# Bayesian KalmanNet: Quantifying Uncertainty in Deep Learning Augmented Kalman Filter

arXiv: https://arxiv.org/abs/2309.03058 · HTML: https://mlsanity.com/paper/2309.03058/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2023.

## Built on by (most cited first, 10 of 10)

- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [DBPnet: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Wheel Load Estimation](https://mlsanity.com/paper/2605.24860/) (2026)
- [Motion Estimation for Multi-Object Tracking using KalmanNet with Semantic-Independent Encoding](https://mlsanity.com/paper/2509.11323/) (2025)
- [Arbitrage-Free Bond and Yield Curve Forecasting with Neural Filters under HJM Constraints](https://mlsanity.com/paper/2511.17892/) (2025)
- [Online Conformal Prediction with Corrupted Feedback](https://mlsanity.com/paper/2605.20515/) (2026)
- [Hybrid Adaptive Kalman Filtering for Data-Efficient Joint Tracking and Classification](https://mlsanity.com/paper/2606.02767/) (2026)
- [Hierarchical Variational Kalman Filtering](https://mlsanity.com/paper/2607.00877/) (2026)
- [Edge-Aware Thermal Infrared UAV Swarm Tracking](https://mlsanity.com/paper/2607.12544/) (2026)
- [Unscented KalmanNet: Structure-Preserving Deep Learning with Calibrated Posterior Uncertainty under Incomplete Physics and Unknown Noise](https://mlsanity.com/paper/2608.04201/) (2026)
- [Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter](https://mlsanity.com/paper/2609.32640/) (2026)

## Abstract (arXiv)

Recent years have witnessed a growing interest in tracking algorithms that augment Kalman Filters (KFs) with Deep Neural Networks (DNNs). By transforming KFs into trainable deep learning models, one can learn from data to reliably track a latent state in complex and partially known dynamics. However, unlike classic KFs, conventional DNN-based systems do not naturally provide an uncertainty measure, such as error covariance, alongside their estimates, which is crucial in various applications that rely on KF-type tracking. This work bridges this gap by studying error covariance extraction in DNN-aided KFs. We begin by characterizing how uncertainty can be extracted from existing DNN-aided algorithms and distinguishing between approaches by their ability to associate internal features with meaningful KF quantities, such as the Kalman Gain (KG) and prior covariance. We then identify that uncertainty extraction from existing architectures necessitates additional domain knowledge not required for state estimation. Based on this insight, we propose Bayesian KalmanNet, a novel DNN-aided KF that integrates Bayesian deep learning techniques with the recently proposed KalmanNet and transforms the KF into a stochastic machine learning architecture. This architecture employs sampling techniques to predict error covariance reliably without requiring additional domain knowledge, while retaining KalmanNet's ability to accurately track in partially known dynamics. Our numerical study demonstrates that Bayesian KalmanNet provides accurate and reliable tracking in various scenarios representing partially known dynamic systems.