  This paper addresses the problem of sound-source localization (SSL) with a
robot head, which remains a challenge in real-world environments. In particular
we are interested in locating speech sources, as they are of high interest for
human-robot interaction. The microphone-pair response corresponding to the
direct-path sound propagation is a function of the source direction. In
practice, this response is contaminated by noise and reverberations. The
direct-path relative transfer function (DP-RTF) is defined as the ratio between
the direct-path acoustic transfer function (ATF) of the two microphones, and it
is an important feature for SSL. We propose a method to estimate the DP-RTF
from noisy and reverberant signals in the short-time Fourier transform (STFT)
domain. First, the convolutive transfer function (CTF) approximation is adopted
to accurately represent the impulse response of the microphone array, and the
first coefficient of the CTF is mainly composed of the direct-path ATF. At each
frequency, the frame-wise speech auto- and cross-power spectral density (PSD)
are obtained by spectral subtraction. Then a set of linear equations is
constructed by the speech auto- and cross-PSD of multiple frames, in which the
DP-RTF is an unknown variable, and is estimated by solving the equations.
Finally, the estimated DP-RTFs are concatenated across frequencies and used as
a feature vector for SSL. Experiments with a robot, placed in various
reverberant environments, show that the proposed method outperforms two
state-of-the-art methods.
