  Speaker localization using microphone arrays depends on accurate time delay
estimation techniques. For decades, methods based on the generalized cross
correlation with phase transform (GCC-PHAT) have been widely adopted for this
purpose. Recently, the GCC-PHAT has also been used to provide input features to
neural networks in order to remove the effects of noise and reverberation, but
at the cost of losing theoretical guarantees in noise-free conditions. We
propose a novel approach to extending the GCC-PHAT, where the received signals
are filtered using a shift equivariant neural network that preserves the timing
information contained in the signals. By extensive experiments we show that our
model consistently reduces the error of the GCC-PHAT in adverse environments,
with guarantees of exact time delay recovery in ideal conditions.
