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A new approach is described for assembling feasible ship trajectories from ship position sightings. The ship may or may not be identified on a particular sighting. The proposed algorithm does not attempt to resolve sighting-trajectory assignment ambiguities. No a priori ship motion model is used except for a bound on the maximum speed. The feasible relative ship motion and identity information are encoded into binary matrices. These binary matrices are computed recursively using logical AND and OR operations. The algorithm is analogous to the Kalman filter.