Echo Simulation Method and System Based on Sparse Scattering Center Clustering

Abstract

This invention discloses an echo simulation method and system based on sparse scattering center clustering, mainly addressing the problem of low efficiency in echo generation in existing technologies. The implementation scheme includes: setting input parameters, calculating the electric field strength and spatial location characterizing the target's scattering properties; projecting the electric field according to its spatial location and dividing the projection plane into uniform resolution cells according to resolution; assigning the electric field to the divided resolution cells; extracting the dominant scattering electric field from the resolution cells, obtaining the dominant conductive electric field strength and location information of all resolution cells; performing neighborhood clustering and merging on the extracted resolution cells, clustering the neighborhoods of weak scattering cells below a threshold towards strong scattering cells to obtain the clustered sparse scattering centers; performing point target echo calculation by traversing different sparse scattering centers with the transmitted signal, and finally synthesizing a time-domain waveform. This invention avoids information loss, reduces data redundancy, and improves echo calculation efficiency, and can be used for target detection and identification.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to an echo simulation method and system that can be used for target detection and identification. Background Technology

[0002] Traditional radar echo simulations often rely on simplified point target models or idealized scattering coefficient distributions, making it difficult to accurately simulate the real electromagnetic scattering behavior of complex targets. While high-frequency electromagnetic methods can achieve accurate calculations of the scattered field, they fail to effectively integrate with signal processing workflows. In traditional radar evaluation, the reflection characteristics are typically characterized by measuring the overall radar cross-section of the target, a method suitable for narrowband, low-resolution conditions. However, with the development of broadband radar technology, radar signals possess higher bandwidth and resolution, providing richer target detail information. Therefore, analytical methods are no longer limited to directly obtaining the overall radar cross-section value at a specific incident angle, but have shifted towards more refined evaluation approaches.

[0003] Among various high-frequency electromagnetic calculation methods, the bouncing ray method (SBR) combines the ray tracing approach of geometric optics with the field integration method of physical optics. Its core is to simulate the multiple reflections of rays on the target surface and accumulate the field intensity to calculate the scattered field. This method ensures both computational accuracy and high solution efficiency, effectively analyzing the scattering characteristics of electrically large and complex targets. Furthermore, after completing ray tracing, it obtains the emission position coordinates and field values ​​of all ray tubes, making it possible to extract the scattering center.

[0004] Patent document CN202010374033.8 discloses "A method for detecting environmental backscattered signals based on clustering analysis." Its core process is as follows: the receiver first calculates the average energy of the received mixed signal according to the bit period, forming an energy set; then, since the tag information "0" and "1" will cause these energy values ​​to exhibit two different clustering states, the K-means clustering algorithm is used to automatically divide them into two clusters; finally, the bit values ​​corresponding to these two clusters are determined by the known preamble, thereby decoding the clustering results to restore the original backscattered signal sequence. This method, because it essentially still belongs to the realm of pure signal processing and mathematical optimization, does not constrain the parameter solution process, does not consider the actual scattering mechanism and characteristics of the target, and does not incorporate the target's physical structure information; therefore, it lacks practical significance for solving real targets.

[0005] Patent document CN202211595819.8 discloses a "radar target scattering center region segmentation method based on local density clustering". This method first applies Frost filtering to the original SAR image to suppress global noise, then uses the level set method for image segmentation to initially extract the target region. Next, area filtering is used to retain the largest connected component to remove interference. Finally, a local density clustering algorithm is used to automatically detect the scattering center within the obtained region and complete the accurate segmentation of each independent scattering region. However, when extracting strong scattering centers, this method only detects local regions of strong scattering sources, resulting in a loss of total energy. Furthermore, this method primarily processes SAR radar images and cannot describe the actual scattering characteristics of the target in detail, thus losing some edge information of the target to a certain extent. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the prior art by proposing an echo simulation method and system based on sparse scattering center clustering. This system combines the actual physical structure and scattering mechanism of the target model for calculation, ensuring that edge information and total energy are not lost, reducing data redundancy, and improving the calculation efficiency of target echoes using a smaller number of scattering center data.

[0007] The technical approach to achieving the objective of this invention is as follows: by using the SBR algorithm to calculate the target scattering characteristics, the true scattering characteristics of the target are obtained, ensuring that edge information and total energy are not lost; by constructing a sparse scattering center clustering model, weak scattering energy is gathered and merged into strong scattering regions to reduce data redundancy and quickly obtain the true echo of the target using a smaller number of scattering center data.

[0008] Based on the above ideas, the technical solution of the present invention includes:

[0009] 1. An echo simulation method based on sparse scattering center clustering, characterized in that it includes:

[0010] (1) Set the input parameters, use the SBR algorithm to calculate the electric field intensity and spatial position that characterize the scattering characteristics of the target, and store them;

[0011] (2) Project the electric field onto any two-dimensional plane in the three-dimensional rectangular coordinate system OXYZ according to its spatial position, and divide the projection plane into uniform square regions according to the resolution, with each region serving as a resolution unit;

[0012] (3) Based on the coordinate values ​​of the electric field on the projection plane, assign the electric field to the predefined resolution unit;

[0013] (4) Compare the magnitudes of all electric field intensities in each resolution cell, extract the dominant scattering electric field in the resolution cell, and obtain the dominant conductive electric field intensity and location information of all resolution cells;

[0014] (5) Set the main conductive field strength threshold, perform neighborhood aggregation and merging on the above-extracted resolution units, and cluster the weak scattering units with a strength below the threshold into strong scattering units to obtain the clustered sparse scattering centers.

[0015] (6) The transmitted signal is traversed through different sparse scattering centers to perform point target echo calculation, that is, the transmitted signal experiences different time delays, and the field strength is superimposed to obtain the echo sequence, and finally synthesizes the time domain waveform.

[0016] Furthermore, in step (5), the extracted resolving units are clustered and merged in their neighborhoods, and the neighborhoods of weak scattering units below a threshold are clustered towards strong scattering units, including:

[0017] (5a) Iterate through each non-edge resolvable cell, denoted as cell P. For each cell P, extract the electric field intensity of itself and the four directly adjacent cells above, below, left and right, and calculate the sum of these five field intensities S.

[0018] (5b) Compare the calculated sum of field strengths S with the preset scattering intensity threshold T:

[0019] if If the unit P and its neighborhood are determined to be weak scattering regions, then (5c) is executed.

[0020] if If so, skip the resolution unit and return to (5a);

[0021] (5c) Set the electric field strength of unit P to the sum of the five field strengths S, and set the electric field strength of the four adjacent units around unit P to zero. Continue to traverse the next resolving unit until all non-edge resolving units have been traversed to complete the clustering operation.

[0022] 2. An echo simulation system based on sparse scattering center clustering, characterized in that it includes:

[0023] The scattering characteristics calculation module is used to set parameters and calculate the electromagnetic scattering characteristics of the target based on the parameters, including the electric field intensity and spatial location of the target scattering.

[0024] The resolution unit division module is used to divide the projection plane into resolution units according to the set parameters.

[0025] The electric field attribution module is used to accurately assign the calculated target scattered electric field to the corresponding resolution cell.

[0026] The main electric field extraction module is used to extract the electric field strength with the largest field strength and its spatial location in the divided resolution cells, and to calculate the total field strength of the scattered electric field of all targets in the resolution cells.

[0027] The resolving unit clustering module is used to cluster all non-edge resolving units based on the comparison results of the extracted total field strength and scattering threshold to obtain sparse scattering centers.

[0028] The echo generation module is used to generate echoes and synthesize the final time-domain waveform based on the sparse scattering center.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] Firstly, this invention sparsifies the scattering centers, causing weak scattering regions to cluster towards strong scattering regions, reducing data redundancy and improving echo calculation efficiency.

[0031] Secondly, since the present invention does not delete the weak region results during the clustering process of weak scattering regions to strong scattering regions, and only processes non-edge resolution units, it can avoid the loss of edge information and total energy.

[0032] Third, since the present invention directly reads the target model, it can combine the target's real physical structure and scattering mechanism to calculate the target's scattering characteristics using the SBR algorithm. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating the implementation of the echo simulation method based on sparse scattering center clustering in this invention.

[0034] Figure 2 This is a block diagram of the echo simulation system based on sparse scattering center clustering of the present invention;

[0035] Figure 3 This is a comparison diagram of the target scattering center results before and after the sparse clustering operation of this invention;

[0036] Figure 4 This is a comparison diagram of the echoes obtained by simulation of the present invention and the traditional time-domain echo method. Detailed Implementation

[0037] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0038] Example 1. Echo simulation method based on sparse scattering center clustering.

[0039] Reference Figure 1 The implementation steps of this example include the following:

[0040] Step 1: Calculate the target scattering characteristics using the SBR algorithm.

[0041] 1.1) Set input parameters, including: the local path of the target model to be calculated, and the calculation frequency. Pitch angle Azimuth , distinguishing the unit size d, where, , , .

[0042] This example selects a fighter jet as the calculation target, with dimensions of 15.16m × 19.87m × 4.20m. Settings include, but are not limited to: the target model's local path being "E:\model\fighter.stl", and the frequency... Pitch angle azimuth The resolution unit size is d=0.05m.

[0043] 1.2) Based on the fact that both the incident elevation angle and azimuth angle are... It can be seen that the incident wave is perpendicular to the top of the fighter jet at this time, and a virtual aperture surface perpendicular to the incident wave can be constructed accordingly.

[0044] 1.3) Calculate the distance between the virtual aperture surface and the target center based on the target's size and operating frequency. and the side length of the X-ray tube :

[0045] ,

[0046] ,in The speed of light;

[0047] 1.4) Based on the virtual aperture surface size and the side length of the ray tube, the number of ray tubes divided on the virtual aperture surface is calculated to be 994 × 759 = 754446;

[0048] 1.5) After the ray tube is divided, the ray propagates towards the target in a straight line and intersects with the target surface element. Calculate the minimum propagation distance. :

[0049] 1.5.1) Initialization ;

[0050] 1.5.2) Based on the expression of any point on the surface element and ray equation Setting them equal, we get the equation: ;

[0051] 1.5.3) Solving the equation Calculate the propagation distance between the ray and the intersection point of the surface element. ;

[0052] 1.5.4) Comparison and Size:

[0053] like ,make After recording the number of the face element, return to 1.5.2).

[0054] like If so, it will directly return to 1.5.2).

[0055] 1.5.4) After traversing all facets, the facet number closest to the ray's origin is identified. That is, the minimum propagation distance of the ray. During the traversal, the space acceleration structure Kd-Tree is used to quickly eliminate a large number of non-intersecting elements, thereby improving computational efficiency.

[0056] 1.6) The distance of the ray's propagation Reflection occurs at the intersection of the smallest surface elements. Based on local geometric features and material properties, the reflection coefficient of the surface element is obtained. Then, according to Snell's law of reflection, the electric field intensity and spatial position change after reflection are obtained:

[0057] ;

[0058] in, For the incident electric field, For the reflected electric field, This is the vertically polarized unit vector. Let be the unit vector of the incident electric field. Let be the horizontally polarized unit vector of the incident electric field. Let be the horizontal polarization unit vector of the reflected electric field. , These are the reflection coefficients for parallel polarization and vertical polarization, respectively. , These represent the amplitudes of parallel polarization and vertical polarization, respectively.

[0059] 1.7) After reflection, the intersection of the ray and the surface element is taken as the new ray starting point. Steps 1.5) to 1.6) are repeated until the spatial position of the ray leaves the target surface element, and the electric field intensity and spatial position that characterize the scattering characteristics of the target are obtained.

[0060] Step 2: Divide the data into resolving units.

[0061] The calculated electric field is projected onto the XOY plane, and the virtual aperture surface is divided into multiple uniformly arranged square regions based on the virtual aperture surface size and the resolution unit size d.

[0062] Each region is treated as a single resolution unit;

[0063] The virtual aperture surface size in this example is: The resolving element size is d = 0.05 m, and the number of resolving elements is: indivual.

[0064] Step 3: The electric field is assigned to the resolution unit.

[0065] Based on the x and y coordinates of the electric field and the positions of the predefined resolution cells, the electric field is assigned to the corresponding resolution cell. In this embodiment:

[0066] When the electric field coordinates satisfy At that time, the electric field is assigned to the first resolution cell in the first row and first column;

[0067] when At that time, the electric field is assigned to the resolution unit in the first row and second column;

[0068] By analogy, all electric fields are assigned to the corresponding resolution units.

[0069] Step 4, extraction of the main conductive field.

[0070] The main conductive field includes the spatial location of the electric field with the strongest intensity within the resolution unit. and the sum of all electric field strengths within the unit. Its implementation includes the following:

[0071] 4.1) For each resolution cell, define an intermediate variable to store information, which includes the maximum scattered electric field intensity. and spatial position vector Two parts, of which:

[0072] Maximum scattered electric field intensity The initial value is set to 0, representing the maximum intensity of all electric fields within the current cell; the spatial position vector is then set to 0. The initial value is set to empty, used to record and Corresponding spatial location;

[0073] 4.3) Iterate through the electric field strength of each cell and compare it with the current field strength. For comparison, the electric field strength of the i-th electric field is... Spatial location is :

[0074] if Then update the intermediate variable. , traverse the next electric field;

[0075] if Then keep and If unchanged, directly iterate through the next electric field;

[0076] 4.4) While traversing the electric field strength of each electric field within the cell, sum up all the electric field strengths to obtain the total scattered field strength of the cell. :

[0077]

[0078] Where N is the total number of electric fields within the unit;

[0079] 4.5) After the traversal is completed, the resolution unit outputs the spatial position of the main conductive field. and total scattered field strength .

[0080] In this embodiment, the final number of resolution units for extracting the main conductive field is 6002.

[0081] Step 5: Identify unit clusters.

[0082] After extracting the main conductive field of the resolving unit in the previous step, a two-dimensional resolving unit matrix of 303×397 is obtained. Iterate through rows 2 to 300 and columns 2 to 396, and for each non-edge cell... Perform the following operations:

[0083] 5.1) Extract each unit field strength The field strength of the four directly adjacent units above, below, left, and right. , , , Calculate its sum. ;

[0084] in , , , , , , ;

[0085] 5.2) Compare the magnitudes of the sum of field strengths S and the preset scattering intensity threshold T:

[0086] if Then determine the resolution unit The region and its neighborhood form a weak scattering region (see section 5.3).

[0087] if If so, skip the resolution unit and return to 5.1).

[0088] 5.3) Unit The field strength is updated to the sum of the field strengths of these five units, that is... ;

[0089] Will The electric field strength of the four adjacent units (top, bottom, left, and right) is set to 0, that is:

[0090] = = = ;

[0091] 5.4) After all non-edge units have been processed according to the above rules, the clustering ends, and all resolving units with non-zero field strength values ​​are formed into sparse scattering centers.

[0092] In this embodiment, the final number of sparse scattering centers after clustering is 317.

[0093] Step 6, Echo generation.

[0094] 6.1) A modulated Gaussian pulse with a carrier frequency of 3 GHz, a pulse width of 8 ns, and a bandwidth of 500 MHz is used as the transmission signal. ;

[0095] 6.2) Calculate the echo signal at any scattering center: ,in The backscattering characteristics of the target are represented by the electric field value at the scattering center obtained in step 5. The propagation loss and antenna gain are set to 1 by default. For two-way delay, The speed of light;

[0096] 6.3) Repeat steps 6.1) to 6.2) to complete the point target echo calculation for all sparse scattering centers, and add all the echoes together to obtain the final time-domain waveform.

[0097] It should be noted that the step numbers in this example and the claims are only for the purpose of clearly and completely describing the embodiments of the present invention and for ease of understanding, and their order is not limited.

[0098] Example 2. Echo simulation system based on sparse scattering center clustering.

[0099] Reference Figure 2 This example includes: a scattering characteristic calculation module 1, a resolution cell partitioning module 2, an electric field assignment module 3, a main conductive field extraction module 4, a resolution cell clustering module 5, and an echo generation module 6. Specifically, the scattering characteristic calculation module 1 includes: a parameter setting submodule 11, a ray tube partitioning submodule 12, a ray-surface element intersection submodule 13, and an electric field tracking submodule 14; the resolution cell clustering module 5 includes: a neighborhood field strength calculation submodule 51, a weak scattering region judgment submodule 52, and a neighborhood merging submodule 53.

[0100] The working principle of the entire system is as follows:

[0101] The scattering characteristic calculation module 1 is used to set parameters and calculate the electromagnetic scattering characteristics of the target based on the parameters, including the electric field intensity and spatial location of the target scattering. The parameter setting submodule 11 is used to set the local path and calculation frequency of the target model. Pitch angle Azimuth The system first resolves the unit size d and passes these parameters to the ray tube partitioning submodule 12 and the resolving unit partitioning module 2. The ray tube partitioning submodule 12 generates a virtual aperture surface based on the elevation and azimuth angles, partitions the ray tubes according to the frequency, and passes the partitioned ray tubes to the ray-surface element intersection submodule 13. The ray-surface element intersection submodule 13 is used to find the target surface element with the smallest propagation distance that intersects with the ray, and passes the surface element intersection point to the electric field tracking submodule 14. The electric field tracking submodule 14 calculates the ray reflection path based on the intersection point of the ray and the target surface element, and records the electric field intensity and spatial position changes according to the ray propagation path, and passes the electric field intensity and spatial position to the resolving unit partitioning module 2.

[0102] The module resolution unit division module 2 is used to divide the projection surface into resolution units according to the set parameters, and to transmit the electric field and the divided resolution units to the electric field attribution module 3.

[0103] The electric field attribution module 3 is used to accurately assign the target scattered electric field to the corresponding resolution unit and transmit the assigned electric field to the main conductive field extraction module 4.

[0104] The main conductive field extraction module 4 is used to extract the spatial location of the electric field with the largest field strength after it has been assigned, calculate the total field strength of the scattered electric fields of all targets in the resolution unit, and transmit the spatial location of the electric field with the largest field strength and the total field strength of all electric fields in the resolution unit to the resolution unit clustering module 5.

[0105] The resolving unit clustering module 5 is used to cluster all non-edge resolving units based on the comparison result of the extracted total field strength and the scattering threshold to obtain sparse scattering centers. The neighborhood field strength calculation submodule 51 is used to calculate the sum of the electric field strengths of all non-edge resolving units and their neighborhoods, and pass the sum of electric field strengths to the weak scattering region judgment submodule 52. The weak scattering region judgment submodule 52 is used to compare the sum of field strengths with the threshold, identify weak scattering regions, and pass the weak scattering regions to the neighborhood merging submodule 53. The neighborhood merging submodule 53 is used to merge the field strengths of the identified weak scattering regions with the central unit, set the field strength of the neighborhood to zero, obtain sparse scattering centers, and pass the scattering centers to the echo generation module 6.

[0106] The echo generation module 6 is used to generate echoes and synthesize the final time-domain waveform based on the sparse scattering center.

[0107] It should be noted that the above functional modules can be implemented, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, they can be implemented, in whole or in part, as program instruction products. A program instruction product includes one or a set of program instructions. When the program instructions are loaded and executed on a computer, the described process or function is generated, in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The program instructions can be stored in a computer-readable and writable storage medium, or transferred from one computer's readable and writable storage medium to another.

[0108] In this embodiment, the direct coupling or communication connection between the modules can be achieved through indirect coupling or communication connection via interfaces, devices, or modules. The functional modules and sub-modules in this embodiment can dynamically reside within a single processing unit, or each module can exist physically independently, or two or more modules can dynamically reside within a single processing unit. When these dynamic components are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable and writable storage medium. This storage medium can be a memory, disk, or optical disc, etc.

[0109] The effectiveness of this invention can be further verified through the following simulation.

[0110] 1. Simulation experimental conditions.

[0111] The hardware platform for the simulation experiment of this invention is as follows: CPU is AMD Ryzen 9 9950X3D 16-Core Processor with a main frequency of 4.3GHz; memory is 192GB; GPU is NVIDIA GeForce RTX 5090 with 126GB of video memory.

[0112] The software platform for the simulation experiment of this invention is: Windows 11 operating system, Visual Studio 2022 and MATLAB R2025a.

[0113] 2. Simulation content and result analysis.

[0114] Simulation 1: Using this invention, the target scattering electric field intensity and spatial location are calculated to obtain the target scattering center before and after clustering. The results are as follows: Figure 3 As shown. Wherein:

[0115] Figure 3 (a) is the image of the uniform scattering centers before clustering.

[0116] Figure 3 (b) is the image of the sparse scattering centers after clustering.

[0117] from Figure 3 It can be seen that before clustering, there are more points and the energy distribution of the scattering centers is uniform. After clustering, the number of points is significantly reduced, which reduces data redundancy and makes the strong scattering points more prominent. Since the edge points are not clustered, some edge information is still retained. For example, a point is retained on both sides of the wing of a fighter jet, which can be used to see the overall outline of the fighter jet, indicating that the present invention has good recognizability.

[0118] Simulation 2 uses the sparse scattering center results of this invention to generate echoes, and compares the results with those calculated by existing traditional time-domain echo methods. The results are as follows: Figure 4 As shown.

[0119] from Figure 4 As can be seen, the two curves have a high degree of similarity. A dual-index geometric mean similarity evaluation system that integrates normalized Euclidean distance and maximum cross-correlation coefficient was used to evaluate the similarity between the two curves. The results show that the similarity can reach 96.53%. However, the echo generation time of the present invention is only 2.09s, while the echo generation time of the prior art is as long as 55.23s, indicating that the present invention has higher fidelity and computational efficiency.

Claims

1. An echo simulation method based on sparse scattering center clustering, characterized in that, include: (1) Set the input parameters, use the SBR algorithm to calculate the electric field intensity and spatial position that characterize the scattering characteristics of the target, and store them; (2) Project the electric field onto any two-dimensional plane in the three-dimensional rectangular coordinate system OXYZ according to its spatial position, and divide the projection plane into uniform square regions according to the resolution, with each region serving as a resolution unit; (3) Based on the coordinate values ​​of the electric field on the projection plane, assign the electric field to the predefined resolution unit; (4) Compare the magnitudes of all electric field intensities in each resolution cell, extract the dominant scattering electric field in the resolution cell, and obtain the dominant conductive electric field intensity and location information of all resolution cells; (5) Set the main conductive field strength threshold, perform neighborhood aggregation and merging on the above-extracted resolution units, and cluster the weak scattering units with a strength below the threshold into strong scattering units to obtain the clustered sparse scattering centers. (6) The transmitted signal is traversed through different sparse scattering centers to perform point target echo calculation, that is, the transmitted signal experiences different time delays, and the field strength is superimposed to obtain the echo sequence, and finally synthesizes the time domain waveform.

2. The method according to claim 1, characterized in that, The input parameters in (1) include: the local path of the target model to be calculated, the calculation frequency. Pitch angle Azimuth , distinguishing unit size d; in, , , .

3. The method according to claim 1, characterized in that, The step (1) of calculating the electric field intensity and spatial location characterizing the scattering properties of the target using the SBR algorithm includes: (1a) Construct a virtual aperture surface containing the target model and perpendicular to the direction of incoming wave, and divide it into ray tubes. Each ray tube consists of a central ray and four edge rays, and the side length of each ray tube is one-tenth of the wavelength. (1b) The ray propagates along a straight line from the starting point and intersects with the target triangular facet. The coordinates of the intersection point, the surface normal vector at the intersection point, and the propagation distance of the ray from the emission point to the intersection point are calculated. All propagation distances are compared to obtain the facet with the smallest ray propagation distance. The ray is reflected at the intersection with this facet. In this process, the spatial acceleration structure Kd-Tree is used to quickly eliminate a large number of non-intersecting facets, thereby improving computational efficiency. (1c) When a ray is reflected on a surface element, the reflection coefficient of the surface element is obtained based on the local geometric features and material properties. Then, the field strength and spatial position change after reflection are obtained according to Snell's law of reflection. ； in, For the incident electric field, For the reflected electric field, This is the vertically polarized unit vector. Let be the unit vector of the incident electric field. Let be the parallel polarization unit vector of the incident electric field. Let be the parallel polarization unit vector of the reflected electric field. , These represent the amplitudes of parallel polarization and vertical polarization, respectively. , These are the reflection coefficients for parallel polarization and vertical polarization, respectively; (1d) After reflection, the intersection of the ray and the surface element is taken as the new starting point of the ray. (1b) and (1c) are repeated continuously until the spatial position of the ray leaves the target surface element, and the final electric field strength and spatial position are obtained.

4. The method according to claim 1, characterized in that: In (2), the two-dimensional plane projection is divided into uniform square regions according to the resolution. This is done by dividing the length and width of the two-dimensional plane into equal parts based on the resolution unit size d, thus obtaining square regions. In step (3), the electric field is assigned to a predefined resolution unit based on the coordinate value of the electric field on the projection plane. This involves traversing the spatial location of all electric fields and assigning the electric field numbers whose coordinate values ​​are within a certain resolution unit range to the array of that resolution unit.

5. The method according to claim 1, characterized in that, Extracting the dominant scattering electric field in the resolving unit in step (4) includes: (4a) For each resolution cell, create an intermediate variable containing two parts: ① Electric field strength: initially set to 0, used to record the maximum scattered electric field amplitude in the current traversal; ② Spatial position: initially set to empty, used to record the spatial position corresponding to the maximum field strength; (4b) Traverse all electric fields assigned to this unit, compare their field strength with the field strength stored in the intermediate variable, find the electric field with the strongest intensity, use the intensity of the electric field as the field strength of the intermediate variable, and use the spatial location of the electric field as the spatial location information of the intermediate variable. (4c) The electric field strengths of all electric fields are summed into an independent summation variable to obtain the sum of all electric field strengths within the cell.

6. The method according to claim 1, characterized in that, The step (5) involves clustering and merging the neighborhoods of the extracted resolving units, clustering the neighborhoods of weak scattering units below a threshold towards strong scattering units, including: (5a) Iterate through each non-edge resolvable cell, denoted as cell P. For each cell P, extract the electric field intensity of itself and the four directly adjacent cells above, below, left and right, and calculate the sum of these five field intensities S. (5b) Compare the calculated sum of field strengths S with the preset scattering intensity threshold T: if If the unit P and its neighborhood are determined to be weak scattering regions, then (5c) is executed. if If so, skip the resolution unit and return to (5a); (5c) Set the electric field strength of unit P to the sum of the five field strengths S, and set the electric field strength of the four adjacent units around unit P to zero. Continue to traverse the next resolution unit until all non-edge resolution units are traversed, and complete the clustering operation to obtain the sparse scattering center.

7. The method according to claim 1, characterized in that, The process in (6) involves calculating point target echoes by traversing different sparse scattering centers of the transmitted signal and finally synthesizing a time-domain waveform, including: (6a) The radar emits a known electromagnetic wave signal. ; (6b) Signals propagate through space, through time delay This causes the signal amplitude to change due to propagation attenuation and the target's radar cross-section (RCS). (6c) Based on the results of (6b), the echo signal received by the radar This is the result of the combined effect of signal delay and attenuation: ,in The attenuation coefficient is a comprehensive factor that includes propagation loss, antenna gain, and target RCS. (6d) Repeat (6a)-(6c) to complete the point target echo calculation for all sparse scattering centers, add all echoes together to obtain the final time-domain waveform.

8. An echo simulation system based on sparse scattering center clustering, characterized in that, include: The scattering characteristics calculation module is used to set parameters and calculate the electromagnetic scattering characteristics of the target based on the parameters, including the electric field intensity and spatial location of the target scattering. The resolution unit division module is used to divide the projection plane into resolution units according to the set parameters. The electric field attribution module is used to accurately assign the calculated target scattered electric field to the corresponding resolution cell. The main electric field extraction module is used to extract the electric field strength with the largest field strength and its spatial location in the divided resolution cells, and to calculate the total field strength of the scattered electric field of all targets in the resolution cells. The resolving unit clustering module is used to cluster all non-edge resolving units based on the comparison results of the extracted total field strength and scattering threshold to obtain sparse scattering centers. The echo generation module is used to generate echoes and synthesize the final time-domain waveform based on the sparse scattering center.

9. The system according to claim 8, characterized in that, The scattering characteristic calculation module includes: The parameter setting submodule is used to set the local path and computation frequency of the target model. Pitch angle Azimuth , distinguishing unit size d; The X-ray tube partitioning submodule is used to generate a virtual aperture surface based on the elevation and azimuth angles, and to partition the X-ray tube according to the frequency. The ray-surface intersection submodule is used to find the target surface element that has the smallest propagation distance and intersects with the ray; The electric field tracking submodule is used to calculate the ray reflection path based on the intersection point of the ray and the target surface element, and to record the changes in electric field intensity and spatial position according to the ray propagation path.

10. The system according to claim 8, characterized in that, The resolution unit clustering module includes: The neighborhood field strength calculation submodule is used to calculate the sum of the electric field strengths of all non-edge-resolved cells and their neighborhoods; The weak scattering region identification submodule is used to compare the sum of the field strengths with a threshold to identify the weak scattering regions. The neighborhood merging submodule is used to merge the field strength of the identified weak scattering regions into the central unit and set the field strength of the neighborhood to zero.

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