Real-Time Quantitative Assessment of UAV Air Risks Based on Nonparametric Error Modeling

The mixed operation of large unmanned aerial vehicles (UAVs) and manned aircraft in complex airspace poses a high collision risk, where the accuracy and real-time performance of risk assessment directly affect airspace safety supervision and operational decision-making. To address the limitations of traditional collision probability models, which inadequately characterize aircraft navigation errors and struggle to adapt to complex dynamic operational environments, this paper proposes a real-time collision probability calculation model based on historical trajectory data and nonparametric error modeling. To address the local anomaly problem caused by the discontinuity of trajectory data, a navigation error calculation method based on B-spline clustering fitting was constructed. The absolute errors under different smoothing factors were compared, and the optimal smoothing factor was determined through the Wilcoxon test to resolve local anomalies caused by overfitting. Kernel density estimation was employed for nonparametric modeling of navigation errors, breaking through the inherent Laplace distribution assumption of traditional models, and an analytical model capable of estimating collision probability at any given time was established. To verify the reliability of the proposed model, Monte Carlo simulations were conducted using operational data from real-world scenarios, and the model calculation results were systematically compared with ground-truth values. The results show that, compared with the double-exponential distribution model, the kernel density estimation model improves the calculation accuracy by 36.85%, with smaller error fluctuations across different scenarios. Furthermore, sensitivity analysis was conducted using the random forest algorithm, identifying relative distance as the dominant factor influencing risk. The research findings can provide theoretical support and methodological reference for risk monitoring and operational strategy optimization in complex airspace.