  The smoothing task is core to many signal processing applications. A widely
popular smoother is the Rauch-Tung-Striebel (RTS) algorithm, which achieves
minimal mean-squared error recovery with low complexity for linear Gaussian
state space (SS) models, yet is limited in systems that are only partially
known, as well as non-linear and non-Gaussian. In this work we propose RTSNet,
a highly efficient model-based and data-driven smoothing algorithm suitable for
partially known SS models. RTSNet integrates dedicated trainable models into
the flow of the classical RTS smoother, while iteratively refining its sequence
estimate via deep unfolding methodology. As a result, RTSNet learns from data
to reliably smooth when operating under model mismatch and non-linearities
while retaining the efficiency and interpretability of the traditional RTS
smoothing algorithm. Our empirical study demonstrates that RTSNet overcomes
non-linearities and model mismatch, outperforming classic smoothers operating
with both mismatched and accurate domain knowledge. Moreover, while RTSNet is
based on compact neural networks, which leads to faster training and inference
times, it demonstrates improved performance over previously proposed deep
smoothers in non-linear settings.
