  Estimating a time-varying spatial covariance matrix for a beamforming
algorithm is a challenging task, especially for wearable devices, as the
algorithm must compensate for time-varying signal statistics due to rapid
pose-changes. In this paper, we propose Neural Integrated Covariance Estimators
for Beamformers, NICE-Beam. NICE-Beam is a general technique for learning how
to estimate time-varying spatial covariance matrices, which we apply to joint
speech enhancement and dereverberation. It is based on training a neural
network module to non-linearly track and leverage scene information across
time. We integrate our solution into a beamforming pipeline, which enables
simple training, faster than real-time inference, and a variety of test-time
adaptation options. We evaluate the proposed model against a suite of baselines
in scenes with both stationary and moving microphones. Our results show that
the proposed method can outperform a hand-tuned estimator, despite the
hand-tuned estimator using oracle source separation knowledge.
