# Unsupervised Learned Kalman Filtering

arXiv: https://arxiv.org/abs/2110.09005 · HTML: https://mlsanity.com/paper/2110.09005/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 17 of 17)

- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [Backprop KF: Learning Discriminative Deterministic State Estimators](https://mlsanity.com/paper/1605.07148/) (2016)
- [KFNet: Learning Temporal Camera Relocalization using Kalman Filtering](https://mlsanity.com/paper/2003.10629/) (2020)
- [Long Short-Term Memory Kalman Filters:Recurrent Neural Estimators for Pose Regularization](https://mlsanity.com/paper/1708.01885/) (2017)
- [Combining Generative and Discriminative Models for Hybrid Inference](https://mlsanity.com/paper/1906.02547/) (2019)
- [Black box variational inference for state space models](https://mlsanity.com/paper/1511.07367/) (2015)
- [ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection](https://mlsanity.com/paper/1905.10750/) (2019)
- [DeepSIC: Deep Soft Interference Cancellation for Multiuser MIMO Detection](https://mlsanity.com/paper/2002.03214/) (2020)
- [State Space LSTM Models with Particle MCMC Inference](https://mlsanity.com/paper/1711.11179/) (2017)

## Built on by (most cited first, 17 of 17)

- [DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup](https://mlsanity.com/paper/2306.03897/) (2023)
- [Radars for Autonomous Driving: A Review of Deep Learning Methods and Challenges](https://mlsanity.com/paper/2306.09304/) (2023)
- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation](https://mlsanity.com/paper/2306.02271/) (2023)
- [A Survey of Machine Learning Techniques for Improving Global Navigation Satellite Systems](https://mlsanity.com/paper/2406.16873/) (2024)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [Neural Augmented Kalman Filtering with Bollinger Bands for Pairs Trading](https://mlsanity.com/paper/2210.15448/) (2022)
- [Hybrid Data-Driven SSM for Interpretable and Label-Free mmWave Channel Prediction](https://mlsanity.com/paper/2411.11576/) (2024)
- [Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements](https://mlsanity.com/paper/2407.07368/) (2024)
- [LQGNet: Hybrid Model-Based and Data-Driven Linear Quadratic Stochastic Control](https://mlsanity.com/paper/2210.12803/) (2022)
- [Learning Flock: Enhancing Sets of Particles for Multi~Sub-State Particle Filtering with Neural Augmentation](https://mlsanity.com/paper/2408.11348/) (2024)
- [DIMM: Decoupled Multi-hierarchy Kalman Filter for 3D Object Tracking](https://mlsanity.com/paper/2505.12340/) (2025)
- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)
- [VSE: Variational state estimation of complex model-free process](https://mlsanity.com/paper/2601.21887/) (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)

In this paper we adapt KalmanNet, which is a recently pro-posed deep neural network (DNN)-aided system whose architecture follows the operation of the model-based Kalman filter (KF), to learn its mapping in an unsupervised manner, i.e., without requiring ground-truth states. The unsupervised adaptation is achieved by exploiting the hybrid model-based/data-driven architecture of KalmanNet, which internally predicts the next observation as the KF does. These internal features are then used to compute the loss rather than the state estimate at the output of the system. With the capability of unsupervised learning, one can use KalmanNet not only to track the hidden state, but also to adapt to variations in the state space (SS) model. We numerically demonstrate that when the noise statistics are unknown, unsupervised KalmanNet achieves a similar performance to KalmanNet with supervised learning. We also show that we can adapt a pre-trained KalmanNet to changing SS models without providing additional data thanks to the unsupervised capabilities.