JPH0242436B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a method for determining statistical distribution characteristics of the amplitude of a received noise signal (hereinafter referred to as clutter) in a radar or the like. The statistical characteristics of radar clutter can be roughly divided into two cases: the case where the amplitude is distributed as Weibull, and the case where the amplitude is distributed as lognormal (LOG/NORMAL). Particularly in the case of sea surface clutter, areas of clutter with a Weibull distribution and areas of clutter with a lognormal distribution may coexist within the same search area. However, in the past, there was no means for distinguishing between these two types of clutter, so it was not possible to perform optimal suppression processing for each type of clutter. In other words, conventional radar systems assume either a Weibull distribution or a lognormal distribution as a clutter signal, and are equipped with a suppression device that is effective only for that one clutter distribution. Therefore, a clutter suppression device designed with Weiple distribution clutter as its main input clutter has the problem of generating a false alarm rate higher than the design value for lognormal distribution clutter; A clutter suppression device designed as a clutter has a problem in that when Weibull distributed clutter is input, the threshold is set high, so that an unnecessarily low target detection rate can be achieved. This high threshold value is set because log-normal distribution clutter has a characteristic that it has a higher probability of having a larger amplitude than Weibull distribution clutter. An object of the present invention is to realize optimal clutter suppression for clutter amplitude characteristics by providing a method for determining statistical distribution characteristics of clutter amplitude. Next, the basic principle of the present invention will be explained. Statistical distribution characteristics of amplitude X, that is, distribution function F
When (U) is known, its distribution function F(U)
Whether it is a log-normal function, a Weibull function, or any other function, the parameters that characterize these functions are measured using the radar clutter amplitude U, and after determining F(U),
Calculate the difference 1.0-F(U) between (U) and the numerical value 1.0, convert the sign of the value calculated by calculating the natural logarithm of the result, raise it to the 1/K power, and multiply the result of this power by σ. Then, the final value Y, that is, Y=σ[−l _o {1.0−F(U)}] ^1/K (1), is obtained by converting the Weipul function with scale parameter σ and shape parameter K into a probability density function. becomes a variable. Here, σ and K are values that can be set arbitrarily. The details of this variable conversion are detailed in another patent application filed by the present inventor, ``General Purpose False Alarm Rate Control Device'', published in Japanese Patent Application Laid-Open No. 57-165774. The variable-converted signal Y has its probability density function P
Since (Y:σ, K) is a Weibull function, is displayed. The property of P(Y:σ, K) is ∫ <sup>Y</sup> <sub>O</sub> P(Y:σ, K)dY=1.0 −exp{−(Y/σ <sup>K</sup> } …(3). Therefore, −(Y/ σ) <sup>K</sup> = l <sub>o</sub> {1.0−∫ <sup>Y</sup> <sub>O</sub> P(Y; σ, K) dY} Kl <sub>o</sub> (Y/σ) = l <sub>o</sub> [−l <sub>o</sub> {1.0−∫ <sup>Y</sup> <sub>O</sub> P(Y; σ, K)
dY}], and finally W=KZ-C...(4), which shows the linear characteristic shown in Figure 1. However, W=l <sub>o</sub> [−l <sub>o</sub> {1.0−∫ <sup>Y</sup> <sub>O</sub> P(Y; σ, K) dY}] (5) Z=l <sub>o</sub> Y (6) C=Kl <sub>o</sub> σ (7). In other words, W is an integral value from Y to ∞ of a Weibull function having a shape parameter K and a scale parameter σ using the output Y of the variable conversion means in an arbitrary radar range cell. The following can be said from the above characteristics of the Weibull function. That is, when the distribution function F(U) indicating the statistical characteristics of the amplitude U of the radar clutter signal is correctly set, the result of variable conversion according to equation (1) Y becomes a variable whose distribution function is the Weibull function. At this time, the calculations of equations (5) and (6) are performed for Y, and the calculation results at this time are defined as W <sub>1</sub> and Z <sub>1</sub> . Also, the Y obtained next
Similar calculations are performed for W <sub>2</sub> and Z <sub>2</sub> . Below, W <sub>i</sub> and Z <sub>i</sub> are obtained in the same way, but in this case, W <sub>i+N</sub> −W <sub>i</sub> /Z <sub>i+N</sub> −Z <sub>i</sub> , (N is an arbitrary value)...(8) is the distribution function F(U ) correctly indicates the statistical characteristics of the received clutter signal, that is, the input signal, it will be correctly converted to a Weibull variable, so i = 1,
It is a constant for all values of 2, 3, 4, . . . and the value of this constant should be equal to the set value K. That is, in order to determine the statistical characteristics of the received clutter signal, several expected distribution functions are set, and the parameter calculation function that characterizes these set distribution functions and the conversion function shown in equation (1) are set for each setting. If each distribution function has one, use the results of calculating equations (5) and (6) for the new variables converted into variables to calculate equation (8), and the result becomes equation (1). When it is determined that the shape parameter K is equal to the shape parameter K, it is determined that the distribution function F(U) set in the variable transformation system of equation (1) is a distribution function that represents the statistical characteristics of the received noise signal. What is necessary is to perform a suppression process on clutter having a distribution characteristic F(U) set as follows. In addition, if the calculation result of equation (8) gives only a value that is far from the set shape parameter K in all variable transformation systems, the statistical characteristics of the input noise signal ) and follows other distribution functions, so
At this time, it is possible to avoid performing suppression processing on clutter having the set distribution characteristics. As a criterion for judgment, when L outputs out of M outputs in equation (8) are equal to the set value of K, the distribution function F( It may be determined that U) is a distribution function representing statistical characteristics of the input received clutter signal. In addition, instead of directly calculating the ratio of the denominator and numerator of the equation (8), a circuit that implements the equation (8) uses a look-up table (look-up table) that uses a memory element such as a ROM.
This can be realized by calculating the difference between the logarithm value of the numerator and the logarithm value of the denominator. Incidentally, in order to be able to sufficiently cope with reception noise signals having very large amplitude levels, it is desirable that the receiver dynamic range be wide. As a means for this purpose, a logarithmic amplifier that logarithmically transforms the received signal is required, so in such a case, equation (1), that is, the variable conversion formula F(U), can be expressed as a probability distribution function of the variable obtained by logarithmically transforming the received signal. Once set, the principle of the present invention can be applied. As can be seen from the above explanation of the principle of the present invention, according to the present invention, it is possible to determine the statistical characteristics of the amplitude of an input clutter signal. Next, the basic configuration of the present invention will be explained with reference to the drawings. The noise amplitude distribution characteristic discriminator according to the present invention has a second
As shown in the figure, it is comprised of a logarithmic amplifier circuit 1 that logarithmically converts the radar received signal, an A/D converter circuit 2, and a circuit 5 that determines the amplitude distribution characteristics of the received signal. Based on the determination result, the clutter suppression circuit Selection section 6
Select the required circuit. Note that the number of circuits for determining amplitude distribution characteristics is equal to the type of distribution characteristics of the target noise signal. For example, the amplitude distribution characteristics of sea surface clutter can be Weibull distributed or lognormal distributed, so two amplitude distribution characteristic discrimination circuits are required for sea surface clutter, so the basic embodiment in this case is the third one. As shown in the figure. Next, an embodiment of the present invention will be described using FIG. The amplitude characteristic device for sea surface clutter includes a logarithmic conversion circuit 1, an A/D conversion circuit 2, a Weibull distribution function setting circuit 3, a Weibull conversion circuit 4, and an amplitude characteristic determination circuit 5 for determining whether the characteristic is a Weibull distribution characteristic. A log-normal distribution function setting circuit 3', a Weibull transform circuit 4', an amplitude characteristic determining circuit 5, and a clutter suppressing circuit for selecting a clutter suppressing circuit based on the results of the amplitude characteristic determining circuit for determining whether the characteristic is a normal distribution characteristic. Selection section 6
Consists of. In these configurations, the other circuits except for the Weibull distribution function setting circuit 3 and the log-normal distribution function setting circuit 3' are common, so the following explanation will focus on the Weibull distribution characteristic discrimination system, and will focus on the log-normal distribution function setting circuit. Additional details regarding circuit 3' will be provided later. Now, the received signal logarithmically converted by the logarithmic amplifier circuit 1 is quantized by the A/D converter circuit 2.
The A/D converted signal is sent to the parameter measurement circuit 31.
Parameters are measured according to the clutter whose characteristics are to be identified. For example, if you want to identify whether clutter has a Weibull distribution or not, the distribution function setting circuit 32 sets the distribution function of the Weibull distribution F(U)=1−exp[U/ν]〓 (9); Measure the shape parameter η and scale parameter ν, which are necessary parameters. In addition, when identifying whether or not the clutter has a lognormal distribution, the distribution function setting circuit 32 sets the distribution function of the lognormal distribution F(U)=1/2+erfU−U/−/σ <sub>u</sub> (10). The average value and standard deviation σ <sub>u</sub> required for this purpose are measured by the parameter measuring circuit 31.
Here erf indicates the error function. As already mentioned, the distribution function setting circuit 32 is a circuit that uses the output U of the A/D conversion circuit 2 and the output of the parameter measurement circuit 31 to calculate the distribution function F(U) according to the characteristics of the clutter to be identified. ,
The calculation result F(U) is sent to the variable conversion circuit 4.
The Weibull transform circuit 42 has a function of converting the output F(X) of the input signal distribution function setting circuit 3 into a new Weibull variable having the shape parameter K and scale parameter σ set by the parameter setting circuit 41. That is, as mentioned earlier, the variable U with the distribution function F(U) is defined as the shape parameter K,
In order to convert the Weibull function with the scale parameter σ into a variable Y having the distribution function, it is necessary to calculate Y = σ [−l <sub>o</sub> {1.0−F(U)}] <sup>1/K</sup> in equation (1). . Therefore, the conversion parameter setting circuit 41 sets σ and K, and the results are sent to the Weibull conversion circuit 42. The Weibull transform circuit 42 first calculates 1.0-F(U) using the output F(U) of the distribution function setting circuit 32, logarithmically transforms this result, then converts the sign and raises the result to the 1/K power. After that, variable conversion is performed by multiplying by σ, and a conversion result Y is obtained. If the variable Y is set so that the distribution function F(X) correctly represents the amplitude characteristics of X, then
It should have been converted into a Weibull variable with K as a shape parameter and σ as a scale parameter.
Therefore, the amplitude characteristic identification circuit 5 calculates K <sub>i</sub> =W <sub>i+N</sub> −W <sub>i</sub> /Z <sub>i+N</sub> −Z <sub>i</sub> (8) and confirms that K <sub>i</sub> is equal to the set value of K. It has a function to determine whether the clutter signal amplitude has a Weibull distribution. However, N is an arbitrary integer, and i=1, 2, 3, 4, . . . represents the number of the radar range cell. There is also a function that uses the relationship between <sub>K i</sub> obtained here and <sub>equation</sub> (4) to confirm that the obtained <sub>C i is</sub> equal to the set value <sub>Klnσ</sub> . I have both. For the values of K <sub>i</sub> and C <sub>i</sub> , we have an identification criterion that states that if they are equal to the set value for L times out of M trials, then they are Weibull distributed. In this case, the amplitude characteristic identification circuit 5 has a function of outputting the identification result of 0. A circuit 6 for selecting a clutter suppression circuit has a function of selecting a clutter suppression circuit most suitable for input clutter suppression based on the output of the amplitude characteristic identification circuit 5. The suppression of Weibull distribution clutter is detailed in the above-mentioned Japanese Patent Application Laid-Open No. 57-165774 entitled ``General Purpose False Alarm Rate Control Device''. The basic embodiment of the present invention has been described above, but the parameter measuring circuit 31 and the distribution function setting circuit 32 that constitute the input signal distribution function setting circuit 3 are
differs depending on the clutter to be identified, so in the following, the distribution function setting circuit 32 is used for the purpose of identifying whether the input signal amplitude has a Weibull distribution or not.
The case where the distribution function is set so that the Weibull distribution function F(U)=1−exp[U/ν] (9) will be described based on FIG. First, the input signal is converted into a quantized signal U by the A/D conversion circuit 2. It is well known that the following relationship holds between the Weibull variable U having the shape parameter η and the scale parameter ν and the logarithmically transformed U. That is, = _lo ν+γ/η (12) ² −() ² =1/η ² π ² /6 (13). Here, 2 represents the average value of U, ² represents the average value of U ² , and γ represents Euler's constant 0.5772. Therefore, the output U of the A/D conversion circuit 2 is input to the square calculation circuit 310, the average value calculation circuit 311, and the division circuit 320. The square calculation circuit 310 is U ²
is output to the average value calculation circuit 312. The average value calculation circuit 312 has a function of calculating the average value of J input U ² , and the average value ² subtraction circuit 314
Output to. Here, J is an arbitrary integer. On the other hand, the average value calculation circuit 311 calculates the average value of the J input U's and outputs it to the square calculation circuit 313. The square calculation circuit 313 calculates the square value ( ) ² of the average value and outputs it to the subtraction circuit 314 .
The subtraction circuit 314 uses the output of the average value calculation circuit 312.
The difference between U ² and the output ( ) ² of the square calculation circuit 313 is calculated. The difference between ² and () ² gives 1/η ² π ² /6 as shown in equation (13). Therefore, the subtraction circuit 31
4 is sent to the shape parameter calculation circuit 318, where the shape parameter η is calculated. Further, the output of the subtraction circuit 314 is sent to a 1/η calculation circuit 315, where 1/η is calculated. The shape parameter calculation circuit 318 and the 1/η calculation circuit 315 are, for example, ROM (Read Only
Memory), etc. can be easily realized. The output of the 1/η calculation circuit 315 is sent to a multiplication circuit 317, where it is multiplied by Euler's constant r to obtain r/η. (12) As can be seen from the equation, the difference between and γ/η gives l _o ν. Therefore, the subtraction circuit 216 calculates the difference between the output of the average value calculation circuit 311 and the output r/η of the multiplication circuit 317, and the result l _o ν is calculated by the index calculation circuit 319.
send to In the exponent calculation circuit 319, exp[l _o
ν] is performed to obtain the scale parameter ν. The configuration and function of the parameter measurement circuit 31 for the Weibull distribution have been described above, and next, the configuration and function of the distribution function setting circuit 32 will be described. In the Weibull distribution function setting circuit 32, first, a division circuit 320 calculates the ratio U/ν between the output of the A/D conversion circuit 2 and the exponent calculation circuit 319, and inputs it to the power calculation circuit 321. The power calculation circuit 321 calculates [U/ν] using U/ν and the output η of the shape parameter calculation circuit 318. This result is input to the exponent calculation circuit 321, and exp[U/ν] can get. Finally, the subtraction circuit 323 obtains the distribution function 1−exp[U/ν]=F(U). Note that the distribution function of the signal after logarithmically amplifying the lognormally distributed noise signal is F(U)=1/2+erfU−U/−/σ. Here, σ is the average value of U, and σ is the variance value of U. Therefore, the parameter measurement circuit 31' and the distribution function circuit 3 for the lognormal distribution
2' is as shown in FIG. In FIG. 5, a logarithmically amplified input signal is converted into a quantized signal by the A/D conversion circuit 2. In FIG.
Next, the output U of the A/D conversion circuit 2 is the square calculation circuit 3.
10', average value calculation circuit 311', subtraction circuit 31
6'. The square calculation circuit 310' outputs U ² to the average value calculation circuit 312'. The average value calculation circuit 311' subtracts the average value for an arbitrary number of data of U by a subtraction circuit 316' and a square calculation circuit 3.
13'. The subtraction circuit 316' calculates U- from the output U of the A/D conversion circuit 2 and the output U of the average value calculation circuit 311', and outputs it to the division circuit 317'. The square calculation circuit 313' is the average value calculation circuit 31
Calculate () ² from the output of 1′ and subtract circuit 31
Output to 4'. The average value calculation circuit 312' outputs the average value ² for an arbitrary number of data of the output U ² of the square calculation circuit 310' to the subtraction circuit 314'. The subtraction circuit 314' is () ² and ² to ² - () ² = σ ²
is calculated and output to the square root calculation circuit 315'. The square root calculation circuit 315' outputs the square root σ of the input σ ² to the division circuit 317'. The division circuit 317' calculates U-U/-/σ for the inputs U- and σ, and outputs the result to the error function calculation circuit 318'. The error function calculation circuit 318' calculates the calculated value erfU- for the input U-U/-/σ.
U/-/σ is output to the adder circuit 319'. here erf
U-U/-/σ is

It is the value defined by [Formula]. Error function calculation circuit 31
8' is a circuit that can be easily realized using a ROM (Read Only Memory) or the like. The adder circuit 319' adds 0.5 to the input erf U-U/-/σ to obtain F(U)=0.5+erf U-U/-/σ. As explained above, the present invention logarithmically amplifies a radar clutter signal, quantizes the signal using an A/D conversion circuit, and then calculates the average value of the quantized signal.
A root mean square value and a variance value are calculated, and parameters necessary for setting a distribution function expected as a statistical characteristic of the amplitude of a radar clutter signal are measured from the calculation results. Thereafter, the distribution function F(U) is calculated using this parameter. Next, variable conversion Y=σ[-l _o {1.0-F(U)}] ^1/K is calculated using this distribution function F(U). Here, σ and K are conversion parameters that are arbitrarily set. Variable Y is distribution function F
If (U) is set to match the statistical distribution characteristics of the amplitude of the radar clutter signal, it is converted into a Weibull variable having a Weibull function with a scale parameter σ shape parameter K as a probability density function. Therefore, confirming that it has been correctly converted into a Weibull variable means that the prediction of the distribution characteristics is correct. The fact that it has been converted to a Weibull distribution means that W _i is defined by W ₁ = l _o [−l _o {1.0−∫ ^Yi _O P [Y; σ, K] dY}] Z _i = l _o Y _i , and W _i+N −W _i /Z _i+N −Z _i is calculated for Z _i , and when this value is equal to K, it is confirmed. Here, P[Y; σ, K] represents a Weibull function with Y as a variable, scale parameter σ, and shape parameter K. It also shows the i-th radar range cell, and W _i , Z _i , and Y _i represent W, Z, and Y in this range cell. Next, when W _i+1 −W _i /Z _i+1 −Z _i =K is confirmed, it means that clutter with the set distribution function is being received, so it is better suited as a clutter suppression circuit. A circuit appropriate for the received signal is selected. Note that each function after the A/D conversion circuit is provided in parallel as many times as there are distribution characteristics that the received signal is expected to have.

[Brief explanation of the drawing]

Fig. 1 is a diagram showing the linear characteristics of the Weibull function, Fig. 2 is a diagram showing the basic configuration of the present invention, Fig. 3 is a diagram showing the basic embodiment of the present invention, and Fig. 4 is a parameter measurement circuit for Weibull distribution. FIG. 5 is a diagram showing the basic configuration of a parameter measuring circuit and a distribution function circuit for log-normal distribution. 1... Logarithmic amplifier circuit, 2... A/D conversion circuit,
3... Weibull distribution function setting circuit, 4... Weibull conversion circuit, 5... amplitude characteristic discrimination circuit, 6... logic AND circuit, 31... Weibull parameter measurement circuit, 32... Weibull distribution function setting circuit, 41
... Conversion parameter setting circuit, 42 ... Conversion circuit, 310 ... Square calculation circuit, 311 ... Average value calculation circuit, 312 ... Average value calculation circuit, 313 ...
... Square calculation circuit, 314 ... Subtraction circuit, 315 ...
... 1/η calculation circuit, 316 ... subtraction circuit, 317 ... multiplication circuit, 318 ... shape parameter calculation circuit, 319 ... index calculation circuit, 320 ... division circuit, 321 ... power calculation circuit, 322 ... ...Exponent calculation circuit, 323...Subtraction circuit, 3'...Log normal distribution function setting circuit, 4'...Log normal conversion circuit, 5'...Amplitude characteristic discrimination circuit, 6'...Logic AND circuit, 31' ...Log normal parameter measurement circuit, 32'...Log normal distribution function setting circuit, 41'...Conversion parameter measurement circuit, 4
2'... Conversion circuit, 310'... Square calculation circuit, 3
11'...Average value calculation circuit, 312'...Average value calculation circuit, 313'...Square calculation circuit, 314'...
Subtraction circuit, 315'...Square root calculation circuit, 31
6'... Subtraction circuit, 317'... Division circuit, 31
8'...Error function calculation, 319'...Addition circuit.

Claims (1)

[Scope of Claims] 1. Parameter measuring means for measuring characteristic parameters of each of a plurality of predetermined distribution functions from a radar reception signal, and a parameter measuring means for measuring characteristic parameters of each of a plurality of predetermined distribution functions from a radar reception signal; Distribution function calculating means for determining the distribution function F(U) of the logarithmically transformed value U; transformation parameter setting means for setting the shape parameter K and the scale parameter σ; and Y=σ[- l _o {1.0
−F(U)}] Variable conversion means for calculating and outputting ^1/K ;
Using Y for each of the plurality of distribution functions obtained by this variable conversion means, logarithmically transformed values of W and Y defined by the integral value from Y to ∞ of the Weibull function with K and σ _are obtained. W _i , W i+N , Z _i , in any radar range cell i and i _+N of Z defined by
Obtain the value of Z _i+N and obtain the slope parameter (W _i+N −W _i )/
(Z _{i + N} − Z _i ) (where N is an arbitrary integer), and a method for determining the K
Clutter amplitude distribution characteristic determination method, comprising: means for determining whether the clutter amplitude distribution characteristic is approximately equal to or within a predetermined range based on K. 2. In claim 1, the parameter measuring means is means for measuring the shape parameter η and scale parameter ν of the Weipul distribution function, and the mean value and variance value σ of the lognormal distribution function, and The function calculation means satisfies F(U)=1−exp(U/ν) and F(U)=1/2+erfU−U/−/σ for the Weibull distribution function and lognormal distribution function, respectively. A method for determining clutter amplitude distribution characteristics.