A Method and System for Measuring and Evaluating Target Scattering Characteristics Based on Solving the Double-Layer Plane Wave Expansion Matrix Equation

Abstract

This invention discloses a method and system for measuring and evaluating target scattering characteristics based on solving a matrix equation derived from a two-layer plane wave expansion. It primarily addresses the problems of inaccurate measurement of targets exhibiting multiple scattering effects, fixed sampling positions, and a lack of unified characterization for different types of near / far-field and single / bi-station scattering information in existing technologies. The solution involves: acquiring near-field scattering data from the target and a calibration object, performing background cancellation and normalization; representing the incident and scattered fields as two-layer plane waves and constructing a matrix equation; solving for the two-layer scattering coefficients using the matrix equation; extrapolating and calibrating the two-layer scattering coefficients to obtain the single-station far-field absolute RCS of the target; and evaluating different types of scattering results using matrix multiplication with the two-layer scattering coefficients. This invention improves the flexibility of antenna sampling positions, enables the evaluation of different types of scattering from complex targets, offers efficient data processing, and has strong universality. It can be used for the analysis of measured and simulated radar cross section (RCS) data.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic measurement technology and relates to a method and system for measuring and evaluating the scattering characteristics of a target, which can be used for near-field measured data and simulation data analysis of radar cross section (RCS). Background Technology

[0002] Radar cross section (RCS) measurement is a core method for evaluating the electromagnetic scattering characteristics of a target and a crucial measurement indicator for stealth design technology, radar detection, and target identification. RCS measurement is mainly divided into three methods: far-field measurement, compact-field measurement, and near-field measurement. Far-field measurement is exposed to the open environment and is limited by the site conditions. For electrically large target RCS testing, far-field conditions require a large test area, which is often susceptible to weather and environmental noise. The test environment not only suffers from severe interference but also has poor confidentiality. Compact-field measurement converts spherical waves into plane waves using a parabolic reflector, forming a quasi-plane wave test area within a limited region and significantly shortening the test distance. However, constructing a large parabolic reflector is expensive, and the equipment operation and maintenance costs are high. Near-field measurement uses a scanning probe to acquire scattering data in the near-radiation zone of the target and extrapolates the target's far-field RCS through certain data processing methods. Currently, plane wave unfolding technology can effectively reduce the acquisition density and eliminate the need for a high-precision scanning rig during the acquisition phase, reducing testing costs and the difficulty of implementing sampling facilities.

[0003] Patent application number 201610901056.3 discloses "a method for obtaining the RCS of a target using high-resolution imaging." This method employs a filtering-inverse projection algorithm to image near-field echo data, extracts the target scattering centers, and uses each scattering center as a point scattering source to perform vector synthesis to reconstruct the target's scattering field. The target's RCS is then obtained based on the RCS of the calibration body. This method does not require far-field measurement distance and has high imaging accuracy. However, because single-station measurements only capture the target's backscattered energy, for targets with multiple scattering effects where the scattering energy is not concentrated in the backscattering direction, single-station measurements will miss these important scattering contributions, resulting in an inability to accurately describe the complex scattering characteristics of targets with multiple scattering effects.

[0004] Patent application No. 202211480281.6 discloses a near-field measurement method for target RCS based on probe compensation and phase center correction. First, phase center correction is performed on the echo signals of the target and the calibrator. Then, the spectral expansion coefficients of the target and the scattering object are obtained, and scanning probe compensation is performed. Finally, the near-field RCS measurement result is obtained by extrapolation. Because this method is a single-station measurement and has strict requirements on the location of the sampling points (requiring orthogonality), it cannot accurately calculate the far-field RCS when the sampling locations are randomly distributed. Furthermore, because single-station measurements involve a single data type, it cannot evaluate different types of scattering results. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a target scattering characteristic measurement and evaluation method and system based on solving the double-layer plane wave expansion matrix. This method aims to accurately obtain the far-field RCS when the sampling positions are randomly distributed, improve the ability to describe the scattering characteristics of multi-scatterer structures such as cavities, and enable the evaluation of different types of scattering results.

[0006] The technical approach to achieving the objective of this invention is as follows: by solving the matrix equation of near-field bistation measurement and double-layer plane wave expansion, the far-field RCS when the sampling position is randomly distributed can be accurately obtained; by solving the double-layer scattering coefficient through double-layer plane wave expansion, the scattering characteristics of scatterers such as cavities can be described; and by using the double-layer scattering coefficient and matrix multiplication, the results of different types of scattering, whether single-station or bistation, near-field or far-field, can be obtained.

[0007] Based on the above ideas, the technical solution of the present invention includes:

[0008] 1. A method for measuring and evaluating the scattering characteristics of a target based on solving a double-layer plane wave expansion matrix, characterized in that it includes:

[0009] (1) Near-field scattering data of the target and the calibration body are obtained by near-field bistatic measurement;

[0010] (2) Perform background cancellation and normalization on the near-field scattering data of the target and the calibration body;

[0011] (3) Based on the normalized near-field scattering data of the target and the calibration body, the incident field and the scattered field are expressed in the form of a two-layer plane wave, and the matrix equation is constructed according to this two-layer plane wave form:

[0012] ,

[0013] in, It is a column vector of near-field measurement data. and These represent the number of transmitter and receiver locations, respectively. The column vector representing the scattering coefficients of the two layers. The transfer matrix is ​​called the double-layer plane wave expansion, where P and Q represent the number of points to discretize the integrals of the incident field and the scattered field, respectively.

[0014] (4) Solve the above matrix equation to obtain the two-layer scattering coefficients of the target and the calibration body. ;

[0015] (5) Using the double-layer scattering coefficients of the target and the calibration body, the single-station far-field absolute radar cross section (RCS) of the target is obtained by extrapolation and calibration. The double-layer scattering coefficients of the target are used to estimate the scattering of the target at any position and of different types by matrix multiplication.

[0016] Furthermore, in step (3), the near-field scattering data based on the normalized target and calibration body are used to combine the incident field and the scattering data.

[0017] The field is represented as a two-layer plane wave, including:

[0018] (3a) By placing the line source along the z-axis in a two-dimensional space, the incident field equation is obtained;

[0019] (3b) Substituting the Hankel function addition theorem and the Bessel integral form into the incident field equation, we obtain the plane wave expansion integral of the incident field equation;

[0020] (3c) Discretize the plane wave expansion integral of the incident field equation numerically to obtain the discretized incident field equation. ;

[0021] (3d) Based on the discretized incident field equation, the surface induced current distribution is obtained by exciting the target with the source excitation coefficient. The scattering field equation is then derived from the surface induced current distribution. The Hankel function addition theorem and the discretized form of the Bessel integral are substituted into the scattering field equation, and the discretized scattering field equation is obtained by numerical discretization. ;

[0022] (3e) By combining the discretized incident field equation and the discretized scattering field equation, we obtain the two-layer plane wave expression. ;

[0023] Furthermore, in step (3), constructing and solving the matrix equation based on the form of a two-layer plane wave includes:

[0024] (3f) The double-layer scattering coefficient in the expression of the double-layer plane wave Represented as a column vector of two-layer scattering coefficients ;

[0025] (3g) Near-field measurement data in the expression of double-layer plane wave Represented as a column vector of near-field measurement data ;

[0026] (3h) Express some terms in the double-layer plane wave expression as a transition matrix. ;

[0027] (3i) Based on the results expressed in (3f), (3g), and (3h), the following matrix equation form is obtained:

[0028] .

[0029] Furthermore, in step (5), the single-station far-field absolute radar cross section (RCS) of the target is obtained by extrapolation and calibration using the two-layer scattering coefficients of the target and the calibration body, including:

[0030] (5a) Perform near-field and far-field transformations on the two-layer scattering coefficients of the target and the calibration body respectively to obtain the single-station far-field radar cross section of the target. and calibration body single-station far-field radar cross section ;

[0031] (5b) The absolute radar cross section of the single-station far field of the calibration body is calculated based on the radius of the calibration body. ;

[0032] (5c) Using the single-station far-field radar cross section of the calibration body and calibration body single-station far-field absolute radar cross section Single-station far-field radar cross section of the target Calibration is performed to obtain the single-station far-field absolute radar cross section of the target. .

[0033] Furthermore, step (5) utilizes the two-layer scattering coefficients of the target under test to achieve scattering estimation of the target at any position and for different types through matrix multiplication, including:

[0034] (5d) Set the positions of the transmitting and receiving antennas of the target to be tested to a random distribution, and calculate the new transfer matrix of the target. ;

[0035] (5e) Based on the double-layer scattering coefficient of the target The new transition matrix of the target to be tested Calculate the new scattering result of the target. ;

[0036] (5f) Based on the location of the transmitting antenna Location of receiving antenna and the radius of the target object, for the newly estimated scattering results An assessment will be conducted.

[0037] 2. A target scattering characteristic measurement and evaluation system based on solving a double-layer plane wave expansion matrix, characterized in that it includes: a measurement module for acquiring near-field measurement data of a calibration body and the target to be measured;

[0038] The normalization module is used to normalize the near-field scattering data of the calibration body and the near-field scattering data of the target under test, respectively.

[0039] The matrix equation construction module is used to express the incident field and the scattered field as a two-layer plane wave form, and to construct a matrix equation based on the two-layer plane wave form.

[0040] The matrix equation solving module is used to calculate the transition matrix in the matrix equation, obtaining the transition matrix of the calibration body and the transition matrix of the target under test. The normalized near-field scattering data of the calibration body and the transition matrix of the calibration body are substituted into the matrix equation to obtain the two-layer scattering coefficient of the calibration body; the normalized near-field scattering data of the target under test and the transition matrix of the target under test are substituted into the matrix equation to obtain the two-layer scattering coefficient of the target under test.

[0041] The scattering result evaluation module is used to extrapolate the single-station far-field absolute radar cross section (RCS) of the target by using the two-layer scattering coefficients of the target and the calibration body. It also uses the two-layer scattering coefficients of the target to achieve scattering estimation of the target at any position and for different types of scattering by matrix multiplication.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] Firstly, this invention utilizes plane wave expansion to construct matrix equations, solves the matrix equations to obtain the double-layer scattering coefficients, and extrapolates the target's single-station far-field RCS from the double-layer scattering coefficients. This can accurately reflect the complex scattering characteristics of the target, adapt to multiple scattering bodies such as cavities, and has high practicality.

[0044] Secondly, since the present invention does not have strict requirements on the sampling points, the sampling positions of the transmitting and receiving antennas can be randomly distributed without affecting the accuracy of the scattering results, thus improving the ability to describe the target scattering characteristics and having strong stability.

[0045] Third, this invention obtains a transfer matrix after randomly distributing the sampling positions. The target scattering result is obtained by matrix multiplication of the transfer matrix and the two-layer scattering coefficients. This result is used to evaluate different types of scattering, such as near-field or far-field, single-station or dual-station. The data conversion efficiency is high. It can not only perform measured data analysis, but also calculate and evaluate simulation data. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the implementation of the target scattering characteristic measurement and evaluation method based on the solution of the double-layer plane wave expansion matrix in this invention.

[0047] Figure 2 This is a schematic diagram of the random distribution and angle truncation of the target sampling position in this invention;

[0048] Figure 3 This is a block diagram of the target scattering characteristic measurement and evaluation system based on the solution of the double-layer plane wave expansion matrix according to the present invention;

[0049] Figure 4 This is a comparison chart of the RCS of a single station with randomly distributed sampling locations according to the present invention;

[0050] Figure 5 This is a diagram showing the scattering results of different types of targets at 10 GHz according to the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions and effects of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] Example 1: A method for measuring and evaluating target scattering characteristics based on solving a double-layer plane wave expansion matrix.

[0053] Reference Figure 1 The implementation steps of this embodiment include the following:

[0054] Step 1: Obtain near-field scattering data of the target and the calibration body through measurement.

[0055] The near-field bistatic array includes a turntable, a transmitting antenna, and a receiving antenna. The receiving antenna is located on a circle with a radius of the turntable center and is used to receive near-field scattering data of the target under test. The transmitting antenna is used to transmit electromagnetic waves.

[0056] The target to be tested is a U-shaped cavity with a base length of 9cm and two side lengths of 9cm.

[0057] The calibration body is a metal sphere with a radius of 150 mm.

[0058] This step obtains near-field scattering data of the target and the calibration body by measuring. First, the target is placed at the center of the turntable, and sampling is performed at each angle. After sampling at all angles, the near-field scattering data of the target is obtained.

[0059] Then, replace the target to be tested with a calibration object and perform the same operation to obtain the near-field scattering data of the calibration object.

[0060] Step 2: Perform background cancellation and normalization on the near-field scattering data of the target and the calibration body.

[0061] 2.1) Based on the near-field scattering data of the target under test and the calibration body, the background interference is removed by background cancellation technique to obtain interference-free near-field scattering data of the target under test and the calibration body.

[0062] 2.2) Normalize the interference-free near-field scattering data of the target under test and the near-field scattering data of the calibration body to unit emission amplitude, respectively, to obtain the normalized near-field scattering data of the target under test and the normalized near-field scattering data of the calibration body.

[0063] Step 3: Represent the incident field and the scattered field as a two-layer plane wave.

[0064] To reduce computational complexity and improve solution speed, the incident and scattered fields need to be represented as superpositions of plane waves, i.e., the original equations are transformed into algebraic calculations. This two-layer plane wave form allows for selective truncation, saving computational resources while maintaining accuracy. The implementation includes:

[0065] 3.1) Placing the line source along the z-axis in a two-dimensional space, we obtain the incident field equation:

[0066] 3.2) Substituting the Hankel function addition theorem and the Bessel integral form into the incident field equation, we obtain the plane wave expansion integral of the incident field equation;

[0067] 3.3) The plane wave expansion integral of the incident field equation is discretized numerically to obtain the discretized incident field equation. :

[0068] ,

[0069] Where C1 represents a constant factor, Here, j is the source excitation coefficient, e is the natural logarithm, P is the number of discretizations of the integral, and k is the wave number. It is the incident field position vector. It is the position vector of the transmitting antenna. It is the integral weight corresponding to the p-th point. It contains the direction vector of the p-th discretized plane wave. It is the azimuth angle relative to the x-axis. The transfer operator representing the expansion of a plane wave;

[0070] 3.4) Based on the discretized incident field equation The surface induced current distribution is obtained by exciting the target with the source excitation coefficient. The scattering field equation is then derived from the surface induced current distribution. The Hankel function addition theorem and the discretized form of the Bessel integral are then substituted into the scattering field equation, and the discretized scattering field equation is obtained by numerical discretization. :

[0071] ,

[0072] Where C2 represents a constant factor, Q is the position vector of the receiving antenna, and Q is the number of points used to discretize the plane wave integral. It is the integral weight corresponding to the q-th point. It is the azimuth angle relative to the x-axis. It is the position vector of the receiving antenna. Represents the transition operator, Fourier transform representing the current distribution;

[0073] 3.5) Discretized incident field equations and discretized scattering field equations After coupling and superposition, the expression for a two-layer plane wave is obtained:

[0074] ,

[0075] in, These are near-field measurement data. It is the double-layer scattering coefficient of the p-th plane wave incident and the q-th plane wave scattered. This represents the integral weight of the p-th plane wave incident. This represents the integral weight of the q-th plane wave scattering.

[0076] Step 4: Construct the matrix equation using the two-layer plane wave form.

[0077] 4.1) The double-layer scattering coefficient in the expression for a double-layer plane wave Represented as a column vector of two-layer scattering coefficients ;

[0078] 4.2) Near-field measurement data in the double-layer plane wave expression Represented as a column vector of near-field measurement data ;

[0079] 4.3) Represent the double-layer plane wave in the equation Represented as a transition matrix ;

[0080] 4.4) Based on the results of steps 4.1) to 4.3), the following matrix equation is obtained. :

[0081] ,

[0082] in, and These represent the number of transmitting antennas and receiving antennas, respectively.

[0083] Step 5: Solve the matrix equation to obtain the two-layer scattering coefficients of the target and the calibration body. .

[0084] 5.1) Transition matrix A single line is represented as:

[0085] ,

[0086] in This represents the transpose operator. Represents the transition matrix The first submatrix in Represents the transition matrix The p-th submatrix in Represents the transition matrix The P-th submatrix in This represents the nth transmitting antenna. This represents the m-th receiving antenna. This represents the position vector of the nth transmitting antenna. This represents the position vector of the m-th receiving antenna;

[0087] 5.2) From the normalized near-field scattering data of the target under test and the normalized near-field scattering data of the calibration body, through the transfer matrix... The expressions calculate the transition matrix of the target under test and the transition matrix of the calibration body, respectively.

[0088] 5.3) Substitute the normalized near-field scattering data of the target and the transfer matrix of the target into the matrix equation and perform the inversion operation to obtain the two-layer scattering coefficient of the target.

[0089] 5.4) Substitute the normalized near-field scattering data of the calibration body and the transfer matrix of the calibration body into the matrix equation and perform the inversion operation to obtain the two-layer scattering coefficients of the calibration body.

[0090] Step 6: Using the two-layer scattering coefficients of the target under test and the calibration body, the single-station far-field absolute radar cross section (RCS) of the target under test is obtained through extrapolation and calibration.

[0091] 6.1) Perform near-field and far-field transformations on the two-layer scattering coefficients of the target and the calibration body respectively to obtain the single-station far-field radar cross section of the target. and calibration body single-station far-field radar cross section ;

[0092] 6.2) The absolute far-field radar cross section of the calibration body at a single station is calculated based on the radius of the calibration body. ;

[0093] 6.3) Utilizing the single-station far-field radar cross-section of the calibration body and calibration body single-station far-field absolute radar cross section Single-station far-field radar cross section of the target Calibration is performed to obtain the single-station far-field absolute radar cross section of the target. ;

[0094] .

[0095] Step 7: Using the two-layer scattering coefficients of the target under test, matrix multiplication is used to estimate the scattering at any position and for different types of the target under test.

[0096] 7.1) Set the positions of the transmitting and receiving antennas of the target under test to be randomly distributed, such as... Figure 2 As shown, where:

[0097] Figure 2 (a) is a schematic diagram showing that the position of the transmitting antenna changes randomly and the radius perturbation is within ±0.5λ.

[0098] Figure 2 (b) is a schematic diagram of a bistatic measurement with the receiving antenna positions randomly distributed at ±45° and the radius perturbation within ±0.5λ.

[0099] 7.2) Calculate the new transfer matrix of the target based on the randomly distributed antenna positions. ;

[0100] 7.3) Based on the two-layer scattering coefficient of the target and the new transfer matrix of the target. Calculate the new scattering result of the target. ;

[0101] ,

[0102] in, and These are the new locations for the transmitting and receiving antennas;

[0103] 7.4) Based on the location of the transmitting antenna Location of receiving antenna And the radius of the target to be measured, for the newly estimated scattering results Conduct an assessment;

[0104] like ,but Indicates a single-station RCS;

[0105] like ,but Indicates a dual-station RCS;

[0106] like ,but Indicates far-field incidence;

[0107] like ,but Indicates far-field scattering;

[0108] in, Indicates the radius of the target to be measured. Indicates wavelength.

[0109] It should be noted that the step numbers in this example and claims are only for the purpose of clearly and completely describing the embodiments of the present invention and for ease of understanding, and their order is not limited.

[0110] Example 2: A target scattering characteristic measurement and evaluation system based on solving a double-layer plane wave expansion matrix.

[0111] Reference Figure 3 This example includes: measurement module 1, normalization module 2, matrix equation construction module 3, matrix equation construction module 4, and scattering result evaluation module 5. The scattering result evaluation module 5 includes: double-layer scattering coefficient extrapolation submodule 51, calibration submodule 52, transfer matrix calculation submodule 53, and scattering type evaluation submodule 54.

[0112] The working principle of the entire system is as follows:

[0113] The measurement module 1 is used to place the target under test at the center of the turntable, perform sampling at each angle, and obtain the near-field scattering data of the target under test after sampling at all angles; then replace the target under test with a calibration body and perform the same operation to obtain the near-field scattering data of the calibration body, and transmit the near-field scattering data of the target under test and the near-field scattering data of the calibration body to the normalization module 2.

[0114] The normalization module 2 is used to remove near-field scattering data of the calibration body and near-field scattering data of the target object using background cancellation technology.

[0115] Background interference in the data is eliminated to obtain interference-free near-field scattering data of the target under test and near-field scattering data of the calibration body; then, the interference-free near-field scattering data of the target under test and the near-field scattering data of the calibration body are normalized to unit emission amplitude, and the normalized near-field scattering data of the target under test and the normalized near-field scattering data of the calibration body are used to solve the data transmission matrix equation module 4.

[0116] The matrix equation construction module 3 is used to express the incident field and the scattered field as a two-layer plane wave form, and to construct a matrix equation based on the two-layer plane wave form. Specifically, the incident field equation is first discretized to obtain a discretized incident field equation; then the scattered field equation is discretized to obtain a discretized scattered field equation; the discretized incident field equation and the discretized scattered field equation are coupled and superimposed to obtain the two-layer plane wave expression; the matrix equation is constructed through the two-layer plane wave form, and the matrix equation is transmitted to the matrix equation solving module 4.

[0117] The matrix equation solving module 4 is used to calculate the transfer matrix in the matrix equation construction module 3, obtaining the transfer matrix of the calibration body and the transfer matrix of the target under test, respectively. The normalized near-field scattering data of the calibration body and the transfer matrix of the calibration body in the normalization module 2 are substituted into the matrix equation to obtain the double-layer scattering coefficient of the calibration body. The normalized near-field scattering data of the target under test and the transfer matrix of the target under test in the normalization module 2 are substituted into the matrix equation to obtain the double-layer scattering coefficient of the target under test. The double-layer scattering coefficient of the calibration body and the double-layer scattering coefficient of the target under test are then transmitted to the scattering result evaluation module 5.

[0118] The scattering result evaluation module 5 is used to extrapolate the single-station far-field absolute radar cross section (RCS) of the target using the two-layer scattering coefficients of the target and the calibration body. It also uses matrix multiplication to estimate the scattering at arbitrary positions and for different types of targets using the two-layer scattering coefficients. Specifically, the two-layer scattering coefficient extrapolation submodule 51 performs near-field and far-field transformations on the two-layer scattering coefficients of the target and the calibration body from the matrix equation solving module 4, obtaining the single-station far-field RCS of the target and the calibration body, respectively. This single-station far-field RCS of the target and the calibration body is then transmitted to the calibration submodule 52. This calibration submodule 52 uses the single-station far-field RCS of the calibration body from the two-layer scattering coefficient extrapolation submodule 51 to calibrate the single-station far-field RCS of the target, obtaining the single-station absolute far-field RCS of the target. The array calculation submodule 53 is used to set the positions of the transmitting antenna and the receiving antenna to a random distribution, obtain the transfer matrix of the target under test, and transmit the transfer matrix of the target under test to the scattering type evaluation submodule 54. The scattering type evaluation submodule 54 is used to perform matrix multiplication between the transfer matrix of the target under test in the transfer matrix calculation submodule 53 and the double-layer scattering coefficient of the target under test in the matrix equation solving module 4, to obtain the scattering result of the target under test, and to judge the near-field or far-field, single-station or dual-station scattering type of the target under test according to the positions of the transmitting antenna and the receiving antenna.

[0119] It should be noted that the above functional modules can be implemented, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, they can be implemented, in whole or in part, as program instruction products. A program instruction product includes one or a set of program instructions. When the program instructions are loaded and executed on a computer, the described process or function is generated, in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The program instructions can be stored in a computer-readable and writable storage medium, or transferred from one computer's readable and writable storage medium to another.

[0120] In this embodiment, the direct coupling or communication connection between the modules can be achieved through indirect coupling or communication connection via interfaces, devices, or modules. The functional modules and sub-modules in this embodiment can dynamically reside within a single processing unit, or each module can exist physically independently, or two or more modules can dynamically reside within a single processing unit. When these dynamic components are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable and writable storage medium. This storage medium can be a memory, disk, or optical disc, etc.

[0121] The effects of this invention can be further illustrated by the following simulation results:

[0122] I. Simulation conditions: The simulation was conducted using the full-wave moment method and MATLAB R2024a;

[0123] II. Simulation Content:

[0124] Simulation 1: Under the above conditions, the monostatic radar cross section (RCS) of randomly distributed antenna locations is calculated using both the method of this invention and the existing method of moments. The results are as follows: Figure 4 .from Figure 4 It is evident that this invention can adapt to antenna position disturbances of varying degrees, and the results are highly consistent with the simulation results of the method of moments.

[0125] Simulation 2: Under the above conditions, the present invention was used to evaluate different types of scattering results, and the results are as follows. Figure 5 ,in:

[0126] Figure 5 (a) The single-station radar cross section (RCS) is calculated using the present invention and the method of moments under near-field incident and near-field scattering conditions, respectively. The dotted line represents the present invention and the solid line represents the method of moments.

[0127] Figure 5 (b) The single-station radar cross section (RCS) is calculated using the present invention and the method of moments under near-field incident and far-field scattering conditions, respectively. The dashed line represents the present invention and the solid line represents the method of moments.

[0128] Figure 5 (c) The bistatic radar cross section (RCS) is calculated using the present invention and the method of moments under far-field incident and near-field scattering conditions, respectively. The dashed line represents the present invention and the solid line represents the method of moments.

[0129] Figure 5 (d) Calculates the bistatic radar cross section (RCS) using the present invention and the method of moments under far-field incident and far-field scattering conditions, respectively. The dashed line represents the present invention, and the solid line represents the method of moments.

[0130] from Figure 5As can be seen, the present invention can arbitrarily combine near-field or far-field, single-station or dual-station methods, and the results are basically consistent with the corresponding simulation results of the method of moments, which reflects the reliability and versatility of the method of the present invention.

[0131] The above description is merely two specific examples of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for measuring and evaluating target scattering characteristics based on solving a double-layer plane wave expansion matrix equation, characterized in that, include: (1) Near-field scattering data of the target and the calibration body are obtained by near-field bistatic measurement; (2) Perform background cancellation and normalization on the near-field scattering data of the target and the calibration body; (3) Based on the normalized near-field scattering data of the target and the calibration body, the incident field and the scattered field are expressed in the form of a two-layer plane wave, and the matrix equation is constructed according to this two-layer plane wave form: ， in, It is a column vector of near-field measurement data. and These represent the number of transmitter and receiver locations, respectively. The column vector representing the scattering coefficients of the two layers. The transfer matrix is ​​called the double-layer plane wave expansion, where P and Q represent the number of points to discretize the integrals of the incident field and the scattered field, respectively. (4) Solve the above matrix equation to obtain the two-layer scattering coefficients of the target and the calibration body. ; (5) Using the double-layer scattering coefficients of the target and the calibration body, the single-station far-field absolute radar cross section (RCS) of the target is obtained by extrapolation and calibration. The double-layer scattering coefficients of the target are used to estimate the scattering of the target at any position and of different types by matrix multiplication.

2. The method according to claim 1, characterized in that, The near-field scattering data of the target and the calibration body obtained by near-field bistatic measurement in (1) includes: First, the target to be tested is placed in the center of the turntable, and electromagnetic waves are emitted by the transmitting antenna. Then, the near-field scattering data of the target to be tested is received by the receiving antenna located on the circumference. Next, the target to be tested is replaced with a calibration body, and the same operation is performed to obtain the near-field scattering data of the calibration body.

3. The method according to claim 1, characterized in that, The near-field scattering data of the target and the calibration body in (2) include background cancellation and normalization, including: Based on the near-field scattering data of the target and the calibration body, background interference is removed using background cancellation technology to obtain interference-free near-field scattering data of the target and the calibration body. The interference-free near-field scattering data of the target under test and the near-field scattering data of the calibration body are normalized to unit emission amplitude, respectively, to obtain the normalized near-field scattering data of the target under test and the normalized near-field scattering data of the calibration body.

4. The method according to claim 1, characterized in that, In (3), based on the normalized near-field scattering data of the target and the calibration body, the incident field and the scattered field are expressed as a two-layer plane wave, including: (3a) By placing the line source along the z-axis in a two-dimensional space, the incident field equation is obtained; (3b) Substituting the Hankel function addition theorem and the Bessel integral form into the incident field equation, we obtain the plane wave expansion integral of the incident field equation; (3c) Discretize the plane wave expansion integral of the incident field equation numerically to obtain the discretized incident field equation. ; ， Where C1 represents a constant factor, Here, j is the source excitation coefficient, e is the natural logarithm, P is the number of discretizations of the integral, and k is the wave number. It is the incident field position vector. It is the position vector of the transmitting antenna. It is the integral weight corresponding to the p-th point. It contains the direction vector of the p-th discretized plane wave. It is the azimuth angle relative to the x-axis. The transfer operator representing the expansion of a plane wave; (3d) Based on the discretized incident field equation, the surface induced current distribution is obtained by exciting the target with the source excitation coefficient. The scattering field equation is then derived from the surface induced current distribution. The Hankel function addition theorem and the discretized form of the Bessel integral are substituted into the scattering field equation, and the discretized scattering field equation is obtained by numerical discretization. : ， Where C2 represents a constant factor, Q is the position vector of the receiving antenna, and Q is the number of points used to discretize the plane wave integral. It is the integral weight corresponding to the q-th point. It is the azimuth angle relative to the x-axis. It is the position vector of the receiving antenna. Represents the transition operator, Fourier transform representing the current distribution; (3e) By combining the discretized incident field equation and the discretized scattering field equation, we obtain the two-layer plane wave expression: ， in, These are near-field measurement data. It is the double-layer scattering coefficient of the p-th plane wave incident and the q-th plane wave scattered. This represents the integral weight of the p-th plane wave incident. This represents the integral weight of the q-th plane wave scattering.

5. The method according to claim 1, characterized in that, The process of constructing and solving the matrix equation based on the two-layer plane wave form in (3) includes: (3f) The double-layer scattering coefficient in the expression of the double-layer plane wave Represented as a column vector of two-layer scattering coefficients ; (3g) Near-field measurement data in the expression of double-layer plane wave Represented as a column vector of near-field measurement data ; (3h) In the expression for a double-layer plane wave Represented as a transition matrix ; (3i) Based on the results expressed in (3f), (3g), and (3h), the following matrix equation form is obtained: ， in, and These represent the number of transmitting antennas and receiving antennas, respectively.

6. The method according to any one of claims 1 to 5, characterized in that, Solving the matrix equation in (4) includes: (4a) Transition matrix A single line is represented as: ， in This represents the transpose operator. Represents the transition matrix The first submatrix in Represents the transition matrix The p-th submatrix in Represents the transition matrix The P-th submatrix in This represents the nth transmitting antenna. This represents the m-th receiving antenna. This represents the position vector of the nth transmitting antenna. This represents the position vector of the m-th receiving antenna; (4b) From the normalized near-field scattering data of the target under test and the normalized near-field scattering data of the calibration body, through the transfer matrix The expressions calculate the transition matrix of the target under test and the transition matrix of the calibration body, respectively. (4c) Substitute the normalized near-field scattering data of the target under test and the transfer matrix of the target under test into the matrix equation and perform the inversion operation to obtain the double-layer scattering coefficient of the target under test; substitute the normalized near-field scattering data of the calibration body and the transfer matrix of the calibration body into the matrix equation and perform the inversion operation to obtain the double-layer scattering coefficient of the calibration body.

7. The method according to claim 1, characterized in that, In step (5), the single-station far-field absolute radar cross section (RCS) of the target is obtained by extrapolation and calibration using the two-layer scattering coefficients of the target and the calibration body, including: (5a) Perform near-field and far-field transformations on the two-layer scattering coefficients of the target and the calibration body respectively to obtain the single-station far-field radar cross section of the target. and calibration body single-station far-field radar cross section ; (5b) The absolute radar cross section of the single-station far field of the calibration body is calculated based on the radius of the calibration body. ; (5c) Using the single-station far-field radar cross section of the calibration body and calibration body single-station far-field absolute radar cross section Single-station far-field radar cross section of the target Calibration is performed to obtain the single-station far-field absolute radar cross section of the target. ; ， Where f represents the sampling frequency, Indicates the sampling angle.

8. The method according to claim 1, characterized in that, In step (5), the scattering coefficients of the target under test are used to estimate the scattering at any position and for different types of targets through matrix multiplication, including: (5d) Set the positions of the transmitting and receiving antennas of the target to be tested to a random distribution, and calculate the new transfer matrix of the target. ; (5e) Based on the double-layer scattering coefficient of the target The new transition matrix of the target to be tested Calculate the new scattering result of the target. ; ， in, and These are the new locations for the transmitting and receiving antennas; (5f) Based on the location of the transmitting antenna Location of receiving antenna And the radius of the target to be measured, for the newly estimated scattering results Conduct an assessment: like ,but Indicates a single-station RCS; like ,but Indicates a dual-station RCS; like ,but Indicates far-field incidence; like ,but Indicates far-field scattering; in, Indicates the radius of the target to be measured. Indicates wavelength.

9. A target scattering characteristic measurement and evaluation system based on solving a two-layer plane wave expansion matrix, characterized in that, include: The measurement module is used to acquire near-field measurement data of the calibration body and the target under test; The normalization module is used to normalize the near-field scattering data of the calibration body and the near-field scattering data of the target under test, respectively. The matrix equation construction module is used to express the incident field and the scattered field as a two-layer plane wave form, and to construct a matrix equation based on the two-layer plane wave form. The matrix equation solving module is used to calculate the transition matrix in the matrix equation, and obtain the transition matrix of the calibration body and the transition matrix of the target to be measured. The normalized near-field scattering data of the calibration body and the transition matrix of the calibration body are substituted into the matrix equation to obtain the double-layer scattering coefficient of the calibration body. The normalized near-field scattering data of the target and the transfer matrix of the target are substituted into the matrix equation to obtain the two-layer scattering coefficient of the target. The scattering result evaluation module is used to extrapolate the single-station far-field absolute radar cross section (RCS) of the target by using the two-layer scattering coefficients of the target and the calibration body. It also uses the two-layer scattering coefficients of the target to achieve scattering estimation of the target at any position and for different types of scattering by matrix multiplication.

10. The method according to claim 1, characterized in that, The scattering result evaluation module includes: The double-layer scattering coefficient extrapolation submodule is used to perform near-field and far-field transformations on the double-layer scattering coefficients of the target under test and the calibration body respectively, so as to obtain the single-station far-field RCS of the target under test and the single-station far-field RCS of the calibration body. The calibration submodule is used to calibrate the far-field RCS of the target single station using the far-field RCS of the calibration body, so as to obtain the absolute far-field RCS of the target single station. The transfer matrix calculation submodule is used to set the positions of the transmitting and receiving antennas to a random distribution to obtain the transfer matrix of the target under test. The scattering type evaluation submodule is used to perform matrix multiplication of the transfer matrix and the two-layer scattering coefficient of the target under test to obtain the scattering result of the target under test, and to determine the scattering type of the target under test based on the positions of the transmitting antenna and the receiving antenna.

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