  Statistical signal processing based speech enhancement methods adopt expert
knowledge to design the statistical models and linear filters, which is
complementary to the deep neural network (DNN) based methods which are
data-driven. In this paper, by using expert knowledge from statistical signal
processing for network design and optimization, we extend the conventional
Kalman filtering (KF) to the supervised learning scheme, and propose the neural
Kalman filtering (NKF) for speech enhancement. Two intermediate clean speech
estimates are first produced from recurrent neural networks (RNN) and linear
Wiener filtering (WF) separately and are then linearly combined by a learned
NKF gain to yield the NKF output. Supervised joint training is applied to NKF
to learn to automatically trade-off between the instantaneous linear estimation
made by the WF and the long-term non-linear estimation made by the RNN. The NKF
method can be seen as using expert knowledge from WF to regularize the RNN
estimations to improve its generalization ability to the noise conditions
unseen in the training. Experiments in different noisy conditions show that the
proposed method outperforms the baseline methods both in terms of objective
evaluation metrics and automatic speech recognition (ASR) word error rates
(WERs).
