Application of Dempster-Shafer theory for the quantification and propagation of the uncertainty caused by the use of AIS data

Abstract

This paper proposes a novel method to quantify the uncertainty inherent to the paths that ships will navigate in the future, from the information provided by the AIS system on the paths followed by the ships in the past. In the framework of the Dempster–Shafer theory, the proposed method analyzes the information contained in a known distribution of vessel traffic on a waterway to construct the corresponding Dempster–Shafer structure. From this structure, using the confidence limits of Kolmogorov–Smirnov, it is possible to estimate the evidential measures (belief and plausibility) of all possible distributions of traffic on that waterway. The interesting facts of this proposal are that these evidential measures are, according to the probabilistic interpretation proposed by Dempster [1], the lower and upper bounds of an interval that contains future distributions of maritime traffic on the waterway under consideration. Therefore, it can be concluded that knowledge of the traffic on a waterway in a given period allows delimit, with a certain confidence level, the uncertainty associated with the randomness of the trajectories that follow the ships during periods of equal duration. The results obtained by the proposed method for the studied case of the Canary Islands are presented, showing reasonable agreement with the results obtained by the software IWRAP Mk2.