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

arXiv: https://arxiv.org/abs/2110.04717 · HTML: https://mlsanity.com/paper/2110.04717/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2021.

## Built on by (most cited first, 11 of 11)

- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [MoE-Gyro: Self-Supervised Over-Range Reconstruction and Denoising for MEMS Gyroscopes](https://mlsanity.com/paper/2506.06318/) (2025)
- [Outlier-Insensitive Kalman Filtering: Theory and Applications](https://mlsanity.com/paper/2309.09505/) (2023)
- [Learning Flock: Enhancing Sets of Particles for Multi~Sub-State Particle Filtering with Neural Augmentation](https://mlsanity.com/paper/2408.11348/) (2024)
- [Q-Net: Queue Length Estimation via Kalman-based Neural Networks](https://mlsanity.com/paper/2509.24725/) (2025)
- [Filtering Jump Markov Systems with Partially Known Dynamics: A Model-Based Deep Learning Approach](https://mlsanity.com/paper/2511.09569/) (2025)
- [Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filter](https://mlsanity.com/paper/2606.28441/) (2026)
- [RTS Smoother-Guided Learning of Physics-Based Neural Differential Models](https://mlsanity.com/paper/2607.15180/) (2026)
- [Unscented KalmanNet: Structure-Preserving Deep Learning with Calibrated Posterior Uncertainty under Incomplete Physics and Unknown Noise](https://mlsanity.com/paper/2608.04201/) (2026)

## Abstract (arXiv)

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.