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中文摘要：
自由飞行是解决空域拥挤的有效方式，为保证飞行安全，对自由飞行下的碰撞风险进行研究。首先，假设自由飞行下飞机的定位误差服从正态分布，在平面直角坐标系内，建立2架飞机水平投影面和垂直投影面的随机运动学模型；其次，当2架飞机在2个投影面上的相对运动距离同时小于最小安全间隔时认为碰撞发生，据此建立飞行碰撞风险模型，并利用欧拉（Euler）方法求解；最后，通过Matlab对一算例进行计算，得出碰撞风险概率。将计算结果与实际安全目标等级对比，验证该模型的合理性。
英文摘要：
Free flight is one of the effective methods for solving airspace congestion, so in order to ensure safety of free flight, the collision risk was studied. Assuming that the positioning errors obey the law of normal distribution in free flight, a random kinematics model was built based on the orthogonal coordinates system having horizontal and vertical planes; When the relative distance of the aircrafts in the two planes is less than the minimum safe separation, the collision happens. So a flight collision risk model was built. The Euler method was used to solve collision risk; Finally an example was calculated through Matlab. Comparing the results and practical safety goal level verifies the model.
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