Bayesian Estimation and Tracking: A Practical Guide

18.3 Implementation of Cartesian and Spherical Tracking Filters

In order to execute any of the tracking filters presented above, one must

1. specify a set of values for q,

2. generate a Monte Carlo set of noisy data that can be used as observations for the filters, and

3. create an initialization state vector and covariance matrix.

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 [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 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 ...