  In hearing aid applications, an important objective is to accurately estimate
the direction of arrival (DOA) of multiple speakers in noisy and reverberant
environments. Recently, we proposed a binaural DOA estimation method, where the
DOAs of the speakers are estimated by selecting the directions for which the
so-called Hermitian angle spectrum between the estimated relative transfer
function (RTF) vector and a database of prototype anechoic RTF vectors is
maximized. The RTF vector is estimated using the covariance whitening (CW)
method, which requires a computationally complex generalized eigenvalue
decomposition. The spatial spectrum is obtained by only considering frequencies
where it is likely that one speaker dominates over the other speakers, noise
and reverberation. In this contribution, we exploit the availability of an
external microphone that is spatially separated from the hearing aid
microphones and consider a low-complexity RTF vector estimation method that
assumes a low spatial coherence between the undesired components in the
external microphone and the hearing aid microphones. Using recordings of two
speakers and diffuse-like babble noise in acoustic environments with mild
reverberation and low signal-to-noise ratio, simulation results show that the
proposed method yields a comparable DOA estimation performance as the CW method
at a lower computational complexity.
