A method for establishing a target-environment composite radar cross section calculation model

Abstract

The application discloses a method for establishing a target-environment combined radar scattering cross section calculation model, which comprises the following steps: S1, calculating the target radar scattering cross section by using a target scattering calculation method to obtain the target radar scattering cross section σ t ; S2, calculating the environment radar scattering cross section by using an improved double-scale method to obtain the environment radar scattering cross section σ s ; S3, calculating the coupled radar scattering cross section by using a kd-tree-based SBR method to obtain the coupled radar scattering cross section σ c ; and S4, obtaining the combined radar scattering cross section calculation model according to the target radar scattering cross section σ t , the environment radar scattering cross section σ s and the coupled radar scattering cross section σ c obtained in steps S1-S3 respectively.

Description

Technical Field

[0001] This invention belongs to the technical field of target-environment characteristics, specifically relating to a method for establishing a target-environment composite radar cross section calculation model. Background Technology

[0002] Target-environment composite scattering is a fundamental problem in radar detection, target recognition, imaging, and long-range remote sensing. Analysis and research on the characteristics of target-environment composite scattering provide essential data support for subsequent signal processing and data analysis.

[0003] Target-environment composite scattering includes not only target scattering and environment scattering, but also target-environment coupled scattering. These problems are typically electrically large and multi-scale, especially since coupled scattering involves target-environment interactions. The key to handling these problems is how to account for coupled scattering. One approach is to use numerical methods to obtain the coupling matrix of the target-environment interaction, and then obtain the coupled electromagnetic current using direct or iterative methods. Another approach is to use high-frequency methods to calculate the contribution of multiple reflections or scatterings. The former approach requires numerical computation, which involves surface partitioning, basis function selection, coupling matrix element construction, matrix behavior analysis, and solving. The environment surface itself is limited by the difficulty of finely partitioning a rough surface model. Even if the coupling matrix can be established, its condition number is usually very large, making direct and iterative solutions ineffective. Therefore, constructing the coupling matrix cannot be considered a general solution. The latter approach accounts for the stronger coupled scattering and discards the weaker scattering, which greatly reduces the computational load and improves efficiency. Although this approach is fast, its computational accuracy is not very high. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing methods and provide a method for establishing a target-environment composite radar cross section calculation model.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for establishing a target-environment composite radar cross section calculation model includes the following steps;

[0007] S1. Calculate the target's radar cross section to obtain the target's radar cross section. ;

[0008] S2. Calculate the environmental radar cross section to obtain the environmental radar cross section. ;

[0009] S3. Calculate the coupled radar cross section to obtain the coupled radar cross section. ;

[0010] S4. The target radar cross section obtained according to steps S1-S3 respectively. Environmental radar cross section and coupled radar cross section The composite radar cross section was obtained. The calculation model for the composite radar cross section is as follows:

[0011] ;

[0012] Among them, the The target's radar cross section. For environmental radar cross section, For the coupled radar cross section, It is a composite radar cross section.

[0013] Preferably, step S1 specifically includes the following steps:

[0014] S11: Based on the improved physical optics method, the complex square root RCS vector of the target surface element is calculated;

[0015] The formula for calculating the complex square root RCS vector of the target surface element is:

[0016] ;

[0017] in, This refers to the complex square root RCS vector of the target surface element. Refers to face unit i visibility function, and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. It refers to the first i The complex square root of the radar cross section of an element. express unit vector, express unit vector, This represents the position vector of the illumination radar. This represents the position vector of the receiving radar. This represents the position vector of the center of a surface element after the target model surface is partitioned;

[0018] S12: Based on the improved physical diffraction theory, the complex square root RCS vector of the target edge diffraction is calculated;

[0019] The formula for calculating the complex square root RCS vector of the target edge diffraction is:

[0020] ;

[0021] in, The complex square root RCS vector of the target edge diffraction. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. It refers to the edge. i visibility function, It refers to the first i The complex square root of the edge of each edge;

[0022] S13. Superimpose the target surface element complex square root RCS vector obtained in step S11 and the target edge complex square root RCS vector obtained in step S12 to obtain the total target complex square root RCS vector, and then obtain the target radar cross section. ;

[0023] The formula for calculating the total target complex square root RCS vector is as follows:

[0024] ;

[0025] in, This refers to the target's complex square root (RCS) vector. This refers to the complex square root RCS vector of the target surface element. The complex square root RCS vector of the target edge diffraction.

[0026] Preferably, step S2 specifically includes the following steps:

[0027] S21: Based on the Kirchhoff approximation method of the surface element, calculate the surface element scattering field under the large-scale scattering characteristics of the environmental surface element, and then calculate the large-scale scattering coefficient of the environmental surface element.

[0028] The formula for calculating the large-scale scattering coefficient of the environmental surface element is as follows:

[0029] ;

[0030] in, This refers to the large-scale scattering coefficient of the environmental surface element. This refers to the scattering field of environmental surface elements. For the horizontal component of the environmental surface element, The amplitude of the incident wave, It refers to the normal vector of a surface unit, and A refers to the area of ​​the environment surface unit;

[0031] S22: The small-scale scattering coefficient of the environmental surface element is calculated based on the first-order small slope approximation method.

[0032] The formula for calculating the small-scale scattering coefficient of the environmental surface element is as follows:

[0033] ;

[0034] in, , And a and b refer to the polarization modes of the scattered wave and the incident wave, respectively. This refers to the horizontal component of the environmental surface. This refers to the correlation function of rough surfaces;

[0035] S23: The large-scale scattering coefficients of the environmental surface elements obtained in step S21 and the small-scale scattering coefficients of the environmental surface elements obtained in step S22 are superimposed to obtain the total environmental scattering coefficients, and thus the environmental radar cross section is obtained. ;

[0036] The formula for calculating the total environmental scattering coefficient is as follows:

[0037] ;

[0038] in, N x and N y They refer to shaft and The number of large face elements along the axial direction. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively.

[0039] Preferably, step S3 specifically includes the following steps:

[0040] S31. Use a kd-tree to segment the target scene until the number of triangles of the relevant nodes meets one of the two conditions for stopping the segmentation. Then, stop segmenting the target scene, that is, stop building the tree, and obtain the kd-tree corresponding to the target scene.

[0041] S32. Starting from the root node of the kd-tree obtained in step S31, start each ray in the target scene and determine whether ray tracing can continue by whether the ray intersects with the target bounding box. If they do not intersect, the tracing stops. If they intersect, traverse each of its child nodes and determine whether the ray intersects with each child node until a leaf node is encountered, and obtain the tracing of each ray.

[0042] S33. Using the SBR method, the complex square root of the coupled radar cross section corresponding to the scattering of each ray is obtained. Then, the complex square root of the total coupled radar cross section is obtained, and thus the coupled radar cross section is obtained. ;

[0043] The formula for calculating the complex square root of the coupled radar scattering cross section corresponding to the scattering produced by each ray is as follows:

[0044] ;

[0045] in, This represents the wave number of the incident wave. Indicates the first m The direction vector after the second reflection, in particular, , Indicates the first m The position vector of the reflection point during the second reflection, in particular, , Indicates after the first n The direction of the electric field vector after the second reflection R T0 Indicates the receiving field point r T With the target center r 0 The distance between them This represents the electric field vector of the receiving antenna. R CT Indicates the first n -1 bounce point position vector r (n-1) With the receiving antenna position vector r T distance, express unit vector, express unit vector, This represents the position vector of the illumination radar. This represents the position vector of the receiving radar. This represents the position vector of the center of a surface element after the target model surface is partitioned. This refers to the surface normal unit vector. Indicates free-space wave impedance;

[0046] The total coupled scattering complex square root RCS is:

[0047] ;

[0048] in, N r This refers to the total number of rays. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. This refers to the visibility function of elements on the path. This refers to the complex square root of the coupled radar scattering cross section corresponding to the scattering produced by each ray;

[0049] Preferably, in step S31, the two conditions are that the number of triangles inside the node is less than the number specified by the user and the depth of the tree exceeds the maximum depth specified by the user.

[0050] Compared with the prior art, the advantages of this invention are as follows:

[0051] (1) The calculation model provided by the present invention can accurately characterize the influence of distance on the composite scattering characteristics of target-environment through the design of the distance factor;

[0052] (2) The calculation model provided by the present invention includes the weighting of the antenna pattern on the composite scattering characteristics, which can more accurately describe the target-environment composite scattering characteristics;

[0053] (3) The target and environment composite scattering calculation method proposed in this invention has relatively high calculation accuracy. The average error in the X-band does not exceed 3dB and the average error in the Ku-band does not exceed 4dB. It can be used under conditions of different target heights, different attitudes, different environmental parameters and small distance between the target and the antenna. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the sphere model segmentation in an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of target surface element scattering calculation in an embodiment of the present invention;

[0056] Figure 3 This is a geometric structure diagram of the cleft edge in an embodiment of the present invention;

[0057] Figure 4 This is the composite dual-scale environment model in the embodiments of the present invention;

[0058] Figure 5 This is a schematic diagram of environmental scattering coordinates in an embodiment of the present invention;

[0059] Figure 6 This is a schematic diagram of the kd-tree partitioning in two-dimensional space in an embodiment of the present invention;

[0060] Figure 7 This is a diagram of the kd-tree data structure in an embodiment of the present invention;

[0061] Figure 8 This is a flowchart of the kd-tree-based SBR algorithm in an embodiment of the present invention;

[0062] Figure 9 This is a schematic diagram of a ray tracing method in the SBR method of this invention.

[0063] Figure 10This is a schematic diagram of the nth reflection in an embodiment of the present invention;

[0064] Figure 11 This is a schematic diagram of the "four-path" model in an embodiment of the present invention;

[0065] Figure 12 This is a schematic diagram of the composite scattering calculation model in an embodiment of the present invention;

[0066] Figure 13 This is a verification diagram of composite scattering under VV polarization in the X-band when the target height is 1m.

[0067] in, Figure 13 (a) is a calm water surface, 1m high, and 0 degrees in orientation; Figure 13 (b) The sea level is Class 1, the altitude is 1m, and the attitude is 0 degrees; Figure 13 (c) is a calm water surface, 1m high, and 45 degrees in orientation; Figure 13 (d) is a Class 1 sea level, 1m high, and 45 degrees in attitude; Figure 13 (e) is a calm water surface, 1m high, with the orientation at 90 degrees; Figure 13 (f) is a Class 1 sea level, 1m high, and 90 degrees in attitude;

[0068] Figure 14 This is a verification diagram of composite scattering under VV polarization in the X-band when the target height is 3m.

[0069] in, Figure 14 (a) is a calm water surface, 3m high, with a 0-degree attitude; Figure 14 (b) The sea level is Class 1, the altitude is 3m, and the attitude is 0 degrees; Figure 14 (c) is a calm water surface, 3m high, and 45 degrees in orientation; Figure 14 (d) is a Class 1 sea level, 3m high, and 45 degrees in attitude; Figure 14 (e) is a calm water surface, 3m high, with a 90-degree angle; Figure 14 (f) is a Class 1 sea level, 3m high, and 90 degrees in attitude;

[0070] Figure 15 This is a verification diagram of composite scattering under VV polarization in the X-band when the target height is 5m.

[0071] in, Figure 15 (a) is a calm water surface, 5m high, and 0 degrees in orientation; Figure 15 (b) The sea level is Class 1, with an altitude of 5m and an attitude of 0 degrees; Figure 15 (c) is a calm water surface, 5m high, and 45 degrees in orientation; Figure 15 (d) is a Class 1 sea level, 5m high, and 45 degrees in attitude; Figure 15 (e) is a calm water surface, 5m high, with a 90-degree angle; Figure 15(f) is a Class 1 sea level, 5m high, and 90 degrees in attitude;

[0072] Figure 16 This is a verification diagram of composite scattering under Ku-band VV polarization when the target height is 1m.

[0073] in, Figure 16 (a) is a calm water surface, 1m high, and 0 degrees in orientation; Figure 16 (b) The sea level is Class 1, the altitude is 1m, and the attitude is 0 degrees; Figure 16 (c) is a calm water surface, 1m high, and 45 degrees in orientation; Figure 16 (d) is a Class 1 sea level, 1m high, and 45 degrees in attitude; Figure 16 (e) is a calm water surface, 1m high, with the orientation at 90 degrees; Figure 16 (f) is a Class 1 sea level, 1m high, and 90 degrees in attitude;

[0074] Figure 17 This is a verification diagram of composite scattering under VV polarization in the X-band when the target height is 3m.

[0075] in, Figure 17 (a) is a calm water surface, 3m high, with a 0-degree attitude; Figure 17 (b) The sea level is Class 1, the altitude is 3m, and the attitude is 0 degrees; Figure 17 (c) is a calm water surface, 3m high, and 45 degrees in orientation; Figure 17 (d) is a Class 1 sea level, 3m high, and 45 degrees in attitude; Figure 17 (e) is a calm water surface, 3m high, with a 90-degree angle; Figure 17 (f) is a Class 1 sea level, 3m high, and 90 degrees in attitude;

[0076] Figure 18 This is a verification diagram of composite scattering under VV polarization in the X-band when the target height is 5m.

[0077] in, Figure 18 (a) is a calm water surface, 5m high, and 0 degrees in orientation; Figure 18 (b) The sea level is Class 1, with an altitude of 5m and an attitude of 0 degrees; Figure 18 (c) is a calm water surface, 5m high, and 45 degrees in orientation; Figure 18 (d) is a Class 1 sea level, 5m high, and 45 degrees in attitude; Figure 18 (e) is a calm water surface, 5m high, with a 90-degree angle; Figure 18 (f) is a Class 1 sea level, 5m high, and 90 degrees in attitude. Detailed Implementation

[0078] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0079] The method for establishing a target-environment composite radar cross section calculation model provided in this embodiment of the invention specifically includes the following steps;

[0080] S1. Calculate the target radar cross section using target scattering calculation methods to obtain the target radar cross section. Specifically, it includes the following steps:

[0081] S11: Based on the improved physical optics method, the complex square root RCS vector of the target surface element is calculated;

[0082] Scattering calculation methods typically involve meshing a 3D model of the object being calculated. The basic unit used in this meshing is often a triangular facet, which allows the resulting model to better simulate the target surface. A schematic diagram of the meshing of a sphere model is shown below. Figure 1 As shown.

[0083] Based on the improved physical optics method, the formula for calculating the scattering electric field of the target surface element is as follows:

[0084] ;

[0085] in, Represents free-space wave impedance. For free space wavenumber, This represents the position vector of the illumination radar. This represents the position vector of the receiving radar. This represents the position vector of the center of a surface element after the target model surface is partitioned. Indicates the direction of the unit vector of the incident magnetic field. The unit normal vector of the surface element. express unit vector, express unit vector, , The imaginary unit;

[0086] The underlined portion represents the incident electric field on the surface element. The amplitude at the point The integral within the integral sign can be calculated using Gordon's formula, i.e.

[0087] ;

[0088] in, The imaginary unit, For free space wavenumber, , , and They represent the first i The position vector at the two endpoints of the edge.

[0089] The complex square root of the radar cross section when the distance between the radar and the target is finite. It can be represented as:

[0090] ;

[0091] in, R T0 Indicates the receiving field point r T Distance from the target center r0 This represents the electric field vector of the receiving antenna. For free space wavenumber;

[0092] The expression for the scattered electric field obtained by combining the PO method, Rewritten as:

[0093] ;

[0094] Vector of each surface element By superimposing these elements, the complex square root RCS vector of the target surface element under physical optics can be obtained. A schematic diagram of the target surface element scattering calculation is shown below. Figure 2 As shown, the formula for calculating the complex square root RCS vector of the target surface element is:

[0095] ;

[0096] in, This refers to the complex square root RCS vector of the target surface element. Refers to face unit i visibility function, and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. It refers to the first i The formula is the complex square root of the radar cross section of each surface element. It is applicable to the calculation of near-field and far-field scattering when the distance between the radar antenna and the target changes.

[0097] S12: Based on the improved physical diffraction theory, the complex square root RCS vector of the target edge diffraction is calculated;

[0098] like Figure 3As shown, the current exhibits a derivative discontinuity at the edge, which generates an equivalent electromagnetic current at the edge, resulting in diffraction. Nπ external wedge ( N > 1), The direction of incidence. To observe the direction, It is the tangential unit vector of the edge. express and The angle between them β 'express and The angle between them and This represents the angle between the incident surface and the scattering surface and the reference surface, respectively.

[0099] The equivalent electromagnetic current at the edge can be derived from the electromagnetic current through physical diffraction (PTD), and its expression is: At this point, the expression for the electric field diffracted from the edge is:

[0100] ;

[0101] in, , , R dS and R dT The edge center vector r d With the incident radar position vector r s and the received radar position vector r T distance, f Let g be the Ufimtsev diffraction coefficient term. Then, we can obtain the complex square root RCS produced by edge diffraction:

[0102] ;

[0103] The complex square root RCS of the target edge is obtained by superimposing the RCS of each edge's diffraction. The formula for calculating the complex square root RCS of the target edge's diffraction is as follows:

[0104] ;

[0105] in, The complex square root RCS vector of the target edge diffraction. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. It refers to the edge. i visibility function, It refers to the first iThe complex square root of the edge of each edge;

[0106] S13: Superimpose the target surface element complex square root RCS vector obtained in step S11 and the target edge complex square root RCS vector obtained in step S12 to obtain the total target complex square root RCS vector, and thus obtain the target radar cross section. ;

[0107] The formula for calculating the total target complex square root RCS vector is as follows:

[0108] ;

[0109] in, This refers to the target's complex square root (RCS) vector. This refers to the complex square root RCS vector of the target surface element. The complex square root RCS vector of the target edge diffraction.

[0110] S2, such as Figure 4 and Figure 5 As shown, the environmental radar cross section is calculated using the dual-scale method, yielding the environmental radar cross section. Specifically, it includes the following steps:

[0111] S21: Based on the Kirchhoff approximation method of the surface element, calculate the surface element scattering field under the large-scale scattering characteristics of the environmental surface element, and then calculate the large-scale scattering coefficient of the environmental surface element.

[0112] The formula for calculating the scattering field of a surface element under the large-scale scattering characteristics of an environmental surface element is as follows:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] in, For free space wavenumber, For the horizontal component of the environmental surface, The amplitude of the incident wave, The surface normal unit vector, This represents the incident wave with local vertical polarization and horizontal polarization. Represents the polarization mode of the incident wave. The dough pieces are respectively in shaft and Projection on the axis, function .

[0121] The scattering coefficient on this surface element can be obtained using the following formula. The formula for calculating the large-scale scattering coefficient of the environmental surface element is as follows:

[0122] ;

[0123] in, This refers to the large-scale scattering coefficient of the environmental surface element. This refers to the scattering field of environmental surface elements. For the horizontal component of the environmental surface element, The amplitude of the incident wave, It refers to the normal vector of a surface unit, and A refers to the area of ​​the environment surface unit;

[0124] S22: Based on the first-order small-slope approximation (SSA1) method, the small-scale scattering coefficients of the environmental surface element are calculated:

[0125] The formula for calculating the small-scale scattering coefficient of the environmental surface element is as follows:

[0126] ;

[0127] in, And a and b refer to the polarization modes of the scattered wave and the incident wave, respectively. This refers to the horizontal component of the environmental surface. This refers to the correlation function of rough surfaces.

[0128] S23: The large-scale scattering coefficients of the environmental surface elements obtained in step S21 and the small-scale scattering coefficients of the environmental surface elements obtained in step S22 are superimposed to obtain the total environmental scattering coefficients, and thus the environmental radar cross section is obtained. ;

[0129] The formula for calculating the total environmental scattering coefficient is as follows:

[0130] ;

[0131] in, N x and N y They refer to shaft and The number of large face elements along the axial direction. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively.

[0132] S3. The coupled radar cross section is calculated using the kd-tree-based SBR method to obtain the coupled radar cross section. The specific calculation steps are as follows:

[0133] S31. Use a kd-tree to segment the target scene until the number of triangles in the relevant nodes meets one of the two conditions for stopping the segmentation. Then, stop segmenting the target scene, i.e., stop building the tree. The kd-tree corresponding to the target scene is obtained, specifically:

[0134] The target scene is segmented using a kd-tree. Here, we take a two-dimensional kd-tree as an example. Figure 6 As shown in the figure, the triangles in the figure represent triangular facets inside the target scene. The partitioning process adopts a recursive approach, attempting to select the partitioning plane based on the degree of concentration or dispersion of triangular facets within the target scene. The partitioning plane divides the target scene into multiple small cuboids, with each cuboid containing approximately the same number of triangular facets. The purpose of this partitioning is to minimize the cost of ray tracing. By continuously partitioning the target scene, the partitioning stops when the number of triangular facets of the relevant nodes meets one of the two conditions for stopping the partitioning: either the number of triangles inside the node is less than the number specified by the user, or the depth of the tree exceeds the maximum depth specified by the user. At this point, the partitioning of the target scene stops, i.e., the tree construction stops. If a triangular facet crosses the partitioning plane (as shown by triangular facet t3 in the figure), both related child nodes need to contain this triangular facet, ultimately resulting in the kd-tree corresponding to the target scene.

[0135] S32. Starting from the root node of the kd-tree obtained in step S31, for each ray in the target scene, determine whether ray tracing can continue by checking if the ray intersects with the target bounding box. If they do not intersect, tracing stops. If they intersect, traverse each of its child nodes and check if the ray intersects with each child node until a leaf node is encountered. This completes the tracing of each ray. Specifically:

[0136] Once the kd-tree subdivision data of the target scene is established, all incident and reflected rays can be efficiently tracked. Each ray starts from the root node of the kd-tree obtained in step S31, such as... Figure 7 As shown, the ability to continue ray tracing is determined by whether the ray intersects with the target bounding box. If they do not intersect, the tracing stops. If they intersect, the ray is traversed through each of its child nodes to determine whether the ray intersects with each child node until a leaf node is encountered, thus obtaining the tracing of each ray. Figure 8 The specific implementation process of ray tracing is given. From Figure 9As can be seen above, the ray tracing process starts from the root node to determine the intersection, gradually delving deeper into the child nodes. When the ray and the child node meet certain conditions in terms of spatial distance, it will continue to enter a deeper level of the tree structure. The deeper the level, the fewer the number of triangular facets that may intersect with the ray. The advantage of kd-tree is that it does not use regular shapes of the same size to divide the structure into octree structures, but uses irregularly sized rectangles, which can balance the time cost of each ray tracing process.

[0137] S33. Using the SBR method, the complex square root of the coupled radar cross section corresponding to the scattering of each ray is obtained. Then, the complex square root of the total coupled radar cross section is obtained, and thus the coupled radar cross section is obtained. ;

[0138] The formula for calculating the complex square root of the coupled radar scattering cross section corresponding to the scattering produced by each ray is as follows:

[0139] ;

[0140] Where, r s This represents the position vector of the illumination radar. k 0 represents the wave number of the incident wave. Indicates the first m The direction vector after the second reflection, in particular, r (m) Indicates the first m The position vector of the reflection point during the second reflection, specifically r (0) =r s , Indicates after the first n The direction of the electric field vector after the second reflection R T0 Indicates the receiving field point r T Distance from the target center r0 Let the electric field vector of the receiving antenna be denoted as , then the total complex square root RCS of the coupled scattering is:

[0141] ;

[0142] in, N r This refers to the total number of rays. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. This refers to the visibility function of elements on the path. This refers to the complex square root of the coupled radar cross section corresponding to the scattering produced by each ray. The specific calculation steps for the coupled radar cross section are as follows:

[0143] Traditional SBR methods typically assume that the incident wave is a plane wave. In reality, the distance between the incident radar and the target environment model is not infinite. Therefore, the incident wave should be considered as a spherical wave, and the radar antenna pattern should also be taken into account.

[0144] To derive a formula for coupled scattering over a finite distance, incorporating antenna pattern amplitude weighting, we assume the electric and magnetic fields of the incident wave can be expressed as:

[0145] ;

[0146] Where, r s This represents the position vector of the illumination radar. and These represent the directions of the incident wave's electric and magnetic field vectors, respectively. k 0 represents the wave number of the incident wave. This indicates the direction of the incident wave vector. The calculation involves... n The incident wave after the second bounce is:

[0147] ;

[0148] ;

[0149] in, Indicates the first m The direction vector after the second reflection, in particular, r (m) Indicates the first m The position vector of the reflection point during the second reflection, specifically r (0) =r s , Indicates after the first n The direction of the electric field vector after secondary reflection can be calculated using the following formula:

[0150] ;

[0151] in, and They represent the first n Reflection coefficients of vertically and parallelly polarized waves during secondary reflection. and These represent the directions of the horizontal and vertical components of the electric field, respectively.

[0152] Figure 10 This is a schematic diagram of the nth reflection. When the nth reflection occurs... n After the first reflection, when the ray stops bouncing and propagates into free space, it is necessary to... n -1 times the reflected wave is taken as r (n)The incident wave at the position vector is used to calculate its scattered field using the PO calculation method. The derivation process is described in the target scattering section. The final result is:

[0153] ;

[0154] in, , indicating the first n -1 bounce point position vector r (n-1) With the receiving antenna position vector r T The distance, in addition

[0155] ;

[0156] ;

[0157] Then, the integral in the above formula is calculated using Gordon's integral formula, and the complex square root RCS corresponding to each ray is finally obtained. In the calculation process, it is still necessary to judge the visibility of the face element. Z-buffer technology can still be used. In this way, the coupled radar cross section corresponding to the scattering of one of the rays can be obtained.

[0158] The SBR method is suitable for solving coupled scattering structures composed of several planes. When the assembled environment surfaces form a planar structure, the method degenerates into a simpler computational model, namely the "four-path" model. For example... Figure 11 As shown, the "four-path" model can calculate target scattering, primary coupled scattering (paths 1 and 2 in the figure), and secondary coupled scattering (path 3 in the figure). Thus, we can obtain:

[0159] ;

[0160] In the formula, ρ 1= ρ s R v,h This refers to the complex reflection coefficient corresponding to path 1. ρ 2= ρ s R v,h This refers to the complex reflection coefficient corresponding to the 2-path. ρ 31 = ρ s R v,h and ρ 32 = ρ s R v,h This refers to the complex reflection coefficient obtained from the two reflections corresponding to the three paths. , and This represents the complex square root RCS of coupled scattering along three paths. ρ s Let be the reflection factor of a rough surface, and its expression is:

[0161] ;

[0162] in, , θ i Let σ be the angle of incidence. h The root mean square height of the environment. λ This is the operating wavelength.

[0163] The "four-path" model is a special case of the SBR method, only considering the contributions of a few strongly coupled scattering events. This method is simple to implement and highly suitable for environments with low roughness. Furthermore, compared to the SBR method, it does not involve pathfinding, thus offering high computational efficiency. The four-path model is typically used for computational estimations where high accuracy is not required. While the SBR method has broad applicability, the ray pathfinding process is time-consuming, and the contribution of coupled scattering rapidly decreases with increasing bounce number due to the increased coupling distance. Therefore, in practical applications, the number of bounces is often limited, discarding higher-order bounces with weaker scattering contributions, which significantly reduces computation time.

[0164] S4. The target radar cross section obtained according to steps S1-S3 respectively. Environmental radar cross section and coupled radar cross section The composite radar cross section calculation model is obtained, such as Figure 12 As shown, the calculation model for the composite radar cross section is as follows:

[0165] ;

[0166] Among them, the The target's radar cross section. For environmental radar cross section, For the coupled radar cross section, It is a composite radar cross section.

[0167] The following verifies the composite radar cross section calculation model provided in the embodiments of the present invention.

[0168] The target was placed above the water surface at heights of 1m, 3m, and 5m, with axial deflection angles of 0°, 45°, and 90°, respectively. The operating frequency was set to the X-band, and the relative permittivity of the water surface was [value missing]. ε r = 61 – j33; Operating frequency in the Ku band, and relative permittivity is ε r = 45 – j38.

[0169] The distance between the target center and the transmitting / receiving antenna is 13 meters, and the water surface size is 100 meters × 60 meters. Both the incident and received signals are VV polarized. First, the combined scattering cross-section of the target and the environment is collected using measurement equipment. Then, the combined scattering cross-section of the target and the environment is calculated using the composite radar scattering cross-section calculation model provided in this embodiment of the invention, obtaining the backscattering cross-section within the range of a grazing angle of 5 degrees to 45 degrees. The measurement and calculation results are as follows: Figures 13-18 As shown, through Figures 13-18 It can be seen that the composite radar cross section calculation model provided in this embodiment of the invention has relatively high calculation accuracy. Furthermore, the target's attitude has a significant impact on the composite scattering results. The average error in the X-band does not exceed 3dB, and the average error in the Ku-band does not exceed 4dB. This also demonstrates that the accuracy of the composite radar cross section calculation model provided in this embodiment of the invention is guaranteed, and it is applicable to targets at different altitudes, with different attitudes, different environmental parameters, and under conditions where the distance between the target and the antenna is small, thus having a wide range of applications.

[0170] In summary, the calculation model provided by the embodiments of the present invention can accurately characterize the influence of distance on the target-environment composite scattering characteristics through the design of the distance factor; moreover, the calculation model provided by the present invention includes the weighting of the antenna pattern on the composite scattering characteristics, which can more accurately describe the target-environment composite scattering characteristics.

[0171] Meanwhile, the target-environment composite scattering calculation model proposed in this invention has relatively high calculation accuracy.

[0172] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for establishing a target-environment composite radar cross section calculation model, characterized in that, Includes the following steps: S1. Calculate the target's radar cross section to obtain the target's radar cross section. ; S2. Calculate the environmental radar cross section to obtain the environmental radar cross section. ; S3. Calculate the coupled radar cross section to obtain the coupled radar cross section. ; Step S3 specifically includes the following steps: S31. Use a kd-tree to segment the target scene until the number of triangles of the relevant nodes meets one of the two conditions for stopping the segmentation. Then, stop segmenting the target scene, that is, stop building the tree, and obtain the kd-tree corresponding to the target scene. S32. Starting from the root node of the kd-tree obtained in step S31, start each ray in the target scene and determine whether ray tracing can continue by whether the ray intersects with the target bounding box. If they do not intersect, the tracing stops. If they intersect, traverse each of its child nodes and determine whether the ray intersects with each child node until a leaf node is encountered, and obtain the tracing of each ray. S33. Using the SBR method, the complex square root of the coupled radar cross section corresponding to the scattering of each ray is obtained. Then, the complex square root of the total coupled radar cross section is obtained, and thus the coupled radar cross section is obtained. ; The formula for calculating the complex square root of the coupled radar scattering cross section corresponding to the scattering produced by each ray is as follows: ； in, This represents the wave number of the incident wave. Indicates the first m The direction vector after the second reflection , Indicates the first m The position vector of the reflection point during the second reflection. , Indicates after the first n The direction of the electric field vector after the second reflection R T0 Indicates the receiving field point r T With the target center r 0 The distance between them This represents the electric field vector of the receiving antenna. R CT Indicates the first n -1 bounce point position vector r (n-1) With the receiving antenna position vector r T distance, express unit vector, express unit vector, This represents the position vector of the illumination radar. This represents the position vector of the receiving radar. This represents the position vector of the center of a surface element after the target model surface is partitioned. This refers to the surface normal unit vector. Indicates free-space wave impedance; The total coupled scattering complex square root RCS is: ； in, N r This refers to the total number of rays. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. This refers to the visibility function of elements on the path. This refers to the complex square root of the coupled radar scattering cross section corresponding to the scattering produced by each ray; S4. The target radar cross section obtained according to steps S1-S3 respectively. Environmental radar cross section and coupled radar cross section The composite radar cross section was obtained. The calculation model for the composite radar cross section is as follows: ； Among them, the The target's radar cross section. For environmental radar cross section, For the coupled radar cross section, It is a composite radar cross section.

2. The method for establishing the target-environment composite radar cross section calculation model as described in claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Based on the improved physical optics method, the complex square root RCS vector of the target surface element is calculated; The formula for calculating the complex square root RCS vector of the target surface element is: ； in, This refers to the complex square root RCS vector of the target surface element. Refers to face unit i visibility function, and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. It refers to the first i The complex square root of the radar cross section of an element. express unit vector, express unit vector, This represents the position vector of the illumination radar. This represents the position vector of the receiving radar. This represents the position vector of the center of a surface element after the target model surface is partitioned; S12: Based on the improved physical diffraction theory, the complex square root RCS vector of the target edge diffraction is calculated; The formula for calculating the complex square root RCS vector of the target edge diffraction is: ； in, The complex square root RCS vector of the target edge diffraction. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively. It refers to the edge. i visibility function, It refers to the first i The complex square root of the edge of each edge; S13. Superimpose the target surface element complex square root RCS vector obtained in step S11 and the target edge complex square root RCS vector obtained in step S12 to obtain the total target complex square root RCS vector, and then obtain the target radar cross section. ; The formula for calculating the total target complex square root RCS vector is as follows: ； in, This refers to the target's complex square root (RCS) vector. This refers to the complex square root RCS vector of the target surface element. The complex square root RCS vector of the target edge diffraction.

3. The method for establishing the target-environment composite radar cross section calculation model as described in claim 1, characterized in that, Step S2 specifically includes the following steps: S21: Based on the Kirchhoff approximation method of the surface element, calculate the surface element scattering field under the large-scale scattering characteristics of the environmental surface element, and then calculate the large-scale scattering coefficient of the environmental surface element. The formula for calculating the large-scale scattering coefficient of the environmental surface element is as follows: ； in, This refers to the large-scale scattering coefficient of the environmental surface element. This refers to the scattering field of environmental surface elements. For the horizontal component of the environmental surface element, The amplitude of the incident wave, It refers to the normal vector of a surface unit, and A refers to the area of ​​the environment surface unit; S22: The small-scale scattering coefficient of the environmental surface element is calculated based on the first-order small slope approximation method. The formula for calculating the small-scale scattering coefficient of the environmental surface element is as follows: ； in, , And a and b refer to the polarization modes of the scattered wave and the incident wave, respectively. This refers to the horizontal component of the environmental surface. This refers to the correlation function of rough surfaces; S23: The large-scale scattering coefficients of the environmental surface elements obtained in step S21 and the small-scale scattering coefficients of the environmental surface elements obtained in step S22 are superimposed to obtain the total environmental scattering coefficients, and thus the environmental radar cross section is obtained. ; The formula for calculating the total environmental scattering coefficient is as follows: ； in, N x and N y They refer to shaft and The number of large face elements along the axial direction. and These refer to the directivity coefficient of the incident antenna and the directivity coefficient of the receiving antenna, respectively.

4. The method for establishing the target-environment composite radar cross section calculation model as described in claim 1, characterized in that, In step S31, the two conditions are that the number of triangles inside the node is less than the number specified by the user and the depth of the tree exceeds the maximum depth specified by the user.

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