# Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models

arXiv: https://arxiv.org/abs/2110.04738 · HTML: https://mlsanity.com/paper/2110.04738/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 10 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [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)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [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)

## Built on by (most cited first, 6 of 6)

- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Outlier-Insensitive Kalman Filtering Using NUV Priors](https://mlsanity.com/paper/2210.06083/) (2022)
- [LQGNet: Hybrid Model-Based and Data-Driven Linear Quadratic Stochastic Control](https://mlsanity.com/paper/2210.12803/) (2022)
- [Uncertainty-Aware Vision-based Risk Object Identification via Conformal Risk Tube Prediction](https://mlsanity.com/paper/2603.23919/) (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)

Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the underlying statistics, however, deep learning based tracking systems struggle to reliably characterize uncertainty. In this paper, we investigate the ability of KalmanNet, a recently proposed hybrid model-based deep state tracking algorithm, to estimate an uncertainty measure. By exploiting the interpretable nature of KalmanNet, we show that the error covariance matrix can be computed based on its internal features, as an uncertainty measure. We demonstrate that when the system dynamics are known, KalmanNet-which learns its mapping from data without access to the statistics-provides uncertainty similar to that provided by the KF; and while in the presence of evolution model-mismatch, KalmanNet pro-vides a more accurate error estimation.