Page 531 - Fundamentals of Radar Signal Processing

(6.173)

where is the estimate of the clutter reflectivity at time n (n usually indexes
complete radar scans of an area) and x[n] is the currently measured clutter

sample at time n. The factor γ controls the relative weight of the current
measurement versus the preceding measurements. This equation is applied
separately to each range-angle cell of interest. The detection threshold is then
set for each range-angle cell as

(6.174)

Note that the threshold for testing for a target on the current scan is based on the
clutter estimate from the previous scan. The current data are not included

because, if the CUT does contain a target, it would distort the clutter
measurement and raise the threshold, creating a self-masking effect. Even with
this precaution, self-masking can cause CFAR losses of several dB if slow-
moving targets are present, so that they persist in a map cell for more than one
scan (Lops and Orsini, 1989). If the target persists in the map cell for a number
of scans approaching the number of scans integrated to form the clutter map,
detectability is essentially lost entirely.

The first-order difference equation (6.173) corresponds to an IIR filter
with the impulse response

(6.175)

where u[n] is the unit step function. Consequently, the output of the filter can
also be expressed as a convolution with h[n]:

(6.176)

This equation shows that, similar to CA CFAR, the threshold will be based on
an average of clutter measurements, but there are several important differences.

In CA CFAR, clutter samples taken during the same pulse or dwell and from
cells adjoining the CUT in spatial position, Doppler, or both are used to
estimate the clutter level. The clutter must be assumed spatially homogeneous so
that these adjoining cells represent the interference in the CUT accurately. The
various CA CFAR extensions discussed previously are all motivated by real-
world violations of this assumption. In clutter mapping, the threshold is based