  The paper considers direction of arrival (DOA) estimation from long-term
observations in a noisy environment. In such an environment the noise source
might evolve, causing the stationary models to fail. Therefore a
heteroscedastic Gaussian noise model is introduced where the variance can vary
across observations and sensors. The source amplitudes are assumed independent
zero-mean complex Gaussian distributed with unknown variances (i.e. the source
powers), inspiring stochastic maximum likelihood DOA estimation. The DOAs of
plane waves are estimated from multi-snapshot sensor array data using sparse
Bayesian learning (SBL) where the noise is estimated across both sensors and
snapshots. This SBL approach is more flexible and performs better than
high-resolution methods since they cannot estimate the heteroscedastic noise
process. An alternative to SBL is simple data normalization, whereby only the
phase across the array is utilized. Simulations demonstrate that taking the
heteroscedastic noise into account improves DOA estimation.
