Ground penetrating radar same-frequency signal separation method based on improved grey wolf algorithm

Abstract

The invention discloses a ground penetrating radar same-frequency signal separation method based on an improved grey wolf algorithm. The method comprises the following steps: improving a standard grey wolf algorithm through Circle chaotic mapping, nonlinear convergence factor adjustment, a Cauchy Gaussian mutation operator and an elimination selection strategy; taking the signal negentropy as a measurement index, and performing Edgeworth expansion on the negentropy to obtain an approximate value of the negentropy; taking the approximate value of the obtained negentropy as a target optimization function, and performing optimization by using an improved standard grey wolf algorithm to obtain a separation matrix, thereby separating a source signal; a separation matrix obtained by using a Givens matrix is further optimized, and the problem dimension is reduced. According to the method, the separation matrix can be effectively obtained under the multi-dimensional problem, and the aim of resisting co-frequency interference under the complex electromagnetic environment is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of radar signal anti-electromagnetic interference, and in particular to a method for separating same-frequency signals of a ground penetrating radar based on an improved grey wolf algorithm. Background Art

[0002] Ground Penetrating Radar (GPR) is a device that uses electromagnetic waves to detect underground objects and structures quickly and non-destructively. It has high resolution and high efficiency, so it is widely used in urban construction, transportation, geology, archaeology, national defense and other fields. GPR technology can obtain information about unknown underground areas without destroying the surface structure, and has become one of the most promising non-destructive underground detection methods.

[0003] The applications of Ground Penetrating Radar (GPR) in military and civilian fields mainly include the following aspects: 1. Underground metal or non-metal buried objects (such as pipelines and cables); 2. The direction of steel bars and cables in buildings (such as bridges and buildings); 3. Road quality inspection, including road quality, thickness and hidden dangers; 4. Geological exploration, such as rock layers, cavities, faults, geological structures, groundwater, underground minerals, etc.; 5. Detection of ancient tombs and ancient sites; 6. Bed mapping of rivers and lakes and detection of underwater targets; 7. Measurement of the thickness of ice and permafrost; 8. Criminal investigation, such as detection of buried weapons, corpses and eavesdropping devices in walls; 9. Military reconnaissance, such as detection of ordnance, mines and underground military facilities.

[0004] The emergence of ground penetrating radar (GPR) provides an important tool for the detection of underground materials and environment, and promotes the continuous innovation of technology. The main challenges faced by GPR technology include system design, hardware implementation, signal processing and data interpretation. Although a large number of studies and experiments have proved the feasibility of GPR, and with the development of hardware technology, complex radar systems can be hardware-based, signal processing technology is relatively lagging and still needs to be studied. The main processes of signal processing include signal preprocessing, target detection, target recognition and target multi-dimensional imaging.

[0005] Due to the rapid development of modern society, electronic devices are diverse, which makes the electromagnetic environment in the detection environment complex and changeable, and the electromagnetic spectrum is becoming more crowded. Electromagnetic interference, led by electromagnetic wave signals, always affects the accuracy and sensitivity of electronic equipment. Among them, co-channel interference is a common clutter signal, which will lead to a decrease in radar detection efficiency and accuracy, and even cause damage to radar hardware. Therefore, avoiding co-channel interference is of great significance to improving GPR detection efficiency and accuracy. Summary of the invention

[0006] In order to study the co-frequency signal interference suppression problem in the GPR signal preprocessing part, the present invention provides a co-frequency signal separation method for ground penetrating radar based on the improved gray wolf algorithm. First, the standard algorithm is improved by Circle chaos mapping, nonlinear convergence factor adjustment, Cauchy-Gaussian mutation operator and elimination selection strategy. Then, the signal negative entropy is used as the target optimization function, and the improved gray wolf algorithm is used to solve it. Finally, Givens transformation is used to optimize the required separation matrix, reduce the problem dimension, and reduce the amount of calculation. This method can effectively obtain the separation matrix under multi-dimensional problems and achieve the purpose of resisting co-frequency interference in complex electromagnetic environments.

[0007] The technical solution adopted by the present invention is:

[0008] The method for separating the same-frequency signals of ground penetrating radar based on the improved gray wolf algorithm includes the following steps:

[0009] Step 1: Improve the standard grey wolf algorithm through Circle chaos mapping, nonlinear convergence factor adjustment, Cauchy-Gauss mutation operator and elimination selection strategy;

[0010] Step 2: Using the signal negative entropy as a measurement indicator, the negative entropy is expanded using Edgeworth to obtain an approximate value of the negative entropy.

[0011] Step 3: Take the approximate value of the negative entropy obtained in step 2 as the target optimization function, use the improved standard grey wolf algorithm in step 1 to find the optimal solution, obtain the separation matrix, and thus separate the source signal;

[0012] Step 4: Use the Givens matrix to further optimize the separation matrix obtained in step 3 to reduce the dimension of the problem.

[0013] In step 1, the standard gray wolf algorithm divides the gray wolf population into four levels: α, β, δ, and ω, which correspond to the optimal solution, the second optimal solution, the third optimal solution, and the remaining solutions, respectively.

[0014] Wolf pack hunting method satisfies:

[0015] D=|C·X p (t)-X(t)|

[0016] X(t+1)=X p (t)-A·D

[0017] Where D is the distance between the prey and the current gray wolf; C is the swing factor; X p (t) represents the position of the prey in the tth iteration; t represents the current number of iterations; X(t) represents the position of the gray wolf individual in the tth iteration; X(t+1) represents the position of the gray wolf individual in the t+1th iteration; A represents the convergence coefficient.

[0018] The convergence coefficient A and the swing factor satisfy:

[0019] A=2ar1-a

[0020] C=2r2

[0021] Where A is the convergence coefficient; C is the swing factor; r1 and r2 are random numbers that obey the uniform distribution of [0, 1]; a is the convergence factor.

[0022] In the process of problem solving, the positions of the three gray wolves α, β, and δ are used to replace the position of the prey, and the three gray wolves α, β, and δ are allowed to jointly guide the ω gray wolf forward.

[0023] First, determine the distance between the ω gray wolf and the α, β, and δ gray wolf individuals. The formula is as follows:

[0024]

[0025]

[0026] In the formula, X α (t), X β (t), X δ (t) represents the position of α, β, δ gray wolf individuals at the tth iteration; X1, X2, X3 represent the distance between ω gray wolf and α, β, δ gray wolf individuals; A α , A β , A δ represents the convergence coefficient of α, β, δ gray wolf individuals; C α , C β , C δ Represents the swing factor of α, β, δ gray wolf individuals.

[0027] Then, use X1, X2, and X3 to determine the current position of the ω gray wolf individual, and the confirmation formula is as follows:

[0028]

[0029] Where X(t+1) represents the position of the gray wolf individual in the t+1th iteration, and X1, X2, and X3 represent the distances between the ω gray wolf and the α, β, and δ gray wolf individuals.

[0030] In step 1, improving the standard grey wolf algorithm includes the following steps:

[0031] S1.1: First, the initial population is optimized by Circle chaos mapping. The optimization process is as follows:

[0032] a): Generate N D-dimensional vectors, each dimension value is a chaotic value in the interval [0,1], and the N vectors are represented by Z1, Z2, …, Z N ,in, They represent the chaotic component values ​​generated by the i-th vector in D dimension respectively; the update formula is as follows:

[0033]

[0034] In the formula, represents the chaotic component value generated by the i-th vector in the j-th dimension; i represents an integer in the interval [1, N]; N is the number of gray wolves in the population; j represents an integer in the interval [1, D]; D represents the dimension of the problem being solved; Represents the randomly generated element value of the jth dimension of the i-th individual;

[0035] b): Load each chaotic component into the value range of the initial position of the gray wolf to generate the initial gray wolf population position X. The element value in the initial gray wolf population position X is:

[0036]

[0037] In the formula, represents the randomly generated element value of the jth dimension of the i-th individual; ub j and lb j are the maximum and minimum values ​​of the j-th dimension element at the individual position of the gray wolf;

[0038] S1.2: Then, the convergence factor a was adjusted, and the improved formula is:

[0039]

[0040] In the formula, t is the number of iterations, t max is the maximum number of iterations.

[0041] S1.3: The Cauchy-Gaussian mutation operator is introduced to perturb the global optimal gray wolf individual, α wolf, to avoid falling into the local optimum. The updated global optimal gray wolf individual formula is:

[0042]

[0043] In the formula, represents the globally optimal gray wolf individual in the updated wolf population α; X α represents the global optimal gray wolf individual in the population; G(0,1) represents the standard Gaussian distribution; C(0,1) represents the standard Cauchy distribution; η is the weight, satisfying

[0044] S1.4: Use the elimination selection strategy to further speed up the convergence of the algorithm. The elimination selection strategy is as follows:

[0045] a) Define the degree of the i-th gray wolf individual in the t-th iteration as The formula satisfies:

[0046]

[0047] In the formula, represents the fitness value of the i-th gray wolf individual in the t-th iteration; Represents the fitness value of the i-th gray wolf individual in the previous iteration.

[0048] b) Define the evolution degree of the i-th gray wolf individual to the optimal gray wolf individual α in the population as The formula satisfies:

[0049]

[0050] In the formula, Represents the fitness value of wolf α at the tth iteration.

[0051] c) Comparison and The size of Then keep the individual; if Then a new gray wolf individual with a higher degree of evolution is selected, and the position of the new gray wolf individual is:

[0052]

[0053] In the formula, It represents the position of the gray wolf individual updated by the i-th gray wolf individual in the t-th iteration. represents the gray wolf individual of α wolf in the tth iteration, represents the position of the i-th gray wolf in the t-th iteration. r is a random number that follows a uniform distribution between [0,1].

[0054] In step 2, the co-frequency signal is essentially a signal with the same or similar frequency as the radar transmission signal. When the antenna receives the signal, it may not be able to process the target echo normally. Depending on whether the signal repetition frequency is similar, co-frequency interference can be divided into co-frequency synchronous interference and co-frequency asynchronous interference. If there is a transmitting source with the same frequency within the radar device range gate, the signal transmission form is the same:

[0055]

[0056] Where a(t) is the amplitude modulation function, f0 is the carrier frequency, is the phase modulation function.

[0057] The same-frequency interference signal must also meet the distance limit. When the same-frequency signal is within the range gate of the radar device, it may interfere with the detection; the range gate R refers to the minimum distance R that the radar can observe. min With the maximum distance Rmax The spacing between. Satisfy:

[0058] R max =cT / 2

[0059] R min =c(T-τ) / 2

[0060] R=R max -R min =cτ / 2

[0061] Where T represents the target echo delay, τ represents the pulse width of the signal transmitted by the radar device, and c is the speed of light.

[0062] The same-frequency interference signal usually comes from different signal transmission sources, so the signals are independent of each other. This signal is usually a non-Gaussian signal, and the signal that obeys the Gaussian distribution has only one Gaussian noise. In signal separation, non-Gaussianity is an important criterion for judging signal independence. Therefore, the interference signal can be separated from the complex signal by measuring the non-Gaussianity of the signal.

[0063] Negative entropy is an important criterion for measuring the non-Gaussianity of a signal. The present invention intends to use negative entropy to measure the non-Gaussianity of a signal as a criterion for separating interference signals. For a random radar signal y, its negative entropy J(y) is expressed as follows:

[0064] J(y)=H(y G )-H(y)

[0065] In the formula, y G represents a Gaussian random vector with the same covariance matrix as the random radar signal y; H(y G ) represents the differential entropy of the Gaussian random vector; H(y) represents the differential entropy of the random radar signal y, which is defined as follows:

[0066] H(y)=-∫p(y)logp(y)dy

[0067] Where p(y) represents the probability density function of the random radar signal y.

[0068] The Edgeworth expansion is used for the negative entropy to obtain the approximate calculated value instead. The negative entropy is expanded as follows:

[0069]

[0070] In the formula, represents the square of the third-order derivative of the negative entropy of the random radar signal y, represents the square of the fourth-order derivative of the random radar signal y, represents the fourth power of the third-order derivative of the random radar signal y, and k4(y) represents the fourth-order derivative of the random radar signal y.

[0071] Usually, the last two terms are ignored, so the approximate value of negative entropy is:

[0072]

[0073] In step 3, the negative entropy approximation value in step 2 is used as the target optimization function, and the improved gray wolf algorithm in step 1 is used for optimization. Specifically, the following steps are included:

[0074] S3.1: Initialize the relevant parameters of the algorithm. Set the problem dimension D, the maximum number of iterations M, the size of the gray wolf population N and other parameters;

[0075] S3.2: randomly generate an initial population X, and generate a new initial population using Circle chaos mapping according to S1.1;

[0076] S3.3: Calculate the fitness value of each gray wolf individual and sort them from high to low according to fitness. The individual with the highest fitness is designated as α wolf, the second best individual is designated as β wolf, the third best individual is designated as δ wolf, and the remaining individuals are designated as δ wolves. Based on the results of this iteration, update the optimal solution of the current population;

[0077] S3.4: Calculate the convergence factor and update the convergence factor according to S1.2;

[0078] S3.5: Update the convergence coefficient, swing factor and position of the individual gray wolf according to the formula in step 1;

[0079] S3.6: Perform Cauchy-Gauss mutation on the current α gray wolf individual according to S1.3 and update its position;

[0080] S3.7: Carry out elimination selection strategy on the current population according to S1.4 to obtain individuals with higher degree of individual evolution;

[0081] S3.8: Repeat the iteration until the maximum number of iterations is reached to obtain the optimization result.

[0082] In step 4, the negative entropy separation matrix obtained by optimizing the improved grey wolf algorithm is further optimized using the Givens matrix, as follows:

[0083] The Givens matrix is ​​used to transform the n-dimensional orthogonal matrix into the product of n×(n-1) / 2 transformation matrices. Using the Givens matrix transformation, the separation matrix is:

[0084]

[0085] In the formula, B(θ) represents the separation matrix after Givens matrix transformation, and θ1, θ2, θ3 are the rotation angles of the separation matrix. At this time, we only need to solve θ = [θ1, θ2, θ3], and the problem dimension becomes 3.

[0086] The present invention provides a method for separating same-frequency signals of ground penetrating radar based on an improved grey wolf algorithm, and the technical effects are as follows:

[0087] 1) The present invention adopts negative entropy as a criterion. Negative entropy can efficiently measure the non-Gaussianity of signals, has high stability, and can provide a more accurate basis for the separation of different signals.

[0088] 2) The present invention adopts the Grey Wolf Algorithm with fewer parameters as the optimization algorithm, and optimizes the algorithm using Circle chaos mapping, nonlinear convergence factor, Cauchy-Gaussian mutation and elimination selection strategy, so that the algorithm's optimization ability and convergence effect are more excellent.

[0089] 3) The present invention uses the Givens matrix to further optimize the separation matrix output by the improved grey wolf algorithm, which can effectively reduce the dimension of the problem and reduce the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] The present invention will be further described below in conjunction with the accompanying drawings and examples;

[0091] Figure 1 Flow chart of the method of the present invention.

[0092] Figure 2 Comparison of the convergence curves of each algorithm on test function 1.

[0093] Figure 3 Comparison of the convergence curves of each algorithm on test function 2.

[0094] Figure 4 Comparison of the convergence curves of each algorithm on test function 3.

[0095] Figure 5 Comparison of the convergence curves of each algorithm on test function 1. DETAILED DESCRIPTION

[0096] The ground penetrating radar same-frequency signal separation method based on the improved gray wolf algorithm includes the following four steps:

[0097] Step 1: Improve the standard grey wolf algorithm through Circle chaos mapping, nonlinear convergence factor adjustment, Cauchy-Gauss mutation operator and elimination selection strategy. The optimization process of Circle chaos mapping is as follows:

[0098]

[0099] In the formula, i represents an integer in the interval [1, N], N is the number of gray wolves in the population; j represents an integer in the interval [1, D], D represents the dimension of the problem being solved, Represents the randomly generated element value of the j-th dimension of the i-th individual.

[0100] b) Load each chaotic component into the value range of the initial position of the gray wolf to generate the initial gray wolf population position X, where the element value of X is:

[0101]

[0102] In the formula, ub j and lb j are the maximum and minimum values ​​of the j-th dimension element of the gray wolf individual position, respectively.

[0103] Then, the convergence factor a was adjusted, and the improved formula is:

[0104]

[0105] In the formula, t is the number of iterations, t max is the maximum number of iterations.

[0106] Then the Cauchy-Gauss mutation operator is introduced to perturb the global optimal gray wolf individual, α wolf, to avoid falling into the local optimum. The updated global optimal gray wolf individual formula is:

[0107]

[0108] In the formula, X α represents the global optimal gray wolf individual in the population, G(0,1) represents the standard Gaussian distribution, C(0,1) represents the standard Cauchy distribution, t is the number of iterations, t max is the maximum number of iterations, η is the weight, satisfying

[0109] The elimination selection strategy is used to further speed up the convergence of the algorithm. The elimination selection strategy is as follows:

[0110] a) Define the degree of the i-th gray wolf individual in the t-th iteration as The formula satisfies:

[0111]

[0112] In the formula, represents the fitness value of the i-th gray wolf individual in the t-th iteration, Represents the fitness value of the i-th gray wolf individual in the previous iteration.

[0113] b) Define the evolution degree of the i-th gray wolf individual to the optimal gray wolf individual α in the population as The formula satisfies:

[0114]

[0115] In the formula, Represents the fitness value of wolf α at the tth iteration.

[0116] c) Comparison and The size of Then keep the individual; if Then a new gray wolf individual with a higher degree of evolution is selected, and the position of the new gray wolf individual is:

[0117]

[0118] Where r is a random number that follows a uniform distribution between [0,1].

[0119] Step 2: Signal separation based on negative entropy.

[0120] Negative entropy J(y) is expressed as follows:

[0121] J(y)=H(y G )-H(y)

[0122] In the formula, y G represents a Gaussian random vector with the same covariance matrix as y, and H(y) represents the differential entropy of the random variable y, which is defined as follows:

[0123] H(y)=-∫p(y)log p(y)dy

[0124] Then the negative entropy is expanded using Edgeworth to obtain the approximate calculated value instead. The negative entropy is expanded as follows:

[0125]

[0126] Usually, the last two terms are ignored, so the approximate value of negative entropy is:

[0127]

[0128] Step 3: Use the improved grey wolf algorithm to optimize the signal negative entropy, obtain the separation matrix, and thus separate the source signal. The overall process is shown in Figure 1 shown.

[0129] Step 4: Use the Givens matrix to optimize the fitness function:

[0130] The Givens matrix can transform an n-dimensional orthogonal matrix into the product of n×(n-1) / 2 transformation matrices. Taking n=3 as an example, we need to solve θ=[θ1, θ2, θ3, θ4, θ5, θ6, θ7, θ8, θ9], with a dimension of 9. Using the Givens matrix transformation, the separation matrix is:

[0131]

[0132] At this time, we only need to solve θ=[θ1, θ2, θ3], and the problem dimension becomes 3.

[0133] In order to prove the rationality of the method, four standard test functions are selected for comparative simulation. The improved grey wolf algorithm (ESGWO) of the present invention is used to optimize the four test functions and compared with the particle swarm algorithm (PSO), crow search algorithm (CSA), chicken swarm optimization algorithm (CSO), and grey wolf algorithm (GWO). Among them, the standard test functions are shown in Table 1 below:

[0134] Table 1 Test function table

[0135]

[0136] Each algorithm is run independently 20 times in each test function, and the optimal value, worst value and average value of the optimization results of the four algorithms are obtained. The experimental results are shown in Table 2 below.

[0137] Table 2 Optimization results of four algorithms

[0138]

[0139]

[0140] It can be seen from Table 2 above that, compared with the four comparison algorithms, the optimization results of the method of the present invention, whether the optimal solution, the worst solution or the average solution, are closest to the theoretical optimum and have better effects.

[0141] Among them, the convergence curves of each algorithm on different test functions are as follows: Figure 2 to Figure 5 As shown,

[0142] Depend on Figure 2 It can be seen that the algorithm of the present invention converges faster on the continuous unimodal function Sphere and has a better optimization effect.

[0143] Depend on Figure 3 It can be seen that the algorithm of the present invention converges faster on the continuous multi-peak function Griewank and has a better optimization effect.

[0144] Depend on Figure 4 It can be seen that the algorithm of the present invention converges faster on the continuous multi-peak function Ackley and has a better optimization effect.

[0145] Depend on Figure 5 It can be seen that the algorithm of the present invention has a faster convergence speed and better optimization effect on the continuous unimodal function Schwefel 2.22. It can be seen that the optimization performance and algorithm robustness of the method of the present invention are better.

Claims

1. A method for separating the same-frequency signals of ground penetrating radar based on the improved grey wolf algorithm, characterized in that The following steps are involved: Step 1: Improve the Grey Wolf Algorithm through Circle Chaos Mapping, nonlinear convergence factor adjustment, Cauchy-Gauss mutation operator and elimination selection strategy; Step 2: Using the signal negative entropy as a measurement indicator, the negative entropy is expanded using Edgeworth to obtain an approximate value of the negative entropy. Step 3: Take the approximate value of the negative entropy obtained in step 2 as the target optimization function, use the improved grey wolf algorithm in step 1 to find the optimal solution, obtain the separation matrix, and thus separate the source signal.

2. The method for separating same-frequency signals of ground penetrating radar based on improved grey wolf algorithm according to claim 1, characterized in that: The method also includes step 4: using the Givens matrix to further optimize the separation matrix obtained in step 3 to reduce the dimension of the problem.

3. The method for separating same-frequency signals of ground penetrating radar based on improved grey wolf algorithm according to claim 1 is characterized in that: In step 1, the improved gray wolf algorithm includes the following steps: S1.1: First, the initial population is optimized by Circle chaos mapping. The optimization process is as follows: a): Generate N D-dimensional vectors, each dimension value is a chaotic value in the interval [0,1], and the N vectors are represented by Z1, Z2, …, Z N ,in, They represent the chaotic component values ​​generated by the i-th vector in D dimension respectively; the update formula is as follows: In the formula, represents the chaotic component value generated by the update of the i-th vector in the j-th dimension; i represents an integer in the interval [1, N]; N is the number of gray wolves in the population; j represents an integer in the interval [1, D]; D represents the dimension of the problem being solved; Represents the randomly generated element value of the jth dimension of the i-th individual; b): Load each chaotic component into the value range of the initial position of the gray wolf to generate the initial gray wolf population position X. The element value in the initial gray wolf population position X is: In the formula, represents the randomly generated element value of the jth dimension of the i-th individual; ub j and lb j are the maximum and minimum values ​​of the j-th dimension element at the individual position of the gray wolf; S1.2: Then, the convergence factor a was adjusted, and the improved formula is: In the formula, t is the number of iterations, t max is the maximum number of iterations; S1.3: The Cauchy-Gaussian mutation operator is introduced to perturb the global optimal gray wolf individual, i.e., α wolf, to avoid falling into the local optimum; the updated global optimal gray wolf individual formula is: In the formula, represents the globally optimal gray wolf individual in the updated wolf population α; X α represents the global optimal gray wolf individual in the population; G(0,1) represents the standard Gaussian distribution; C(0,1) represents the standard Cauchy distribution; η is the weight, satisfying S1.4: Use the elimination selection strategy to further speed up the convergence of the algorithm; the elimination selection strategy is as follows: a) Define the degree of the i-th gray wolf individual in the t-th iteration as The formula satisfies: In the formula, represents the fitness value of the i-th gray wolf individual in the t-th iteration; Represents the fitness value of the i-th gray wolf individual in the previous iteration; b) Define the evolution degree of the i-th gray wolf individual to the optimal gray wolf individual α in the population as The formula satisfies: In the formula, represents the fitness value of wolf α at the tth iteration; c) Comparison and The size of Then keep the individual; if Then a new gray wolf individual with a higher degree of evolution is selected, and the position of the new gray wolf individual is: In the formula, It represents the position of the gray wolf individual updated by the i-th gray wolf individual in the t-th iteration. represents the gray wolf individual of α wolf in the tth iteration, represents the position of the i-th gray wolf individual in the t-th iteration; r is a random number that obeys the uniform distribution between [0,1].

4. The method for separating same-frequency signals of ground penetrating radar based on improved grey wolf algorithm according to claim 1, characterized in that: In step 2, in signal separation, non-Gaussianity is an important criterion for judging signal independence; therefore, interference signals can be separated from complex signals by measuring signal non-Gaussianity; negative entropy is used to measure signal non-Gaussianity as a criterion for interference signal separation; for a random radar signal y, its negative entropy J(y) is expressed as follows: J(y)=H(y G )-H(y) In the formula, y G represents a Gaussian random vector with the same covariance matrix as the random radar signal y; H(y G ) represents the differential entropy of the Gaussian random vector; H(y) represents the differential entropy of the random radar signal y, which is defined as follows: H(y)=-∫p(y)logp(y)dy Where p(y) represents the probability density function of the random radar signal y.

5. The method for separating same-frequency signals of ground penetrating radar based on improved grey wolf algorithm according to claim 4 is characterized in that: The Edgeworth expansion is used for the negative entropy to obtain the approximate calculated value instead. The negative entropy is expanded as follows: In the formula, represents the square of the third-order derivative of the negative entropy of the random radar signal y, represents the square of the fourth-order derivative of the random radar signal y, represents the fourth power of the third-order derivative of the random radar signal y, k4(y) represents the fourth-order derivative of the random radar signal y; The approximate value of negative entropy is:

6. The method for separating same-frequency signals of ground penetrating radar based on improved grey wolf algorithm according to claim 3 is characterized by: The step 3 includes the following steps: S3.1: Initialize the relevant parameters of the algorithm; set the problem dimension D, the maximum number of iterations M, the size of the gray wolf population N and other parameters; S3.2: randomly generate an initial population X, and generate a new initial population using Circle chaos mapping according to S1.1; S3.3: Calculate the fitness value of each gray wolf individual and sort them from high to low according to fitness; designate the individual with the highest fitness as α wolf, the second best individual as β wolf, the third best individual as δ wolf, and the remaining individuals as δ wolves; based on the results of this iteration, update the optimal solution of the current population; S3.4: Calculate the convergence factor and update the convergence factor according to S1.2; S3.5: Update the convergence coefficient, swing factor and position of the individual gray wolf according to the formula in step 1; S3.6: Perform Cauchy-Gauss mutation on the current α gray wolf individual according to S1.3 and update its position; S3.7: Carry out elimination selection strategy on the current population according to S1.4 to obtain individuals with higher degree of individual evolution; S3.8: Repeat the iteration until the maximum number of iterations is reached to obtain the optimization result.

7. The method for separating same-frequency signals of ground penetrating radar based on improved grey wolf algorithm according to claim 2 is characterized in that: In step 4, the negative entropy separation matrix obtained by optimizing the improved grey wolf algorithm is further optimized using the Givens matrix, as follows: The Givens matrix is ​​used to transform the n-dimensional orthogonal matrix into the product of n×(n-1) / 2 transformation matrices. Using the Givens matrix transformation, the separation matrix is: Where B(θ) represents the separation matrix after Givens matrix transformation, θ1, θ2, θ3 are the rotation angles of the separation matrix respectively; At this time, we only need to solve θ=[θ1, θ2, θ3], and the problem dimension becomes 3.

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