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INTRODUCTION
The Closest Point of Approach (CPA) is an estimated point at which the distance between the own ship and another object target will reach the minimum value. CPA is a valuable quantity in assessing ship safety with regards collision avoidance. CPA is presented in Automatic Radar Plotting Aids (ARPA) to assist in direct estimation of collision risk. CPA consists of two parameters: the Distance at Closest Point of Approach (DCPA) and the Time to Closest Point at Approach (TCPA). These should be obtained by the ship officer on target vessels in order to determine whether the risk of collision exists (Bole et al., 2014). A ship officer then makes the collision avoidance decision taking into account the manoeuvring characteristics of the ship, the tactical situation (course, speed and aspect of target vessels) and the DCPA/TCPA. Furthermore, the CPA may be considered in judging the responsibility of the involved ships in a maritime accident investigation.
Figure 1 (left) shows two ships: ship A and ship B. Over the time series t 1, t 2, t 3, t 4 and t 5, ship A navigates from A 1 to A 5 following a straight trajectory, while ship B navigates from B 1 to B 5 also linearly. Suppose ship A is the own ship and considered as the relative object. The relative motion of the object ship (ship B) is illustrated in Figure 1 (right). Based on both the initial positions and the true velocity vectors of ship A and ship B, the CPA can then be obtained (Sameshima, 1961).
Figure 1.
A situation of ships approaching each other.
[Figure Omitted; See PDF]
As a crucial factor for collision avoidance, CPA is widely used in the maritime industry to obtain the ship domain and assess the navigational risk. CPA was originally introduced when radar was first used to avoid the collision. Radar is an essential safety facility also used by aircraft and other systems. CPA is therefore not only useful for ship safety, but also helpful for aircraft collision avoidance (Kim et al., 2013) and vehicles (Huang and Lin, 2012). Pimontel (2007) looked at the factors that might...