Bayesian Estimation and Tracking: A Practical Guide

7.4 Application of the EKF to the DIFAR Ship Tracking Case Study

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.

7.4.1 The Ship Motion Dynamics Model

The dynamic model can be obtained in vector–matrix form by using the ships state vector defined by (4.1) and combining (4.2) and (4.3) into

(7.76)

where we have added a Gaussian white noise acceleration noise term v_n−1 to allow for small variations and maneuvers in the ships track. Here, we define the time-invariant transition matrix F as

(7.77)

and note that

(7.78)

7.4.2 The DIFAR Buoy Field Observation Model

Define the buoy field observation vector at time t_n as

(7.79)

The observation model for each buoy can be defined ...