Cosine Density Distribution Based Probabilistic Risk Approach for Modeling Ship Overtaking Candidates in Channels

A method for calculating collision probability is proposed to analyze the risk of collision accidents when ships navigate in free navigation sea areas. Ships navigate in the channel, not in the entire range from negative infinity to positive infinity. Therefore, the normal distribution is not in accordance with the actual situation, which will cause calculation errors. For Gaussian distribution, different channels have different values for the mean mu and standard deviation sigma. It requires a significant amount of work and large sample data to determine the channel parameters. According to the approximately symmetrical distribution and boundedness of ship traffic flow in the channel, we use cosine distribution to describe the overtaking possibility. The error between the overtaking probability corresponding to different density functions and the statistical results of actual automatic identification system (AIS) data are compared. Results show that cosine distribution can better fit the actual ship overtaking probability than that of the Gaussian distribution.