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Aircraft proximity termination conditions for 3D turn centric modes

机译：3D转弯中心模式的飞机接近终止条件

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International airspace design is undergoing significant change that requires formal and rigorous mathematical specifications to assure the safety of flight operations. Aircraft proximity management is one such area. The Point of Closest Approach (PCA) between aircraft flightpaths is the position along a flightpath at which the minima in relative range occurs. To date, PCA has been estimated primarily based on the assumption of a linear extrapolation of the velocity vectors of each aircraft involved, however, this assumption is limiting and aircraft in turning flight must also be considered. A generalised geometric and vector construction for the determination of PCA is presented. A solution based on a characterization of Fermat's method for stationary points is presented that results in a complex transcendental equation. By casting the equation in a determinant structure a co-linearity condition is revealed between three unique 2D points. A novel aspect is that one of these points is a fixed reference point that lies on either the vector between the aircraft turn centres or on one of its extensions providing a reference to determine the location of the PCA. The analytic method can be readily applied in a laboratory test environment or in an automated guidance context. The rigorous proof enables a higher confidence in achieving dependable operations in a safety critical context and in the adequacy of test strategies when developing algorithms for aircraft avionics.
机译：国际空域设计正在发生重大变化，需要正式和严格的数学规范来确保飞行操作的安全性。飞机接近管理就是这样的领域之一。飞机飞行路径之间的最接近进近点（PCA）是沿飞行路径的相对范围最小值发生的位置。迄今为止，PCA的估计主要是基于对所涉及的每架飞机的速度矢量进行线性外推的假设，但是，这种假设是有限的，还必须考虑飞机在转弯飞行中的情况。介绍了用于确定PCA的广义几何和矢量构造。提出了基于费马方法定点特征的解决方案，该解决方案导致了一个复杂的超越方程。通过将方程式转换为行列式结构，可以在三个唯一的2D点之间揭示共线性条件。一个新颖的方面是，这些点之一是固定参考点，该参考点位于飞机转弯中心之间的向量上或其延伸部分之一上，以提供确定PCA位置的参考。该分析方法可以轻松地应用于实验室测试环境或自动化指导环境中。严格的证明使人们更有信心在开发安全的航空电子算法时，在安全关键的情况下实现可靠​​的运行以及测试策略的充分性。

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