Probability Distributions in Coastal Regions for Association of Naval Vessels

A multi-target tracking method requires a data association algorithm to decide which measurements, from a set of many, to use for updating each track. In this paper we will consider a case where the position of multiple marine vessels is measured in a coastal region, and the time span between each measurement set is large. The vessels of interest are assumed to be sufficiently inert in the sense that the vessels intend to maintain a particular cruising speed while traveling to their destination. Moreover, by assuming that the vessels intend to travel the shortest route possible, we have a foundation to assign conditional probabilities to each measured position. We use the fast marching method (FMM) to compute a time-of-arrival (ToA) map which indicates where the vessel can be at a particular time, provided that the initial speed is known and remains constant. The ToA map is then evaluated with respect to a Gaussian distribution which provides a probability density function (pdf) used to evaluate the probability that a new measurement originate from the same vessel as a track.