GB2184626A

GB2184626A - Detecting signals in clutter

Info

Publication number: GB2184626A
Application number: GB08531354A
Authority: GB
Inventors: Matsuo Sekine
Original assignee: Individual
Current assignee: Individual
Priority date: 1985-12-20
Filing date: 1985-12-20
Publication date: 1987-06-24
Anticipated expiration: 2005-12-20
Also published as: GB8531354D0; GB2184626B

Abstract

A target signal detecting apparatus and method are described for detecting a target signal in a cluttered signal having an amplitude characteristic which exhibits the Weibull distribution. An input signal X is subjected to logarithmic transformation, y = 1nX, and the values <y<2>> and <y><2> are calculated along with a distributed parameter C given by <IMAGE> The value of C is then compared with a predetermined threshold to determine whether a target signal is present. The value of C may also be amplified non-linearly before being compared with the threshold. <IMAGE>

Description

SPECIFICATION Target Signal Detecting Apparatus and Method The present invention relates to a target signal detecting apparatus and method for discriminating and detecting a target signal from a noise signal whose amplitude characteristic exhibits the Weibull distribution.

In recent years, it has been observed that various kinds of noise included in signals such as the noise accompanying a radar signal due to the reflection of the transmitted signal from the surface of the sea, and the noise accompanying a signal received by an ultrasonic detecting apparatus, are distributed in accordance with the Weibull distribution.

Assuming now that the amplitude intensity x of a signal X follows the Weibull distribution, the probability density function Pc(x) of the Weibull distribution is given as follows:

where b is a constant determined by the nature of the signal and Ca distributed parameter. This probability density function Pc(x) exhibits any one of various distribution forms depending on the value of the distributed parameter C. For example, it exhibits the exponential distribution when the value of the distributed parameter C is 1, the Rayleigh distribution when the value is 2 and the Gaussian distribution when the value is 2.5.

Where the amplitude of a target signal is smaller than the amplitude of a noise signal, the detection of the target signal is impossible by a conventional discrimination method in which a suitable amplitude threshold is established to discriminate the two signals from each other.

The present invention has been made to attempt to overcome the foregoing deficiency in the prior art and it is the primary object of the invention to provide a target signal detecting apparatus so designed that a target signal, not distributed according to the Weibull distribution, is detected within noise which is distributed in accordance with the Weibull distribution.

According to the present invention a method of detecting a target signal from a received signal X having an amplitude intensity distribution which generally follows a Weibull distribution having a probability density function Pc(x) given by

where b and C are constants which are determined by the nature of said received signal; comprises calculating a transformed signal y=1nxwherexisthe amplitude of the signal X, calculating and the square of the mean value < y > 2, calculating a distributed parameter C in accordance with the following equation

comparing function of the calculated distributed parameter with a predetermined threshold and determining that a target signal is present in the signal X when the value of the function is greater than the threshold.

Also according to the present invention a target signal detecting apparatus comprises logarithmic transformation means for logarithmically transforming a received signal X having an amplitude intensity distribution generally following a Weibull distribution having a probability density function Pc(x) given by

where b and C are constants which are determined by the nature of said received signal, by a transformed signal y= 1 nx where xis the amplitude of the signal X; means-square value computing means for calculating the mean-square value < y2 > ; square value computing means for calculating the squared-mean value < y > 2; distributed parameter computing means for computing a distributed parameter C in accordance with the said mean-square and squared-mean values, according to the equation

means for generating a value Z=C" obtained by raising the distributed parameter C to an nth power, where n is a number greater than or equal to 1; and target signal detecting means for comparing the said value Z with a predetermined threshold and for determining that a target signal is present in the signal X when the value of Z is greater than the threshold.

The invention may be carried into practice in various ways and one specific example of a target signal detecting apparatus embodying the invention will be described with reference to the diagrams, in which Figure lisa block circuit diagram of a target signal detecting apparatus; Figure 2 is a graph showing the variation (a) with the time t of the amplitude X, (b) distributed parameter C and (c) distributed parameter Z raised to nth power (null) of a received signal; Figure 3 is a graph showing examples of the variation with the amplitude X of the probability density function Pc(x); Figure 4 is a graph showing the variation with time t of the amplitude X of a received signal.

Figure 5 shows a prior art radar system; Figure 6 shows how the invention may be applied to the radar system shown in Figure 5; and Figure 7 shows in greater detail the system of Figure 6.

Firstly, Figure 3 illustrates some examples of the probability density function shown by the above equation (1). In the Figure, the broken line and the solid line respectively show the probability density functions Pc(x) respectively corresponding to the distributed parameters of C=1.5 and C=2. Figure 4 is a graph showing the variation of the amplitude x (the ordinate) of a received signal including a target signal OS and noise signals NS in a time sequence with the time t (the abscissa). If the amplitude of the target signal OS is lower than the amplitude of the noise signal as shown in Figure 4, it is impossible to detect the target signal OS by the conventional method in which a suitable threshold is established to discriminate the target signal OS and the noise signal NS from each other.

Next, the signal processing theory of the target signal detecting apparatus according to the invention will be described.

An input signal X having an amplitude intensity x following the Weibull distribution with its probability density function Pc(x) given by the previously mentioned equation (1),that is:

This is logarithmically transformed in terms of a variable y in which is given by y=lnx (2) The mean-square value < y2 > of the variable y is as follows:

Here, y is the Euler constant and its value is 0.5772. . .

Also, the mean value < y > of the variable y is as follows:

Thus, < y > 2, the square of the mean of the variable Y is as follows:

Therefore, the variance E(y) about the mean of the variable y is given by the following equation (6), since it is the difference between the mean-square value < y2 > of the variable y and the square value < y > 2 of the mean of the variable y: E(y)= < y2 > < y > 2 (6) n2 6c2 Thus, the distributed parameter C can be written as

Referring now to Figure 1, there is illustrated a block circuit diagram of a target signal detecting apparatus.In the Figure, a logarithmic amplifier 10 (more generally, a logarithmic transformation means) logarithmically transforms the signal shown in Figure 4 (that is, the received signal X which has an amplitude x) so that a signal Y having an amplitude y=1 nx is generated. This signal Y is then applied to mean-square value computing means 20 and square value computing means 20 includes a square computing element 21, a delay circuit 22 composed for example of a shift register or the like, an integrator 23 and a divider 24 and it computes the mean-square value < y2 > of the signal Y as shown by the equation (3).In other words, the square computing element 21 squares the amplitude y of the signal Y to produce an amplitude y2 and the delay circuit 22 samples and quantizes the signal Y to extract N (N is a natural number) sampled values y:, y221 ---, YN corresponding to the amplitude y2 of the signal Y.The integrator 23 calculates an integrated value

of the N sampled values y:, y22, ---, YN and then the divider 24 divides the integrated value

by N to calculate a mean-square value < y2 > of the signal Y as follows:

On the other hand, the square value computing means 30 of the mean value includes a delay circuit 31, and integrator 32, a divider 33 and a square computing element 34 and it calculates a square value < y > 2 of the mean of the signal Y as shown by the equation (5). In other words, the delay circuit 31 samples and quantizes the signal Y to extract N sampled values y1, y2, ---, y, corresponding to the amplitude y of the signal Y and the integrator 32 calculates an integrated value

of the N sampled values y1, Y2, ---, y. Then, the divider 33 divides the integrated value

by N to calculate a mean value

of the integrated value

and then the square value computing element 34 squares the mean value

to calculate a square value < y > 2 of the mean value of the signal Y as follows::

Then, a distributed parameter computing means 40 including a subtractor 41 and a computing element 42 calculates a distributed parameter C in accordance with the mean-square value and the square value of the mean value. This distributed parameter C is calculated as follows: the subtractor 41 calculates the variance E(y) about the mean of the sinnal Y as shown bv the equation (6) and then the comDutina element 42 calculates a square root

of the variance E(y)= < y2 > - < v > 2, calculates a reciprocal

of the square root and then multiplies the thus obtained reciprocal by a constant rU.

Figure 2 shows the distributed parameter C obtained in the above-mentioned manner. In the Figure, even if the signal X applied to the logarithmic amplifier 10 is such that the target signal OS is lower in amplitude than the noise signals NS (See the curve (a) in Figure 2), the distributed parameter C generated from the distributed parameter computing means 40 has a greater value in the portion corresponding to the target signal OS and has substantially a constant value with small variations (See the curve (b) in Figure 2) in the portions corresponding to the noise signals making it easy to detect the distributed parameter C corresponding to the target signal OS.

In this embodiment, the distributed parameter C corresponding to the target signal OS is applied to a non-linear amplifier 50 (non-linear amplifying means) so as to make easier the detection of the distributed parameter C.

The non-linear amplifier 50 raises the distributed parameter C to the nth power (where n is a number greater than or equal to 1 ) and generates a new distributed parameter Z (Z=C"). It is to be noted that a square amplifier with n=2 or the like is well known as a specific example of the non-linear amplifier 50. With the new distributed parameter Z generated from the non-linear amplifier 50, as shown by the curve (c) in Figure 2, the variations of the portions corresponding to the noise signals NS are suppressed and the portion corresponding to the target signal OS is amplified considerably as compared with the distributed parameter C (See the curve (b) in Figure 2) thus further simplifying the detection of the distributed parameter Z corresponding to the target signal OS or the establishment of a threshold value.

Then a target signal detector 60 (target signal detecting means) compares the new distributed parameter Z generated from the non-linear amplifier 50 and a threshold ZTH preset manually or automatically in the target signal detector 60 so that the distributed parameter Z greater than the threshold ZTH is delivered as one corresponding to the target signal.

While the threshold ZTH is preset manually or automatically as mentioned previously, the manual presetting is effected while observing the distributed parameter Z on the display screen of an A scope, B scope, PPI scope or the like. On the other hand, the automatic presetting is effected by calculating a mean value < Z > of the distributed parameter Z and a variance Var about the mean value < Z > and then selecting a suitable threshold value in accordance with the calculated mean value < Z > and variance Var such that the false alarm rate that a noise signal NS is detected mistakenly for a target signal OS or the detection probability of target signal OS attains a given value.

The method of calculating the threshold ZTH will now be described. If P(Z) represents the probability density function of the distributed parameter Z, then the mean value < Z > and the mean-square value < Z2 > of the distributed parameter Z respectively become as follows:

Then, the variance Var about the mean < Z > of the distributed parameter Z becomes as follows Var= < Z2 > - < Z > 2 (10) Also, the false alarm rate Pfa becomes as follows:

where ZTH is the threshold. Then, where the amplitude t of a target signal OS is superposed on the distributed parameter Z, the detection probability Pa of the target signal OS becomes as follows:

Then, the threshold is fixed in such a manner that the false alarm rate Pfa or the detection probability Pa, as desired, attains the required value.

Specific values of the threshold ZTH calculated in the above-mentioned manner will now be described.

In other words, by letting < Z > represents the mean value of the distributed parameter Z, < Z2 > the mean-square value, < Z > 2 the square value of the mean value Z, < Z2 > - < Z > 2 the variance about the mean value < Z > and K a constant (K is any given constant including 1) and considering the mean value tZ > , the mean-square value < Z2 > and the variance < Z2 > - < Z > 2 as the amplitude levels of the noise signals, the threshold ZTH iS given by any one of the following expression (13) to (17).

K. < Z > ( (13)

Also, using a constant A, the threshold ZTH may be established in accordance with any one of the following expressions (18) to (22) in addition to those shown by the above expressions (13) to (17) K. < Z > +A (18)

In short, it is only necessary to establish the threshold ZTH in such a manner that the false alarm rate Pfa or the detection probability Pa reaches the required value.

A specific example of the prior art, and the application of the present invention to that prior art will now be described with reference to Figures 5 to 7.

Figure 5 shows a prior art radar system. The pulse-type RF (radio frequency) electromagnetic wave generated from a transmitter 120 is radiated as an electromagnetic wave into the air through an antenna 100. A duplexer 110, serving as a change-over switch, is provided between the two and is here switched to the antenna side. If the radar is a ship-board radar, the electromagnetic wave radiated into the air is reflected from the surface of the sea, the land, other ship or the like so that it is again received by the antenna 100 from which it is then supplied to an RF front end unit 130 through the duplexer 100 (now switched to the RF front end unit 130). The RF front end unit 130 converts the RF signal to an IF (intermediate frequency) signal and supplies it to a receiver 140.The receiver 140 amplifies and finally converts the IF signal to a video signal which in turn is supplied to a display unit 150. This comprises, for example, a PPI display; the video signal is displayed on the screen of its CRT.

Figure 6 shows an embodiment of the invention which is applied to the system of Figure 5. This system differs in essence from the system of Figure 5 in that a logarithmic receiver 160 which has a large dynamic range (e.g. about 100 dB) is provided. This large range prevents its output from saturating even in the case of an excessively large input signal. A signal processing unit 170 is also provided. This performs the calculation of variance values and the signal detection by the separation between signals and noise or the like.

The logarithmic receiver 160 and the signal processing unit 170 are in fact shown as a whole by the block diagram of Figure 1, and they are indicated generally by the numeral 180 in Figure 6.

Figure 7 shows in greater detail the system shown in Figure 6. Only the differences between Figure 7 and 6 will be described. The RF front end unit 130 includes components 131 to 134 of Figure 7. The waveguide to microstrip transition 131 is a unit for passing the RF signal from the waveguide or the RF signal transmission line to a microstrip line. After amplification in a radio frequency amplifier 132, the RF signal is mixed with the output of a local oscillator 134 in a mixer 133, thereby producing the desired intermediate frequency signal (e.g., a 60 MHz signal). In this case, the function of rejecting any undesired image signal is also performed.

The IF signal is supplied to the receiver and signal processing unit 180. The unit 180 differs from Figure 1 in that an A/D converter 181 is inserted after the logarithmic amplifier 10 so as to convert the IF signal to a digital signal of the desired number of bits and thereby permit the performance of digital computations. As a result, the computations of the units 20,30 and 40 are all performed by the use of digital signals. To reconvertthe output of the unit 40 to an analogue signal, the output is supplied to a D/A converter 182.

This analogue signal is supplied to the non-linear amplifier 50 so that the signal detection is performed by the target signal detector 60. Also, the output of the D/A converter 182 is used as a monitor through a linear amplifier 51.

The output of the target signal detector 60 is applied to the cathode of a CRT 155 through a video amplifier 151 in a display unit 150. Simultaneously, a system trigger (a trigger synchronized with the RF transmission of the transmitter) is supplied to the display unit 150 so that in the case of the PPI, a sweep generator 152 generates and supplies a sawtooth sweep waveform to a deflection coil 156 through a sweep amplifier 153. At the same time, the system trigger drives an unblanking circuit 154 so that a voltage is supplied to the grid of the CRT 155 so as to permit the output of the video amplifier 151 to be displayed on the CRT screen for a given period of time.

In this way, the output of the target signal detector 60 is displayed on the screen of the CRT 155.

It is to be noted that while the respective component parts of this embodiment are provided by means of electric circuitry, they may also be provided by means of a micro-computer or the like.

Claims

1. A method of detecting a target signal from a received signal X having an amplitude intensity distribution which generally follows a Weibull distribution having a probability density function Pc(x) given by

where b and care constants which are determined by the nature of said received signal; comprising calculating a transformed signal y=1 nx where x is the amplitude of the signal X, calculating the mean-square value < y2 > and the square of the mean value < y > 2, calculating a distributed parameter C in accordance with the following equation.

comparing a function of the calculated distributed parameter with a predetermined threshold and determining that a target signal is present in the signal X when the value of the function is greater than the threshold.

2. A method as claimed in Claim 1 in which the function of the distributed parameter is Z=C where n is a number greater than or equal to one.

3. A method as claimed in Claim 1 or Claim 2 in which the threshold is determined such that the probability of correct detection of a target signal, or the rate of incorrect determination that a target signal is present, attains a predetermined value.

4. A method as claimed in Claim 1 or Claim 2 or Claim 3 in which the threshold is determined in terms of a variable Z=C", where n is a number greater than or equal to one, and in terms of the variance of the mean value of Z, < Z > .

5. A method as claimed in Claim 3 in which the threshold has a value of K < Z > . where K is a constant.

6. A method as claimed in Claim 3 in which the threshold has a value of K.

where K is a constant.

7. A method as claimed in Claim 3 in which the threshold has a value of K

where K is a constant.

8. A method as claimed in Claim 3 in which the threshold has a value of < Z > +K.

where K is a constant.

9. A method as claimed in Claim 3 in which the threshold has a value of

where K is a constant.

10. A method as claimed in Claim 3 in which the threshold has a value of K < Z > +A, where K and A are constants.

11. A method as claimed in Claim 3 in which the threshold has a value of K

where K and A are constants.

12. A method as claimed in Claim 3 in which the threshold has a value of K

where K and A are constants.

13. A method as claimed in Claim 3 in which the threshold has a value of < Z > +K

where K and A are constants.

14. A method as claimed in Claim 3 in which the threshold has a value of K.

where K and A are constants.

15. A target signal detecting apparatus comprising logarithmic transformation means for logarithmically transforming a received signal X having an amplitude intensity distribution generally following a Weibull distribution having a probability density function Pc(x) given by

where b and Care constants which are determined by the nature of the received signal, to a transformed signal y= 1 nx where x is the amplitude of the signal X; mean-square value computing means for calculating the mean-square value < y2 > ; square value computing means for calculating the squared-mean value < y > 2; distributed parameter computing means for computing a distributed parameter C in accordance with the said mean-square and squared-mean values, according to the equation

16. Apparatus as claimed in Claim 15 in which the means for generating a value Z=C" comprises a non-linear amplifier.

17. Apparatus as claimed in Claim 15 or Claim 16 in which the logarithmic transformation means comprises a logarithmic amplifier.

18. Apparatus as claimed in Claim 15 or Claim 16 or Claim 17 in which the mean-square value computing means comprises means for calculating the square of the signal y, means for sampling the squared signal, means for calculating the sum of these sampled values, and means for dividing the sum by a number N1 equal to the number of samples.

19. Apparatus as claimed in any one of Claims 15 to 18 in which the square value computing means comprises means for sampling the signal y, means for calculating the sum of these sampled values, means for dividing the sum by a number N2 equal to the number of samples, and means for squaring the resulting value.

20. Apparatus as claimed in any one of Claims 15 to 19 including means for displaying the value Z, and means for varying the threshold value.

21. A target signal detecting apparatus substantially as specifically herein described with reference to the diagrams.

22. A target signal detecting apparatus arranged to operate by a method as claimed in any one of claims 1 to 14.

23. A method of detecting a target signal substantially as specifically herein described.