  The generalized cross correlation (GCC) is regarded as the most popular
approach for estimating the time difference of arrival (TDOA) between the
signals received at two sensors. Time delay estimates are obtained by
maximizing the GCC output, where the direct-path delay is usually observed as a
prominent peak. Moreover, GCCs play also an important role in steered response
power (SRP) localization algorithms, where the SRP functional can be written as
an accumulation of the GCCs computed from multiple sensor pairs. Unfortunately,
the accuracy of TDOA estimates is affected by multiple factors, including
noise, reverberation and signal bandwidth. In this paper, a sub-band approach
for time delay estimation aimed at improving the performance of the
conventional GCC is presented. The proposed method is based on the extraction
of multiple GCCs corresponding to different frequency bands of the cross-power
spectrum phase in a sliding-window fashion. The major contributions of this
paper include: 1) a sub-band GCC representation of the cross-power spectrum
phase that, despite having a reduced temporal resolution, provides a more
suitable representation for estimating the true TDOA; 2) such matrix
representation is shown to be rank one in the ideal noiseless case, a property
that is exploited in more adverse scenarios to obtain a more robust and
accurate GCC; 3) we propose a set of low-rank approximation alternatives for
processing the sub-band GCC matrix, leading to better TDOA estimates and source
localization performance. An extensive set of experiments is presented to
demonstrate the validity of the proposed approach.
