Mathematics Model for Collision Avoidance in Traffic Alert and Collision Avoidance System

In the system of traffic alert and collision avoidance system (TCAS), the time of closest point of approach of the aircraft, horizontal miss distance (HMD), and vertical miss distance (VMD) are the primary parameters to describe the concept of collision avoidance. Firstly, the time of Tau is explained physically which approximates the time to closest point of approach (CPA), and then the formal expression of HMD is induced via the transforming of coordinate which is expressed by relative distance, relative distance rate, and relative acceleration between aircrafts. Finally, the modified model for engineering application is considered.