In applying the EKF to the problem of tracking the Cartesian position and velocity of a ship as it transits a buoy field, a dynamic model of the ships kinematics over time is required along with a model linking the bearing observations to the ships position. Two additional things need to be discussed: how to initialize and how to choose a proper acceleration noise q.
where we have added a Gaussian white noise acceleration noise term vn−1 to allow for small variations and maneuvers in the ships track. Here, we define the time-invariant transition matrix F as
and note that
Define the buoy field observation vector at time tn as
The observation model for each buoy can be defined ...