A Bayesian and Markov Chain Approach to Short-Term Personal Watercraft Trajectory Forecasting

Abstract

In this work, vessel position for a single future step 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. One or two previous actual or estimated values are used for forecasting. The information comes from a cloud-based marine watercraft tracking system that enables remote control of the vessels. One proposed approach to trajectory estimation uses the longitude and latitude offsets, while another uses the speed, heading, and time intervals. Another estimation method uses a fixed time interval of one second. The fourth and final trajectory estimation method used the actual time intervals. The calculated and the original trajectory are compared using the average Euclidean distances of the corresponding point. The most accurate estimates are for the x and y offsets; however, the y offset is slightly easier to estimate than the x offset. The estimated time interval between points is the least accurate of all the variables. The most successful trajectory estimation method forecasted the x and y offsets with a Bayesian approach using two previous actual values. The limitation of forecasting a single step inspires more sophisticated machine-learning approaches.

Keywords: personal watercraft, trajectory forecasting, Markov chain