Adaptive UAV Visual Localisation Based on Improved Gradient-Damping Newton Method

The role of unmanned aerial vehicles (UAVs) in time-sensitive missions such as low-altitude reconnaissance and disaster rescue has gained increasing significance. To address the challenge of visual localisation for UAVs operating in complex terrains under Global Navigation Satellite System (GNSS)-denied environments, this paper proposes an improved adaptive gradient-damped Newton approach to mitigate the trade-off between terrain non-convexity and computational real-time performance. The proposed approach incorporates a terrain-gradient-based dynamic step-size adjustment mechanism that adaptively captures non-linear terrain characteristics in real time and effectively reduces the numerical oscillations typically observed in steep regions when using the standard Newton method. In addition, a tightly coupled vision–geometry framework was developed to constrain cumulative drift during long-range flight. Monte Carlo simulation results demonstrate that the proposed algorithm maintains submeter localisation accuracy while achieving approximately a three-fold improvement in computational efficiency compared with traditional grid-based methods, and a 27.4% increase in convergence speed relative to the standard Newton method. Experiments conducted under high-noise conditions and highly undulating terrains indicate that the approach exhibits strong convergence stability, offering a computationally efficient and robust solution for UAV navigation.