Radar target multi-scattering center forward modeling method based on grid model

Abstract

The present application relates to a radar target multi-scattering center forward modeling method based on a grid model, and belongs to the technical field of electromagnetic calculation. The method is based on a scattering center parameterized model of a target, utilizes a bounce ray technique and a multi-scattering center forward modeling technique, and performs forward modeling on the radar target. After modeling is completed, electromagnetic calculation can be performed through a scattering center parameterized representation form of the target, the complexity during electromagnetic calculation is simplified, the simulation efficiency is significantly improved, and electromagnetic calculation of a large target or scene can be realized.

Description

Technical Field

[0001] This invention relates to a forward modeling method for radar targets with multiple scattering centers based on a grid model, belonging to the field of electromagnetic computation technology. It involves bouncing ray technology and forward modeling technology for multiple scattering centers, enabling forward modeling of radar targets or scenes based on a grid model. The modeling results can efficiently simulate the radar scattering characteristics, echo data, and image data of targets or scenes with arbitrary structures, thereby supporting subsequent research in areas such as target characteristic analysis, intelligent interpretation of radar data, and semantic information extraction. Background Technology

[0002] The scattering center model is a parameterized simulation algorithm for electromagnetic scattering, following the full-wave numerical method and the high-frequency approximation method. The scattering center model does not include complex electromagnetic scattering processes; instead, it parameterizes different scattering mechanisms using analytical expressions with a small number of parameters. It can describe the variation of the electromagnetic scattering response of a radar target with incident frequency, line-of-sight angle, polarization, and the target's physical properties. Therefore, the scattering center model simplifies the complexity of electromagnetic calculations, significantly improves simulation efficiency, and is one of the most effective simulation methods for electromagnetic simulation of large targets or scenes.

[0003] For different scattering mechanisms, there are various typical parametric representations of the scattering center. The ideal point scattering center model has the simplest representation, with the amplitude of the scattering center unaffected by frequency and line-of-sight, but it cannot meet the simulation requirements of broadband conditions. The Prony scattering center model, based on the point scattering center model, uses a decay exponential function to correct the frequency dependence of the amplitude term, but when the bandwidth of the incident electromagnetic wave is large, the frequency dependence behavior of the scattering response will have a large deviation. The frequency dependence term of the GTD scattering center model is represented by a power function with a half-integer exponent, whose value corresponds one-to-one with the scattering mechanism and geometry, making it more accurate than the point scattering center model and the Prony model, but it does not consider the angular domain characteristics of the scattering properties. The attribute scattering center model (ASC), based on the GTD model, uses a decay exponential function and a sinc function to describe the angular dependence of the scattering center amplitude, and is currently the most widely used scattering center model.

[0004] After clarifying the representation of the scattering center, it is necessary to estimate the unknown parameters of the scattering center model. Parameter estimation is a crucial step in scattering center modeling and mainly falls into two categories: data-driven methods based on scattering data and model-driven methods based on geometric models. Data-driven methods, belonging to the inverse modeling approach for scattering centers, are currently the most widely used. They typically require prior scattering characteristic data and optimization methods such as genetic algorithms and particle swarm optimization to inversely retrieve the unknown parameters. Currently, besides experimental methods, methods for obtaining prior scattering characteristics fall into two main categories: full-wave numerical methods and high-frequency approximation methods. Full-wave methods can meet the accuracy requirements for simulating the scattering characteristics of radar targets. Classical full-wave algorithms include the Method of Moments (MOM), the Discrete Functional Variational Finite Element Method (FEM), the Time-Domain Integral Equation (TDIE), the Finite-Difference Time-Domain (FDTD), and the Multilevel Fast Multipole (MLFMA) technique. High-frequency approximation methods, such as Physical Optics (PO), Bouncing Ray Method (SBR), and Geometric Optics (GO), have significant advantages in solution efficiency and can be used to analyze the electromagnetic scattering characteristics of complex radar targets.

[0005] However, data-driven scattering center modeling schemes require a large amount of prior scattering data for frequency and angle sweeping, resulting in enormous computational load and cost. Therefore, model-driven scattering center modeling schemes are more suitable for modeling the scattering centers of large and complex radar targets. The core idea is to use the target's geometric structure information to determine the type, amplitude, location, and other parameters of the scattering center model. Model-driven methods are forward modeling methods, with typical schemes including scattering center modeling methods based on the component-level decomposition of complex targets, and methods for rapid generation and extraction of 3D inverse synthetic aperture radar images based on numerical methods.

[0006] Since the accuracy and efficiency of data-driven scattering center modeling methods are inextricably linked to prior scattering characteristic data, there are numerous technical challenges in modeling the scattering centers of large and complex radar targets. On one hand, the sheer volume and accuracy of prior scattering characteristic data are difficult to guarantee. The scattering process of actual radar targets is extremely complex, encompassing various scattering components such as surface scattering, edge diffraction, peak diffraction, diffuse scattering, and multiple scattering. Using precise full-wave numerical methods to obtain prior scattering characteristic data requires significant computational resources and time; while high-frequency asymptotic methods suffer from poor modeling accuracy and limited applicability, resulting in relatively weak scattering characteristic data precision. On the other hand, the representation of scattering centers needs improvement. The accuracy of data-driven modeling methods depends on the completeness of the scattering centers; each scattering component corresponds to a different scattering center. For example, reflection components correspond to distributed scattering centers, sliding scattering centers, etc.; diffraction components correspond to local scattering centers; and multiple scattering corresponds to multiple scattering centers. Different types of scattering center characterization require clarifying the amplitude, position, frequency dependence, and angle dependence of the scattering center. However, the characterization of scattering centers for diffracted, multiple, and medium-type targets is still in the research and development stage. In particular, for multiple scattering centers, due to the complexity of ray paths, the estimation of parameters such as position and amplitude of multiple scattering centers is limited to typical regular structures, such as dihedral and right-angle cavity structures. Existing multiple scattering center modeling methods are difficult to generalize and apply. Summary of the Invention

[0007] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and propose a forward modeling method for multiple scattering centers of radar targets based on a grid model. This method is based on a grid model and combines the bouncing ray method, the equivalent optical path difference theory, and the parametric characterization model of scattering centers. According to the performance characteristics of rays on different types of surface elements (such as the number of bounces, the spatial angular domain characteristics of rays, etc.), the type, location, and amplitude of scattering centers are determined. This effectively reduces the universality of forward modeling of target scattering centers, solves the technical difficulties of modeling multiple scattering centers, and the process is easy to automate, reducing the manual intervention in the scattering center modeling process and facilitating subsequent software integration.

[0008] The technical solution of this invention is:

[0009] A forward modeling method for radar target multiple scattering centers based on a grid model, the steps of which include:

[0010] Step 1: Establish a grid model of the radar target. The specific method is as follows:

[0011] 1) Use the software CATIA to create a surface model of the target geometry;

[0012] 2) Import the surface model created in step 1) into the FEKO software for mesh generation to obtain the target mesh model;

[0013] The mesh model includes parameters such as mesh vertex coordinates, normal orientation, and material properties;

[0014] Mesh models can also be obtained from other 3D model data, such as publicly available or measured DEM data, point cloud data, etc.

[0015] Step 2: Generate an initial ray tube based on the mesh model established in Step 1, and record the intersection coordinates, bounce count, and electromagnetic information of the ray tube.

[0016] The method for generating the initial ray tube is as follows: Project the target mesh model onto an equivalent surface at infinity (this equivalent surface is perpendicular to the incident field direction), and establish a virtual aperture surface for electromagnetic wave incident on the projection of the equivalent surface. Divide the virtual aperture surface according to a set step size (typically, to ensure path accuracy during ray bouncing, the step size of the virtual aperture surface is 1 / 10λ, where λ is the incident wavelength). The divided virtual aperture surface is a series of square meshes, ultimately forming the initial ray tube. One ray tube consists of four corner points and one center point; the corner points of the ray tube are the vertices of the square meshes, and the center of the ray tube is the center of the square meshes.

[0017] The recording of ray bounce information is as follows: the propagation of the ray is tracked unit by unit, and the intersection between the mesh and the ray tube is determined. When the ray tube intersects with a cell of the target mesh model, it is determined whether the cell is occluded. If the cell is not occluded, the intersection coordinates, bounce count, and electromagnetic information of the ray tube are recorded. If the cell is occluded, it is not calculated. If the ray tube does not intersect with a cell of the target mesh model, the ray tube is not calculated, until all ray tubes leave the surface of the target mesh model.

[0018] Step 3: Based on the coordinates of the intersection point of the ray tube, the number of bounces and electromagnetic information recorded in Step 2, the ray is divided into groups, and the grouped ray sets are characterized in the form of scattering centers.

[0019] The ray diversity is divided into multiple ray sets C. m And the set of single rays, which includes the hyperboloid ray set C s C, a single-curved ray set ds and planar ray sets;

[0020] The number of intersections between rays and the mesh model is counted. When the number of intersections between a ray and a surface element of the target model is greater than 1, it is considered multiple reflection, and the corresponding rays are grouped into a multiple ray set C. m ;

[0021] When the number of intersections is equal to 1, it is a single reflection, and the corresponding ray set is called a single ray set;

[0022] The method for characterizing the results after diversity using the form of scattering centers is as follows:

[0023] The number of intersections between rays and the mesh model is counted. When the number of intersections between a ray and a surface element of the target model is greater than 1, it is considered multiple reflection, and the corresponding rays are grouped into a multiple ray set C. m Ray set information includes ray number, ray bounce order, ray direction, and mesh information. Multiple ray sets C m The resulting scattering center is a multi-type scattering center (MSC), and its parameterized expression is as follows:

[0024]

[0025] Where N is the number of scattering centers, f is the incident wave frequency, and f c For the center frequency, A n Let x be the complex amplitude parameter of the scattering center. n ,y n ,z n Let α be the three-dimensional position parameters of the scattering center, θ and φ be the azimuth and elevation angles of the incident wave in the target coordinate system, respectively, and α be the scattering center. n For MSC, α is a frequency-dependent parameter of the scattering center. n =1 / 2, where k is the wave number in free space;

[0026] A set of hyperboloid rays for single-reflection is established to clarify the characterization of the sliding scattering center (SSC). Specifically, a single reflection occurs when the number of intersections is 1. The rays of a single reflection are traversed according to their ray numbers. The surface element numbers intersecting the rays and their normal vectors are extracted. The elevation angle θ and azimuth angle φ of the surface element normal vectors in the target coordinate system are calculated. The values ​​of the intensity I of each ray and the angles θ and φ of the intersecting surface element normal vectors are recorded, forming (I,θ) and (I,φ) curves, labeled as I... θ Curve and I φ Curve. When I θ Curve and I φ When all curves are continuously changing, their curve information is statistically analyzed, and the corresponding rays are grouped into a hyperboloid ray set C. s The corresponding surface structure is a hyperboloid, forming an SSC (Surface Set Corner), which records the ray numbers and mesh information of intersecting surface elements. Hyperboloid ray set C s Sliding scattering centers (SSCs) can be formed, and their parameterized characterization is as follows:

[0027]

[0028] Where A(ξ) is the amplitude term, ξ = ξ(θ,φ), and θ and φ are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively; (jk) α The amplitude frequency dependence of the scattering center is characterized by α, which is the frequency dependence factor. For SSC, α = 1, and k is the wave number in free space. This indicates the radar's line-of-sight direction.

[0029] Establish a single-curved surface ray set to clarify the characterization form of the distributed scattering center DSC-S. When I θ curves and When only one curve is a continuously varying curve and the other is a pulse-type discontinuous curve, the corresponding structure is a single-surface type, and the corresponding rays are grouped into a single-surface ray set C. ds This can form a distributed scattering center DSC-S, whose parameterized characterization is as follows:

[0030]

[0031] Where A(ξ) is the amplitude term, ξ = ξ(θ, φ), and θ and φ are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively. (jk) α The amplitude frequency dependence of the scattering center is characterized by α, which is the frequency dependence factor. For DSC-S, α = -1 / 2, k is the wave number in free space, and L is the generatrix length of the monolith. Let ξ = ξ(θ,φ) be the radar line of sight direction. The spatial angle, ξ′, is the radar line-of-sight angle when the radar line of sight and the normal vector of the reflective structure are parallel. r is the location-orientation characteristic dependency function. i ′ is the equivalent location of the scattering center.

[0032] Establish a planar ray set to clarify the characterization form of the distributed scattering center DSC-P. When I θ curves and When all curves are pulse-type discontinuous curves, the corresponding target geometry is planar, and the corresponding ray set is classified as a planar ray set C. dp The resulting scattering center type is planar distributed scattering center DSC-P. The parameterization of DSC-P is consistent with formula (3), and the frequency dependence factor α = 1.

[0033] Step 4: Determine the location parameters of the scattering center based on the coordinates of the ray tube intersection, the number of bounces, and the electromagnetic information recorded in Step 2.

[0034] The positional parameters include the three-dimensional position of the scattering center MSC, the three-dimensional position of the scattering center SSC, the three-dimensional position of the scattering center DSC-S, and the three-dimensional position of the scattering center DSC-P.

[0035] Among them, the three-dimensional position of the scattering center MSC is determined based on the equivalent optical path difference;

[0036] The method for determining the three-dimensional position of the scattering center SSC is as follows: traverse the ray number corresponding to the hyperboloid ray set in step three and the mesh information of the intersecting surface element, count the angle Θ between the ray and the normal vector of the intersecting surface element, set a minimum value as the threshold ε, and when Θ < ε, the position of the surface element is the three-dimensional position of the SSC.

[0037] The method for determining the three-dimensional position of the scattering center DSC-S is as follows: traverse the ray number and intersecting surface mesh information corresponding to the single-curved surface ray set in step three, count the angle Θ between the ray and the corresponding surface, when Θ is the minimum value, mark the position of the corresponding surface and connect them into a straight line, the position of the center point of the straight line is the three-dimensional position of DSC-S, and the length of the straight line is the length of DSC-S, that is, L in formula (3).

[0038] The method for determining the three-dimensional position of the scattering center DSC-P is as follows: the angle Θ formed by the ray set of DSC-P and the corresponding surface element is a fixed value, the position of the corresponding surface element is marked, the position of the center point of the surface element region is the position of DSC-P, and the length of the intersection line between the plane where the ray set center is located and the region plane is the length of the scattering center, i.e. L in formula (3).

[0039] Step 5: Determine the amplitude parameters of the scattering center based on the coordinates of the ray tube intersection, the number of bounces, and the electromagnetic information recorded in Step 2.

[0040] Traversing ray set C m The intensity of rays of the same order concentrated in the ray pool is accumulated and used as the amplitude parameter of the corresponding order MSC, i.e., A in formula (1). n .

[0041] SSC: Based on ray set C s Extract the surface element normal corresponding to the scattering center location, and then extract the surface element normal near the surface element normal. The sum of the ray intensities corresponding to neighboring surface elements within the angular range is the amplitude of SSC. That is, A(ξ) in formula (2). The initial value is 5°.

[0042] DSC-S: Based on ray set C ds Taking the surface element normal vector corresponding to the straight line L in step four as the center vector, and its vicinity... The sum of the ray intensities corresponding to the neighboring surface elements within the angular range is the amplitude of DSC-S, which is A(ξ) in formula (3).

[0043] DSC-P: Based on ray set C dpThe amplitude parameter of DSC-P is obtained by summing the ray intensities corresponding to all surface elements in the plane, which is A(ξ) in formula (3).

[0044] Step six: Based on the position parameters determined in step four and the amplitude parameters determined in step five, obtain the scattering center model;

[0045] Further optimization is needed. If the RCS error is less than 3dB, the scattering center modeling is complete; otherwise, return to step five to increase the number of scattering centers (often referring to the order of multi-order scattering centers) and expand the range. The range of values ​​is determined until the RCS error calculated by the scattering center model meets the accuracy requirements.

[0046] Beneficial effects:

[0047] (1) This method is based on the parametric model of the target's scattering center and uses bouncing ray technology and multi-scattering center forward modeling technology to perform forward modeling of radar targets. After modeling, electromagnetic calculations can be performed through the parametric representation of the target's scattering center, which simplifies the complexity of electromagnetic calculations, significantly improves simulation efficiency, and enables electromagnetic calculations of large targets or scenes.

[0048] (2) Commonly used scattering center modeling methods often require estimating unknown parameters of the scattering center model after clarifying its representation. If the number of unknown parameters is too large, a large amount of data is needed for estimation, resulting in a huge computational load and resource consumption. This method, however, is based on the geometric structure of the radar target, using target geometric information to determine the type, amplitude, and location parameters of the scattering center model. Therefore, this method can effectively save modeling time and cost.

[0049] (3) The scattering process of actual radar-detected objects is very complex, usually consisting of multiple scattering components. Obtaining accurate data requires a lot of computational resources and time. If an approximate algorithm is used, the data may contain errors and the applicability is limited. However, this method is based on modeling the scattering center of the target's geometric structure, and is not affected by modeling errors caused by computational methods. At the same time, it can analyze the scattering components at various locations of the target through geometric structure analysis, which is more conducive to determining the parameterized representation of the scattering center. Attached Figure Description

[0050] Figure 1 Flowchart for forward modeling of multiple scattering centers based on SBR;

[0051] Figure 2 For the target geometric model;

[0052] Figure 3 For target mesh model information;

[0053] Figure 4 This is a schematic diagram of ray splitting;

[0054] Figure 5 This is a schematic diagram of the equivalent optical path difference for secondary effects;

[0055] Figure 6 This is a schematic diagram of the dihedral geometry.

[0056] Figure 7 This is a schematic diagram of the equivalent path for secondary scattering at a right-angled dihedral angle;

[0057] Figure 8 A schematic diagram of the equivalent scattering center of a right-angled dihedral angle;

[0058] Figure 9 This is a schematic diagram of the geometric structure of a sphere;

[0059] Figure 10 This is a schematic diagram of the geometric structure of a flat plate;

[0060] Figure 11 This is a schematic diagram of the cylindrical geometry.

[0061] Figure 12 This is a schematic diagram of the geometric structure of a cone;

[0062] Figure 13 This is a schematic diagram of the geometry of the Agni missile;

[0063] Figure 14 A schematic diagram of the geometric structure of the Agni missile with a flat plate.

[0064] Figure 15 Comparison of positive modeling results for dihedral angles;

[0065] Figure 16 This is the location of the dihedral scattering center;

[0066] Figure 17 Comparison of forward and inverse modeling results for the sphere scattering center;

[0067] Figure 18 The location of the sphere's scattering center;

[0068] Figure 19 Comparison of forward and reverse modeling results for a flat plate;

[0069] Figure 20 The location of the scattering center of the flat plate;

[0070] Figure 21 Comparison of forward and reverse modeling results for a cylinder;

[0071] Figure 22 The location of the scattering center of the cylinder;

[0072] Figure 23Comparison of forward and reverse modeling results for a cone;

[0073] Figure 24 Location of the cone scattering center;

[0074] Figure 25 Comparison of forward and reverse modeling results for the Agni missile;

[0075] Figure 26 This is the location of the Agni missile's scattering center.

[0076] Figure 27 Comparison of forward modeling results for Agni missile with added flat plate;

[0077] Figure 28 The location of the scattering center of the Agni missile with a flat plate. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0079] A forward modeling method for radar target multiple scattering centers based on a grid model, the steps of which include:

[0080] Step 1: Obtain the target mesh model.

[0081] The present invention uses the commercial software CATIA to create a surface model of the target geometry (see schematic diagram of the surface model as shown). Figure 2 (As shown). The surface model is imported into the commercial software FEKO for mesh generation to obtain the corresponding mesh model. The mesh model includes parameters such as mesh vertex coordinates, normal orientation, and material properties. The mesh model information is as follows: Figure 3 As shown. In addition to the examples of this invention, the mesh model can also be obtained from other 3D model data, such as publicly available or measured DEM data, point cloud data, etc.

[0082] Step 2: Generate an initial ray tube and track the ray bouncing process.

[0083] Project the target mesh model onto an equivalent surface at infinity (this equivalent surface is perpendicular to the incident field direction) to establish a virtual aperture surface for the electromagnetic wave incident. Divide the virtual aperture surface into sections with a certain step size (typically, to ensure path accuracy during ray bouncing, the step size is 1 / 10λ, where λ is the incident wavelength). The resulting virtual aperture surface is a series of square meshes, ultimately forming the initial ray tube. Each ray tube consists of four corner points and a center point; the corner points are the vertices of the square meshes, and the center of the ray tube is the center of the square meshes, as shown below. Figure 4 As shown.

[0084] The propagation of rays is tracked unit by unit. The intersection of the grid and the ray tubes is determined. When a ray tube intersects with a target cell, it is determined whether the cell is occluded. If the cell is not occluded, the intersection coordinates, bounce count, and electromagnetic information of the ray tube are recorded. Ray tubes that do not intersect with the target cell are not counted. This process continues until all ray tubes have left the target surface.

[0085] Step 3: Based on the spatial domain characteristics and bounce number of the rays, complete the ray diversity and clarify the representation form of the scattering center.

[0086] (1) Divide the multiple ray set and clarify the characterization form of the multiple scattering center MSC. The specific method is: count the number of intersections between the ray and the mesh. When the number of intersections between the ray and the target surface element is greater than 1, it is a multiple reflection, and the corresponding ray is collected into the multiple ray set C. m The ray set information includes ray number, ray bounce order, ray direction, and mesh information. Ray set C m The resulting scattering center is a multi-type scattering center (MSC), and its parameterized expression is as follows:

[0087]

[0088] Where N is the number of scattering centers, f is the incident wave frequency, and f c For the center frequency, A n Let x be the complex amplitude parameter of the scattering center. n ,y n ,z n Let α be the three-dimensional position parameters of the scattering center, θ and φ be the azimuth and elevation angles of the incident wave in the target coordinate system, respectively, and α be the scattering center. n For MSC, α is a frequency-dependent parameter of the scattering center. n =1 / 2.

[0089] (2) Establish a hyperboloid ray set to clarify the characterization form of the sliding scattering center (SSC). The specific method is as follows: when the number of intersections equals 1, it is considered a single reflection. Traverse the rays of a single reflection according to their ray numbers, extract the surface element numbers intersecting with the rays and their normal vectors, calculate the elevation angle θ and azimuth angle φ of the surface element normal vector in the target coordinate system, record the values ​​of the intensity I of each ray and the angles θ and φ of the intersecting surface element normal vectors, forming (I,θ) and (I,φ) curves, labeled as I... θ Curve and I φ Curve. When I θ Curve and I φ When all curves are continuously changing, their curve information is statistically analyzed, and the corresponding rays are grouped into a hyperboloid ray set C. s The corresponding surface structure is a hyperboloid, forming an SSC (Surface Set Corner), which records the ray numbers and mesh information of intersecting surface elements. Hyperboloid ray set Cs Sliding scattering centers (SSCs) can be formed, and their parameterized characterization is as follows:

[0090]

[0091] Where A(ξ) is the amplitude term, ξ = ξ(θ,φ), and θ and φ are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively; (jk) α The amplitude frequency dependence of the scattering center is characterized by α, which is the frequency dependence factor. For SSC, α = 1, and k is the wave number in free space. This indicates the radar's line-of-sight direction.

[0092] (3) Establish a single-curved surface ray set to clarify the characterization form of the distributed scattering center DSC-S. When I θ curves and When only one curve is a continuously varying curve and the other is a pulse-type discontinuous curve, the corresponding structure is a single-surface type, and the corresponding rays are grouped into a single-surface ray set C. ds This can form a distributed scattering center DSC-S, whose parameterized characterization is as follows:

[0093]

[0094] Where A(ξ) is the amplitude term, ξ = ξ(θ, φ), and θ and φ are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively. (jk) α The amplitude frequency dependence of the scattering center is characterized by α, which is the frequency dependence factor. For DSC-S, α = -1 / 2, k is the wave number in free space, and L is the generatrix length of the monolith. Let ξ = ξ(θ,φ) be the radar line of sight direction. The spatial angle, ξ′, is the radar line-of-sight angle when the radar line of sight and the normal vector of the reflective structure are parallel. r is the location-orientation characteristic dependency function. i ′ is the equivalent location of the scattering center.

[0095] (4) Establish a planar ray set to clarify the characterization form of the distributed scattering center DSC-P. When I θ curves and When all curves are pulse-type discontinuous curves, the corresponding target geometry is planar, and the corresponding ray set is classified as a planar ray set C. dp The resulting scattering center type is planar distributed scattering center DSC-P. The parameterization of DSC-P is consistent with formula (3), and the frequency dependence factor α = 1.

[0096] Step 4: Determine the position and length parameters of the scattering center.

[0097] (1) MSC: The position of the MSC is determined using the equivalent optical path difference theory. The principle of equivalent optical path difference is as follows: Figure 5 As shown. First, select a plane P that satisfies the condition that the incident ray intersects with the plane. a P b (i.e., the plane containing the two faces of the dihedral angle), with a line passing through point Q. b The direction of the dihedral angle intersection line is oriented along the axis. Rotate the face containing the face so that the plane containing the face becomes P. b ', when P is satisfied a ⊥P b When ' ', these two faces become two faces of a right-angled dihedron (shown by the dashed lines in the figure), and their ray paths also satisfy the condition of using the intersection line of the right-angled dihedron with perpendicular incident light. Let ' ' For plane P a P b The point of intersection between the line of intersection and the reference plane can be determined based on the above analysis of the right-angled dihedral angle. Just click Q a Q b The equivalent point where the two surfaces interact secondaryly is the desired 3D position parameter (x). n ,y n ,z n ).

[0098] (2) SSC: Traverse the ray number and intersecting surface information corresponding to the hyperboloid ray set in step three, count the angle Θ between the ray and the normal vector of the intersecting surface, set a minimum value as the threshold ε, and when Θ < ε, the position of the surface is the position of SSC.

[0099] (3) DSC-S: Traverse the ray number and intersecting surface information of the single surface ray set in step three, count the angle Θ between the ray and the corresponding surface, when Θ is the minimum value, mark the position of the corresponding surface and connect them into a straight line, the position of the center point of the straight line is the position of DSC-S, and the length of the straight line is the length of DSC-S, that is, L in formula (3).

[0100] (4) DSC-P: For DSC-P, the angle Θ formed by its ray set and the corresponding surface element is a fixed value. Mark the position of the corresponding surface element. The position of the center point of the surface element region is the position of DSC-P. The length of the intersection line between the plane where the ray set center is located and the region plane is the length of the scattering center, i.e. L in formula (3).

[0101] Step 5: Determine the amplitude parameters of the scattering center

[0102] (1) MSC: Traversal of ray sets C m The intensity of rays of the same order concentrated in the ray pool is accumulated and used as the amplitude parameter of the corresponding order MSC, i.e., A in formula (1). n .

[0103] (2) SSC: Analysis of ray set C s Extract the surface element normal corresponding to the scattering center location, and then extract the surface element normal near the surface element normal. The sum of the ray intensities corresponding to neighboring surface elements within the angular range is the amplitude of SSC. That is, A(ξ) in formula (2). The initial value is 5°.

[0104] (3) DSC-S: Analysis of ray set C ds Taking the surface element normal vector corresponding to the straight line L in step four as the center vector, and its vicinity... The sum of the ray intensities corresponding to the neighboring surface elements within the angular range is the amplitude of DSC-S, which is A(ξ) in formula (3).

[0105] (4) DSC-P: Analysis of ray set C dp The amplitude parameter of DSC-P is obtained by summing the ray intensities corresponding to all surface elements in the plane, which is A(ξ) in formula (3).

[0106] Step 7: Model Verification. Compare the obtained scattering center model with the SBR algorithm in FEKO software. If the RCS error is less than 3dB, the scattering center modeling is complete; otherwise, return to Step 5 and increase the number of scattering centers (referring to the order of multiple scattering centers) to expand the model. The range of values ​​is determined until the RCS error calculated by the scattering center model meets the accuracy requirements.

[0107] Example

[0108] Step 1: Obtain the target mesh model.

[0109] The present invention uses the commercial software CATIA to create a surface model of the target geometry (see schematic diagram of the surface model as shown). Figure 2 (As shown). The surface model is imported into the commercial software FEKO for mesh generation to obtain the corresponding mesh model. The mesh model includes parameters such as mesh vertex coordinates, normal orientation, and material properties. The mesh model information is as follows: Figure 3 As shown. In addition to the examples of this invention, the mesh model can also be obtained from other 3D model data, such as publicly available or measured DEM data, point cloud data, etc.

[0110] Step 2: Generate an initial ray tube and track the ray bouncing process.

[0111] Project the target mesh model onto an equivalent surface at infinity (this equivalent surface is perpendicular to the incident field direction) to establish a virtual aperture surface for the electromagnetic wave incident. Divide the virtual aperture surface into sections with a certain step size (typically, to ensure path accuracy during ray bouncing, the step size is 1 / 10λ, where λ is the incident wavelength). The resulting virtual aperture surface is a series of square meshes, ultimately forming the initial ray tube. Each ray tube consists of four corner points and a center point; the corner points are the vertices of the square meshes, and the center of the ray tube is the center of the square meshes, as shown below. Figure 4 As shown.

[0112] The propagation of rays is tracked unit by unit. The intersection of the grid and the ray tubes is determined. When a ray tube intersects with a target cell, it is determined whether the cell is occluded. If the cell is not occluded, the intersection coordinates, bounce count, and electromagnetic information of the ray tube are recorded. Ray tubes that do not intersect with the target cell are not counted. This process continues until all ray tubes have left the target surface.

[0113] Step 3: Based on the spatial domain characteristics and bounce number of the rays, complete the ray diversity and clarify the representation form of the scattering center.

[0114] The characteristics of multiple ray sets (MSCs) are defined. Specifically, the number of intersections between rays and the mesh is counted. When the number of intersections between a ray and a target surface element is greater than 1, it is considered a multiple reflection, and the corresponding rays are grouped into a multiple ray set C. m The ray set information includes ray number, ray bounce order, ray direction, and mesh information. Ray set C m The resulting scattering center is a multi-type scattering center (MSC), and its parameterized expression is as follows:

[0115]

[0116] Where N is the number of scattering centers, f is the incident wave frequency, and f c For the center frequency, A n Let x be the complex amplitude parameter of the scattering center. n ,y n ,z n Let α be the three-dimensional position parameters of the scattering center, θ and φ be the azimuth and elevation angles of the incident wave in the target coordinate system, respectively, and α be the scattering center. n For MSC, α is a frequency-dependent parameter of the scattering center. n =1 / 2.

[0117] A hyperboloid ray set is established to clarify the characterization of the sliding scattering center (SSC). Specifically, when the number of intersections equals 1, it is considered a single reflection. The rays of a single reflection are traversed according to their ray numbers. The surface element numbers intersecting the rays and their normal vectors are extracted. The elevation angle θ and azimuth angle φ of the surface element normal vectors in the target coordinate system are calculated. The values ​​of the intensity I of each ray and the angles θ and φ of the intersecting surface element normal vectors are recorded, forming (I,θ) and (I,φ) curves, labeled as I... θ Curve and I φ Curve. When I θ Curve and I φ When all curves are continuously changing, their curve information is statistically analyzed, and the corresponding rays are grouped into a hyperboloid ray set C. s The corresponding surface structure is a hyperboloid, forming an SSC (Surface Set Corner), which records the ray numbers and mesh information of intersecting surface elements. Hyperboloid ray set C s Sliding scattering centers (SSCs) can be formed, and their parameterized characterization is as follows:

[0118]

[0119] Where A(ξ) is the amplitude term, ξ = ξ(θ,φ), and θ and φ are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively; (jk) α The amplitude frequency dependence of the scattering center is characterized by α, which is the frequency dependence factor. For SSC, α = 1, and k is the wave number in free space. This indicates the radar's line-of-sight direction.

[0120] Establish a single-curved surface ray set to clarify the characterization form of the distributed scattering center DSC-S. When I θ curves and When only one curve is a continuously varying curve and the other is a pulse-type discontinuous curve, the corresponding structure is a single-surface type, and the corresponding rays are grouped into a single-surface ray set C. ds This can form a distributed scattering center DSC-S, whose parameterized characterization is as follows:

[0121]

[0122] Where A(ξ) is the amplitude term, ξ = ξ(θ, φ), and θ and φ are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively. (jk) α The amplitude frequency dependence of the scattering center is characterized by α, which is the frequency dependence factor. For DSC-S, α = -1 / 2, k is the wave number in free space, and L is the generatrix length of the monolith. Let ξ = ξ(θ,φ) be the radar line of sight direction. The spatial angle, ξ′, is the radar line-of-sight angle when the radar line of sight and the normal vector of the reflective structure are parallel. r is the location-orientation characteristic dependency function. i ′ is the equivalent location of the scattering center.

[0123] Establish a planar ray set to clarify the characterization form of the distributed scattering center DSC-P. When I θ curves and When all curves are pulse-type discontinuous curves, the corresponding target geometry is planar, and the corresponding ray set is classified as a planar ray set C. dp The resulting scattering center type is planar distributed scattering center DSC-P. The parameterization of DSC-P is consistent with formula (3), and the frequency dependence factor α = 1.

[0124] Step 4: Determine the position and length parameters of the scattering center.

[0125] MSC: The location of the MSC is determined using the equivalent optical path difference theory. The principle of equivalent optical path difference is as follows: Figure 5 As shown. First, select a plane P that satisfies the condition that the incident ray intersects with the plane. a P b (i.e., the plane containing the two faces of the dihedral angle), with a line passing through point Q. b The direction of the dihedral angle intersection line is oriented along the axis. Rotate the face containing the face so that the plane containing the face becomes P. b ', when P is satisfied a ⊥P b When ' ', these two faces become two faces of a right-angled dihedron (shown by the dashed lines in the figure), and their ray paths also satisfy the condition of using the intersection line of the right-angled dihedron with perpendicular incident light. Let ' ' For plane P a P b The point of intersection between the line of intersection and the reference plane can be determined based on the above analysis of the right-angled dihedral angle. Just click Q a Q b The equivalent point where the two surfaces interact secondaryly is the desired 3D position parameter (x). n ,y n ,z n ).

[0126] SSC: Traverse the ray numbers and intersecting surface elements corresponding to the hyperboloid ray set in step three, calculate the angle Θ between the ray and the normal vector of the intersecting surface element, set a minimum value as the threshold ε, and when Θ < ε, the position of the surface element is the position of SSC.

[0127] DSC-S: Traverse the ray number and intersecting surface mesh information corresponding to the single surface ray set in step three, count the angle Θ between the ray and the corresponding surface, when Θ is the minimum value, mark the position of the corresponding surface and connect them into a straight line, the position of the center point of the straight line is the position of DSC-S, and the length of the straight line is the length of DSC-S, that is, L in formula (3).

[0128] DSC-P: For DSC-P, the angle Θ formed by its ray set and the corresponding surface element is a fixed value. The position of the corresponding surface element is marked. The position of the center point of the surface element region is the position of DSC-P. The length of the intersection line between the plane where the ray set center is located and the region plane is the length of the scattering center, i.e., L in formula (3).

[0129] Step 5: Determine the amplitude parameters of the scattering center

[0130] MSC: Traversal Ray Set C m The intensity of rays of the same order concentrated in the ray pool is accumulated and used as the amplitude parameter of the corresponding order MSC, i.e., A in formula (1). n .

[0131] SSC: Analysis of ray set C s Extract the surface element normal corresponding to the scattering center location, and then extract the surface element normal near the surface element normal. The sum of the ray intensities corresponding to neighboring surface elements within the angular range is the amplitude of SSC. That is, A(ξ) in formula (2). The initial value is 5°.

[0132] DSC-S: Analysis of ray set C ds Taking the surface element normal vector corresponding to the straight line L in step four as the center vector, and its vicinity... The sum of the ray intensities corresponding to the neighboring surface elements within the angular range is the amplitude of DSC-S, which is A(ξ) in formula (3).

[0133] DSC-P: Analysis of ray set C dp The amplitude parameter of DSC-P is obtained by summing the ray intensities corresponding to all surface elements in the plane, which is A(ξ) in formula (3).

[0134] Step Six: Model Verification. Compare the obtained scattering center model with the SBR algorithm in FEKO software. If the RCS error is less than 3dB, the scattering center modeling is complete; otherwise, return to Step Five and increase the number of scattering centers (referring to the order of multiple scattering centers) to expand the model. The range of values ​​is determined until the RCS error calculated by the scattering center model meets the accuracy requirements.

[0135] The simulation results are as follows:

[0136] Example 1: Dihedral Model

[0137] The geometric structure and coordinate diagram of the dihedral target established by this invention are shown below. Figure 6 As shown in the diagram. Surfaces A and B each have a width of 1m, and the dihedral angle formed by the two surfaces has a length of 1m. The included angle of the dihedral angle is set to a right angle. The incident wave frequency is 3GHz, the incident angle is θ = 0–90°, and φ = 0°. According to the principle of equivalent optical path difference, the equivalent position of the MSC is as follows: Figure 7 As shown in Table 1, the results of the forward modeling of the dihedral scattering center are compared with those of the FEKOSBR simulation. Figure 15 As shown. The forward modeling time for the dihedral scattering center is approximately 30 seconds, and the root mean square error between the result and FEKO's calculation is 0.8 dB.

[0138] Table 1. Results of forward modeling of dihedral scattering centers

[0139]

[0140] Example 2: Ball

[0141] The sphere's geometric parameters are: radius 1m, incident wave frequency 3GHz, incident angle θ = 0–90°, φ = 0°, and VV polarization. See the sphere's geometric structure. Figure 8 The comparison results of RCS and FEKO based on the scattering center model are as follows: Figure 17 As shown in Table 2, the forward modeling time for the sphere scattering center is approximately 150 seconds, while the reverse modeling time is approximately 2400 seconds. Furthermore, the RCS result calculated using the forward modeling method has a smaller error than the result obtained using the reverse modeling method. This indicates that the forward modeling method for the sphere scattering center is highly efficient and achieves the required accuracy. The location of the scattering center is marked as follows. Figure 18 As shown.

[0142] Table 2. Results of positive modeling of the spherical scattering center.

[0143] Amplitude (0°) 2.7745 2.738 Location of the scattering center (0°) {1.06e-18,0.01,0.9} {-0.049,0.019,0.99} RMSE 0.114 0.1097 Modeling time 2400s 149.5s

[0144] Example 3: Flat Panel

[0145] The geometric parameters of the plate are: length 1m, incident wave frequency 3GHz, incident angle θ=0~90°, φ=0°, and polarization mode VV polarization. See the geometric structure of the plate. Figure 10 The comparison results of RCS and FEKO based on the scattering center model are as follows: Figure 19As shown in Table 3, the forward modeling time for the scattering center of the flat plate is approximately 27 seconds, while the reverse modeling time is approximately 1800 seconds. Furthermore, the RCS result calculated using the forward modeling method has a smaller error than the result obtained using the reverse modeling method. This indicates that the forward modeling method for the scattering center of the flat plate is highly efficient and achieves the required accuracy. The scattering center locations are marked as follows. Figure 20 As shown.

[0146] Table 3. Results of positive modeling of the scattering center of the flat plate.

[0147] Amplitude (0°) 1141.223 1267.33 Location of the scattering center (0°) {0.50,0.50,0} {0.5,0.5,-5.96e-08} RMSE 1.31 0.5456 Modeling time 1800s 26.5s

[0148] Example 4: Cylinder

[0149] The cylinder has the following geometric parameters: height 1m, base radius 0.5m, incident wave frequency 3GHz, incident angle θ = 0–90°, φ = 0°, and VV polarization. See [link to cylinder geometry diagram]. Figure 11 The comparison results of RCS and FEKO based on the scattering center model are as follows: Figure 21 As shown in Table 4, the forward modeling time for the cylindrical scattering center is approximately 55 seconds, while the reverse modeling time is approximately 3000 seconds. Furthermore, the RCS result calculated using the forward modeling method has a smaller error than the result obtained using the reverse modeling method. This demonstrates that the forward modeling method for the cylindrical scattering center is highly efficient and achieves the required accuracy. The scattering center locations are labeled as follows. Figure 22 As shown.

[0150] Table 4. Results of forward modeling of the scattering center of the cylinder

[0151] DSC1 Amplitude (0°) 699.59 773.03 DSC1 scattering center location (0°) {0,0,1}；{0.5,0,1} {2.2e-05,3.5e-05,1} DSC2 amplitude (90°) 0.05 37.31 DSC2 scattering center location (90°) {0.5,0,0} {0.49,0.004,0.49} RMSE 3.93 1.1835 Modeling time 3000s 54.9s

[0152] Example 5: Cone

[0153] The cone's geometric parameters are: height 1m, base radius 1m, incident wave frequency 3GHz, incident angle θ=0~90°, φ=0°, and VV polarization. See the diagram for the cone's geometric structure. Figure 12 The comparison results of RCS and FEKO based on the scattering center model are as follows: Figure 23 As shown in Table 5, the forward modeling time for the conical scattering center is approximately 95 seconds, while the reverse modeling time is approximately 3600 seconds. Furthermore, the RCS calculation using the forward modeling method yields a smaller error than the reverse modeling method. This indicates that the forward modeling method for the conical scattering center is highly efficient and achieves the required accuracy. The scattering center locations are labeled as follows. Figure 24 As shown.

[0154] Table 5. Results of forward modeling of the cone scattering center.

[0155] Amplitude (0°) 0.1284 0.0734 Location of the scattering center (0°) {0.5,0,0.5}；{0.5,0,0} {0.504,0.014,0.49} RMSE 2.517 2.2847 Modeling time 3600s 95.9s

[0156] Example 6: Agni Missile

[0157] The missile is approximately 2 meters long and 0.9 meters wide, with an incident wave frequency of 4 GHz, an incident angle of θ = 0–90°, φ = 0°, and VV polarization. The geometry of the Agni missile is shown below. Figure 13 The comparison results of RCS and FEKO based on the scattering center model are as follows: Figure 25 As shown in Table 6, the forward modeling time for the Agni missile scattering center is approximately 95 seconds, while the reverse modeling time is approximately 3600 seconds. Furthermore, the RCS result calculated using the forward modeling method has a smaller error than the result obtained using the reverse modeling method. This indicates that the forward modeling method for the Agni missile scattering center is highly efficient and achieves the required accuracy. The scattering center locations are marked as follows. Figure 26 As shown.

[0158] Table 6. Results of Forward Modeling of the Scattering Center of the Agni Missile

[0159]

[0160] Example 7: Agni missile plus flat plate

[0161] The missile is approximately 2 meters long and 0.9 meters wide, with an incident wave frequency of 5 GHz, an incident angle of θ = 0–90°, φ = 0°, and VV polarization. The geometry of the Agni missile with a flat plate is shown below. Figure 14 The comparison results of RCS and FEKO based on the scattering center model are as follows: Figure 27 As shown in Table 7, the forward modeling time for the Agni missile plus flat plate scattering center is approximately 1070 seconds, with a root mean square error of 3 dB compared to FEKO's calculation. The scattering center positions obtained from the forward modeling of the Agni missile plus flat plate are shown in Table 7. In summary, this demonstrates that the forward modeling of the dihedral scattering center is highly efficient and meets the required accuracy. The scattering center positions are labeled as follows. Figure 28 As shown.

[0162] Table 7. Results of Forward Modeling of Agni Missile Radiation Center Using Flat Plate

[0163]

[0164] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A forward modeling method for multiple scattering centers of radar targets based on a grid model, characterized in that... The steps of this method include: Step 1: Establish a grid model of the radar target; Step 2: Generate an initial ray tube based on the mesh model established in Step 1, and record the intersection coordinates, bounce count, and electromagnetic information of the ray tube. Step 3: Based on the coordinates of the intersection point of the ray tube, the number of bounces and electromagnetic information recorded in Step 2, the ray is divided into groups, and the grouped ray sets are characterized in the form of scattering centers. Step 4: Determine the location parameters of the scattering center based on the coordinates of the ray tube intersection, the number of bounces, and the electromagnetic information recorded in Step 2. Step 5: Determine the amplitude parameters of the scattering center based on the coordinates of the ray tube intersection, the number of bounces, and the electromagnetic information recorded in Step 2. Step six: Based on the position parameters determined in step four and the amplitude parameters determined in step five, obtain the scattering center model; In step three, the ray diversity is divided into multiple ray sets C. m And the set of single rays, which includes the hyperboloid ray set C s C, a single-curved ray set ds and planar ray sets; When the number of intersections between a ray and a surface element of the target model is greater than 1, it is considered multiple reflection, and the corresponding ray set is called the multiple ray set C. m Multiple ray sets C m The resulting scattering centers are multi-type scattering centers (MSCs), and their parameterized form is as follows: （1） in, The number of scattering centers f The incident wave frequency, f c For the center frequency, The complex amplitude parameter of the scattering center, The three-dimensional position parameters of the scattering center. and These are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively. For MSC, the frequency-dependent parameter of the scattering center is... = 1 / 2, The wave number in free space; A single reflection occurs when the number of intersections between a ray and a surface element of the target model is equal to 1. For each single reflection ray, the ray number is used to traverse the model, extracting the surface element numbers that intersect with the ray and their normal vectors. The elevation angle of the surface element normal vector in the target coordinate system is then calculated. θ and azimuth Record the intensity of each ray. I intersecting surface element normal vector θ Angle and The value of the angle forms ( I , θ )and( I , ) curve, marked as I θ curves and I curve; when I θ curves and I When all curves are continuously changing, their curve information is statistically analyzed, and the corresponding rays are grouped into a hyperboloid ray set C. s The corresponding surface structure is a hyperboloid, forming an SSC (Surface Set Corner), which records the ray numbers and mesh information of intersecting surface elements. The hyperboloid ray set C s The sliding scattering center (SSC) is formed, and its parameterized characterization is as follows: （2） in, For the amplitude term, , and These are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively. Characterizing the amplitude-frequency dependence of the scattering center, For SSC, it is a frequency-dependent factor; =1, Let be the wave number in free space. In the direction of the radar line of sight; when I θ curves and I φ When only one curve is a continuously varying curve and the other is a pulse-type discontinuous curve, the corresponding structure is a single-surface type, and the corresponding rays are grouped into a single-surface ray set C. ds This forms a distributed scattering center DSC-S, whose parameterized characterization is as follows: （3） in, For the amplitude term, , and These are the azimuth and elevation angles of the incident wave in the target coordinate system, respectively. Characterizing the amplitude-frequency dependence of the scattering center, As a frequency-dependent factor, DSC-S =-1 / 2, Let be the wave number in free space. L Let be the generatrix length of the simple surface. In the direction of radar line of sight, for spatial angle, The radar line-of-sight angle is the angle when the normal vectors of the radar line of sight and the reflective structure are parallel. For location and orientation characteristic dependent feature function, The equivalent location of the scattering center; when I θ curves and I φ When all curves are pulse-type discontinuous curves, the corresponding target geometry is planar, and the corresponding ray set is classified as a planar ray set C. dp The resulting scattering center type is planar distributed scattering center DSC-P. The parameterization of DSC-P is consistent with formula (3), and the frequency dependence factor is... .

2. The forward modeling method for radar target multiple scattering centers based on a grid model according to claim 1, characterized in that: The specific method for establishing the grid model of the radar target in step one is as follows: use the software CATIA to establish a surface model of the target's geometric structure, import the established surface model into the software FEKO for mesh generation, and obtain the grid model of the radar target.

3. The forward modeling method for radar target multiple scattering centers based on a grid model according to claim 2, characterized in that: The mesh model includes mesh vertex coordinates, normal vector orientation, and material property parameters.

4. The forward modeling method for radar target multiple scattering centers based on a grid model according to claim 1, characterized in that: In step two, the method for generating the initial ray tube is as follows: project the target mesh model onto an equivalent surface at infinity, and establish a virtual aperture surface for electromagnetic wave incident on the projection of the equivalent surface. Divide the virtual aperture surface according to a set step size to form the initial ray tube.

5. The forward modeling method for radar target multiple scattering centers based on a grid model according to claim 4, characterized in that: The recording of ray bounce information is as follows: the propagation of the ray is tracked unit by ray tube, and the intersection between the mesh and the ray tube is determined. When the ray tube intersects with a surface element of the target mesh model, it is determined whether the surface element is occluded. When the surface element is not occluded, the intersection coordinates, bounce count, and electromagnetic information of the ray tube are recorded. When the surface element is occluded, it is not calculated. When the ray tube does not intersect with a surface element of the target mesh model, the ray tube is not calculated, until all ray tubes leave the surface of the target mesh model.

6. The method for forward modeling of multiple scattering centers of radar targets based on a grid model according to claim 1, characterized in that: In step four, the position parameters include the three-dimensional position of the scattering center MSC, the three-dimensional position of the scattering center SSC, the three-dimensional position of the scattering center DSC-S, and the three-dimensional position of the scattering center DSC-P. Among them, the three-dimensional position of the scattering center MSC is determined based on the equivalent optical path difference; The method for determining the three-dimensional position of the scattering center SSC is as follows: traverse the ray numbers corresponding to the hyperboloid ray sets in step three and the mesh information of the intersecting surface elements, and calculate the angle between the ray and the normal vector of the intersecting surface element. Set a minimum value as the threshold. ,when At that time, the position of the surface element is the three-dimensional position of the SSC; The method for determining the three-dimensional position of the scattering center DSC-S is as follows: traverse the ray numbers and intersecting surface mesh information corresponding to the single-curved surface ray set in step three, and count the angles between the rays and the corresponding surface elements. , When the value is at its minimum, mark the position of the corresponding surface element and connect them with a straight line. The center point of the straight line is the three-dimensional position of DSC-S, and the length of the straight line is the length of DSC-S, which is the value in formula (3). L ; The method for determining the three-dimensional position of the ray center DSC-P is as follows: the angle formed by the ray set of DSC-P and the corresponding surface element. For fixed values, mark the position of the corresponding surface element. The center point of the surface element region is the position of DSC-P. The length of the intersection line between the plane where the ray set center is located and the region plane is the length of the scattering center, i.e., in formula (3). L ; In step five, the ray set C is traversed. m The intensity of rays of the same order in the ray concentration is accumulated and used as the amplitude parameter of the corresponding order MSC, i.e., in formula (1). ; According to ray set C s Extract the surface element normal corresponding to the scattering center location, and then extract the surface element normal near the surface element normal. The sum of the ray intensities corresponding to neighboring surface elements within the angular range is the amplitude of the SSC, i.e., the value in formula (2). , The initial value is 5°; According to ray set C ds Using the straight line in step four L The corresponding surface element normal vector is the center vector, and its vicinity... The sum of the ray intensities corresponding to neighboring surface elements within the angular range is the amplitude of DSC-S, i.e., the sum of the ray intensities in formula (3). ; According to ray set C dp The amplitude parameter of DSC-P is obtained by summing the ray intensities corresponding to all surface elements in the plane, i.e., the amplitude parameter of formula (3). .

7. The method for forward modeling of multiple scattering centers of radar targets based on a grid model according to claim 1, characterized in that: In step six, when the RCS error is less than 3dB, the scattering center modeling is complete. Conversely, return to step five to increase the number of scattering centers and expand... The range of values ​​is determined until the RCS error calculated by the scattering center model meets the accuracy requirements.

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