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

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 nonlinear 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 nonlinearities while retaining the efficiency and interpretability of the traditional RTS smoothing algorithm. Our empirical study demonstrates that RTSNet overcomes nonlinearities 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 nonlinear settings.