Unscented KalmanNet: a hybrid deep learning filter with calibrated posterior covariance for nonlinear state estimation

2026-08-04

AI Summary

This work addresses the degraded accuracy and poor covariance calibration of conventional Unscented Kalman Filters (UKF) in nonlinear dynamic systems subject to time-varying noise statistics and model mismatch. To this end, we propose Unscented KalmanNet (UKN), a hybrid recursive estimator that integrates deep learning with the UKF framework. UKN preserves the UKF’s explicit sigma-point covariance propagation and positive definiteness while introducing two neural modules: NoiseNet for bounded multiplicative correction of time-varying noise covariances and GainNet for bounded residual-based adjustment of the analytical gain. A calibration-aware adaptive loss function is designed to jointly optimize state error, covariance consistency, and innovation consistency. Experiments on three synthetic systems and real-world UZH-FPV flight data demonstrate that UKN consistently outperforms UKF, achieving 22.4%–49.7% lower state RMSE and yielding uncertainty estimates—measured by NEES and coverage probability—that are closest to nominal levels, with superior generalization stability.

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.

Problem

• nonlinear state estimation
• covariance calibration
• model mismatch
• time-varying noise
• Unscented Kalman filter

Innovation

• Unscented KalmanNet
• covariance calibration
• hybrid deep learning filter
• noise adaptation
• gain correction