A Bayesian and Markov chain approach to short-term and long-term personal watercraft trajectory forecasting

Abstract

In this work, vessel position is estimated using a Bayesian approach based on heading, speed, time intervals, and offsets of latitude and longitude. An additional approach using a Markov chain is presented. The trajectory data comes from a cloud-based marine watercraft tracking system that enables remote control of the vessels. Wave height and meteorological reports were used to evaluate the impact of weather on personal watercraft trajectories. One proposed approach to trajectory estimation uses the longitude and latitude offsets, while another uses the speed, heading, and actual time intervals. A long-term forecasting window of up to ten seconds is achieved by dividing trajectories into segments that do not overlap. The limitation this method faces in long-term forecasting inspires more sophisticated machine-learning approaches. The most successful estimation method used one or two previous actual values and a Bayesian approach, proving that using previously predicted values in a chain accumulates errors. Considering environmental variables did not improve the model, highlighting that small watercrafts operate well even in unstable sea states. This occurs because they generate and ride waves, having a larger impact than oceanic currents.