# 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

(18.100)

Thus, and it follows immediately that q_{x} has units of [distance^{2}/time^{3}]. Or, we could write this as [acceleration^{2}× time] or [acceleration^{2}/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 q_{x}. Since our dynamic model is one of constant velocity with zero-mean Gaussian acceleration noise, the value for q_{x} 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

(18.101)

If a is given in g's (the acceleration due to gravity), we must ...

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