct signal. We analyze several time-delay estimators that exploit this information. In order that they can operate in the presence of co-channel interference (CCI), it is assumed that the noise field has an arbitrary and unknown spatial correlation. We show that the maximum likelihood (ML) estimator is the only one that presents a sufficient robustness against calibration or modeling errors. Starting from the ML estimator, we derive a new method that takes the uncertainty about the steering vector of the LOSS into account.