Page 400 - Introduction to Information Optics

7.4. Target Tracking 385

of the targets. Any prior knowledge of the targets before tracking will also be
helpful in this association process. For example, if one target is known to travel
much faster than the others, its correlation peak is more likely to be located
farther away from the origin in the velocity plane than those of slower ones.
In the following, a parameter-based data association algorithm using a
Kalman filtering model is described. Assume that the sampling interval dt is
sufficiently short that the dynamic parameters (velocity, acceleration, angular
velocity, etc.) of the targets are fairly consistent within a few sequential frames.
Thus, given the dynamic parameters of a target in the k frame, the parameters
in the next frame should be rather predictable. Let z(k) be the measurement at
the k frame and z(k\k — 1) be the predicted measurement in the k frame, based
upon the information evaluated up to the k — I frame. Then the innovation (or
measurement residue), defined as

v(k) = z(k) - z(k\k - 1), (7.30)

can be used to evaluate the likelihood of association between z(k) and the
target under consideration. In stochastic models, one would evaluate the
normalized squared distance D from the measured z(k) to the current track,
l
D-v'S~ v (7.31)

where v' is the transpose of v and S is the innovation covariance of the target,
which is basically the variance of the estimated states. The values of
z(k\k — 1), S, and the like can be evaluated by applying a standard Kalman filter
to the dynamic model. (The use of Kalman filtering in stochastic modeling is
a well-known subject on its own and will not be discussed here.)
A data association process can be carried out as follows:

Step 1: At the A' — 1 frame, the dynamic parameters of the N targets are
determined at track 1 to N.
Step 2: At the k frame, N new measurements are made, given as a,h,..., N,
The normalized square distances are then computed:

l
D la - v' laSi v la, D }h = v\ hSi '?',;„...,etc.,
and similarly for D 2a, D 2b,..., D 3a,..., and so on.
Step 3: The most likely association is given by choosing the possible combina-
tion of Ds that yields the minimum sum.

To initiate the tracker, all the measurements in the first few tracking cycles
are used to set up multiple potential tracks. Tracks that have inconsistent
dynamic parameters are dropped until only a single track is assigned to each