RTSNET: Learning to Smooth in Partially Known State-Space Models

The smoothing task, which considers recovery of a sequence of hidden state variables from a sequence of noisy observations, 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 in dynamic systems that are represented as linear Gaussian state space (SS) models. However, this modelbased algorithm 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 model-based RTS 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 is shown to outperform previously proposed deep smoothers in non-linear settings.