Unscented KalmanNet: a hybrid deep learning filter with calibrated posterior covariance for nonlinear state estimation
Summary
This paper introduces Unscented KalmanNet (UKN), a hybrid deep learning filter that augments the Unscented Kalman Filter with learned components to improve state estimation accuracy and covariance calibration under unknown noise statistics and model mismatch. Experiments show significant RMSE reductions over UKF and other KalmanNet variants.
View Cached Full Text
Cached at: 08/06/26, 07:46 AM
# Unscented KalmanNet: a hybrid deep learning filter with calibrated posterior covariance for nonlinear state estimation Source: [https://arxiv.org/abs/2608.04201](https://arxiv.org/abs/2608.04201) [View PDF](https://arxiv.org/pdf/2608.04201) > Abstract:State estimation for nonlinear dynamical systems is commonly performed with the Unscented Kalman filter \(UKF\), which propagates the state moments through deterministic sigma points and reports a posterior covariance at every step\. In practice, however, unknown and time\-varying noise statistics and model mismatch degrade both estimation accuracy and covariance calibration\. Existing learned filters improve accuracy but are largely built on the extended Kalman filter and either forgo an explicit covariance or learn uncertainty without correcting mismatch\-induced gain bias\. This paper introduces the Unscented KalmanNet \(UKN\), a hybrid recursive estimator that augments the UKF with two structurally distinct learned components while preserving its explicit sigma\-point covariance recursion\. NoiseNet predicts time\-varying process and measurement covariances as bounded multiplicative corrections to fixed baselines, guaranteeing positive definiteness, while GainNet applies a bounded residual correction to the analytical gain\. A calibration\-aware training objective combines state error with covariance\- and innovation\-consistency terms through adaptive weights, jointly optimizing accuracy and calibration\. UKN is benchmarked against UKF, KalmanNet, and Bayesian KalmanNet on three synthetic systems and UZH\-FPV real\-flight data\. It achieves the lowest aggregate state\-estimation error in all four examples and reduces RMSE by $26\.4$\-$49\.7\\%$ compared to UKF in the synthetic cases\. Leave\-one\-sequence\-out cross\-validation over 11 flights shows $22\.4\\%$ and $34\.3\\%$ reductions in mean position and velocity RMSE, respectively\. UKN also yields the lowest fold\-to\-fold variability, with normalized NEES and empirical coverage closest to nominal values among the other filters\. ## Submission history From: Minhyeok Ko \[[view email](https://arxiv.org/show-email/c1dd1483/2608.04201)\] **\[v1\]**Tue, 4 Aug 2026 19:58:01 UTC \(7,698 KB\)
Similar Articles
Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filter
This paper presents CA-NKCF, a novel distributed latent state estimator combining partial domain knowledge with deep neural networks, achieving robust performance without noise statistics knowledge, outperforming traditional filters in linear, chaotic, and wireless tracking environments.
Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators
This paper introduces a structured parameterization for noise models in ELTO-based Kalman filters, enabling dynamic adaptation to non-stationary processes and improving state estimation performance in noisy, time-varying environments.
Kalman Delta Networks: Uncertainty-aware Associative Memory
Introduces Kalman Delta Networks, which improve language modeling by reformulating linear attention as a linear-Gaussian state-space model with Kalman-filter updates to track memory uncertainty, yielding efficient approximations that outperform existing linear-attention models.
Response-state Learning for Transferable Vibrational Spectroscopic Characterization with Electron Prior
This paper introduces SO(3) Equivariant Neural Kalman Networks (SENK) for accurate and transferable vibrational spectral prediction, outperforming existing methods and integrating tensor prediction with physics-informed calibration.
A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements
This paper presents a Bayesian filtering approach to learn Lagrangian dynamics from partial, noisy measurements by parameterizing kinetic and potential energies with neural networks and jointly estimating states and parameters via maximum likelihood.