Collision risk model for independently operated homogeneous air traffic flows in terminal area

Abstract

Collision risk models (CRM) have been developed and applied so as to determine the safe separation minima and monitor the collision risk level of the airspace. CRMs estimate the expected number of aircraft collisions. Each model employs some assumptions. For instance, the curved trajectories cannot be treated in some CRMs. These models cannot be generally applied for the collision risk estimation of the terminal airspace operation because the trajectories are curved in the terminal airspace. In addition, some CRMs cannot treat the time-dependent position error. The Rice CRM can handle time-dependent position errors and does not assume straight flight contrary to other CRMs. However, it estimates the expected number of collisions of a single pair of aircraft during a specific time interval though most of the other CRMs estimate the ‘total’ collision risk of all the aircraft in the airspace. The total number of possible collisions is often required rather than the expected number of collision of a single pair of aircraft in the application of collision risk models.

Our motivation is to extend the Rice formula so as to calculate the ‘total’ collision risk. We developed a CRM for the ‘total’ collision risk even in the curved-trajectory and time-dependent position error cases. The assumption we made for the derivation of our CRM formula was ‘independently operated homogeneous air traffic flow.’ The Rice CRM was used as the basis of this CRM. We also applied our CRM to the collision risk estimation of independently operated arrival and departure flows.