IMPACT OF THE CROSS-TRACK ERROR DISTRIBUTION LAW ON SAFE NAVIGATION IN NARROW WATERS

The paper indicates that navigation in narrow waters requires navigators to use means of passage safety assessment prior to choosing a route. It is pointed out that a relevant factor when assessing the safe passage probability is the cross-track error distribution law, whose impact is the subject of the research. The article analyses recent developments and publications that have begun investigating this subject, and highlights previously unsolved parts of the general problem. The results revealed two equivalent approaches, as well as a navigational safety parameter, which are used to determine the probability of safe navigation in narrow waters on the chosen route. The need to develop advanced predictive vessel motion models is noted, while many researchers study the design of an information system for vessel motion simulation with complex dynamic models and an intelligence system for vessel motion prediction that imitates the learning process of an autonomous control unit created with the use of the artificial neural network. Methods for identification of vessel manoeuvring models are shown. Based on the analysis of vessel hydrodynamics, a nonlinear model frame of vessel manoeuvring is established. The available publications suggest using compound laws of the first and second types for describing random errors in navigation measurements as an alternative to the normal distribution law. The article examines the dependence of the safe narrow waters passage probability on the cross-track error distribution law. The normal law and compound laws of the first and second types are considered as the cross-track error distribution laws. A formula for estimating the safe passage probability in the manoeuvring area is given, and expressions for the distribution function of the normal law and compound laws of both types are obtained. To assess the impact of the cross-track error distribution law for the same route, the safe passage probability for the normal distribution law, as well as compound laws of the first and second types, was calculated. For the same route, the probability of safe passage was calculated with the use of onedimensional and two-dimensional density models. It is shown that the average relative difference between the estimated safe passage probability for both models is 0.3%, which confirms the validity of using a one-dimensional cross-track error distribution density.