  Horizontal line arrays are often employed in underwater environments to
estimate the direction of arrival (DOA) of a weak signal. Conventional
beamforming (CB) is robust but has wide beamwidths and high-level sidelobes.
High-resolution methods such as minimum-variance distortionless response (MVDR)
and subspace-based MUSIC algorithm, produce low sidelobe levels and narrow
beamwidths, but are sensitive to signal mismatch and require many snapshots and
the knowledge of number of sources. In addition, heteroscedastic noise where
the variance varies across observations and sensors due to nonstationary
environments degrades the conventional methods significantly. This paper
studies DOA in heteroscedastic noise (HN) environment, where the variance of
noise is varied across the snapshots and the antennas. By treating the DOAs as
random variables and the nuisance parameters of the noise variance different
across the snapshots and the antennas, multi-snapshot variational line spectral
estimation (MVALSE) dealing with heteroscedastic noise (MVHN) is proposed,
which automatically estimates the noise variance, nuisance parameters of the
prior distribution, number of sources, and provides the uncertain degrees of
DOA estimates. When the noise variance only varies across the snapshots or the
antennas, the variants of MVHN, i.e., MVHN-S and MVHN-A, can be naturally
developed. Finally, substantial numerical experiments are conducted to
illustrate the proposed algorithms' performance, including a real data set in
DOA application.
