In order to associate observations from successive scans, a model for the expected motion of the underlying target is required. The system model used throughout the Sim89 tracker is based on a simple kinematic Kalman filter. Consider, for the moment, motion in one dimension. The model used to describe this motion is
where x, v, a and j are position, velocity, acceleration and jerk () and is a stochastic (noise) contribution to the jerk. The Kalman filter based on Equation 18.1 is completely straightforward, and ultimately depends on a single parameter
The system model of Equation 18.1 is appropriate for describing targets travelling along trajectories with unknown but approximately smooth accelerations. The size of the noise term in Equation 18.2 determines the magnitude of abrupt changes in the acceleration which can be accommodated by the model without loss of track. For the typical noise value quoted in Equation 18.2, scan-to-scan variations are easily accommodated.
During boost phase, the actual trajectories of the targets are, in principle, not known, and the substantial freedom for unanticipated maneuvering implicit in Equations 18.1 and 18.2 is essential. On the other hand, the exact equation of motion for ballistic target (i.e., RVs) is completely known, so that the uncertainties in predicted positions according to the kinematic model are much larger than is necessary. Nonetheless, Equation 18.1 is maintained as the primary system model throughout all phases of the Sim89 tracker. This choice is based primarily on considerations of speed. Evaluations of predicted positions according to Equation 18.1 require only polynomial arithmetic and are much faster than predictions done using the exact equations of motion. Moreover, for the scan times under consideration, the differences between exact and polynomial predictions are certainly small compared to expected sensor measurement errors.
While ``exact'' system models for target trajectories are not used in the tracker per se, they are used for the collection of tracking ``answers'' which are exchanged between tracking systems or between trackers and other elements in the full Sim89 environment. (This ``handover'' issue is discussed in more detail in the next section.)