6.1 Detection of Radio Signals
129
Fig. 6.2 Realization of random output signal y out and corresponding conditional probability
distribution density, describing statistical properties of read-out values y out
P cd =
∞
y thr
p(y out |S t = 0)dy out ,
(6.1)
and conditional probability of false alarm as follows:
P f a =
∞
y thr
p(y out |S t = 0)dy out ,
(6.2)
In Fig. 6.2, the shaded areas of conditional distributions to the right of threshold
y thr correspond to probabilities P cd and P f a .
Threshold selection criterion. Probabilities P cd and P f a essentially depend on
selection of threshold y thr . Finally, certainty and reliability of target detection depend
on correct selection of y thr value. Threshold depends on criterion, which should be
admitted at testing of statistical hypothesis. Nowadays, a several different approaches
to threshold selection are known in mathematical statistics. However, not all the
known criteria can be applied in target radar detection theory. This is explained
that the most required parameters at criterion setting cannot be preset beforehand
or defined during radar surveillance. Clarify this on example of ideal observer
criterion. Based on this criterion, the threshold is selected in a way that to minimize average losses C ls at decisions-making, which are stipulated by false decisions
probabilities P f a and P tm . Average losses C ls can be written down as follows:
C ls = β m P m P t + β f a P f a (1 − P t ),
(6.3)
129
Fig. 6.2 Realization of random output signal y out and corresponding conditional probability
distribution density, describing statistical properties of read-out values y out
P cd =
∞
y thr
p(y out |S t = 0)dy out ,
(6.1)
and conditional probability of false alarm as follows:
P f a =
∞
y thr
p(y out |S t = 0)dy out ,
(6.2)
In Fig. 6.2, the shaded areas of conditional distributions to the right of threshold
y thr correspond to probabilities P cd and P f a .
Threshold selection criterion. Probabilities P cd and P f a essentially depend on
selection of threshold y thr . Finally, certainty and reliability of target detection depend
on correct selection of y thr value. Threshold depends on criterion, which should be
admitted at testing of statistical hypothesis. Nowadays, a several different approaches
to threshold selection are known in mathematical statistics. However, not all the
known criteria can be applied in target radar detection theory. This is explained
that the most required parameters at criterion setting cannot be preset beforehand
or defined during radar surveillance. Clarify this on example of ideal observer
criterion. Based on this criterion, the threshold is selected in a way that to minimize average losses C ls at decisions-making, which are stipulated by false decisions
probabilities P f a and P tm . Average losses C ls can be written down as follows:
C ls = β m P m P t + β f a P f a (1 − P t ),
(6.3)