Page 80 - Fundamentals of Radar Signal Processing

the required threshold is set using interference statistics estimated from the data

itself, a process called constant-false-alarm rate (CFAR) detection. Detection
processing is described in detail in Chap. 6.

1.5.6 Measurements and Track Filtering
Radar systems employ a wide variety of processing operations after the point of
target detection. One of the most common postdetection processing steps, and
one of the three major functions of interest in this text, is tracking of targets, an

essential component of many radar systems. Tracking is comprised of (usually
multiple) measurements of the position of detected targets followed by track
filtering.
The radar signal processor detects the presence of targets using threshold
detection methods. The range, angle, and Doppler resolution cell in which a
target is detected provide a coarse estimate of its location in those coordinates.
Once detected, the radar will seek to refine the estimated range by using signal

processing methods to more precisely estimate the time delay after pulse
transmission at which the threshold crossing occurred, the angle of the target
relative to the antenna mainbeam direction, or its radial velocity. Individual
measurements will have some error due to interference, and so provide a noisy
snapshot of the target location and motion at one instant in time.
The term track filtering describes a higher-level, longer time scale process

of integrating a series of such measurements to estimate a complete trajectory of
the target over time. It is often described as data processing rather than signal
processing. Because there may be multiple targets with crossing or closely
spaced trajectories, track filtering must deal with the problems of determining
which measurements to associate with which targets being tracked, and with
correctly resolving nearby and crossing trajectories. A variety of optimal
estimation techniques have been developed to perform track filtering. An

excellent reference in this area is Bar-Shalom (1988).
Figure 1.25 illustrates a series of noisy measurements in one dimension of
the position of two targets and the filtering of that noisy trajectory using an
extremely simple alpha-beta filter, to be discussed in Chap. 9. The position in
the x dimension versus time for each target is shown by the gray lines, so the
two targets are moving at different velocities along the x axis and one passes the

other at around time step 32. The circle and diamond markers indicate the noisy
radar measurements of position for each. The solid black lines are the smoothed
estimates of position produced by the alpha-beta filter. In part (a) of the figure,
the filter correctly associates the measurements with each target when they
cross, so that each smoothed estimate follows the same target over the
observation time. In Fig. 1.25b, the noise variance is higher, causing the filter to
incorrectly swap the tracks around time step 40. This represents an error in

measurement-to-track data association. A variety of techniques are available to
attempt to address this problem; a few are discussed in Chap. 9.