# Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification

arXiv: https://arxiv.org/abs/2506.11639 · HTML: https://mlsanity.com/paper/2506.11639/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 9 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)

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

- [Recursive KalmanNet: Analyse des capacit'es de g'en'eralisation d'un r'eseau de neurones r'ecurrent guid'e par un filtre de Kalman](https://mlsanity.com/paper/2507.14144/) (2025)
- [Learned Memory Attenuation in Sage-Husa Kalman Filters for Robust UAV State Estimation](https://mlsanity.com/paper/2605.18704/) (2026)
- [FW-NKF: Frequency-Weighted Neural Kalman Filters](https://mlsanity.com/paper/2606.02251/) (2026)
- [Hybrid Adaptive Kalman Filtering for Data-Efficient Joint Tracking and Classification](https://mlsanity.com/paper/2606.02767/) (2026)
- [Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning](https://mlsanity.com/paper/2609.28425/) (2026)
- [Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter](https://mlsanity.com/paper/2609.32640/) (2026)

## Abstract (arXiv)

State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Our approach propagates error covariance using the recursive Joseph's formula and optimizes the Gaussian negative log-likelihood. Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.