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A Two-Stage Residual Extended Kalman Filter using Extreme Gradient Boosting and Kolmogorov–Arnold Networks for terrain-aided Unmanned Aerial Vehicle Localization in Global Navigation Satellite System-denied environments.

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Title: A Two-Stage Residual Extended Kalman Filter using Extreme Gradient Boosting and Kolmogorov–Arnold Networks for terrain-aided Unmanned Aerial Vehicle Localization in Global Navigation Satellite System-denied environments.
Authors: Abdelkader, Mohamed1 (AUTHOR), Jarraya, Imen1 (AUTHOR) imenjarraya85@gmail.com, Gabr, Khaled1 (AUTHOR), Al-Batati, Abdulrahman S.1 (AUTHOR), AlMusalami, Abdullah1 (AUTHOR), Alahmed, Fatimah1 (AUTHOR), Boulila, Wadii1 (AUTHOR)
Source: Engineering Applications of Artificial Intelligence. Jun2026, Vol. 173, pN.PAG-N.PAG. 1p.
Subjects: Kalman filtering, Machine learning, Drone aircraft, Boosting algorithms, Digital elevation models, Multisensor data fusion
Geographic Terms: Saudi Arabia
Abstract: Unmanned Aerial Vehicles (UAVs) localization in Global Navigation Satellite Systems-denied environments faces significant challenges due to sensor limitations, environmental factors, and the absence of absolute positioning references. Visual-based methods degrade under sparse textures and illumination changes, while traditional sensor fusion approaches suffer from cumulative drift and poor adaptability to dynamic conditions. We propose the Two-Stage Residual Extended Kalman Filter (TSR-EKF), a hybrid framework that incorporates Machine Learning (ML)-based residual corrections into a probabilistic state estimator. The core novelty lies in a clear two-stage residual learning strategy: the approach employs eXtreme Gradient Boosting (XGBoost) for coarse bias removal from terrain-induced and inertial errors, followed by Dense Kolmogorov–Arnold Networks (DenseKAN) for fine nonlinear residual refinement. These corrections are fused with Inertial Measurement Unit velocities and terrain-referenced measurements within an Extended Kalman Filter framework without altering its standard probabilistic structure. We conducted experimental validation using seven UAV flight trajectories over the Taif region, Saudi Arabia. These tests were performed in high-fidelity Gazebo simulations using actual terrain Digital Elevation Models (DEM). The results demonstrate clear and measurable performance gains. The TSR-EKF achieves root-mean-square error (RMSE) reductions of 57.4% to 98.9% compared to traditional EKF methods while maintaining sub-6m positioning accuracy and real-time computational feasibility with processing times under 2.1 ms per update. The framework exhibits exceptional robustness to sparse measurement conditions, making it suitable for mission-critical UAV operations in contested environments. Overall, these results highlight TSR-EKF as a practical and effective solution that combines Kalman filtering reliability with ML adaptability for robust autonomous navigation. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:Unmanned Aerial Vehicles (UAVs) localization in Global Navigation Satellite Systems-denied environments faces significant challenges due to sensor limitations, environmental factors, and the absence of absolute positioning references. Visual-based methods degrade under sparse textures and illumination changes, while traditional sensor fusion approaches suffer from cumulative drift and poor adaptability to dynamic conditions. We propose the Two-Stage Residual Extended Kalman Filter (TSR-EKF), a hybrid framework that incorporates Machine Learning (ML)-based residual corrections into a probabilistic state estimator. The core novelty lies in a clear two-stage residual learning strategy: the approach employs eXtreme Gradient Boosting (XGBoost) for coarse bias removal from terrain-induced and inertial errors, followed by Dense Kolmogorov–Arnold Networks (DenseKAN) for fine nonlinear residual refinement. These corrections are fused with Inertial Measurement Unit velocities and terrain-referenced measurements within an Extended Kalman Filter framework without altering its standard probabilistic structure. We conducted experimental validation using seven UAV flight trajectories over the Taif region, Saudi Arabia. These tests were performed in high-fidelity Gazebo simulations using actual terrain Digital Elevation Models (DEM). The results demonstrate clear and measurable performance gains. The TSR-EKF achieves root-mean-square error (RMSE) reductions of 57.4% to 98.9% compared to traditional EKF methods while maintaining sub-6m positioning accuracy and real-time computational feasibility with processing times under 2.1 ms per update. The framework exhibits exceptional robustness to sparse measurement conditions, making it suitable for mission-critical UAV operations in contested environments. Overall, these results highlight TSR-EKF as a practical and effective solution that combines Kalman filtering reliability with ML adaptability for robust autonomous navigation. [ABSTRACT FROM AUTHOR]
ISSN:09521976
DOI:10.1016/j.engappai.2026.114430