CN117572373A - Method for obtaining wide-angle RCS of medium target based on compressed sensing algorithm - Google Patents
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Abstract
The invention discloses a method for acquiring a medium target wide-angle single-station RCS based on a compressed sensing algorithm, which comprises the following implementation steps: setting wide-angle uniform incident plane waves for irradiating a medium target; defining RWG basis functions and calculating excitation vectors for each incident angle; the excitation vector is sparse and compressed respectively; generating a PMCHWT equation of the target surface and solving to obtain a compressed induction electromagnetic current matrix; recovering each column of the compressed induction electromagnetic current matrix into an original induction electromagnetic current matrix through an OMP algorithm; and calculating the radar scattering cross section of the medium target according to the induction electromagnetic current vector. According to the invention, the RCS result at any angle can be solved by combining less PMCHWT equation solving times with OMP recovery algorithm, and the solving time of the RCS at the wide angle of the medium target is reduced on the premise of ensuring accuracy.
Description
Technical Field
The invention belongs to the technical field of radars, and further relates to a method for acquiring a wide-angle radar cross section RCS (Radar Cross Section) of a medium target based on a compressed sensing algorithm CS (Compressed Sensing) in the technical field of electromagnetic simulation. The method can be used for acquiring the radar cross section of the medium target at a wide angle.
Background
Currently, in the low frequency digital method, a moment method MoM (Moment of Moment) is widely applied to obtain a simple ideal conductor target wide angle RCS, and a traditional medium target wide angle RCS obtaining method is a moment method based on a PMCHWT (Poggio-Miller-Chan-Harrington-Wu-Tsai) integral equation. When analyzing a radar scattering cross section of a medium target, a moment method based on a PMCHWT integral equation is used for establishing the PMCHWT integral equation for each angle, current and magnetic flow are respectively simulated through two RWG basis functions, then an electromagnetic current mixing matrix equation is established, current and magnetic flow are solved, and finally the radar scattering cross section is calculated through the current and the magnetic flow. However, when the method is used for solving the wide-angle radar scattering cross section of the medium target, two RWG basis functions are needed to be used for establishing an equation set and solving, so that the dimension of the equation set is increased, the calculation time and the memory are increased sharply, the calculation efficiency is low, and feasibility is not achieved.
The university of Beijing university discloses a moment method-based electromagnetic simulation method for a dielectric substrate antenna in patent literature (2023, 4, 18, 202310273517.7, CN 115983053A) of the moment method-based electromagnetic simulation method for a dielectric substrate antenna. Firstly, marking the surfaces and lines of antenna feed and impedance loading ports; secondly, adding mesh dissection auxiliary lines along the edge of the metal patch of the antenna on the adjacent medium surface and the inside of the metal patch; setting an antenna port according to the mark, and setting a solving condition; then, carrying out mesh triangle unit subdivision on the structure of the antenna according to the mesh subdivision auxiliary line, and recording subdivision mesh information; and finally, electromagnetic simulation is carried out according to the solving conditions and the subdivision grid information. According to the method, the mesh subdivision auxiliary lines are added in the antenna metal patch and on the surface of the medium, so that accuracy and calculation efficiency in simulating electromagnetic characteristics of the antenna with the medium substrate structure by using a moment method are effectively improved. However, this method still has the disadvantages: firstly, the network subdivision auxiliary lines are required to be manually added, so that the number of RWG basis functions is increased, and the calculation time is increased due to the fact that the dimension of the equation is increased. Secondly, the method needs to use two RWG basis functions to build an equation set and solve the equation set, so that the dimension of the equation set is increased to lead to the rapid increase of the calculation time and the memory, and the calculation efficiency is low.
The university of Anhui discloses a method for rapidly solving the three-dimensional target double-station RCS in the patent literature (application date 2022, 3 month and 22 days, application number 202210286946.3, application publication number CN 114722589A) applied by the university of Anhui, the field of electromagnetic numerical calculation is designed, and the solving efficiency of the three-dimensional conductor target double-station RCS can be effectively improved. The method comprises the steps of firstly solving the effective mode of each block by adopting a regional decomposition strategy and constructing a characteristic mode basis function. Then, sparse conversion is carried out on the induced current corresponding to the characteristic mode basis function. And finally, constructing a low-dimensional compressed sensing model and reconstructing the induced current. The invention provides a new sparse basis construction method for a moment method based on compressed sensing, realizes sparse conversion of induced current on the surface of a three-dimensional target, and improves filling and solving efficiency of a matrix equation. However, this method still has the disadvantages: firstly, the method adopts a method of randomly extracting an impedance matrix and an excitation vector according to rows, and can not ensure that all effective information extracted into the matrix, so that a calculation result has larger error than a traditional moment method result. Secondly, the method is only suitable for solving the conductor target, but not suitable for solving the medium target.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a method for acquiring a medium target wide-angle radar cross section RCS based on a compressed sensing algorithm, which is used for solving the technical problems of low medium target RCS calculation efficiency caused by excessive calculation times and large medium target RCS calculation result error caused by randomly extracting matrix elements according to rows in the prior art.
In order to achieve the above purpose, the technical idea of the invention is that excitation vectors generated by each angle are used as row vectors to form an excitation matrix, each column in the excitation matrix is thinned and compressed, the problem of effective information loss in an original matrix equation caused by randomly extracting an impedance matrix and the excitation vectors in a target double-station RCS in the prior art is avoided, the calculation accuracy in calculating a wide angle RCS of a medium target is improved, the compressed excitation matrix is decomposed into compressed excitation vectors by rows and substituted into a moment equation for solving, the compressed induction current vectors are obtained, the compressed induction current vectors are formed into compressed induction current matrices by rows, the original compressed induction current matrices are restored into the original induction current matrices by utilizing an orthogonal matching pursuit OMP (Orthogonal Matching Pursuit) algorithm for each column in the compressed induction current matrices, and the problem of low calculation efficiency in the process of solving the PMCHWT moment equation due to larger dimension of the PMWT moment equation in the electromagnetic simulation method of the substrate antenna based on the moment method in the prior art is avoided, and therefore the wide angle radar cross section of the medium target is calculated rapidly.
The technical scheme adopted by the invention comprises the following steps:
step 1, setting wide-angle uniform incident plane waves of an irradiation medium target;
step 2, defining RWG basis functions and calculating excitation vectors of each incident angle;
step 3, sparse and compression are respectively carried out on the excitation vectors;
step 4, generating a PMCHWT equation of the target surface;
step 5, solving a PMCHWT equation to obtain a compressed induction electromagnetic current vector;
step 6, recovering an original induction electromagnetic current matrix through an OMP algorithm;
and 7, calculating the radar scattering cross section of the medium target according to the restored induced electromagnetic current vector.
Compared with the prior art, the invention has the following advantages:
firstly, the column vectors of the excitation matrix are thinned and compressed, and then the column vectors are brought into a PMCHT moment equation for solving, so that the problem of low calculation efficiency caused by oversized dimensions of the PMCHWT moment equation in the electromagnetic simulation method of the substrate antenna containing the medium based on the moment method is solved, the wide-angle RCS of the medium target is rapidly obtained on the premise that the PMCHWT moment equation needs to be solved for a small number of times, the calculation complexity of solving the PMCHWT moment equation is reduced, and the calculation efficiency of the RCS of the radar scattering cross section is effectively improved.
Secondly, when the column vectors of the excitation matrix are compressed, the random Gaussian matrix is multiplied by each column vector in the excitation matrix, namely, each element in each column of the excitation matrix is multiplied by a corresponding coefficient and then summed, so that all effective information extracted into a PMCHWT moment equation is ensured, errors in the process of calculating the original induced current are reduced, the problem of losing equation effective information caused by randomly extracting the impedance matrix and the excitation vector in a method for rapidly solving the three-dimensional target double-station RCS in the prior art is solved, and the accuracy of calculating the radar scattering cross section RCS of the medium target is effectively improved.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a model of a simulation experiment of the present invention;
FIG. 3 is a graph showing the comparison of the calculated medium target wide angle RCS with the calculated medium target wide angle RCS based on the PMCHWT moment method according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the specific examples.
The implementation steps of the embodiment of the present invention will be described in further detail with reference to fig. 1.
Step 1, setting wide-angle uniform incident plane waves of an irradiation medium target.
Incidence angle θ= { θ of plane wave 1 ,θ 2 ,…,θ i ,…,θ N Comprises 360 angles, where n=360, θ i Refers to the ith incident angle, the angle range is [1 DEG, 360 DEG ]]The step size is 1 deg..
Step 2, defining RWG basis functions and calculating excitation vectors of each incident angle.
The invention adopts positiveThe square sheet structure is positioned in a xoz plane, the length and the thickness of the medium square sheet are respectively 2m and 0.01m, and a triangular splitting method is adopted to split the medium target surface to obtain 1328 triangular surface patches omega= { omega 1 ,Ω 2 ,...,Ω u ,...,Ω U U=1328, each triangular patch Ω u The two triangular patches with common edges form 1992 triangular patch pairs, and the RWG basis function f (r) = { f with the position vector of r 1 (r),f 2 (r),…,f d (r),…,f n (r) }, where n=1992, f d (r) represents f n The d-th RWG basis function in (r) has the expression:
wherein f d (r) an expression representing the d-th basis function, r representing a distance between a field point and a source point, l d Representing the side length of the common edge of two triangular face sheets, omega + u,d 、Ω - u,d Respectively represent f d (r) the corresponding side length is l d And the current reference direction is from Ω + u,d Flow direction omega - u,d Is provided with a pair of triangular face pieces, respectively represent triangular dough pieces omega + u,d 、Ω - u,d Area of->Representing triangular dough sheet omega + u,d Vertex points not on a common edge + u,d Is>Representing triangular dough sheet omega - u,d Is directed to omega - u,d Is not on the common edge.
Incidence angle theta i Corresponding electric excitation vectorMagnetic excitation vector->The calculation formulas of (a) are respectively as follows:
wherein,respectively represent the ith incident angle theta i Corresponding to the electric excitation vector and the magnetic excitation vector with the length of n, the value of n is equal to the total number of the basis functions, E θ Representing the pitch angle->Amplitude of electric field in direction, < >>Representing azimuth +.>The electric field amplitude in the direction exp represents an exponential function based on a natural constant e, j represents an imaginary unit symbol, c represents a propagation direction vector, k represents the propagation direction of an incident uniform plane wave,electric excitation vector->Is>Composing excitation vectorsThe length of which is 2n, and the upper corner mark T indicates the transpose operation.
And 3, respectively carrying out sparsity and compression on the excitation vectors.
The step of sparse excitation vectors is to combine each incident angle excitation vector into an excitation matrix according to rows, and then multiply each column excitation vector by a Fourier sparse matrix to obtain a sparse excitation matrix x. The specific expression is:
wherein x= { x 1 ,x 2 ,…,x d ,…,x n X, where x d Represents the d-th sparse column vector with dimensions N x 1, ψ N×N Represents a Fourier orthogonal transformation matrix, and M < N.
And multiplying each sparse column vector in the sparse matrix by a random Gaussian matrix to obtain a compression excitation matrix, wherein the specific expression is as follows:
wherein,represents the compression excitation value, phi, before the d-th basis function at the t-th compression angle M×N Represents a random gaussian matrix, m=65.
Step 4, generating a PMCHWT equation of the target surface as follows:
wherein Z is 2n×2n An impedance matrix representing a dimension of 2n×2n;representing a compressed electromagnetic current vector of length 2n×1,>representing a compressed excitation vector of length 2n×1.
And 5, solving a PMCHWT equation to obtain a compressed induction electromagnetic current vector.
Will compress the excitation matrixEach row vector in>Is carried into an LMCHWT equation, a PMCHWT moment equation is solved through an LU decomposition method, and a compressed induction electromagnetic current vector is obtained through calculationComposing a compressed induction electromagnetic current matrix->
And 6, recovering the original induction electromagnetic current matrix through an OMP algorithm.
Matrix of induced electromagnetic current for compressionOMP recovery calculation is carried out on each column vector in the matrix to obtain an induction electromagnetic current matrix I N×2n The specific calculation formula is as follows:
wherein,represents the d-th compression excitation value at the t-th compression angle, phi M×N For a random gaussian matrix (consistent with the random gaussian matrix in step 3), x' represents the recovered induced electromagnetic current sparse vector.
And then carrying out inverse Fourier transform on the induced current sparse vector x', wherein the calculation formula is as follows:
wherein,represents the d-th induction electromagnetic current value at the restored i-th incident angle,/th>Representing the inverse fourier matrix.
And 7, calculating the radar scattering cross section of the medium target according to the restored induced electromagnetic current vector.
Based on recovered N induced electromagnetic current vectors I 2n The RCS of the medium target is calculated, and the RCS calculation formula of the specific medium target is as follows:
wherein E is θ Andrespectively the incident electric fields E inc θ and +.>The electric field amplitude of the direction, and the propagation vector k can be expressed as:
wherein k represents the wave number,the direction coordinates of the propagation vector k are indicated.
The effects of the present invention will be further described with reference to simulations.
1. And (5) simulating experimental conditions.
The hardware platform of the simulation experiment of the invention is: the processor is Intel (R) Core (TM) i7-11700F CPU, the main frequency is 2.50GHZ, and the memory is 64.0GB.
The software platform of the simulation experiment of the invention is: windows 10 operating system, intel Visual Fortran2019, altair Feko 2020.
The simulation experiment of the invention uses a dielectric cube thin plate target, as shown in fig. 2, the size of the dielectric cube thin plate is about 2 x 2m x 0.01m, and the relative dielectric constant of the dielectric plate is 2. The incident wave is a uniform plane wave, the polarization mode is theta polarization, the number of triangular patches on the surface of the medium plate is 1238, the number of RWG basis functions is 1992, and the number of unknowns is 3984 after subdivision.
2. Simulation content and simulation result comparison analysis:
the simulation experiment of the invention is to simulate the wide-angle radar scattering cross section of a medium square sheet model by adopting the invention and a prior art (PMCHWT equation), so as to obtain a wide-angle radar scattering cross section diagram of the model, as shown in figure 3.
In simulation experiments, one prior art technique employed refers to:
umashankar, et al, published paper "Electromagnetic scattering by arbitrary shaped three dimensional homogeneous lossy dielectric objects [ J ]. IEEE Transactions on Antennas and Propagation.1986,34:758-766," describe a solution to the matrix method of the integral equation of the surface of the medium, abbreviated as PMCHWT equation.
The abscissa in fig. 3 represents the azimuth angle of the incident wave in degrees, the angular range is 1 ° -360 °, and the ordinate represents the single-station radar cross section obtained by simulation of a simple dielectric cube sheet. When a matrix method based on PMCHWT is used for solving, uniformly selecting at equal intervals of 1 DEG within an angle range of 1 DEG to 360 DEG, corresponding to 360 matrix equations, solving the equations to obtain current, calculating a wide-angle radar cross section and drawing a curve; when the wide angle RCS of the medium target is obtained based on the compressed sensing algorithm, the excitation vectors under different angles are compressed, the solving frequency of an equation is reduced to 65 times, the solved induced current is restored to the induced current under the original 360 angles through the OMP algorithm, the obtained wide angle radar scattering cross section result is drawn into the curve in the figure 3, wherein the curve marked by a black circle represents the curve of the wide angle RCS of the medium target obtained by simulation in the prior art, and the curve marked by a red triangle represents the curve of the wide angle RCS of the medium target obtained by the method provided by the invention.
As can be seen from FIG. 3, compared with the conventional PMCHWT-based moment method, the method provided by the invention has the advantages that curves drawn from wide-angle radar cross section results obtained by simulating a simple medium cube sheet have good consistency, and the accuracy of the simulation of the medium target is proved.
In order to further prove the rapidity of acquiring the wide-angle RCS of the medium target, the simulation results of the two methods are respectively evaluated by using one index (CPU calculation time), the calculation time of the CPU when the simple medium cube thin plate model simulates the wide-angle radar cross section is respectively counted by adopting the technology of the invention and the prior art, and the statistical results are plotted into a table 1.
Table 1 CPU calculation time comparison table for two methods in simulation experiment
| Simulation method | Matrix solving time(s) | OMP calculation time(s) | Total duration of time |
| PMCHWT moment method | 14.5s | / | 14.5s |
| The method of the invention | 4.1s | 3.8s | 7.9s |
By using the following formula, the calculation efficiency of the present invention is improved compared with the prior art.
As can be seen from the combination of Table 1, the simulation calculation time of the method is obviously lower than that of the conventional PMCHWT moment method, and compared with the PMCHWT moment method, the method can reduce the CPU calculation time of a simple square dielectric sheet model by 45.5%, and the method can obviously shorten the wide-angle RCS calculation time and maintain good precision.
The simulation experiment shows that: according to the method, excitation vectors are firstly sparse and then compressed, original N excitation vectors are compressed into M excitation vectors, equations are solved through a moment method to obtain M compressed induction magnetic currents, the M compressed induction magnetic currents are restored into the original N electromagnetic currents through an OMP algorithm, and finally a medium target wide angle RCS is solved. The method solves the problems of excessive unknowns, low calculation efficiency and long calculation time caused by solving the PMCHWT moment equation in the prior art, maintains higher accuracy, and is a method for rapidly acquiring the wide-angle radar cross section of the medium target accurately and efficiently.
Claims (8)
1. A method for acquiring a medium target wide-angle single-station RCS based on a compressed sensing algorithm is characterized in that excitation vectors are subjected to sparseness and compression respectively to generate a PMCHWT equation of a target surface, the PMCHWT equation is solved to obtain a compressed induction magnetic current vector, and an original induction magnetic current matrix is recovered through an OMP algorithm; the method comprises the following steps:
step 1, setting wide-angle uniform incident plane waves of an irradiation medium target;
step 2, defining RWG basis functions and calculating excitation vectors of each incident angle;
step 3, sparse and compression are respectively carried out on the excitation vectors;
step 4, generating a PMCHWT equation of the target surface;
step 5, solving a PMCHWT equation to obtain a compressed induction electromagnetic current vector;
step 6, recovering an original induction electromagnetic current matrix through an OMP algorithm;
and 7, calculating the radar scattering cross section of the medium target according to the restored induced electromagnetic current vector.
2. The compressed sensing algorithm-based medium target wide-angle single-station RCS acquisition method according to claim 1, wherein the expression of the RWG basis function in step 2 is:
wherein f d (r) represents the expression of the d-th basis function, r represents the distance between the field point and the source point, ld represents the side length of the common side of two triangular patches, Ω + u,d 、Ω - u,d Respectively indicate that the side length corresponding to fd (r) is l d And the current reference direction is from Ω + u,d Flow direction omega - u,d Is provided with a pair of triangular face pieces, respectively represent triangular dough pieces omega + u,d 、Ω - u,d Area of->Representing triangular dough sheet omega + u,d Vertex points not on a common edge + u,d Is>Representing triangular dough sheet omega - u,d Is directed to omega - u,d Is not on the common edge.
3. The compressed sensing algorithm-based medium target wide-angle single-station RCS acquisition method according to claim 2, wherein the expression of the excitation vector in step 1 is:
wherein,respectively represent the ith incident angle theta i Corresponding to the electric excitation vector and the magnetic excitation vector with the length of n, the value of n is equal to the total number of the basis functions, E θ Representing the pitch angle->Amplitude of electric field in direction, < >>Representing azimuth +.>The electric field amplitude in the direction exp represents an exponential function based on a natural constant e, j represents an imaginary unit symbol, c represents a propagation direction vector, k represents the propagation direction of an incident uniform plane wave, and the electric excitation vector +.>Is>Composing excitation vectorsThe length of which is 2n, and the upper corner mark T indicates the transpose operation.
4. The method for acquiring the medium target wide-angle single-station RCS based on the compressed sensing algorithm according to claim 1, wherein the step 3 of performing sparse excitation vector means that each incident angle excitation vector is combined into an excitation matrix according to rows, and each column of excitation vectors is multiplied by a fourier sparse matrix to obtain a sparse excitation matrix.
5. The method for obtaining the medium target wide-angle single-station RCS based on the compressed sensing algorithm according to claim 1, wherein the compressing the excitation vectors in the step 3 refers to multiplying each column vector in the sparse excitation matrix by a random gaussian matrix to obtain a compressed excitation matrix.
6. The compressed sensing algorithm-based medium target wide-angle single-station RCS acquisition method according to claim 3, wherein the PMCHWT equation for generating the target surface in step 4 is as follows:
wherein Z is 2n×2n An impedance matrix representing a dimension of 2n×2n;representing a compressed electromagnetic flow vector of length 2n x 1,representing a compressed excitation vector of length 2n×1.
7. The method for obtaining the medium target wide-angle single-station RCS based on the compressed sensing algorithm according to claim 1, wherein the solving of the PMCHWT equation in the step 5 refers to obtaining the compressed induction magnetic current vector through LU decomposition solving.
8. The method for obtaining the medium target wide-angle single-station RCS according to claim 1, wherein the recovering of the original induction magnetic current matrix in step 6 means that the compressed induction magnetic current vectors are combined into a compressed induction magnetic current matrix according to rows, and then the compressed induction magnetic current matrix is recovered into the original induction magnetic current matrix for each column through an OMP algorithm.
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