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

TL;DR

RTSNet is a novel hybrid smoothing algorithm that combines model-based and data-driven approaches, effectively handling model mismatch and non-linearities in state-space models with improved efficiency and accuracy.

Contribution

RTSNet introduces a trainable, deep unfolding-based extension of the RTS smoother, enhancing performance in partially known, non-linear, and non-Gaussian systems.

Findings

RTSNet outperforms classic smoothers under model mismatch.

RTSNet handles non-linearities more effectively than previous methods.

RTSNet achieves faster training and inference with improved accuracy.

Abstract

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.