18.3 Implementation of Cartesian and Spherical Tracking Filters
In order to execute any of the tracking filters presented above, one must
We address each of these in the sections below.
18.3.1 Setting Values for q
Consider the prediction equation for the Cartesian state covariance matrix given in (18.15). If we compare the upper left 2 × 2 set of components of the left-hand side of (18.15) with the similar set of components of Q from (18.8), it follows that
Thus, and it follows immediately that qx has units of [distance2/time3]. Or, we could write this as [acceleration2× time] or [acceleration2/Hz].
Assuming that we know something about the maneuverability characteristics of the object we are trying to track, we can estimate the value required for qx. Since our dynamic model is one of constant velocity with zero-mean Gaussian acceleration noise, the value for qx can be set to twice the largest possible maneuver acceleration of the object. It is doubled to account for turns to the left or right. So we set
If a is given in g's (the acceleration due to gravity), we must ...