A method for obtaining the wide-angle RCS of a medium target based on compressed sensing algorithm

Abstract

This invention discloses a method for obtaining the wide-angle single-station RCS of a medium target based on a compressed sensing algorithm. The steps are as follows: setting a wide-angle uniform incident plane wave illuminating the medium target; defining RWG basis functions and calculating the excitation vector for each incident angle; performing sparsification and compression on the excitation vectors respectively; generating the PMCHWT equations for the target surface and solving to obtain the compressed induced electromagnetic current matrix; recovering the original induced electromagnetic current matrix from each column of the compressed induced electromagnetic current matrix using the OMP algorithm; and calculating the radar cross section of the medium target based on the induced electromagnetic current vectors. This invention can obtain the RCS result at any angle with fewer PMCHWT equation solutions and combined with the OMP recovery algorithm, reducing the solution time for the wide-angle RCS of the medium target while ensuring accuracy.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to the field of electromagnetic simulation technology, a method for obtaining the wide-angle radar cross section (RCS) of a medium target based on the compressed sensing algorithm (CS). This invention can be used to obtain the wide-angle radar cross section of a medium target. Background Technology

[0002] Currently, in low-frequency numerical methods, the Moment of Moment (MoM) is widely used to obtain the wide-angle RCS of simple ideal conducting targets. However, traditional methods for obtaining the wide-angle RCS of dielectric targets are based on the MoM of Moment (PMCHWT) integral equation. When analyzing the radar cross section of dielectric targets, this method, based on the PMCHWT integral equation, establishes a PMCHWT integral equation for each angle, simulates current and magnetic current using two RWG basis functions, constructs an electromagnetic-current hybrid matrix equation, solves for the current and magnetic current, and finally calculates the radar cross section using the current and magnetic current. However, when solving for the wide-angle radar cross section of dielectric targets, this method requires establishing and solving a system of equations using two RWG basis functions. This increases the dimensionality of the equation system, leading to a sharp increase in computation time and memory usage, resulting in low computational efficiency and making it impractical.

[0003] Beijing Institute of Technology disclosed an electromagnetic simulation method for antennas with dielectric substrates based on the method of moments (MoM) in its patent application, "An Electromagnetic Simulation Method for Antennas with Dielectric Substrates Based on the Method of Moments" (Application Date: April 18, 2023, Application No.: 202310273517.7, Publication No.: CN 115983053A). This method first marks the surfaces and lines of the antenna feed and impedance loading ports; secondly, it adds grid partitioning auxiliary lines along the edge of the antenna's metal patch, on the adjacent dielectric surface and inside the metal patch; then, it sets the antenna ports according to the markings and sets the solution conditions; next, it partitions the antenna structure into triangular elements according to the grid partitioning auxiliary lines and records the partitioned grid information; finally, it performs electromagnetic simulation based on the solution conditions and the partitioned grid information. This method, by adding grid partitioning auxiliary lines inside the antenna metal patch and on the dielectric surface, effectively improves the accuracy and computational efficiency when simulating the electromagnetic characteristics of antennas with dielectric substrate structures using the method of moments. However, this method still has some shortcomings: First, it requires manually adding auxiliary lines for network partitioning, which increases the number of RWG basis functions, leading to an increase in equation dimensionality and computation time. Second, it requires establishing and solving a system of equations using two RWG basis functions, which further increases the dimensionality of the equation system, resulting in a sharp increase in computation time and memory usage, and ultimately, low computational efficiency.

[0004] Anhui University of Science and Technology disclosed a method for rapidly solving the bistatic RCS of a three-dimensional target in its patent application "A Method for Rapidly Solving the Bistatic RCS of a Three-Dimensional Target" (application date: March 22, 2022, application number: 202210286946.3, publication number: CN 114722589A). Designed for the field of electromagnetic numerical computation, this method effectively improves the efficiency of solving the bistatic RCS of three-dimensional conductor targets. The method first employs a domain decomposition strategy to solve for the effective modes of each block and constructs characteristic mode basis functions. Then, it uses the characteristic mode basis functions to perform sparse transformation on the induced current. Finally, it constructs a low-dimensional compressed sensing model and reconstructs the induced current. This invention provides a new sparse basis construction method for the method of moments based on compressed sensing, realizing the sparse transformation of the induced current on the surface of a three-dimensional target and improving the efficiency of matrix equation filling and solution. However, this method still has shortcomings: firstly, the method uses a row-wise random sampling method for the impedance matrix and excitation vector, which cannot guarantee the extraction of all effective information in the matrix, resulting in a significant error between the calculation results and those of the traditional method of moments. Secondly, this method is only applicable to solving conductor targets, not to solving dielectric targets. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by proposing a method for obtaining the wide-angle radar cross section (RCS) of a medium target based on a compressed sensing algorithm. This method solves the technical problems of low calculation efficiency of medium target RCS due to excessive calculations and large errors in the calculation results of medium target RCS caused by randomly selecting matrix elements row by row.

[0006] To achieve the above objectives, the technical approach of this invention is to use the excitation vector generated at each angle as row vectors to form an excitation matrix. Each column of the excitation matrix is ​​then sparsified and compressed, avoiding the loss of effective information in the original matrix equation caused by randomly selecting the impedance matrix and excitation vector in a fast solution for the bistatic RCS of a target in existing technologies. This improves the computational accuracy when calculating the wide-angle RCS of a medium target. The compressed excitation matrix is ​​then decomposed row-wise into compressed excitation vectors and substituted into the method of moments (MoM) equations to obtain compressed induced current vectors. These compressed induced current vectors are then used to form a compressed induced current matrix. For each column of the compressed induced current matrix, the Orthogonal Matching Pursuit (OMP) algorithm is used to restore the original compressed induced current matrix to its original form. This avoids the problem of low computational efficiency when solving the PMCHWT method of moments equations in existing electromagnetic simulation methods for dielectric substrate antennas, where the PMCHWT equations have a large dimension. This allows for the rapid calculation of the wide-angle radar cross section of a medium target.

[0007] The technical solution adopted in this invention includes the following steps:

[0008] Step 1: Set up a wide-angle uniform incident plane wave to irradiate the target medium;

[0009] Step 2: Define the RWG basis functions and calculate the excitation vector for each incident angle;

[0010] Step 3: Perform sparsification and compression on the excitation vectors respectively;

[0011] Step 4: Generate the PMCHWT equation for the target surface;

[0012] Step 5: Solve the PMCHWT equations to obtain the compression induced electromagnetic current vector;

[0013] Step 6: Recover the original induced electromagnetic current matrix using the OMP algorithm;

[0014] Step 7: Calculate the radar cross section of the medium target based on the recovered induced electromagnetic current vector.

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

[0016] First, this invention sparsifies and compresses the column vectors of the excitation matrix before substituting them into the PMCHT method of moments equations for solving. This solves the problem of low computational efficiency caused by the excessively large dimension of the PMCHT method of moments equations in an existing electromagnetic simulation method for antennas with dielectric substrates. This invention enables the rapid acquisition of the wide-angle RCS of dielectric targets with only a few solutions to the PMCHT method of moments equations, reducing the computational complexity of solving the PMCHT method of moments equations and effectively improving the computational efficiency of radar cross section (RCS).

[0017] Secondly, when compressing the column vectors of the excitation matrix, this invention multiplies each column vector in the excitation matrix by a random Gaussian matrix on the left. That is, each element in each column of the excitation matrix is ​​multiplied by the corresponding coefficient and then summed. This ensures that all effective information in the PMCHWT method of moments equations is extracted, thereby reducing the error when calculating the original induced current. This invention solves the problem of loss of effective information in the equations caused by the random extraction of the impedance matrix and excitation vector in a method for quickly solving the RCS of a three-dimensional target bistatic target in the prior art, and effectively improves the accuracy of calculating the radar cross section (RCS) of the target in the medium. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0019] Figure 2 This is the model used in the simulation experiment of this invention;

[0020] Figure 3 This is a comparison of the RCS of the target medium calculated by this invention and the RCS of the target medium calculated by the method of moments based on PMCHWT. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0023] Step 1: Set up a wide-angle uniform incident plane wave to irradiate the target medium.

[0024] The incident angle of a plane wave is θ = {θ1, θ2, ..., θ}. i ,…,θ N It contains 360 angles, where N = 360, θ i The i-th incident angle is defined as [1°, 360°] with a step size of 1°.

[0025] Step 2: Define the RWG basis functions and calculate the excitation vector for each incident angle.

[0026] This invention employs a cubic thin-plate structure located in the xoz plane. The length and thickness of the medium cubic plate are 2m and 0.01m, respectively. A triangular partitioning method is used to partition the surface of the medium target, resulting in 1328 triangular facets Ω = {Ω1, Ω2, ..., Ω...}. u ,...,Ω U}, where U = 1328, and each triangular facet Ω u There are 1992 triangle facet pairs that share a common edge with the triangle facets. The RWG basis function for the position vector r is f(r) = {f1(r), f2(r), ..., f d (r),…,f n (r)}, where n=1992, f d (r) represents f n The expression for the d-th RWG basis function in (r) is:

[0027]

[0028] Among them, f d (r) represents the expression of the d-th basis function, where r represents the distance between the field point and the source point, and l d Ω represents the length of the common side of two triangular faces. + u,d Ω - u,d They represent f respectively d The side length corresponding to (r) is l d The common side and the current reference direction is from Ω + u,d Flow to Ω - u,d Two triangular facets, Representing the triangular facet Ω + u,d Ω - u,d area, Represents a triangular facet Ω + u,d The vertex that is not on the common edge points to Ω. + u,d The vector of the source point, Represents a triangular facet Ω - u,d The source point points to Ω - u,d Vectors of vertices that are not on a common edge.

[0029] incident angle θ i Corresponding electric excitation vector and magnetic excitation vector The calculation formulas are as follows:

[0030]

[0031]

[0032]

[0033] in, Let θ represent the i-th incident angle. i For the corresponding electric and magnetic excitation vectors of length n, where the value of n equals the total number of basis functions, E θ Indicates along the pitch angle The amplitude of the electric field in the direction, Indicates along the azimuth angle The electric field amplitude in the direction, exp represents the exponential function with the natural constant e as the base, j represents the imaginary unit sign, c represents the propagation direction vector, k represents the propagation direction of the incident uniform plane wave, and the electric excitation vector. With magnetic excitation vector Composition of excitation vector Its length is 2n, and the superscript T indicates the transpose operation.

[0034] Step 3: Sparsify and compress the excitation vectors respectively.

[0035] The aforementioned sparsification of the excitation vectors refers to combining each incident angle excitation vector into an excitation matrix row by row, and then left-multiplying each column of excitation vectors by a Fourier sparse matrix to obtain a sparse excitation matrix x. The specific expression is:

[0036]

[0037] Where x = {x1, x2, ..., x} d ,…,x n}, where x d Represents the d-th sparse column vector, with dimensions N×1, Ψ N×N Let M denote the Fourier orthogonal transformation matrix, and M << N.

[0038] Then, multiply each sparse column vector in the sparse matrix by a random Gaussian matrix on the left to obtain the compressed excitation matrix, as shown in the following expression:

[0039]

[0040] in, Φ represents the compression excitation value before the d-th basis function at the t-th compression angle. M×N Let M represent a random Gaussian matrix, where M = 65.

[0041] Step 4, the PMCHWT equation for the target surface is generated as follows:

[0042]

[0043] Among them, Z 2n×2n This represents an impedance matrix with dimensions 2n×2n; This represents a compressed electromagnetic current vector with a length of 2n×1. This represents a compression excitation vector with a length of 2n×1.

[0044] Step 5: Solve the PMCHWT equation to obtain the compression induced electromagnetic current vector.

[0045] Compress the excitation matrix Each row vector in Substituting the equations into the LMCHWT equations, the PMCHWT method of moments equations is solved using the LU decomposition method to calculate the compression induced electromagnetic current vector. Composition of compressive induction electromagnetic current matrix

[0046] Step 6: Recover the original induced electromagnetic current matrix using the OMP algorithm.

[0047] For the compression induction electromagnetic current matrix OMP recovery calculation is performed on each column vector in the matrix to obtain the induced electromagnetic current matrix I. N×2n The specific calculation formula is as follows:

[0048]

[0049] in, Φ represents the d-th compression excitation value at the t-th compression angle. M×N is a random Gaussian matrix (consistent with the random Gaussian matrix in step 3), and x' represents the recovered sparse vector of induced electromagnetic current.

[0050] Then, perform an inverse Fourier transform on the sparse vector x' of the induced current, and the calculation formula is as follows:

[0051]

[0052] in, This represents the recovered induced electromagnetic current value at the i-th incident angle, d-th. This represents the Fourier inverse matrix.

[0053] Step 7: Calculate the radar cross section of the medium target based on the recovered induced electromagnetic current vector.

[0054] Based on the recovered N induced electromagnetic current vectors I 2nThe RCS of the medium target is calculated using the following formula:

[0055]

[0056]

[0057]

[0058] Among them, E θ and These are the incident electric fields E inc θ and The magnitude of the electric field in the direction, and the propagation vector k can be expressed as:

[0059]

[0060] Where k represents the wave number, This represents the direction coordinate of the propagation vector k.

[0061] The effects of the present invention will be further illustrated below with simulation results.

[0062] 1. Simulation experimental conditions.

[0063] The hardware platform for the simulation experiment of this invention is: Intel(R) Core(TM) i7-11700F CPU with a main frequency of 2.50GHz and 64.0GB of memory.

[0064] The software platform for the simulation experiment of this invention is: Windows 10 operating system, Intel VisualFortran 2019, and Altair Feko 2020.

[0065] The simulation experiment used in this invention is a dielectric cubic thin plate target, such as... Figure 2 As shown, the dimensions of the dielectric cubic thin plate are approximately 2m * 2m * 0.01m, and the relative permittivity of the dielectric plate is 2. The incident wave is a uniform plane wave with θ polarization. After partitioning, the number of triangular facets on the surface of the dielectric plate is 1238, the number of RWG basis functions is 1992, and the number of unknowns is 3984.

[0066] 2. Comparative analysis of simulation content and results:

[0067] The simulation experiment of this invention uses this invention and a prior art (PMCHWT equation) to simulate the wide-angle radar cross-section of a dielectric square thin plate model, obtaining a wide-angle radar cross-section diagram of the model, as shown below. Figure 3 As shown.

[0068] In simulation experiments, one existing technology used is:

[0069] The method of moments (PMCHWT) for solving the integral equation of dielectric surfaces, as proposed by K. Umashankar et al. in their paper “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects [J]. IEEE Transactions on Antennas and Propagation. 1986, 34: 758-766”, is referred to as the PMCHWT equation.

[0070] Figure 3 The horizontal axis represents the incident wave azimuth angle in degrees, ranging from 1° to 360°, while the vertical axis represents the single-station radar cross section obtained from simulation of a simple medium cube thin plate. When using the PMCHWT-based method of moments, 360 angle points are uniformly selected at 1° intervals within the 1°-360° angle range, corresponding to 360 matrix equations. Solving these equations yields the current, and the wide-angle radar cross section is calculated and plotted as a curve. When using the compressed sensing algorithm of this invention to obtain the wide-angle RCS of the medium target, the excitation vectors at different angles are first compressed, reducing the number of equation solutions to 65. Then, the induced current obtained is restored to the original induced current at the 360° angle using the OMP algorithm. The resulting wide-angle radar cross section is then plotted. Figure 3 The curves in the figure represent the target width angle RCS obtained by simulation using existing technology, marked with black circles, and the target width angle RCS obtained by the method proposed in this invention, marked with red triangles.

[0071] from Figure 3 It can be seen that, compared with the existing method of moments based on PMCHWT, the curve plotted using the technology of this invention for the wide-angle radar cross section obtained from the simulation of a simple medium cube thin plate has good consistency, proving the accuracy of the invention in simulating medium targets.

[0072] To further demonstrate the speed of obtaining the wide-angle RCS of a medium target using the present invention, the simulation results of the two methods were evaluated using a single metric (CPU computation time). The CPU computation time of simulating the wide-angle radar cross section using the present invention and a prior art was statistically analyzed using a simple medium cube thin plate model, and the statistical results are plotted in Table 1.

[0073] Table 1 Comparison of CPU computation time between the two methods in the simulation experiment.

[0074] Simulation method Matrix solution time (s) OMP calculation time (s) Total duration PMCHWT Method of Moments 14.5s / 14.5s Method of the present invention 4.1s 3.8s 7.9s

[0075] The following formula is used to calculate the improved computational efficiency of the present invention compared to the prior art.

[0076]

[0077] As can be seen from Table 1, the simulation calculation time of the present invention is significantly lower than that of the existing PMCHWT method of moments. Compared with the PMCHWT method of moments, the method of the present invention can reduce the CPU calculation time of a simple square dielectric thin plate model by 45.5%, proving that the method of the present invention can significantly shorten the calculation time of wide-angle RCS while maintaining good accuracy.

[0078] The simulation experiments above demonstrate that the method of this invention first sparsifies and then compresses the excitation vectors, reducing the original N excitation vectors to M. The method of moments (MoM) is then used to solve the equations to obtain the compressed M induced electromagnetic currents. Finally, the OMP algorithm is used to restore the original N electromagnetic currents from the compressed M induced electromagnetic currents, and the wide-angle RCS of the medium target is calculated. This method solves the problems of excessive unknowns, low computational efficiency, and long computation time in existing technologies when solving the PMCHWT MoM equations, while maintaining high accuracy. It is a highly accurate and efficient method for rapidly obtaining the wide-angle radar cross section of a medium target.

Claims

1. A method for obtaining the wide-angle single-station RCS of a medium target based on compressed sensing algorithm, characterized in that, The method involves sparsening and compressing the excitation vector to generate the PMCHWT equations for the target surface, solving the PMCHWT equations to obtain the compressed induced electromagnetic current vector, and then recovering the original induced electromagnetic current matrix using the OMP algorithm. The method includes the following steps: Step 1: Set up a wide-angle uniform incident plane wave to irradiate the target medium; Step 2: Define the RWG basis functions and calculate the excitation vector for each incident angle; Step 3, perform sparsification and compression on the excitation vectors respectively: Sparsification of the excitation vectors means combining each incident angle excitation vector into an excitation matrix by row, and then multiplying each column of excitation vectors by a Fourier sparse matrix to obtain a sparse excitation matrix; Compression of the excitation vectors means multiplying each column vector in the sparse excitation matrix by a random Gaussian matrix to obtain a compressed excitation matrix. Step 4: Generate the PMCHWT equation for the target surface; Step 5: Solve the PMCHWT equations to obtain the compression induced electromagnetic current vector; Step 6: Restore the original induced electromagnetic current matrix using the OMP algorithm; the restoration of the original induced electromagnetic current matrix refers to combining the compressed induced electromagnetic current vectors into a compressed induced electromagnetic current matrix by row, and then restoring the original induced electromagnetic current matrix for each column using the OMP algorithm. Step 7: Calculate the radar cross section of the medium target based on the recovered induced electromagnetic current vector.

2. The method for obtaining the wide-angle single-station RCS of a medium target based on compressed sensing algorithm according to claim 1, characterized in that, The expression for the RWG basis function mentioned in step 2 is: ； in, Indicates the first The expression for each basis function, This represents the distance between the field point and the source point. This represents the side length of the common side of two triangular faces. , They represent The corresponding side length is The common side and the current reference direction is from Flow direction Two triangular facets, , Representing triangular facets , area, Represents a triangular facet The vertex that is not on the common edge points to The vector of the source point, Represents a triangular facet The source point points to Vectors of vertices that are not on a common edge.

3. The method for obtaining the wide-angle single-station RCS of a medium target based on compressed sensing algorithm according to claim 2, characterized in that, The expression for the excitation vector mentioned in step 1 is: ； ； ； in, , They represent the first Angle of incidence The corresponding length is The electric excitation vector and the magnetic excitation vector, The value of is equal to the total number of basis functions. Indicates along the pitch angle The amplitude of the electric field in the direction, Indicates along the azimuth angle The amplitude of the electric field in the direction, Represented by natural constant An exponential function with base 0. The symbol representing the imaginary unit. Represents the propagation direction vector. The electric excitation vector represents the propagation direction of the incident uniform plane wave. With magnetic excitation vector Composition of excitation vector Its length is Superscript This indicates the transpose operation.

4. The method for obtaining the wide-angle single-station RCS of a medium target based on compressed sensing algorithm according to claim 3, characterized in that, The PMCHWT equation for generating the target surface described in step 4 is as follows: ； in, The dimension is The impedance matrix; Indicates length is The compressed electromagnetic current vector, Indicates length is The compression excitation vector.

5. The method for obtaining the wide-angle single-station RCS of a medium target based on compressed sensing algorithm according to claim 1, characterized in that, The solution to the PMCHWT equations mentioned in step 5 refers to obtaining the compressed induced electromagnetic current vector through LU decomposition.

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