For the purpose of localizing a distant noisy target, or, conversely, calibrating a receiving array, the time delays defined by the propagation across the array of the target-generated signal wavefronts are estimated in the presence of sensor-to-sensor-independent array self-noise. The Cramér-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered beamformers or properly filtered systems of multiplier-correlators can be used to provide efficient estimates. The effect of suboptimally filtering the array outputs is discussed.