Probabilistic Closest Point of Approach (CPA) for Collision Risk Monitoring and Analysis

Closest Point of Approach (CPA) is widely used in surveillance-based collision-risk monitoring to estimate the time and minimum lateral and vertical separation between projected aircraft trajectories over a bounded future horizon. Deterministic CPA performs this calculation from the current position, speed, and heading of each aircraft, making it interpretable and computationally efficient. However, in terminal airspace, where aircraft frequently turn, straighten, and capture approach paths, a single projected trajectory may not adequately represent plausible short-term heading evolution. This study develops a probabilistic extension of bounded-horizon CPA, denoted probabilistic P-CPA, that preserves the familiar CPA-family outputs while estimating the probability that a predefined safety volume is entered under short-term heading uncertainty. State-dependent maneuver-transition probabilities and heading-change distributions were learned from historical trajectories and propagated through Monte Carlo simulation, with the assessment recomputed at each synchronized 5 s observation. The method was evaluated using six months of arrivals to San Francisco International Airport runways 28L and 28R. The results show that probabilistic P-CPA identifies scenarios in which deterministic CPA outcomes are sensitive to plausible short-term heading evolution, particularly when aircraft are entering, continuing, or exiting turns. Implications of this capability, limitations, and future work are discussed.