Page 129 - Radar Technology Encyclopedia

detection criterion, likelihood-ratio detection criterion, minimax 119

The procedures performed in the detector when likeli- Mean detection compares the mean value of n received
hood ratio L(u) is calculated are determined by the shape of pulses to a predetermined threshold. The conventional
f(y,u) and f(y,0) and can be worked out in detail for known receiver typically uses mean detection. SAL
statistical characteristics of interference n(t) and signal plus Ref.: Skolnik (1980), p. 486.
interference combination, y(t) = u(t) + n(t). The ratios of a
Detection-measurement is detection of a signal in an inter-
priori probabilities of target presence and absence can be
ference background with simultaneous evaluation of parame-
taken for the threshold values.
ters (e.g., range, azimuth, elevation) in case a target-present
The likelihood-ratio detector based on this criterion is a
decision is made. The separation of these tasks is quite arbi-
distribution-dependent detector. The Marcus-Swerling detec-
trary and concerns only the differences in practical implemen-
tor is a version of a sequential detector for use in search radar. tation of evaluating signal parameters in detection and
It operates on multiple detector cells but does not test all 2 k
measurement modes.
possibilities (where k is the number of resolution cells) but
Due to the random nature of interference and parameters
makes a decision as to target presence on the basis of the like-
of received signals, the tasks of detection and measurement
lihood ratio. The Wald detector is a sequential detector using
are statistical. In statistical decision theory, a number of crite-
the theory of sequential analysis developed by Wald. AIL
ria for detection of signals have been developed (see detec-
Ref.: Dulevich (1978), pp. 60–62; Dillard (1989), pp. 139–142.
tion criteria). One can distinguish tasks of detection-
M-ary [multialternative] detection makes the decision as to measurement of two kinds: (1) when measured parameters do
signal presence or absence using more than two hypotheses not change during the observation interval and (2) when one
(as opposed to binary detection). The common example of a cannot disregard such a change. Optimization of detection-
multialternative detector is the detector making a decision measurement of the first kind reduces to single-stage minimi-
about the target presence for each of the range cells. In this zation based on the average risk criterion. A rigorous solution
k
case, the number of possible decisions is M = 2 , where k is to such problems for the total set of targets on the whole is
the number of range resolution cells. It can consist from the quite complex. If minimization is conducted for each target,
set of binary detectors: one binary detector per one resolution then detection-measurement reduces to discovery of excesses
cell. In a more generic case, the problem of range and veloc- of the threshold by the likelihood-ratio logarithm. In practice,
ity detection can be solved by means of a multialternative for example, if the measured parameter is delay time, this
detector, Fig. D22. amounts to using the matched filter with an amplitude detec-
There are K range channels and K = mK velocity tor. Optimization of detection-measurement of the second
R
R
u
channels, where m is the number of velocity channels per kind requires one to introduce certain models describing the
range channel. From the output of the Kth range channel 1, change for the measured parameters in time. In the majority
the signal goes to a velocity channel 2, and then to switch 3 of cases, Markovian discrete or continuous models are appli-
and threshold unit 4. If output voltage of the Kth channel cable. This amounts to multistage tracking detection-mea-
exceeds the threshold voltage, the decision about the target surement; for example, for detection of trajectory. The most
presence is made, and the signal goes to decision-making unit common circuits for implementation of detection-measure-
5, which determines in what cell the target was detected (i.e., ment are plot extractors. AIL
determines target range and velocity). Multialternative detec- Ref.: Skolnik (1980), p. 388; Shirman (1981), pp. 293–300.
tors are typically used in multichannel phased-array radars.
Median detection is a process in which the median value of n
AIL
received pulses is found and compared against a threshold.
Ref.: Skolnik (1970), p. 179; Lukoshkin (1982), p. 42.
The process is robust, as the threshold values and the detec-
tion probabilities do not depend on the detailed shape of the
Input
clutter probability density function but depends only on the
median value. This method of detection has better perfor-
mance in non-Rayleigh clutter than mean detection. SAL
Range data Range data Range data
processing processing processing Ref.: Skolnik (1980), p. 486.
channel 1 channel 1 channel 1
m-out-of-n detection (see double-threshold detection,
Velocity data Velocity data
processing processing INTEGRATION, binary).
channel 2 channel 2
The minimax detection criterion is the optimum detection
criterion that ensures minimum average risk for unknown a
Threshold Threshold
unit Switch unit Switch priori probability of occurrence of the signal. This criterion is
4 3 4 3
a particular case of the minimum-average-risk criterion, when
a priori probabilities P of appearance of signals from targets
Decision-making unit a
5
are unknown, but losses r and r due to selection of an
pr
lt
Output
invalid hypothesis (r is the loss for a false alarm, r is the
pr
lt
loss for a target miss). When using this criterion, one calcu-
Figure D22 Multialternative detector for range and velocity.