Radar cross section (RCS) acquisition method based on CBFM-AIM-EDM

Abstract

The application provides a radar scattering cross section (RCS) acquisition method based on CBFM-AIM-EDM, and the implementation steps are as follows: initializing parameters; calculating main characteristic basis functions of each sub-region based on CBFM-AIM; calculating secondary characteristic basis functions of each sub-region based on CBFM-AIM-EDM; constructing a reduction matrix and acquiring the radar scattering cross section (RCS). The main characteristic basis functions and the secondary characteristic basis functions of each sub-region are calculated by using the characteristic basis function method (CBFM), then the RWG basis functions and their divergence on each sub-region can be projected on the matrix grid respectively by using the adaptive integration method (AIM) to obtain the Topelitz matrix, so that the calculation speed is accelerated, the RCS acquisition efficiency is improved under the condition of ensuring the accuracy, and the coupling between two sub-regions of the target is equivalent to the coupling between equivalent dipoles by using the equivalent dipole moment method (EDM), so that the RCS acquisition efficiency is further improved.

Description

Technical Field

[0001] This invention belongs to the field of communication technology and relates to a method for obtaining the radar cross section (RCS) of a target, specifically a method for obtaining the RCS of a target based on CBFM-AIM-EDM. Background Technology

[0002] Radar Cross Section (RCS) is a measure of the intensity of radar waves reflected by a target within a radar system. It is a unit of area used to represent a target's ability to scatter radar waves, and its magnitude indicates the target's visibility on the radar detector. The size of the RCS is not directly equivalent to the actual physical area of ​​the object, but depends on various factors, including the target's size, shape, material, and the angle and frequency of the incident wave.

[0003] The technical approach or principle of radar cross section (RCS) acquisition is to transform the electromagnetic scattering problem into a solvable system of linear algebraic equations. First, the target object is geometrically modeled, and its surface is discretized into multiple small elements. Next, using Maxwell's equations, the electromagnetic scattering problem is described as an integral equation, and appropriate basis functions are chosen to represent the current distribution on the surface. Then, by substituting the basis functions into the integral equation and weighting it with test functions, the integral equation is discretized, forming a matrix equation system. The elements of the matrix represent the interaction between the current and the electric field.

[0004] Existing methods for obtaining radar cross section (RCS) face a challenge: calculating the target's RCS requires the computation of numerous impedance matrices, leading to increased computation time and low efficiency. For example, Xi'an University of Electronic Science and Technology, in its patent application "A Broadband RCS Acquisition Method for Periodic Structures Based on CBFM and AWE" (Application Date: May 15, 2023, Application No.: 202310540021.1, Publication No.: CN 116484642 A), proposed a broadband RCS acquisition method for periodic structures based on CBFM and AWE. The implementation steps are: initializing parameters; calculating the excitation vector for each sub-region; calculating the induced current of each sub-region at each frequency corresponding to the wavenumber; and obtaining the broadband RCS of the periodic structure. This invention divides the entire target into many sub-regions, constructs basis functions in each sub-region using the characteristic basis function method (CBFM), and reflects the interaction between sub-regions through secondary characteristic basis functions, thereby reducing the order of the impedance matrix. This avoids the complexity of solving the problem caused by an excessively large impedance matrix due to too many basis functions. Simultaneously, it uses asymptotic waveform estimation (AWE) to calculate the current at other frequencies based on the induced current at the center frequency, avoiding the repetitive filling of the impedance matrix at each frequency and effectively improving computational efficiency. However, calculating the characteristic basis functions requires calculating a high-dimensional impedance matrix, which still consumes considerable time and memory. Furthermore, solving the secondary characteristic basis functions requires calculating a large number of double integrals, which still consumes a significant amount of time, resulting in relatively low efficiency in obtaining the RCS. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects in the prior art and propose a method for obtaining target RCS based on CBFM-AIM-EDM, which solves the technical problem of low acquisition efficiency in the prior art.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Initialize parameters:

[0008] Divide the target Each subregion is divided into several sub-regions. The first triangular facet, then the second... Sub-regions The Middle A triangular facet Each edge forms a common edge. Pairs of triangular facets are used to initialize each sub-region. The incident wave electric field is , No. The RWG basis functions for the triangular facet pairs are: ,in, , It is the position vector in each triangular facet;

[0009] (2) Calculate the principal characteristic basis functions of each sub-region based on CBFM-AIM:

[0010] According to each sub-region incident wave electric field RWG basis functions for each triangle facet pair Calculate each sub-region excitation vector Then, based on the characteristic basis function method CBFM, according to the RWG basis function... With excitation vector Calculate each sub-region Main characteristic basis functions In calculation When using the adaptive integral method (AIM) RWG basis functions on The projection coefficient matrix is ​​obtained by projecting the divergence of the matrix onto the matrix grid, and then obtaining the Topelitz matrix.

[0011] (3) Calculate the minor characteristic basis functions of each sub-region based on CBFM-AIM-EDM:

[0012] Based on the Equivalent Dipole Moment (EDM) method, the coupling between two sub-regions of the target is equivalent to the coupling of equivalent dipoles. This makes the integration of a large number of triangle facet pairs between the two sub-regions equivalent to the multiplication of two dipoles. Then, based on each sub-region... Main characteristic basis functions Each subregion is calculated using the length of the common edge of each pair of triangle faces with other subregions and the position vector of each triangle face. Coupled excitation vector Then, based on the CBFM method, according to the RWG basis functions Coupled excitation vector obtained by coupling between sub-regions Calculate each sub-region Secondary characteristic basis functions In calculation When using the adaptive integral method (AIM) RWG basis functions on The divergence and its divergence are projected onto the matrix grid to obtain the Topelitz matrix;

[0013] (4) Construct the reduced matrix and obtain the radar cross section (RCS):

[0014] According to each sub-region Main characteristic basis functions With secondary characteristic basis functions Construct a reduced matrix, and calculate the value of each sub-region using the reduced matrix. Surface current and according to Calculate the radar cross section (RCS) of the target.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] First, this invention uses the CBFM method to calculate the primary and secondary characteristic basis functions of each sub-region, and then uses the adaptive integration method AIM to project the RWG basis functions and their divergences on each sub-region onto the matrix grid to obtain the Topelitz matrix, thereby accelerating the calculation. This overcomes the problem of existing technologies consuming a lot of memory and time when calculating the impedance matrix, and improves the efficiency of obtaining RCS while ensuring accuracy.

[0017] Second, the present invention uses the Equivalent Dipole Moment (EDM) method to convert the coupling between two sub-regions of the target into the coupling of equivalent dipoles. This makes the integral operation of a large number of triangular facet pairs in the two sub-regions equivalent to the multiplication operation of two dipoles, thereby transforming a large number of double integrals when calculating minor feature basis functions into simple vector operations, further improving the efficiency of RCS acquisition. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the implementation of the present invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0020] Reference Figure 1 The present invention includes the following steps.

[0021] Step 1: Initialize parameters.

[0022] The target is divided into 5 sub-regions, and each sub-region is further divided into 1250 triangular patches. Then, the... Sub-regions The Middle A triangular facet Each edge is used as a common edge to form 1125 pairs of triangular facets, and then each sub-region is initialized. The incident wave electric field is , No. The RWG basis functions for the triangular facet pairs are: ,in, It is the position vector in each triangular facet.

[0023] No. Sub-regions The Middle RWG basis functions The expression is:

[0024] ,

[0025] in, Indicates the first Sub-regions The first in A pair of triangular facets, Indicates the first Sub-regions The first in The length of the common edge of a pair of triangular facets. Indicates the first Sub-regions The first in The area of ​​a pair of triangular facets. Indicates the first Sub-regions The first in The vertices of the triangular facets that are not on the common edge point to... The vector.

[0026] Step 2: Calculate the principal feature basis functions for each sub-region based on CBFM-AIM:

[0027] According to each sub-region incident wave electric field RWG basis functions for each triangle facet pair Calculate each sub-region excitation vector ;

[0028] Each sub-region incident wave electric field With excitation vector The expression is:

[0029] ,

[0030] ,

[0031] in, and These are the angles of elevation in the spherical coordinate system. Direction and azimuth The unit vector of direction, and They are and The amplitude of the electric field, The propagation direction vector, The imaginary unit, Represented by natural constant An exponential function with base 0.

[0032] In the characteristic basis function method CBFM, based on the RWG basis functions With excitation vector Calculate each sub-region Main characteristic basis functions ;

[0033] ,

[0034] AIM acceleration based on adaptive integral method: key feature basis functions The calculation will be performed on each sub-region. Enclose each sub-region in a Cartesian grid. RWG basis functions on Both the green function impedance matrix and its divergence can be projected onto the matrix grid. The projected Green's function impedance matrix becomes the Topelitz matrix. Then, Fourier transform is used to accelerate the matrix calculation, and the multipole expansion can be used to obtain the values ​​of each sub-region. Projection coefficient matrix on , , and Then, based on the projection coefficient matrix , , and Then each sub-region can be calculated. Main characteristic basis functions ;

[0035] Each sub-region solved based on AIM Main characteristic basis functions The calculation formula is:

[0036] ,

[0037] in, It is the near-field impedance matrix obtained by the method of moments (MOM). It is a Fourier transform operation. It is the inverse Fourier transform operation. It is free-space wave impedance. It is the free space wavenumber. , , and They are the first The RWG basis function of each subregion along direction, direction, The projection coefficient matrix of direction and divergence, , , and They are , , and The transpose of the matrix, It is the first Topelitz matrices for each subdomain.

[0038] Step 3: Calculate the secondary feature basis functions for each sub-region based on CBFM-AIM-EDM:

[0039] Based on the EDM method, according to each sub-region Main characteristic basis functions Each subregion is calculated using the length of the common edge of each pair of triangle faces with other subregions and the position vector of each triangle face. Coupled excitation vector Then, based on the CBFM-AIM method, according to the RWG basis functions... Coupled excitation vector obtained by coupling between sub-regions Calculate each sub-region Secondary characteristic basis functions ;

[0040] Considering the coupling between each sub-region, it is necessary to consider the coupling between each sub-region. Calculate minor characteristic basis functions The scattering fields generated by the main characteristic basis functions of other sub-regions are taken as sub-regions. The incident field is calculated for each sub-region. Secondary characteristic basis functions Secondary characteristic basis functions The expression is:

[0041] ,

[0042] Coupled excitation vectors between solution domains To accelerate the coupling between regions, the equivalent dipole moment method (EDM) is used to represent the coupling between regions as equivalent to the coupling generated by equivalent dipoles. This transforms the integration of numerous triangular facet pairs between two sub-regions into the multiplication of two dipoles, thereby converting the large number of double integrals used to calculate minor characteristic basis functions into simple vector operations. The first in the region The triangular element pair and the first The first in the region The equivalent dipole moment of a pair of triangular elements can be expressed as:

[0043] ,

[0044] in, and They represent the first The first sub-region The common side length of the triangular facet pairs and the length of the first triangle facet. The first sub-region The length of the common side of a pair of triangular facets. and They represent the first The first sub-region The centroid position vectors of the two triangles in the triangular patch and the first triangle... The first sub-region The position vector of the centroid of two triangles for each triangular facet;

[0045] No. The first in the region The radiated electric field generated by an equivalent dipole can be expressed as:

[0046] ,

[0047] ,

[0048] ,

[0049] ,

[0050] in, express , unit vector;

[0051] Therefore, the coupling excitation vector This can be represented by EDM as:

[0052] ,

[0053] Based on the adaptive integral AIM method, the speed of each sub-region is accelerated. Secondary characteristic basis functions computational speed, characteristic basis functions The expression is:

[0054] ,

[0055] in, Indicates the first Sub-regions The coupled excitation vector.

[0056] Step 4: Construct the reduced matrix and obtain the radar cross section (RCS):

[0057] According to each sub-region Main characteristic basis functions With secondary characteristic basis functions Construct a reduced matrix, and calculate the value of each sub-region using the reduced matrix. Surface current and according to Calculate the radar cross section (RCS) of the target.

[0058] To obtain the surface current of the target It is necessary to construct a reduced matrix to obtain the main characteristic basis functions. With secondary characteristic basis functions The weighting coefficients reduce the self-impedance matrix required in the reduced matrix. and mutual impedance matrix The self-impedance matrix has already been obtained in step 3. and mutual impedance matrix The calculation formula is:

[0059] ,

[0060] ,

[0061] Weighting coefficients and Weighting coefficients The calculation formula is:

[0062] ,

[0063] Therefore, each sub-region Surface current Based on the main characteristic basis functions With secondary characteristic basis functions respectively with weighting coefficients and weighting coefficients Linear combination calculation;

[0064] ,

[0065] According to each sub-region Surface current The radar cross section (RCS) of a target is calculated using the following formula:

[0066] ,

[0067] ,

[0068] ,

[0069] in, The scattering unit vector, The field point position vector, For each sub-region Surface area, This represents the squaring operation. Indicates the distance between the radar and the target. Indicates to Take the extreme operation.

Claims

1. A method for obtaining radar cross section (RCS) based on CBFM-AIM-EDM, characterized in that, Includes the following steps: (1) Initialize parameters: Divide the target Each subregion is divided into several sub-regions. The first triangular facet, then the second... Sub-regions The Middle A triangular facet Each edge forms a common edge. Pairs of triangular facets are used to initialize each sub-region. The incident wave electric field is , No. The RWG basis functions for the triangular facet pairs are: ,in, , It is the position vector in each triangular facet; (2) Calculate the principal characteristic basis functions of each sub-region based on CBFM-AIM: According to each sub-region incident wave electric field RWG basis functions for each triangle facet pair Calculate each sub-region excitation vector Then, based on the characteristic basis function method CBFM and the adaptive integral method AIM, according to the RWG basis function... With excitation vector Calculate each sub-region Main characteristic basis functions In the calculation When using the adaptive integral method (AIM) RWG basis functions on The projection coefficient matrix is ​​obtained by projecting the divergence of the matrix onto the matrix grid, and then obtaining the Topelitz matrix. (3) Calculate the minor characteristic basis functions of each sub-region based on CBFM-AIM-EDM: Based on the Equivalent Dipole Moment (EDM) method, the coupling between two sub-regions of the target is equivalent to the coupling of equivalent dipoles. This makes the integration of a large number of triangle facet pairs between the two sub-regions equivalent to the multiplication of two dipoles. Then, based on each sub-region... Main characteristic basis functions Each subregion is calculated using the length of the common edge of each pair of triangle faces with other subregions and the position vector of each triangle face. Coupled excitation vector Then, based on the CBFM method, according to the RWG basis functions Coupled excitation vector obtained by coupling between sub-regions Calculate each sub-region Secondary characteristic basis functions In calculation When using the adaptive integral method (AIM) RWG basis functions on The divergence and its divergence are projected onto the matrix grid to obtain the Topelitz matrix; (4) Construct the reduced matrix and obtain the radar cross section (RCS): According to each sub-region Main characteristic basis functions With secondary characteristic basis functions Construct a reduced matrix, and calculate the value of each sub-region using the reduced matrix. Surface current and according to Calculate the radar cross section (RCS) of the target.

2. The method according to claim 1, characterized in that, The RWG basis functions mentioned in step (1) are The calculation formula is: ； in, Indicates the first Sub-regions The first in A pair of triangular facets, Indicates the first Sub-regions The first in The length of the common edge of a pair of triangular facets express The area of ​​the triangular facet. Indicates the first Sub-regions The first in The vertices of the triangular facets that are not on the common edge point to... The vector.

3. The method according to claim 1, characterized in that, The excitation vector for each sub-region described in step (2) The calculation formula is: ； ； in, and These are the angles of elevation in the spherical coordinate system. Direction and azimuth The unit vector of direction, and They are and The amplitude of the electric field, The propagation direction vector, The imaginary unit, Represented by natural constant An exponential function with base 0.

4. The method according to claim 3, characterized in that, The principal characteristic basis functions of each sub-region described in step (2) The calculation formula is: ； in, It is the near-field impedance matrix obtained by the method of moments (MOM). It is a Fourier transform operation. It is the inverse Fourier transform operation. It is free-space wave impedance. It is the free space wavenumber. , , and They are the first The RWG basis function of each subregion along direction, direction, The projection coefficient matrix of direction and divergence, , , and They are , , and The transpose of the matrix, It is the first Topelitz matrices for each subdomain.

5. The method according to claim 4, characterized in that, The coupling excitation vector of each sub-region mentioned in step (3) The calculation formula is: ； ； ； ； ； in, and They represent the first The first sub-region The common side length of the triangular facet pairs and the length of the first triangle facet. The first sub-region The length of the common side of a pair of triangular facets. and They represent the first The first sub-region The centroid position vectors of the two triangles in the triangular patch and the first triangle... The first sub-region The position vectors of the centroids of two triangles relative to the triangular facet. express The unit vector.

6. The method according to claim 5, characterized in that, The secondary characteristic basis functions of each sub-region described in step (3) The calculation formula is: ； in, Indicates the first Sub-regions The coupled excitation vector.

7. The method according to claim 5, characterized in that, Each sub-region described in step (4) Surface current The calculation formula is: ； ； in, and They represent Weighting coefficients and The weighting coefficients.

8. The method according to claim 5, characterized in that, The target radar cross section (RCS) mentioned in step (4) is calculated using the following formula: ； ； ； in, The scattering unit vector, The field point position vector, For each sub-region Surface area, This represents the squaring operation. Indicates the distance between the radar and the target. Indicates to Take the extreme operation.

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