Far-field RCS calculation method for cylindrical near-field scattering data hierarchical preprocessing and MoM inversion
By employing a probe compensation method based on data hierarchical preprocessing and regularization optimization, the numerical ill-conditioning problem in near-field RCS calculation of cylindrical targets is solved, improving the reliability and accuracy of the inversion results. This method is suitable for high-precision RCS measurement of large or complex targets.
Patent Information
- Application Number
- CN202511300208.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-12
- Publication Date
- 2025-11-07
AI Technical Summary
In existing methods for calculating near-field RCS of cylindrical targets based on MoM inversion, numerical ill-conditioning occurs when the probe pattern function approaches zero in higher-order modes, leading to noise gain and affecting the reliability and accuracy of the inversion results, especially in the measurement of large or complex targets.
A hierarchical data preprocessing method is adopted, including systematic error calibration, background noise suppression, and regularization-based probe compensation. By constructing a regularization optimization problem and using the conjugate gradient iteration method, the probe compensation process is optimized to ensure numerical stability and data accuracy.
It significantly improves the numerical stability and accuracy of inversion calculations, enhances the realism of the target surface current distribution and the accuracy of far-field RCS calculations, strengthens the adaptive capability and robustness of the calculations, and reduces the sensitivity to the measurement environment and target characteristics.
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Figure CN120908773A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of electromagnetic scattering measurement and calculation, and particularly provides a far-field RCS calculation method for columnar near-field scattering data hierarchical preprocessing and MoM precise inversion. BACKGROUND
[0002] In the fields of radar target characteristic measurement, stealth technology research, and military target identification, the radar cross section (Radar Cross Section, RCS) of a target is a crucial core parameter. Far-field RCS measurement is a traditional method for obtaining the parameter, but it requires that the test distance must satisfy the far-field condition R > 2D 2 / λ, where D is the maximum size of the target and λ is the wavelength. This requires the construction of an extremely large and expensive microwave anechoic chamber for large targets or low-frequency tests, which is difficult to implement and costly.
[0003] To overcome the limitations of far-field measurement, near-field measurement technology has emerged and been widely applied. This technology acquires scattering field data of a target at a close distance and uses strict electromagnetic field transformation theory to inversely calculate the far-field characteristics. Among various near-field inversion algorithms, the inversion method based on the Method of Moments (MoM) is favored due to its strict electromagnetic basis. The core of this method is as follows: first, the columnar near-field complex data (amplitude and phase) are acquired by a probe, and after a series of data preprocessing, they are used as excitation sources. By solving the MoM equation set established based on the Electric Field Integral Equation (EFIE), the induced current distribution on the target surface is directly inverted. Finally, by performing far-field radiation integral calculation on the current distribution, the precise far-field RCS value can be obtained. This method avoids the truncation error problem in the traditional mode expansion method and has higher accuracy in theory.
[0004] The standard process of the existing columnar near-field RCS calculation method based on MoM inversion generally includes: columnar near-field data measurement, system error calibration, background noise suppression, probe compensation, MoM inversion calculation, and far-field calculation. In the key step of probe compensation, the existing technology generally adopts a "direct inverse filtering" method. Specifically, after transforming the measured near-field data from the spatial domain to the modal domain (i.e., the columnar wave spectrum domain), the technology simply divides the data by the directional diagram function P(n, k z), in order to eliminate the disturbance caused by the non-ideal probe pattern to the measurement results, and restore the ideal field distribution, this method assumes that the probe pattern is reversible in the entire mode domain. However, the inventors of the present application found through in-depth analysis and a large number of practices that the prior art has a deep and rare technical defect: the value of the probe pattern function P(n, k z ) tends to zero at high-order modes (i.e. when the mode order |n| or the axial wave number |k z | is large), which is an unavoidable physical fact; the "direct inverse filtering" operation is mathematically equivalent to dividing a value that tends to zero, which will cause a numerically ill-conditioned problem; therefore, any small noise and error remaining in the measurement and pre-processing will be amplified sharply in this division operation, especially in these high-order mode channels, resulting in serious noise gain.
[0005] The consequences of the above technical problems are serious and hidden. The illegally amplified high-order mode domain noise will be treated as valid field information in the subsequent MoM inversion process. The MoM inversion, as an accurate inverse problem solving process, will try to fit all the data containing huge noise, resulting in non-physical high-frequency oscillations and artifacts in the target surface current distribution obtained by inversion, and the errors in the current distribution will be further amplified in the final far-field RCS calculation, which will result in significant distortion and deviation of the calculated RCS value at specific observation angles such as lateral and tail directions, and the reliability of the results will decrease sharply. The problem is particularly troublesome for targets with large electrical size and complex structure (whose high-order mode components are more significant) or in frequency bands where the probe performance is limited, which seriously restricts the application of this technology in high-end precision measurement scenarios.
[0006] Therefore, there is an urgent need in the art for a new cylindrical near-field data processing and inversion method that can overcome the above numerical ill-conditioned problem, ensure the numerical stability of the entire calculation process while effectively compensating for the probe effect, and provide reliable technical support for high-precision far-field RCS calculation. SUMMARY
[0007] The present application aims to provide a cylindrical near-field scattering data hierarchical preprocessing and MoM inversion far-field RCS calculation method to overcome the deficiencies of the prior art in cylindrical near-field scattering data processing and far-field RCS calculation. Through new data preprocessing and accurate inversion strategy, the present application improves the data processing accuracy and the accuracy and efficiency of far-field RCS calculation.
[0008] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:
[0009] The application discloses a far-field RCS calculation method of cylindrical near-field scattering data layering preprocessing and MoM inversion, and is characterized by comprising the following steps.
[0010] Step 1. Obtain an original cylindrical near-field scattering data matrix E by measuring through cylindrical near-field scattering data raw ;
[0011] Step 2. Perform data layering preprocessing on the original cylindrical near-field scattering data matrix E raw , and the data layering preprocessing comprises sequentially performed system error calibration, background noise suppression and probe compensation based on regularization, to obtain ideal field data E ideal ;
[0012] Step 3. Project the ideal field data E ideal to obtain an excitation vector, and obtain a surface current distribution J through current distribution inversion based on the method of moments (MoM);
[0013] Step 4. Calculate a far-field scattering field E s according to the surface current distribution J, and combine incident plane wave field intensity E i to obtain a far-field RCS value.
[0014] Further, the specific process of step 1 is as follows: a darkroom environment is constructed, a probe carrying a vector antenna is controlled to perform two-dimensional scanning on a cylindrical scanning frame with the to-be-measured target as the center in the darkroom environment, and complex amplitude and phase information of scattered waves are recorded at each sampling point, and finally an original cylindrical near-field scattering data matrix E is obtained. Wherein, N z and N φ are the number of sampling points in the axial direction and the azimuth direction, respectively.
[0015] Further, in step 1, the scanning range is as follows: the axial height range is denoted as H, and the value of H is greater than the geometric height of the to-be-measured target, so as to ensure that the target is completely covered in the scanning process; and the scanning angle range in the azimuth direction is set to cover the whole circle angle from 0 to 360°.
[0016] The sampling interval is as follows: the axial sampling interval Δz satisfies λ0 represents the working wavelength; and the azimuth sampling interval Δφ satisfies k is the wave number, and a is the cylindrical scanning radius.
[0017] Further, in step 2, the specific process of system error calibration is as follows:
[0018] A multi-target calibration method is applied to extract a system error coefficient matrix C err , and the calibrated data E cal is generated through operation , and the symbol represents element-by-element multiplication.
[0019] The specific process of the multi-target calibration method is as follows: select at least three standard metal spheres of different diameters as calibration targets, and record the theoretical value of the radar cross section σ. theory ;
[0020] Each calibration sphere is placed at the center of the cylindrical scanning frame and measured according to the same scanning trajectory and sampling method as the target object, thus obtaining the corresponding raw measurement data matrix. Compare the original measurement data matrix Near-field distribution of an ideal cylindrical surface The difference is used to solve the complex coefficient error matrix C using the least squares fitting method. err The solution takes the form: C is a constant.
[0021] Furthermore, in step 2, the specific process of background noise suppression is as follows:
[0022] Collect background data matrix E bkg Through the calculation E sub =E cal -E bkg Generate background-suppressed data E sub ;
[0023] Background data matrix E bkg The acquisition process is as follows: The target to be measured is removed in a dark room environment, the same two-dimensional motion as in step 1 is completed, and the complex values of the scattered field received at each sampling point are recorded. The results constitute the background data matrix E. bkg .
[0024] Furthermore, in step 2, the specific process of probe compensation based on regularization is as follows:
[0025] Construct a positive operator that includes the probe pattern function. Optimization problem: Among them, E sub This is the data after background suppression. The regularization operator is λ, and the regularization parameter is λ. The ideal cylindrical near-field data matrix E is obtained by solving the problem using the conjugate gradient iteration method. ideal .
[0026] Furthermore, in step 4, the far-field RCS value σ is specifically: Where r is the observation distance.
[0027] Based on the above technical solution, the beneficial effect of the present invention is that it provides a far-field RCS calculation method for cylindrical near-field scattering data layer preprocessing and accurate MoM inversion, which has the following advantages:
[0028] 1) Significantly improve the numerical stability and reliability of the inversion calculation;
[0029] By using the inverse problem solving framework based on regularization optimization to replace the direct division, the compensation process is converted into an optimization problem of minimizing a cost function, which includes a data fidelity term and a regularization constraint term, the latter effectively suppresses the amplification of noise in the high-order mode channel, ensuring the robustness of the solving process to ill-conditioned conditions, thereby obtaining physically credible and stable ideal field data, laying a reliable foundation for subsequent MoM inversion;
[0030] 2) Obtain higher precision and more realistic target surface current distribution, and further improve the calculation accuracy of far-field RCS;
[0031] Since the more accurate ideal field data E ideal As the excitation source of the moment method equation, the inverse process can converge to a current solution that is closer to the real physical situation, which is smoother and has fewer artifacts, thereby significantly improving the accuracy of the far-field scattering field calculated by radiation integration and the final output RCS value, especially at high frequencies and at harsh observation angles such as lateral and tail directions;
[0032] 3) Enhance the adaptability and robustness of far-field RCS calculation, and reduce its sensitivity to specific measurement environments or target characteristics;
[0033] An adaptive regularization parameter selection mechanism (L-curve method) is introduced, which can objectively and automatically determine the optimal regularization strength according to the characteristics of the current measurement data and the forward model, meaning that the invention can intelligently achieve the best balance between measurement data and solution stability without manual intervention for parameter adjustment. Therefore, the invention exhibits more consistent and reliable performance for targets of different sizes, materials, scattering characteristics, and different measurement systems. BRIEF DESCRIPTION OF DRAWINGS
[0034] Figure 1 The flowchart of the columnar near-field scattering data layering preprocessing and MoM inversion far-field RCS calculation method in the present invention.
[0035] Figure 2 The flowchart of the data layering preprocessing in the present invention.
[0036] Figure 3 The flowchart of the probe compensation based on regularization in the present invention.
[0037] Figure 4 The flowchart of the current distribution inversion based on the moment method in the present invention.
[0038] Figure 5 Flowchart for the process of far-field RCS calculation in the present application. DETAILED DESCRIPTION
[0039] In order to make the objectives, technical solutions and advantages of the present application clearer, further detailed description will be made to the present application in combination with the drawings and examples.
[0040] The present embodiment provides a far-field RCS calculation method of cylindrical near-field scattering data layering preprocessing and MoM precise inversion, the flowchart of which is shown in Figure 1 , and specifically includes the following steps:
[0041] Step 1. Obtain the original cylindrical near-field scattering data matrix E raw through cylindrical near-field scattering data measurement.
[0042] Construct a darkroom environment, control the probe carrying a vector antenna to perform two-dimensional motion on a cylindrical scanning frame centered on the target to be measured in the darkroom environment, and record the complex amplitude and phase information of the scattered wave at each sampling point, finally obtain an original cylindrical near-field scattering data matrix , where N z and N φ are the number of sampling points in the axial and azimuth directions respectively.
[0043] The acquisition of cylindrical near-field scattering data firstly depends on the motion range and sampling interval design of the scanning frame; the axial height range is denoted as H, which must be greater than the actual geometric height of the target to be measured, and a certain margin is reserved on this basis to ensure that the target is completely covered in the entire scanning process and avoid field information loss due to boundary truncation; the azimuth scanning angle range is set to cover a full circle from 0 to 360°, so that the scattering characteristics of the target in the full azimuth range can be completely recorded, thereby providing sufficient input conditions for subsequent electromagnetic inversion and far-field calculation; the sampling interval design follows the Nyquist sampling theorem to avoid aliasing error, where the axial sampling interval satisfies λ0 represents the working wavelength, which ensures that the spatial variation of the electric field distribution in the axial direction can be accurately captured, and the azimuth sampling interval satisfies k is the wave number, a is the cylindrical scanning radius, and this condition ensures that the sampling density in the circumferential direction is sufficient to analyze the scattering information of the target at different azimuths.
[0044] The vector antenna receives the scattered wave of the target to be measured at each sampling point (z i ,φ j ) of the scanning frame and records the complex amplitude and phase information thereof, and the obtained original measurement value is denoted as E raw (z i ,φ j), by applying all axial positions z i and azimuth φ j The measured values were organized to form the original cylindrical near-field scattering data matrix. Where, N z N represents the number of axial sampling points. φ This matrix represents the number of sampling points in the azimuth direction. It serves as the input and basis for subsequent hierarchical preprocessing steps such as system error calibration, background noise suppression, and regularized probe compensation. The completeness and accuracy of this matrix directly determine the reliability of the method of moments inversion solution for the current distribution J and the far-field radar cross section σ.
[0045] Step 2. Process the original cylindrical near-field scattering data matrix E raw Data hierarchical preprocessing is performed, which includes sequentially executing system error calibration, background noise suppression, and regularization-based probe compensation to obtain ideal field data E. ideal ;
[0046] The data layering preprocessing is as follows: Figure 2 As shown, this includes sequentially performed system error calibration, background noise suppression, and regularization-based probe compensation; specifically as follows:
[0047] System error calibration uses a multi-target calibration method to extract the system error coefficient matrix C. err And through calculation Generate calibration data E cal The symbol ⊙ indicates element-wise multiplication;
[0048] In the multi-target calibration method, at least three standard metal spheres of different diameters are first selected as calibration targets, and their theoretical radar cross-section is denoted as σ. theory This value is directly given by the analytical solution of electromagnetic scattering of the sphere, and has strict theoretical computability. Each calibration sphere is placed at the center of the cylindrical scanning frame and measured according to the same scanning trajectory and sampling method as the target under test, thus obtaining the corresponding original measurement data matrix. Based on the theoretical scattering cross-section σ theory And by measuring geometric relationships, the ideal near-field distribution of the cylindrical surface can be derived. This distribution should be completely consistent with the actual measurement results under conditions without systematic errors; through comparison and The difference is used to solve the complex coefficient error matrix C using the least squares fitting method. err The solution is in the form of C is a constant; matrix Each element in the matrix contains information on the amplitude error, phase error, and port isolation error of the measurement system at the corresponding sampling point; after obtaining the error matrix, the original data matrix E of the target to be measured is obtained.raw The calibration is performed point by point, and the specific operation is wherein, represents element-wise multiplication, represents error matrix element-wise inverse; for each element in the matrix, the operation is wherein, E raw (i,j) represents the original scattering field complex value collected at the axial position z i and the azimuth angle φ j ; represents the complex calibration coefficient corresponding to the point;
[0049] After this processing, the calibrated matrix E cal has eliminated systematic errors, and the amplitude and phase information can truly reflect the scattering characteristics of the target itself, providing accurate input for subsequent background noise suppression and probe compensation steps;
[0050] Background noise suppression, receive E cal and collect the background data matrix E bkg ; sub = E cal - E bkg ; sub ;
[0051] The acquisition of the background data matrix is performed under conditions completely consistent with the formal measurement, and the specific operation is to remove the target to be measured in a darkroom environment, so that the vector antenna mounted on the scanning frame completes the same two-dimensional motion on the cylindrical trajectory as the calibration measurement, and the scattering field complex value received at each sampling point (z i , φ j ) is recorded to obtain the background data matrix , the dimensions of which are consistent with the calibrated matrix E cal ; the data in the background matrix mainly includes electromagnetic clutter in the darkroom environment, parasitic coupling of the measurement device itself, and fixed interference components such as field area reflection, and does not include the scattering contribution of the target to be measured;
[0052] To separate the target scattering signal, the calibrated data matrix and the background matrix are subtracted element by element, and the operation formula is E sub = E cal - E bkg ; this operation is a point-by-point subtraction in the complex domain, and for each element in the matrix, it is expressed as E sub (i,j) = E cal (i,j) - E bkg (i,j), wherein E cal (i,j) represents the scattering field complex value collected at the sampling point (z i , φ j) measured at the same position containing both the target scattering and the background scattering, E bkg (i,j) represents the complex electric field value measured at the same position containing only the background scattering;
[0053] The matrix E sub contains only the scattering contribution of the target under test, the background clutter and the system fixed interference are effectively canceled out, thus improving the purity and reliability of the input data in the subsequent probe compensation and matrix inversion steps;
[0054] The probe compensation based on regularization is shown as Figure 3 , receives E sub and constructs a forward operator containing the probe pattern function P(n,k z ); The ideal, undisturbed cylindrical near-field data E ideal is reconstructed by solving the minimization problem , where is the regularization operator and λ is the regularization parameter;
[0055] The construction of the forward operator is based on the cylindrical wave spectrum expansion theory, and its core element is the probe pattern function P(n,k z ), which describes the receiving sensitivity of the vector probe to different modal electromagnetic waves, where n represents the order in the azimuthal direction, and k z represents the axial wave number component; by introducing this function, the forward operator can associate the ideal field data E ideal with the actual receiving characteristics of the probe, thus obtaining a simulated result consistent with the real measurement data
[0056] To realize the compensation of the probe effect, an optimization problem is constructed The objective function consists of two parts, the first part is the data fidelity term , which physically means that the ideal field after the action of the forward operator should be as close as possible to the data matrix E sub after background suppression, ensuring that the reconstruction result conforms to the experimental observation; the second part is the regularization term , where , the first-order difference operator is taken to introduce the total variation constraint to suppress the high-frequency oscillation of the solution, and the parameter λ is the regularization coefficient, which is determined by the L-curve method to achieve a balance between data fidelity and solution smoothness;
[0057] The solution of the optimization problem adopts the conjugate gradient iteration method, which gradually updates the solution vector in the complex domain space, and realizes fast convergence through the combination of the steepest descent direction and orthogonality condition; the final solution obtained through the iteration process is the ideal cylindrical near-field data matrix Eideal The matrix effectively eliminates the distortion effect introduced by the probe directional diagram function, and the complex amplitude and phase characteristics can truly reflect the spatial distribution of the target scattering field, thereby providing reliable input for the construction of the subsequent inversion equation ZJ=V of the moment method;
[0058] Step 3. According to the ideal field data E ideal The projection obtains an excitation vector, and the surface current distribution J is obtained through current distribution inversion based on the moment method;
[0059] The current distribution inversion process based on the moment method is shown in Figure 4 E ideal The triangular mesh is divided based on the geometry model of the target to be measured, and the moment method equation set ZJ=V is established based on the electric field integral equation, wherein, Z represents the impedance matrix, J represents the surface current vector to be solved, E ideal The projection obtains an excitation vector; the surface current distribution J is obtained by solving the equation set through a stable iterative algorithm;
[0060] Step 4. According to the surface current distribution J, the far-field scattering field E s is calculated by using the radiation integral formula, and the far-field RCS value is calculated by combining the incident plane wave field intensity E i ;
[0061] The far-field RCS value σ is specifically: Wherein, r is the observation distance;
[0062] As shown in Figure 5 , the results are logarithmically transformed, and the results are output in the form of a two-dimensional directional diagram or a three-dimensional color mapping diagram.
[0063] The beneficial effects of the present application will be described in detail in combination with simulation tests.
[0064] (I) Experimental environment construction
[0065] Darkroom environment: a microwave darkroom with a size of 15m*10m*8m is selected, the darkroom is designed and built according to GB50826-2012 “Electromagnetic wave darkroom engineering technical specification”; the electromagnetic shielding performance of the darkroom is excellent, and the shielding effectiveness can reach more than 100dB in the frequency range of 10kHz-18GHz, which can effectively isolate external electromagnetic wave interference, and provide a stable electromagnetic environment for high-precision cylindrical near-field scattering data measurement; high-performance wave-absorbing materials are laid on the inner wall of the darkroom, and the reflectivity of the wave-absorbing materials is less than-40dB in the working frequency band, which can greatly reduce the influence of indoor reflected waves on the measurement results.
[0066] Measurement device: A high-precision vector network analyzer is used, with a frequency range of 10 MHz-50 GHz, an amplitude measurement accuracy of ±0.05 dB, and a phase measurement accuracy of ±0.1°, which can accurately measure the complex amplitude and phase information of the scattered wave; the matching vector antenna is ETS-Lindgren 3166, with a working frequency range of 1-18 GHz, good directivity and low sidelobe characteristics, and can accurately receive the scattered wave of the target to be measured; the cylindrical scanning frame is electrically controlled and has a high-precision positioning system with a positioning accuracy of ±0.1 mm, which can ensure the movement accuracy of the probe on the cylindrical trajectory and the accuracy of the sampling points.
[0067] (ii) Parameter setting
[0068] Sampling interval: During the data measurement process, the sampling interval is determined according to the working wavelength λ0; when the working wavelength λ0 = 30 mm, the axial sampling interval Δz is set to 10 mm according to the principle of Δz ≤ λ0 / 2, ensuring that the spatial variation of the electric field distribution can be accurately captured in the axial direction. The azimuthal sampling interval Δφ is calculated according to Δφ ≤ π / (ka), where the cylindrical scanning radius a = 1 m and the wave number k = 2π / λ0, and Δφ ≤ 0.0157 rad, which is about 0.9°. The actual setting is 0.5° to ensure that the sampling density in the circumferential direction is sufficient to analyze the scattering information of the target at different azimuths.
[0069] Regularization parameter: In the probe compensation step based on regularization, the regularization parameter λ is determined by the L-curve method; first, define the regularization term norm as The data fidelity term residual norm is Take the regularization parameter λ as a variable, calculate the regularization term norm and residual norm at different λ, and draw a curve in logarithmic coordinates; as λ increases, the residual norm monotonically increases and the regularization term norm monotonically decreases. The corner point of the curve is automatically identified by the curvature analysis method, and the corresponding regularization parameter is determined as λopt; through multiple experimental verification, for general electromagnetic scattering measurement scenes, when the noise level of the measurement system is low, λopt takes a value between 0.01 and 0.1; when the noise level is high, λopt takes a value between 0.1 and 1.
[0070] Grid subdivision accuracy: When performing triangular mesh subdivision on the geometric model of the target to be measured, the grid accuracy is determined according to the working wavelength λ0; when the working wavelength λ0 = 30 mm, the length of each side of the facet ls needs to satisfy ls < λ / 10, i.e. ls < 3 mm. In actual operation, ls is set to 2 mm to ensure the accuracy of the discrete grid in numerical integration and current expansion.
[0071] (iii) Far-field RCS calculation
[0072] (1) Cylindrical near-field scattering data measurement;
[0073] Scan frame setup: Place the target to be measured at the center of the cylindrical scan frame, ensuring that the center axis of the target coincides with that of the cylindrical scan frame; Set the axial height range H according to the height of the target to be measured. Assuming the height of the target to be measured is 1 m, to ensure that the target is completely covered during the entire scanning process and to reserve a certain amount of margin, set H to 1.2 m;
[0074] Sampling point measurement: Control the probe carrying the vector antenna to move in two dimensions on the cylindrical scan frame according to the set sampling interval; At each sampling point (zi, φj), the vector network analyzer receives the scattered wave of the target to be measured and records its complex amplitude and phase information to obtain the raw measurement value Eraw(zi, φj); Sample the axial position zi from 0 to 1.2 m at an interval of 10 mm, obtaining Nz=121 axial sampling points; Sample the azimuth angle φj from 0° to 360° at an interval of 0.5°, obtaining Nφ=721 azimuthal sampling points;
[0075] Data matrix construction: Organize the measurement values of all sampling points to construct the raw cylindrical near-field scattering data matrix Eraw;
[0076] (2) Data layering preprocessing:
[0077] System error calibration:
[0078] Target selection and measurement: Select three standard metal spheres with different diameters as calibration targets, with diameters of 50 mm, 100 mm, and 150 mm; Place each calibration sphere in turn at the center of the cylindrical scan frame and measure it according to the same scanning trajectory and sampling method as the target to be measured, obtaining the corresponding raw measurement data matrix
[0079] Error matrix solution: According to the theoretical value of the radar cross section σtheory of the standard metal sphere and the measurement geometry, derive the ideal cylindrical near-field distribution Solve the complex coefficient error matrix Cerr using the least squares fitting method;
[0080] Data calibration: After obtaining the error matrix Cerr, calibrate the raw data matrix Eraw of the target to be measured point by point to obtain the calibrated matrix Ecal;
[0081] Background noise suppression: Remove the target to be measured in a darkroom environment, and make the vector antenna mounted on the scan frame complete the same two-dimensional motion on the cylindrical trajectory as the calibration measurement, recording the scattering field complex value at each sampling point to obtain the background data matrix E bkg; subtract the calibrated data matrix Ecal from the background matrix Ebkg element by element to obtain the background-suppressed data Esub;
[0082] Regularization-based probe compensation: construct the forward operator based on the cylindrical wave spectrum expansion theory Introduce the probe directional pattern function P(n, kz); construct the optimization problem Solve the optimization problem by using the conjugate gradient iteration method, and set the iteration termination condition as the error of the results of the adjacent two iterations being less than 10 -6 After multiple iterations, the ideal cylindrical near-field data matrix Eideal is finally obtained;
[0083] (3) Current distribution inversion based on the method of moments:
[0084] Geometric model subdivision: the geometric surface of the target to be measured is triangular meshed, and the continuous curved surface is discretized into M planar triangular facets; ensure that the edge length of each facet ls = 2 mm, which satisfies the condition ls < λ / 10; select Rao-Wilton-Glisson basis function fm(r) as the expansion function, and the surface current vector expansion is
[0085] Matrix equation system establishment and solution: establish the matrix equation system based on the electric field integral equation, construct the impedance matrix Z through the Galerkin test method; pre-process the system by using the preconditioner based on incomplete LU decomposition, and combine the generalized minimum residual method to iteratively solve, and set the termination condition as the residual norm ||ZJ-V||2<10 -4 Finally, the surface current distribution solution J is obtained;
[0086] (4) Far-field RCS calculation:
[0087] The far-field scattering field is calculated using the radiation integral formula, the target surface has been discretized into Ntri facets, and the integral calculation is converted into the summation of each term of the discrete facets E s (θ, φ), and the radiation integral process is executed in parallel at multiple frequency points and multiple observation directions, the wave number k is different for each frequency, and the observation direction is defined by the azimuth angle φ and the elevation angle θ, and the far-field scattering electric field distribution E s (θ, φ) is finally output.
[0088] Receive the far-field scattering electric field distribution E s (θ, φ) and the electric field intensity E i of the incident plane wave at the center position of the target, calculate the RCS value according to the radar cross-sectional area definition formula, execute the calculation for each combination of (θ, φ, f) to obtain the radar cross-sectional area function σ(θ, φ, f), perform a logarithmic scale transformation on the result, and output the result through a two-dimensional directional pattern or a three-dimensional color mapping chart.
[0089] The above description is only a specific implementation of the present application. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equally effective or equivalent features. Any feature disclosed in this specification, or any method or process disclosed in this specification, can be combined with any other disclosed feature or method or process, unless otherwise stated.
Claims
1. A method for calculating the far-field RCS of a cylindrical near-field scattering data by layering preprocessing and MoM inversion, characterized in that, The method comprises the following steps: Step 1. Obtain raw cylindrical near-field scattering data matrix E by cylindrical near-field scattering data measurement raw ; Step 2. Data stratification pre-processing is performed on the raw cylindrical near-field scattering data matrix E raw , which includes systematic error calibration, background noise suppression and probe compensation based on regularization, in sequence, to obtain ideal field data E ideal ; Step 3. Obtain the excitation vector from the ideal field data E ideal The surface current distribution J is obtained by the current distribution inversion based on the method of moments. Step 4. Calculate the far-field scattering field E according to the surface current distribution J using the radiation integral formula s , combined with the incident plane wave field intensity E i to obtain the far-field RCS value.
2. The method of claim 1, wherein the method is characterized by, The specific process of step 1 is: a darkroom environment is constructed, a probe carrying a vector antenna is controlled to perform two-dimensional scanning on a cylindrical scanning frame with the target to be measured as the center, and the complex amplitude and phase information of scattered waves are recorded at each sampling point, so as to finally obtain an original cylindrical near-field scattering data matrix Wherein, N z and N φ are the number of sampling points in the axial and azimuth directions respectively.
3. The method of claim 2, wherein the method further comprises: In step 1, the scanning range is as follows: the axial height range is recorded as H, and the value of H is greater than the geometric height of the target to be measured, so as to ensure that the target is completely covered in the scanning process; the scanning angle range in the azimuth direction is set to cover the whole circle angle from 0 to 360°. The sampling interval is: the axial sampling interval Δz satisfies λ0 represents the working wavelength; the azimuthal sampling interval Δφ satisfies k is the wave number, and a is the cylindrical scanning radius.
4. The method of claim 1, wherein the method further comprises: In step 2, the specific process of system error calibration is as follows: A multi-target calibration method is applied to extract the system error coefficient matrix C err , and the calibrated data E is generated by operation cal , and the symbol ⊙ represents element-by-element multiplication; The specific process of the multi-target calibration method is: selecting at least three standard metal spheres with different diameters as calibration targets, recording the theoretical value σ theory of the radar scattering cross section area of each target Each calibration sphere is placed at the center of the cylindrical scanning frame and measured according to the same scanning trajectory and sampling method as the target object, thus obtaining the corresponding raw measurement data matrix. Compare the original measurement data matrix Near-field distribution of an ideal cylindrical surface The difference is used to solve the complex coefficient error matrix C using the least squares fitting method. err The solution takes the form: C is a constant.
5. The method of claim 1, wherein the method further comprises: In step 2, the specific process of background noise suppression is as follows: Collecting background data matrix E bkg , by operating E sub = E cal - E bkg Generate background-suppressed data E sub ; Background data matrix E bkg The acquisition procedure is: remove the object to be measured in a dark room environment, complete the same two-dimensional motion in step 1, record the received scattered field complex value at each sampling point, and the obtained result constitutes the background data matrix E bkg .
6. The method of claim 1, wherein the method is characterized by: In step 2, the specific process of probe compensation based on regularization is as follows: In step 2, the specific process of probe compensation based on regularization is as follows: Constructing a forward operator comprising a probe directivity function Constructing an optimization problem: where E sub is the data after background suppression, is a regularization operator, and λ is a regularization parameter; the ideal cylindrical near-field data matrix E ideal is obtained by solving using a conjugate gradient iteration.
7. The method of claim 1, wherein the method further comprises: calculating the far-field RCS of the object based on the MoM inversion of the pre-processed cylindrical near-field scattering data. In step 4, the far-field RCS value σ is given in particular by: where r is the observation distance.