Page 548 - Fundamentals of Radar Signal Processing

interference sources such as clutter and jamming, and hardware limitations. For

instance, the scanning antenna’s received power would be measured only at
discrete angles determined by the radar’s PRF and the antenna scan rate rather
than on the dense sampling grid used in the preceding example. In a search
mode, there might be only one to two samples per beamwidth and the peak
estimator used here would not be practical. The peak estimator is also a poor
choice because it takes no advantage of multiple samples to average out the

effects of the noise. More practical estimators will be considered shortly.

7.1 Estimators

7.1.1 Estimator Properties
Suppose that one has a vector of N measured data samples x = {x , i = 0,…, N –
i
1} that depends on a deterministic but unknown parameter Θ. Θ might be the
actual target angle, time delay (equivalent to range), or Doppler shift. An

estimator f(x) is an algorithm for computing an estimate of the actual value of
Θ from the data x:

(7.1)

If the data is noisy, will be an RV with its own PDF and moments. Because
the quality of different estimators will vary it is reasonable to ask what
properties characterize a good estimator?
Before answering that question, it is useful to define two important metrics

of estimator quality, accuracy and precision. Figure 7.3 illustrates these two
ideas heuristically with the example of target shooting. The hits on the left target
are centered roughly on the bull’s-eye (center of the target) but are widely
dispersed. Because the average location is near the center of the target, this set
of hits is said to exhibit good accuracy. However, because they are widely
dispersed, they are said to exhibit poor precision. In the middle target, the hits

are tightly clustered but the center of the cluster is far from the bull’s-eye. These
hits are precise but inaccurate. In the target on the right the hits are both tightly
clustered and centered on the bull’s-eye: both precise and accurate.