Page 131 - Radar Technology Encyclopedia

detection, noncoherent detection probability 121

The optimum detector for a noncoherent pulse train typi- where L is the detection threshold; f (y,u) and f (y,0) are the
0
cally consists of the matched filter (matched to single pulse in probability density functions of the received signal y(t) in
a train), an amplitude detector, a noncoherent integrator, and a interference when the desired signal u(t) is present in the
threshold unit (Fig. D25). The dependence of the signal-to- observation interval T and when it is absent, respectively. The
noise ratio versus the number of pulses required for detection likelihood ratio determines by what factor the observed pres-
with specified probabilities of detection and false alarm can ence of u(t) is more probable in the actual presence of a signal
be determined from detection curves for chosen target-fluctu- than during its absence.
ation model and detector model. AIL, SAL The decision “there is a signal,” given by the detector, is
Ref.: Blake (1980), p. 41; Sosulin (1992), p. 64. written in the form R[u(t)] = 1 and the decision “there is no
signal” is given in the form R[u(t)] = 0. As a result we can
Alarm
Matched Envelope Video Threshold write
filter detector integrator
1 L ³, L 0
Rut ()[ ] æ ö
=
Figure D25 Optimum detector for a noncoherent pulse train. è 0 L <, L ø
0
In place of the likelihood ratio L sometimes one uses the
nonparametric detection (see distribution-free detection,
logarithmic function of this ratio
CFAR).
fy u )
,
(
Open-loop automatic detection is used in an ESM system in l = log L = log ---------------
,
fy 0 )
(
which a certain number of many cells are available for incom-
In this case the decision rule for detection is written in the
ing pulses (Fig. D26). The available cells are labeled with
form
information about the instantaneous parameters of the emis-
sion (i.e., direction-of-arrival or pulsewidth) and when a pulse 1 l ³, log L 0
=
arrives, a free cell will declare itself available to accept other Rut ()[ ] æ ö
è 0 l <, log L ø
0
pulses with the same parameters as those of the first pulse,
Such detection frequently is called logarithmic. There is a
within a certain tolerance. The agility of the parameters may
large number of variants for detection of different signals in
be taken into account to use the appropriate criterion. SAL
the background of different kinds of interference, and in each
Ref.: Neri (1991), p. 309.
case the likelihood ratio or its algorithm can be specified for
PW, DOA, frequency Detection Analysis, tracking,
histogram and identification known characteristics of interference and mixture of a signal
with interference to find the optimum detection algorithm.
Cell 1 Association
Verification of new Optimum detection is discussed in radar detection theory for
of time emitters finding maximum achievable signal detection performance in
relation with
between Emitter old ones; a background of interference. In practice it is difficult to
the pulses frame comparison
Front Pulse in each with library implement completely optimum detection algorithms, and
end frame
histogram and updating simplified detectors with parameters close to optimum are
and of track file
automatic used (e.g., the binary detector, m-out-of-n detector, etc.).
detection
Library These detectors experience some detector loss with respect to
Cell N Track the true optimum and are termed quasioptimum detectors.
file
AIL
Figure D26 Open-loop automatic detection (from Neri, 1991, Ref.: Skolnik (1970), p. 15.5; Dulevich (1973), pp. 60–62; Blake (1980),
Fig. 4.27, p. 310). p. 45.
Operator detection is the detection of echo signals by the Detection probability is “the probability that a signal, when
human operator using visual observation of radar displays actually present at the input to the receiver, will be correctly
(sometimes called visual detection). Operator detection declared a target signal based on observation of the receiver
depends not only on the signal-to-noise ratio but on the output.” This probability is typically referred to in terms of
visual-mental acuity of the operator, his alertness and experi- single-pulse, single-scan, or cumulative probability of detec-
ence, and the resolution of the display (which may cause a tion. Single-scan probability of detection is often called the
collapsing loss). In modern radars this method is usually blip-scan ratio, for which the usual notation is P . For sur-
d
replaced with automatic detection. SAL veillance radars, the probability that the target is detected at
Ref.: Barton (1964), p. 6; Skolnik (1990), p. 2.24. least once in N successive scans is called the cumulative prob-
ability of detection.
Optimum detection is detection of a signal in an interference
The probability of detection is associated with the proba-
background using optimum detection criteria. In the optimum
bility of false alarm in a way that depends on the detection
detection a decision on presence of a target is made in the
criterion. For a given receiver configuration if the detection
case when the likelihood ratio
threshold is reduced to increase the probability of detection,
,
fy u )
(
,
=
(
L yu ) --------------- ³ L 0 there will be an increase in false-alarm probability, and simi-
(
,
fy 0 )
larly for decreased probabilities if the threshold is raised. The