An analysis of domain-based ship collision risk parameters

According to a lot of contemporary research on ship collision avoidance the classic approach parameters - distance at closest point of approach (DCPA) and time to the closest point of approach (TCPA) - are not sufficient for estimating ship collision risk and for planning evasive manoeuvres. Consequently new measures are introduced, often utilizing the concept of a ship domain. Their drawback, up to this point, was the lack of analytic solutions that would make it possible to efficiently use ship domains in real-time systems where computational time is of essence. The current paper aims to change this, offering analytic formulas for domain-based collision risk parameters: degree of domain violation (DDV) and time to domain violation (TDV). Explicit derivations of formulas for DDV and TDV are presented here for any elliptic domain. For domains of other shapes elliptic approximations are discussed, so that the derived formulas could still be used. A comparison of TCPA/DCPA with domain-based parameters is presented, evidencing the superiority of the latter.