SIMO bridge flaw detection radar dielectric coefficient high-precision tomography inversion method and system based on corner method

Abstract

The invention discloses an SIMO bridge flaw detection radar dielectric coefficient high-precision tomographic inversion method and system based on an angle rotation method, which are used for improving the refraction angle estimation precision and dielectric coefficient inversion precision of an SIMO bridge flaw detection radar at each dielectric interface. According to the method, the refraction point coordinates of each receiving array element of the SIMO system on each layer of interface are calculated by adopting an improved corner method, near-field beam forming is performed on each layer of steel bar target based on a minimum entropy criterion, and the dielectric coefficient of each dielectric layer is subjected to high-precision tomography inversion. Simulation experiment results show that the refraction point estimation error can be effectively reduced, the accuracy of dielectric coefficient inversion is improved by about 6.03%, the accuracy of inversion results is remarkably enhanced, and the method has engineering application prospects.

Description

Technical Field

[0001] The present invention belongs to the field of ground penetrating radar, and in particular relates to a dielectric constant inversion method and system for layered media. Background Art

[0002] Bridge flaw detection radar is a non-destructive underground detection technology that uses high-frequency electromagnetic waves to penetrate the surface for imaging and detection. It can detect differences in the electromagnetic properties of different underground materials. Its operating principle is based on the transmission and reception of electromagnetic waves. The transmitting antenna emits high-frequency electromagnetic waves into the ground. When the electromagnetic waves encounter different underground media, they are reflected, refracted, and scattered due to differences in dielectric constant and conductivity. The receiving antenna picks up the echo signals that pass through the interfaces of different materials. By measuring parameters such as the echo signal's intensity and time delay, it infers the physical properties of the underground target and obtains information on the distribution of the underground medium, thereby enabling imaging and analysis of underground structures.

[0003] In recent years, researchers have been exploring and researching GPR technology, proposing methods such as acoustic emission (AE), ultrasonic pulse (UT), impact echo (IE), and infrared thermography (IT). Most of these existing technologies rely on single-transmitter, single-receiver (SISO) radar systems. While SISO systems offer a simple structure and facilitate real-time processing, they suffer from lower resolution and weaker anti-interference capabilities compared to multi-channel systems. In contrast, the single-input, multiple-output (SIMO) mode simultaneously captures echo signals from the same target through multiple receiving channels, effectively improving the system's coherence and resolution. This allows the radar system to more accurately locate targets and enhances its detection capabilities in complex environments. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: in view of the large error between the estimated coordinates of the refraction point of the medium interface and the true value during the inversion process and the low efficiency and poor precision of the self-focusing technology, a refraction point calculation method based on the improved rotation angle method is adopted to solve the error problem caused by the different medium incident angles in the application of the traditional MAST algorithm in array antennas, and an iterative search self-focusing algorithm based on the minimum entropy criterion is introduced to achieve high-precision tomographic inversion of the dielectric constant.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] First, the present invention proposes a high-precision tomographic inversion method for dielectric coefficient of SIMO bridge flaw detection radar based on the rotation angle method, comprising the following steps:

[0007] S1. Using a SIMO radar to receive echo signals. The radar is a single-transmitter, multiple-receiver bistatic system that transmits a single-cycle Gaussian pulse signal. Multiple array elements receive the signal simultaneously. The echo signals are processed by range migration correction and near-field beamforming.

[0008] S2. Inverting the dielectric constant of the first layer of medium, including iterative search based on the initial value combined with the step size, optimizing the distance migration compensation matrix using the minimum entropy criterion, and determining the dielectric constant of the first layer by minimizing the entropy value;

[0009] S3. Estimate the coordinates of the refraction points of each array element at the interface of the second layer of dielectric material using the rotation angle method based on angle iteration and boundary constraints. Combine the inversion results of the first layer as initial values and iteratively invert the dielectric coefficient of the second layer.

[0010] S4. Perform layer-by-layer inversion on the dielectric coefficient of the nth layer of medium, where n≥3. Use the inversion result of the previous layer as prior information and repeat step S3 to achieve tomographic inversion of the dielectric coefficients of multiple layers.

[0011] Furthermore, in the method proposed by the present invention, the single-cycle Gaussian pulse emission signal a(t) in step S1 is:

[0012]

[0013] Where A is the amplitude of the Gaussian pulse, σ is the standard deviation of the Gaussian pulse, and f0 is the radar operating center frequency.

[0014] If the target is in the nth layer of the medium, in SIMO mode, the echo signal S(t n ,M) is

[0015]

[0016] Where t=[t1,t2,…t W ] T , W is the number of sampling points of the range signal, t1, t2, ...t W is the sampling time corresponding to the corresponding sampling point, M is the total number of array elements, S(t n ,M) is the W×M B-scan two-dimensional signal matrix, τ in is the transmission delay from the target to the i-th array element in the n-layer medium, R in A is the propagation path distance from the target to the i-th array element in the n-th layer of the medium, i is the amplitude of the echo signal of the i-th array element, ε n is the dielectric constant of the nth layer of medium, and C is the speed of light.

[0017] Furthermore, the distance migration compensation matrix in step S2 of the method of the present invention is defined as:

[0018]

[0019] Where l represents the number of searches, f W is the frequency of the Wth frequency point, is the estimated dielectric constant of the first layer of medium during the l-th search.

[0020] Furthermore, in step S2 of the method of the present invention, the range migration compensation first performs a fast Fourier transform (FFT) on the first layer target S(t1,M) received by the array along the range direction, and converts the signal into the range frequency domain. In this domain, the array signal is compared with the range migration compensation matrix Multiply and convert the signal to the range time domain through inverse fast Fourier transform IFFT to compensate for the range migration offset of the target, that is:

[0021]

[0022] In the formula is the Hadamard product, IFFT W To perform inverse fast Fourier transform on the range direction, is the two-dimensional time domain signal after range migration correction in the lth autofocusing process;

[0023] According to the propagation characteristics of near-field spherical waves, the receiving array is phase compensated, and after compensation, the fast Fourier transform (FFT) is performed along the array aperture direction to convert the signal into the beam domain to achieve energy focusing and target imaging in the near-field area, namely:

[0024]

[0025] Where FFT M Perform a fast Fourier transform on the array element.

[0026] Furthermore, in step S3 of the method of the present invention, the coordinates of the refraction points of each array element at the interface of the second medium are estimated based on the angle iteration and boundary constraint rotation method, and the formula is:

[0027]

[0028] Where x1 is the horizontal coordinate of the emission source, h1 is the height of the emission source from the ground, and h2 is the depth of the target underground. is the refraction angle.

[0029] Furthermore, in step S3 of the method of the present invention, the dielectric constant of the second layer is iteratively inverted, specifically:

[0030] Assume that in the first self-focusing iteration, the second layer medium element distance migration compensation matrix is for:

[0031]

[0032] Where, is the estimated dielectric constant of the second layer of medium during the l-th search, is the propagation path distance in the first layer of medium during the l-th search, is the propagation path distance in the second layer of the medium during the lth search;

[0033] Range migration compensation first performs fast Fourier transform (FFT) on the second layer target S(t2,M) received by the array along the range direction, and converts the signal into the range frequency domain. In this domain, the array signal is compared with the range migration compensation matrix Multiply and convert the signal to the range time domain through inverse fast Fourier transform IFFT to compensate for the range migration offset of the target, that is:

[0034]

[0035] In the formula is the Hadamard product, is the two-dimensional time domain signal after range migration correction;

[0036] In the first self-focusing, after the range migration correction, the near-field guidance vector of the target in each receiving array element of the second layer of medium is for:

[0037]

[0038] According to the propagation characteristics of near-field spherical waves, the receiving array is phase compensated to eliminate the phase difference of the spherical wavefront curvature caused by the spatial distribution of the array elements. After compensation, the fast Fourier transform FFT is performed along the array aperture direction to convert the signal into the beam domain, realizing energy focusing and target imaging in the near-field area, that is,

[0039]

[0040] In the near-field beamforming self-focusing imaging process, when the target entropy value reaches the minimum, the search process stops, and the dielectric constant result of the second layer of the medium in the tomographic inversion is obtained at this time. If the minimum entropy value is not reached, the dielectric constant is updated and the steps are repeated until the target minimum entropy value is obtained.

[0041] At the same time, the present invention also proposes an electronic system, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method proposed by the present invention.

[0042] Furthermore, the electronic system further comprises: a signal transmitting module for generating a single-cycle Gaussian pulse signal;

[0043] Multi-channel receiving module, synchronously collecting echo signals from each array element;

[0044] The tomographic inversion module performs range migration correction, near-field beamforming, and iterative inversion of dielectric constants.

[0045] Finally, the present invention provides a computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable the computer to execute the method provided by the present invention.

[0046] The present invention adopts the above technical solution, which has the following technical effects compared with the prior art:

[0047] This paper provides an efficient minimum entropy-based SIMO bridge flaw detection radar tomography inversion method and system. By incorporating the angle rotation method into the MAST algorithm and using angle rotation to calculate the coordinates of the refraction point, the accuracy of the refraction point position estimation is improved. High-precision focused imaging of each layer of steel bars is then performed based on the minimum entropy criterion, and focused search is performed using an iterative search. Finally, the dielectric constant of each layer of medium is inverted. This method significantly improves the accuracy and stability of the inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a double-layer medium model diagram.

[0049] Figure 2 This is a process flow chart of the present invention.

[0050] Figure 3 Angle iteration model diagram for double-layer media.

[0051] Figure 4 This is a comparison chart of the coordinate analysis of the refraction point on the interface between the MAST algorithm and the TAMST algorithm.

[0052] Figure 5 Figure 2 is the mean square error plot of the two refraction point estimation algorithms.

[0053] Figure 6 This is a comparison chart of the two self-focusing algorithms based on the minimum entropy criterion and the maximum energy criterion.

[0054] Figure 7 This is a cross-sectional diagram of the minimum entropy criterion and the maximum energy criterion. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is described in detail below with reference to the accompanying drawings:

[0056] This invention primarily studies the tomographic inversion method for SIMO bridge flaw detection radar based on the minimum entropy criterion. A single-transmitter, multiple-receiver dual-base system based on an array-based ground-penetrating radar is proposed. The system receives the target's echo signal via the SIMO radar and performs a tomographic inversion of the dielectric constant of the first layer of the medium. This information serves as prior information for the layer-by-layer inversion of the dielectric constants of subsequent layers. During the inversion process, the system first estimates the coordinates of the refraction point of the current layer of the medium. Then, combining range migration correction with near-field beamforming, the dielectric constant is tomographically inverted based on the principle of minimizing the target's entropy value. Furthermore, the dielectric constant is dynamically updated by checking whether the entropy value meets the minimization condition. This invention enables high-precision tomographic inversion of the dielectric constant, significantly improving the accuracy and stability of the inversion.

[0057] Example 1: Figure 1 The tomographic inversion model of SIMO ground penetrating radar in double-layer media is demonstrated. Figure 2 The method processing flow of the present invention is as follows:

[0058] Step 1: SIMO radar receives the echo signal, specifically:

[0059] The SIMO bridge flaw detection radar is a single-transmitter, multiple-receiver bistatic system that transmits a single-cycle Gaussian pulse signal, which is received simultaneously by multiple array elements. The single-cycle Gaussian pulse transmission signal a(t) is as follows:

[0060]

[0061] Where A is the amplitude of the Gaussian pulse, σ is the standard deviation of the Gaussian pulse, and f0 is the radar operating center frequency. If the target is in the nth layer of the medium, in SIMO mode, the echo signal S(t n ,M) is

[0062]

[0063] Where t=[t1,t2,…t W ] T , W is the number of sampling points of the range signal, t1, t2, ...t W is the sampling time corresponding to the corresponding sampling point, M is the total number of array elements, S(t n ,M) is the W×M B-scan two-dimensional signal matrix, τ in is the transmission delay from the target to the i-th array element in the n-layer medium, R in A is the propagation path distance from the target to the i-th array element in the n-th layer of the medium, i is the amplitude of the echo signal of the i-th array element, ε n is the dielectric constant of the nth layer of medium, and C is the speed of light.

[0064] Step 2: High-precision inversion of the dielectric constant of the first layer, specifically:

[0065] In the first layer of medium, set The initial value of the dielectric constant is 0.05, and the step size is 0.05. The range migration correction and near-field beamforming are combined with the self-focusing technology to estimate the first layer of medium information. Since the target is in the near field of the radar, its propagation mode is spherical wave. The echo signal received by the array element is a range-azimuth coupling function, and accurate phase compensation is required for the received signal. During the first self-focusing iteration, the dielectric constant is 0.05. Assume that the range migration compensation matrix of the receiving array is for:

[0066]

[0067] Where l represents the number of searches, f W is the frequency of the Wth frequency point, is the estimated dielectric constant of the first layer of medium during the l-th search.

[0068] Range migration compensation first performs a fast Fourier transform (FFT) on the first layer target S(t1,M) received by the array along the range direction, converting the signal into the range frequency domain. In this domain, the array signal is compared with the range migration compensation matrix Multiply and convert the signal to the range time domain through inverse fast Fourier transform (IFFT) to compensate for the range migration offset of the target, that is:

[0069]

[0070] In the formula is the Hadamard product, IFFT W To perform inverse fast Fourier transform on the range direction, is the two-dimensional time domain signal after range migration correction during the lth autofocusing process.

[0071] In the first self-focusing, after the range migration correction, the near-field guidance vector of the target in each receiving array element of the first layer of medium is for

[0072]

[0073] Where k represents the reference array element, r kj It represents the straight-line propagation distance from the target to the reference array element in the j-th layer of the medium.

[0074] According to the propagation characteristics of near-field spherical waves, the receiving array is phase compensated to eliminate the phase difference of the spherical wavefront curvature caused by the spatial distribution of the array elements. After compensation, a fast Fourier transform (FFT) is performed along the array aperture direction to convert the signal into the beam domain, that is, Realize energy focusing and target imaging in the near field area, where FFT M Performs a fast Fourier transform on the array.

[0075] By searching for the dielectric constant, a focusing process combining range migration correction and near-field beamforming is achieved. When the dielectric constant deviates significantly from its true value, the focused signal energy will disperse at different frequencies within the beam domain, resulting in weakened signal energy at the focused position. During the autofocusing process, the entropy-based monotonicity can reflect the degree of image focus. Optimizing the dielectric constant inversion using a target entropy minimization method can improve inversion accuracy and enhance focusing.

[0076] The entropy value of the lth focused image is Estimation by iterative search make The entropy value is minimized, thereby achieving dielectric coefficient tomographic inversion. Therefore, the self-focusing process is essentially an optimization process to solve the local optimal solution of the cost function:

[0077]

[0078] Where arg min[·] represents the independent variable value at which the function obtains the minimum value. The iterative search range is set to 1 to 30. When the focused target entropy value is the minimum, the iterative search ends and the dielectric constant inversion result of the first layer of medium is obtained.

[0079] Step 3: High-precision inversion of the dielectric constant of the second layer, specifically:

[0080] 3.1. Estimation of the refraction point of each array element based on the improved rotation angle method

[0081] From step 2, we can see that the dielectric constant has an impact on the accuracy of self-focusing and tomographic inversion. The complex propagation environment inside the medium, the uneven layered structure and the signal refraction will cause the actual echo signal to deviate from the line of sight of the SIMO radar, and thus mismatch with the actual position of the target. Therefore, accurately knowing the coordinates of the signal refraction point is the prerequisite for realizing the layer-by-layer inversion of the dielectric constant. When the target is in the second layer of the medium, according to the output dielectric constant of the first layer of the medium As the initial value of the dielectric constant of the second layer, that is:

[0082]

[0083] Add angle iteration based on MAST. Figure 3 This is the angle iteration model diagram of the improved rotation angle method in a double-layer medium. In the first self-focusing iteration, the dielectric constant When electromagnetic waves are refracted at an angle During propagation, the intersection position x with the horizontal plane where the i-th receiving array element is located is i_2_l for:

[0084]

[0085] Where x1 is the horizontal coordinate of the emission source, h1 is the height of the emission source from the ground, and h2 is the depth of the target underground.

[0086] 3.2. Second layer dielectric coefficient inversion, specifically:

[0087] Assume that in the first self-focusing iteration, the second layer medium element distance migration compensation matrix is for:

[0088]

[0089] Where, is the estimated dielectric constant of the second layer of medium during the l-th search, is the propagation path distance in the first layer of medium during the l-th search, is the propagation path distance in the second layer of the medium during the lth search.

[0090] Range migration compensation first performs a fast Fourier transform (FFT) on the second layer target S(t2,M) received by the array along the range direction, and converts the signal into the range frequency domain. In this domain, the array signal is compared with the range migration compensation matrix Multiply and convert the signal to the range time domain through inverse fast Fourier transform (IFFT) to compensate for the range migration offset of the target, that is:

[0091]

[0092] In the formula is the Hadamard product, is the two-dimensional time domain signal after range migration correction.

[0093] In the first self-focusing, after the range migration correction, the near-field guidance vector of the target in each receiving array element of the second layer of medium is for:

[0094]

[0095] According to the propagation characteristics of near-field spherical waves, the receiving array is phase compensated to eliminate the phase difference of the spherical wavefront curvature caused by the spatial distribution of the array elements. After compensation, a fast Fourier transform (FFT) is performed along the array aperture direction to convert the signal into the beam domain, that is, Realize energy focusing and target imaging in the near field area.

[0096] During near-field beamforming self-focusing imaging, the search stops when the target entropy reaches a minimum, and the dielectric constant of the second layer in the tomographic inversion is obtained. If the minimum entropy value is not reached, the dielectric constant is updated and step 3 is repeated until the target minimum entropy value is achieved.

[0097]

[0098] The accuracy of the refraction point estimation depends on the accuracy. The higher the accuracy, the more concentrated the focused target energy is. The refined search results can be used as prior information for layer-by-layer inversion to perform multi-layer medium inversion.

[0099] Step 4: High-precision inversion of multi-layer dielectric constants, specifically:

[0100] When the dielectric layer is ≥3, when inverting the dielectric coefficient of the nth layer, the dielectric coefficient of the n-1th layer is used. As the prior information of the inversion of this layer, that is,

[0101]

[0102] During the lth self-focusing iteration, when the nth layer of medium is present, the intersection position x of the electromagnetic wave and the horizontal plane where the i-th receiving array element is located is i_n_l The iterative equation is:

[0103]

[0104] Where h n is the height of the nth dielectric layer, is the dielectric constant of the nth layer medium.

[0105] Repeat step 3 to invert the dielectric constant layer by layer.

[0106] The effectiveness of the proposed method was verified through Matlab simulation. High-precision refraction point estimation was investigated, using the MAST and TAMST algorithms, respectively, to determine the refraction point position of a double-layer medium. Using the array's horizontal coordinate as a variable, the incident layer's thickness d1 = 0.2 μm, its dielectric constant ε1 = 8, and the refraction layer's thickness d2 = 0.4 μm, its dielectric constant ε2 = 16, the refraction point position at the interface of the double-layer medium was calculated. The results are shown in Table 1.

[0107] Table 1 Calculation results of refraction point position

[0108]

[0109] The present invention provides a refraction point estimation algorithm based on an improved rotation angle method, which is suitable for high-precision refraction point estimation of multi-layer media. Figure 4 This is a comparison chart of the refraction point coordinates at the interface between the two algorithms. Compared to the traditional MAST algorithm, the TAMST algorithm used in this paper effectively improves the accuracy of refraction point estimation, reducing the error by 1.24%. Experimental results show that the refraction point coordinates calculated by the MAST algorithm for each channel deviate significantly from the exact values, while the refraction point coordinate curves calculated by the TAMST algorithm are basically consistent with the exact values. Figure 5 A comparison of the mean squared error (MSE) of the MAST algorithm and the improved rotation angle method for refraction point location is presented. The results show that when the array element is far from the target, the error in the refraction point coordinates calculated by the MAST algorithm increases rapidly. TAMST, by introducing a boundary constraint mechanism, stabilizes the change in the refraction point coordinates when the array element is sufficiently far away, significantly reducing the error. Furthermore, the TAMST method employed in this invention is less affected by dielectric constants, exhibits greater stability and applicability, and can be widely used for high-precision refraction point coordinate estimation in complex media environments.

[0110] Figure 6 The two focused points in the image represent point targets in the first and second layers. The 2D focused image obtained using the maximum energy criterion exhibits significant defocusing, resulting in an inversion error of approximately 1.78%. In contrast, the focused image obtained using the minimum entropy criterion exhibits no significant defocusing, and the inversion error is approximately 0.31%, a 1.47% improvement over the maximum energy criterion. Figure 7 The azimuthal cross-sections of the two methods are shown. It can be seen that there are obvious side lobes in the azimuthal direction of the maximum energy criterion algorithm, indicating that complete focusing cannot be achieved and the energy of the pulse signal is dispersed, resulting in reduced stability of the self-focusing method based on the maximum energy criterion and difficulty in focusing on the precise dielectric constant.

[0111] Example 2:

[0112] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method of the present invention are implemented, which will not be described in detail here.

[0113] Example 3:

[0114] This embodiment further provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor.

[0115] It should be noted that the processing flow of Examples 2 to 3 corresponds to the specific steps of the method provided in Example 1 of the present invention, and has the functional modules and beneficial effects corresponding to the execution method. For technical details not fully described in this embodiment, please refer to the method provided in the embodiment of the present invention.

[0116] The program code for implementing the methods of the present application can be written in any combination of one or more programming languages. Such program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that when the program code is executed by the processor or controller, the functions / operations specified in the flow charts and / or block diagrams are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0117] In the context of the present application, a machine-readable medium can be a tangible medium that can contain or store a program for use by an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, device or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium can include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0118] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A high-precision tomographic inversion method for dielectric coefficient of SIMO bridge flaw detection radar based on the rotation angle method, characterized in that: The following steps are involved: S1. Using a SIMO radar to receive echo signals. The radar is a single-transmitter, multiple-receiver bistatic system that transmits a single-cycle Gaussian pulse signal. Multiple array elements receive the signal simultaneously. The echo signals are processed by range migration correction and near-field beamforming. S2. Inverting the dielectric constant of the first layer of medium, including iterative search based on the initial value combined with the step size, optimizing the distance migration compensation matrix using the minimum entropy criterion, and determining the dielectric constant of the first layer by minimizing the entropy value; S3. Estimate the coordinates of the refraction points of each array element at the interface of the second layer of dielectric material using the rotation angle method based on angle iteration and boundary constraints. Combine the inversion results of the first layer as initial values and iteratively invert the dielectric coefficient of the second layer. S4. Perform layer-by-layer inversion on the dielectric coefficient of the nth layer of medium, where n≥3. Use the inversion result of the previous layer as prior information and repeat step S3 to achieve tomographic inversion of the dielectric coefficients of multiple layers.

2. The method according to claim 1, characterized in that The single-cycle Gaussian pulse emission signal a(t) in step S1 is: Where A is the amplitude of the Gaussian pulse, σ is the standard deviation of the Gaussian pulse, and f0 is the radar operating center frequency.

3. The method according to claim 1, characterized in that If the target is in the nth layer of the medium, in SIMO mode, the echo signal S(t n ,M) is Where t=[t1,t2,…t W ] T , W is the number of sampling points of the range signal, t1, t2, ...t W is the sampling time corresponding to the corresponding sampling point, M is the total number of array elements, S(t n ,M) is the W×M B-scan two-dimensional signal matrix, τ in is the transmission delay from the target to the i-th array element in the n-layer medium, R in A is the propagation path distance from the target to the i-th array element in the n-th layer of the medium, i is the amplitude of the echo signal of the i-th array element, ε n is the dielectric constant of the nth layer of medium, and C is the speed of light.

4. The method according to claim 1, wherein The distance migration compensation matrix in step S2 is defined as: Where l represents the number of searches, f W is the frequency of the Wth frequency point, is the estimated dielectric constant of the first layer of medium during the l-th search.

5. The method according to claim 4, characterized in that In step S2, the range migration compensation first performs a fast Fourier transform (FFT) on the first layer target S(t1,M) received by the array along the range direction, and converts the signal into the range frequency domain. In this domain, the array signal is compared with the range migration compensation matrix Multiply and convert the signal to the range time domain through inverse fast Fourier transform IFFT to compensate for the range migration offset of the target, that is: In the formula is the Hadamard product, IFFT W To perform inverse fast Fourier transform on the range direction, is the two-dimensional time domain signal after range migration correction in the lth autofocusing process; According to the propagation characteristics of near-field spherical waves, the receiving array is phase compensated, and after compensation, the fast Fourier transform (FFT) is performed along the array aperture direction to convert the signal into the beam domain to achieve energy focusing and target imaging in the near-field area, namely: Where FFT M Perform a fast Fourier transform on the array element.

6. The method according to claim 1, characterized in that In step S3, the coordinates of the refraction points of each array element at the interface of the second layer of medium are estimated based on the angle iteration and boundary constraint rotation method. The formula is: Where x1 is the horizontal coordinate of the emission source, h1 is the height of the emission source from the ground, and h2 is the depth of the target underground. is the refraction angle.

7. The method according to claim 1, characterized in that In step S3, the dielectric coefficient of the second layer is iteratively inverted, specifically: Assume that in the first self-focusing iteration, the second layer medium element distance migration compensation matrix is for: Where, is the estimated dielectric constant of the second layer of medium during the l-th search, is the propagation path distance in the first layer of medium during the l-th search, is the propagation path distance in the second layer of the medium during the lth search; Range migration compensation first performs fast Fourier transform (FFT) on the second layer target S(t2,M) received by the array along the range direction, and converts the signal into the range frequency domain. In this domain, the array signal is compared with the range migration compensation matrix Multiply and convert the signal to the range time domain through inverse fast Fourier transform IFFT to compensate for the range migration offset of the target, that is: In the formula is the Hadamard product, is the two-dimensional time domain signal after range migration correction; In the first self-focusing, after the range migration correction, the near-field guidance vector of the target in each receiving array element of the second layer of medium is for: According to the propagation characteristics of near-field spherical waves, the receiving array is phase compensated to eliminate the phase difference of the spherical wavefront curvature caused by the spatial distribution of the array elements. After compensation, the fast Fourier transform FFT is performed along the array aperture direction to convert the signal into the beam domain, realizing energy focusing and target imaging in the near-field area, that is, In the near-field beamforming self-focusing imaging process, when the target entropy value reaches the minimum, the search process stops, and the dielectric constant result of the second layer of the medium in the tomographic inversion is obtained at this time. If the minimum entropy value is not reached, the dielectric constant is updated and the steps are repeated until the target minimum entropy value is obtained.

8. An electronic system, characterized in that: include: at least one processor; a memory in communication with the processor, storing executable instructions; When the processor executes the instructions, the method according to any one of claims 1 to 7 is implemented.

9. The system according to claim 8, characterized in that Also includes: A signal transmitting module, used for generating a single-cycle Gaussian pulse signal; Multi-channel receiving module, synchronously collecting echo signals from each array element; The tomographic inversion module performs range migration correction, near-field beamforming, and iterative inversion of dielectric constants.

10. A computer-readable storage medium, characterized in that Computer instructions are stored, and when the instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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