Control-Theoretic Framework for Autonomous UAV Navigation in GNSS-Denied Environments via Adaptive Multi-Sensor Fusion

  • Jiafeng Li orcid

    School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China
Article ID: 4733
DOI: https://doi.org/10.59400/adecp4733
Keywords: adaptive control; stochastic differential equations; multi-sensor fusion; optimal control; stability analysis; UAV systems

Abstract

This paper develops a control-theoretic framework for autonomous unmanned aerial vehicle (UAV) navigation in environments where Global Navigation Satellite System (GNSS) signals are degraded or denied. The navigation problem is posed as a stochastic dynamical system: vehicle kinematics and inertial error states are modelled by a nonlinear Itô stochastic differential equation, and heterogeneous sensor observations enter through a family of nonlinear output maps. State estimation is formulated as a matrix Riccati differential equation in which measurement confidence is modulated by a bounded, continuously differentiable weighting law governed by its own first-order differential equation. We prove that, under uniform observability and boundedness of the weighting law, the estimation error is exponentially bounded in mean square, and we obtain an explicit convergence rate that degrades continuously rather than discontinuously as individual sensors lose reliability — a formal statement of graceful degradation. Learning-based feature extraction is incorporated as a bounded exogenous perturbation, and the estimator is shown to be input-to-state stable with respect to it. Trajectory generation is cast as a constrained optimal control problem solved in receding-horizon form, and the estimator–controller interconnection is established as stable by a small-gain argument. A schedulability analysis bounds the sensing-to-actuation latency, making the real-time claim a proved property of the task set. Experiments across five scenarios yield 0.38 m RMSE indoors and 0.72 m in urban canyons, improving on visual-inertial odometry by 41.5% and conventional extended Kalman filtering by 66.1% in indoor flight.

Published
2026-09-01
How to Cite
Li, J. (2026). Control-Theoretic Framework for Autonomous UAV Navigation in GNSS-Denied Environments via Adaptive Multi-Sensor Fusion. Advances in Differential Equations and Control Processes, 33(3). https://doi.org/10.59400/adecp4733
Issue
Vol. 33 No. 3 (2026): In Progress
Section
Article

Copyright (c) 2026 Jiafeng Li

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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