自由飞行下,飞行员可以灵活地选择飞行路线,从而提升了空域的利用率,是解决航路拥挤问题的一种有效方式。为保证自由飞行下的飞行安全,需要对自由飞行下的最小安全间距进行研究,从而为安全间距标准的制定提供理论依据。考虑CNS(通信、导航、监视)性能引起的飞机定位误差和飞机速度误差,以及它们导致飞机间距的误差,建立了基于二维随机变量概率密度的碰撞风险模型。针对所建立的碰撞风险模型,提出了采用最优8阶Steffensen迭代法对最小安全间距进行求解的方法,从而求出自由飞行下基于CNS性能的最小安全间距。算例结果验证了求最小安全间距方法的可行性。 Under free flight, pilots have the flexibility to choose the route of flight, thus improving the airspace utilization, which is an effective way to solve the problem of overcrowding. In order to ensure the flight safety under free flight, the minimum safety clearance under free flight needs to be studied so as to provide a theoretical basis for the establishment of safety clearance standards. Taking into account the errors caused by CNS (communication, navigation and surveillance) performance and aircraft speed errors, and the errors caused by them, this paper establishes a collision risk model based on probability density of two-dimensional random variables. Aiming at the established collision risk model, a method of solving the minimum safety clearance using the optimal 8-order Steffensen iteration method is proposed to find the minimum safety clearance based on CNS performance under free flight. The result of the example verifies the feasibility of finding the minimum safety distance.