A near field RCS test method for shortening near field sampling distance

Abstract

The application discloses a near-field RCS test method for shortening a near-field sampling distance, comprising the following steps: 1, using a plane wave synthesis algorithm to solve the emission coefficient of each transmitting antenna; 2, determining the box size of the gathered plane wave spectrum according to the target size, using the dichotomy to divide the box, and determining the total number N of non-empty boxes of the bounding box; 3, using the fast irregular antenna field change algorithm of the multi-plane wave gathering center to solve the far-field field value through the near-field test data; 4, multiplying the emission coefficient corresponding to each transmitting antenna with the far-field electric field corresponding to the target direction, superimposing the results of all the transmitting antennas, obtaining the far-field electric field of the target direction and converting the far-field electric field into the RCS; the application can guarantee the calculation precision of the algorithm under the near-distance sampling, and meanwhile, the loss of the calculation resources is avoided.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic measurement technology, specifically relating to a near-field RCS testing method that shortens the near-field sampling distance. Background Technology

[0002] Radar Cross Section (RCS) measures the ability of radar-detected objects such as aircraft, vehicles, and ships to scatter electromagnetic waves. Therefore, RCS measurement and evaluation are essential when designing stealth targets of significant military value. However, measuring the RCS of a target aircraft is difficult because RCS calculation requires plane wave incidentness and that the receiver meets far-field (FF) conditions. Depending on the architecture of the RCS measurement system, the actual measurement of target RCS characteristics can be categorized into three types: far-field measurement, compressed-field measurement, and near-field measurement. Near-field measurement uses the measured near-field (NF) information of the target, assisted by a Near-Field–Far-Field Transformation (NFFFT) algorithm, to obtain the far-field RCS test results. Common post-processing algorithms are divided into imaging approximation algorithms and full-wave algorithms. Imaging approximation algorithms use near-field monostation measurement information to extrapolate the target's far-field monostation information. However, when dealing with complex targets involving multiple scattering and other complex coupling effects, approximation methods may not provide accurate calculation results. The full-wave method requires bistatic measurements of the near field and the use of plane-wave synthesis (PWS) to approximate the field distribution within a certain region as if it were a plane wave incident state. When high accuracy is required, bistatic near-field measurements are typically performed, followed by near-field to far-field conversion using a correlated full-wave method.

[0003] While the bistatic full-wave method offers higher accuracy, it places high demands on the distance, size, and distribution of antennas. Using specific wavefunction expansions to calculate near-field extrapolation can effectively reduce the antenna distribution range. Furthermore, the Fast Fourier Transform (FFT) can quickly solve the inverse problem to obtain the near-field extrapolation results. However, these methods only allow near-field sampling points to be distributed on regular classical measurement surfaces, such as spheres, cylinders, and planes. If there is any offset between the near-field measurement points and the classical measurement surface, the calculation accuracy will be significantly affected.

[0004] The Fast-Irregular Antenna Field Transformation Algorithm (FIAFTA) uses equivalent current, plane spectrum, or spherical spectrum as unknowns for calculation. Its advantages include flexible antenna placement and strong robustness to sampling region truncation, thus reducing the near-field sampling area. FIAFTA can perform both multi-layer and single-layer transfer calculations. The matrix elements of the single-layer transfer are explicit, resulting in faster iteration speeds during iterative inversion. The core of the original single-layer algorithm is to focus the plane spectrum at the center of the target and then transfer it to the near-field measurement area. Due to the constraint of the Green's function addition theorem required for the transfer, a near-field sampling distance of at least twice the target size is needed to ensure accuracy, which may be difficult to meet in actual measurements. Dividing the target area into multiple small boxes and focusing the plane wave at the center of each box can effectively reduce the near-field sampling distance, but this increases the number of unknowns and reduces computational efficiency. Therefore, this invention adds a box division determination process for the convergent plane spectrum to the original near-field extrapolation calculation process, which not only ensures the calculation accuracy of the algorithm under close-range sampling, but also avoids the consumption of computing resources. Summary of the Invention

[0005] In view of this, the present invention provides a near-field RCS testing method that shortens the near-field sampling distance, which can ensure the calculation accuracy of the algorithm under near-field sampling while avoiding the consumption of computing resources.

[0006] The technical solution for implementing the present invention is as follows:

[0007] A near-field RCS testing method that shortens the near-field sampling distance includes the following steps:

[0008] Step 1: Use the plane wave synthesis algorithm to solve for the transmission coefficient of each transmitting antenna;

[0009] Step 2: Determine the box size of the focused plane spectrum based on the target size, divide the box using the bisection method, and determine the total number N of non-empty boxes in the bounding box;

[0010] Step 3: Using near-field test data, solve for the far-field values ​​using the fast irregular antenna field change algorithm of the multi-plane wave focusing center;

[0011] Step 4: Multiply the transmission coefficient corresponding to each transmitting antenna by the far-field electric field corresponding to the target direction, and superimpose the results of all transmitting antennas to obtain the far-field electric field in the target direction and convert it into RCS.

[0012] Furthermore, in step two, the box size must ensure that the distance of the transfer operation is greater than twice the size of the box itself, and ensure that the target fills the total range of multiple boxes as much as possible. In the framework of Multilevel Fast Multipole Algorithm (MLFMA), the bisection method is used to divide the maximum size of the target into U parts.

[0013] Furthermore, the box size d must satisfy:

[0014]

[0015] Among them, D min R is the location of the nearest test site. max The maximum target radius is α, which is a calculation accuracy parameter, ranging from 0 to 2.

[0016] Furthermore, the formula for calculating U is:

[0017]

[0018] Furthermore, step three specifically involves:

[0019] After determining the bisection degree U, the number of non-empty boxes N under this division is obtained. The plane wave in each box is treated as an independent unknown, and the spectrum of each plane wave is calculated. Correlation with near-field values. The expression is:

[0020]

[0021] Where N is the total number of non-empty boxes, K n Here, q represents the effective plane spectrum number within each box, and q is the label of the receiving antenna. Represents θ q The unit vector of direction, express The unit vector of direction, θ is the near-field electric field value q Directional components, It is the near-field electric field value Directional components; using a near-field extrapolation algorithm, the correlation matrix between the plane wave spectrum and the near-field value is filled and solved, and the magnitude of each plane wave spectrum is solved simultaneously; finally, the plane wave spectra of multiple boxes in the same direction are phase-shifted and superimposed, and the electric field value in the target direction is obtained after interpolation calculation. The expression is:

[0022]

[0023] Where r c Let r be the center coordinates of each box.o Using the origin coordinates, when superimposing the coefficients, the shift factor from the box to the origin needs to be considered. It refers to the plane spectrum θ or Unknown coefficients in the components.

[0024] Beneficial effects:

[0025] 1. This invention uses a fast irregular antenna field change algorithm for multi-plane wave focusing centers to ensure calculation accuracy under close-range sampling conditions. At the same time, it provides a method for determining the size of the focusing plane wave spectrum and a segmentation method to avoid the box being too small and affecting the calculation performance.

[0026] 2. This invention divides the target into different regions, with the plane wave in each region as an independent unknown, and calculates the correlation between the plane wave spectrum and the near-field value. After solving the plane wave unknowns, the plane wave spectra of each box are shifted and superimposed, realizing a near-field testing method for measuring closer field points.

[0027] 3. Starting from the Green's function superposition formula for plane spectrum transfer, this invention obtains the relationship between the box size of the aggregated plane spectrum and the near-field measurement distance, and finally derives the relationship between the number of segmentations and the near-field measurement distance under the multilayer fast multipole frame, which can be applied to calculations under different near-field measurement environments. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the near-field RCS testing technology of the present invention, which shortens the near-field sampling distance.

[0029] Figure 2 This is a graph showing the trend of the calculation error results of Example 1 as a function of the near-field measurement distance and the number of bisections.

[0030] Figure 3 Example 1 is in D min =70m calculation error, total number of unknowns, and calculation time as a function of the number of bisections.

[0031] Figure 4 This is the result of dividing the central box of the planar spectrum in Example 2.

[0032] Figure 5 The results are the near-field measurement calculations of the single-station RCS in Example 2. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0034] This invention provides a near-field RCS testing method that shortens the near-field sampling distance, such as... Figure 1As shown, the main implementation steps are: plane wave synthesis, determination of the box size and segmentation method for focusing the plane wave spectrum, near-field extrapolation, and RCS synthesis. These steps will be described in detail below:

[0035] Step 1: Plane wave synthesis

[0036] Step 1.1: Use the commercial CAD software CATIA to create the plane wave synthesis region covering the target and perform subdivision.

[0037] Step 1.2: Based on the actual test distribution of the transmitting antenna (Tx), use it as the input for plane wave synthesis. The distribution of the transmitting antenna should satisfy the spacing requirements of the Nyquist sampling theorem and the range requirements of the projection theorem.

[0038] Step 1.3: Solve for the emission coefficient of each Tx using the plane wave synthesis algorithm. The field distribution of the plane wave is synthesized from the electromagnetic field radiated by the antenna, and its expression is shown in formula (1).

[0039]

[0040] Where M is the total number of transmitting antennas, E syn For the electromagnetic field of the synthesized plane wave, E m For each Tx, the radiated electromagnetic field, a m The emission coefficient for each Tx.

[0041] In order to solve the composition problem in numerical computation, it is necessary to establish a test function and test the boundary conditions at the boundary of the test region, as shown in (2).

[0042]

[0043] Where, β p (r) is the test function defined on the surface of the plane wave synthesis region. Generally, RWG basis functions are used. There are a total of P basis functions discrete on the surface of the plane wave synthesis region. Formula (2) can be used to establish an M×P dimensional linear matrix C for solution. However, since the matrix is ​​not invertible, an approximate solution method is required to minimize the root mean square error of the problem. The expression is shown in (3).

[0044]

[0045] Where C matrix is ​​the matrix spanned by the left side of formula (2), and x is a m Zhang Cheng's column vector, b is Zhang Cheng's column vector calculated from the right side of formula (2). Formula (3) can be equivalent to solving equation (4).

[0046] C H Cx = C H b Cx=b (4)

[0047] Where C H Let C be the conjugate transpose of matrix C. This equation is solved using the GMRES iterator.

[0048] Step 1.4: Substitute the calculated unit radiation field of each antenna into the matrix elements. The electromagnetic field expressions for the unit radiation of the antenna are shown in (5) and (6).

[0049]

[0050]

[0051] in, Let k be the unit vector of the plane wave expansion, k be the beam, and r be the field point. O Let D be the coordinates of the center of the box where the field point is located, and D be the transfer direction vector. The plane wave expansion representing the equivalent current at the Tx antenna is expressed as shown in (7).

[0052]

[0053] Where r' is the source point, r S J represents the center coordinates of the box containing the source point. m This represents the equivalent surface current at the source point.

[0054] T L (k,x) represents the transfer function of the plane wave, expressed as (8).

[0055]

[0056] in, For the second type of Hankel function, P l Let L be the Legendre function. The upper limit L of the summation has the following values:

[0057]

[0058] Where d is the maximum size of the planar spectral focusing box, and d0 is the accuracy parameter, which is generally between 3 and 4.

[0059] In formulas (5) and (6), This is generally referred to as a focusing operation because it focuses the surface current into a point centered at r. S The area where a spherical wave converges is generally called a box, which is a cube with a side length of d; T L (k,x) is generally called the transfer operation, which transfers the spherical wave from its center r. S The box is moved to the center as r O The box; This is called a divergence operation, where the center is r.O The plane wave is converted into the field value at the sampling point.

[0060] Step 2: Determine the box size and segmentation method for the focused plane spectrum.

[0061] To satisfy the accuracy of the superposition theorem in formula (8), the distance of the transfer operation should be more than twice the size of the box itself. Therefore, the formula that the box size d needs to satisfy is (10).

[0062]

[0063] Where D min R is the location of the nearest test site. max The maximum target radius is α, which is the calculation accuracy parameter. When α is 0, it is exactly twice the size of the box, but the calculation accuracy is not high at this time. Therefore, α is generally taken between 0 and 2 as the ratio increment.

[0064] In actual calculations, the determination of the box size d also needs to consider the actual target's segmentation to ensure that the target fills the total area of ​​multiple boxes as much as possible. In the framework of Multilevel Fast Multipole Algorithm (MLFMA), a bisection method is usually used. By bisecting the maximum size of the target U times, the expression for the box size is (11).

[0065]

[0066] Therefore, the formula for calculating U is (12).

[0067]

[0068] Finally, the total number N of non-empty boxes in the bounding box is determined based on the box size and the division method.

[0069] Step 3: Algorithm for Fast Irregular Antenna Field Variation at Multi-Plane Wave Focusing Center

[0070] Step 3.1: For each Tx antenna, establish a receiving antenna (Rx) array and measure the electric field value at that point. Use the Rx antenna distribution location and the measured field strength as inputs for near-field extrapolation.

[0071] Step 3.2: Use the near-field extrapolation algorithm to solve for the magnitude of each plane spectrum. The field distribution at Rx can be calculated from the plane spectrum, as shown in expression (13).

[0072]

[0073] Where N is the total number of non-empty boxes, K nThe effective plane spectrum number is obtained within each box, and q is the label of the receiving antenna. Represents θ q The unit vector of direction, θ q This represents the θ component of point q in spherical coordinates. express The unit vector of direction, This indicates that point q is in spherical coordinates. Quantity, θ is the near-field electric field value q Directional components, It is the near-field electric field value Directional components; a total of Q Rx points are used to receive the electric field. At this time, the field values ​​of the Rx points are all scalars, so there is no need to use the test function to calculate the inner product for scalarization. Formula (13) will form an NK×Q dimensional linear matrix, and its solution method is similar to that of formula (4), so it will not be repeated.

[0074] Step 3.3: Substitute the correlation between each plane spectrum and the near-field value into the matrix elements. The formula for calculating the near-field value from the plane spectrum is shown in (14).

[0075]

[0076] Where D is the distance from the center of the box to each Rx. This is the corresponding distance direction unit vector. For the plane wave expansion at the target location, the expression is consistent with (7). For the near-field extrapolation method, if the plane wave spectrum is used as the unknown, there is no need to use formula (7) for further calculation; only the transfer matrix T needs to be calculated. L and use Refers to the plane wave spectrum θ and Unknown coefficients in the components.

[0077] Step 3.4: Use the interpolated plane wave spectrum obtained from the solution to obtain the electric field value in the target direction.

[0078] First, the planar wave spectra of multiple boxes in the same direction need to be superimposed, and the superposition formula is (15).

[0079]

[0080] Where r c Let r be the center coordinates of each box. o The coordinates are those of the origin. When superimposing the coefficients, the shift factor from the box to the origin needs to be considered.

[0081] For the far-field electric field in the target direction, since the Green's function is quite smooth in the far field, it is only necessary to perform Lagrange linear interpolation on the plane wave spectrum. Considering the coefficients of the plane wave spectrum at four points around the target direction, the expression is shown in (16).

[0082]

[0083] Where ω i These are the Lagrange interpolation coefficients.

[0084] Step 4: RCS Synthesis

[0085] Step 4.1: Far-field electric field synthesis. Multiply the emission coefficient corresponding to each Tx antenna by the far-field electric field corresponding to the target direction, and then superimpose the results of all Tx antennas to finally obtain the far-field electric field in that direction.

[0086] Step 4.2: Calculate the far-field RCS. The calculation formula is shown in (17).

[0087]

[0088] Example 1: Flat Cylindrical Model

[0089] This invention establishes a flat cylindrical model as follows: Figure 2 The interior shows a cylinder 4.5m high and 32m in radius. The integrated test area is consistent with the model, with a mesh size of 0.1 times the free-space electrical wavelength. The plane wave frequency is 50MHz, and the incident direction is the x-direction. The polarization direction is the z-direction. In the near-field extrapolation method, only the extrapolation results for a single station are calculated. The required dual-station near-field measurement points are distributed over a radius of D. min On the surface of a sphere, the distribution range in the spherical coordinate system is: The measurement interval is 1.8°.

[0090] Figure 2 The distance D of the near-field point distribution is given. min The graph shows the trend of the change in the number of binary divisions calculated by near-field extrapolation and the change in calculation error. Figure 2 The test distances considered were 70m, 60m, and 45m, with the number of bisections increasing from 1 to 5, corresponding to a gradual decrease in box size from 16m to 1m, and an increase in the number of non-empty boxes from 4 to 1836. The calculation error was calculated as the difference between the single-station scattered field calculated directly using MLFMA and the single-station scattered field calculated using near-field extrapolation. Figure 2It can be seen that when the near-field test distance remains constant, the smaller the size and the greater the number of boxes in the plane spectrum aggregation, the more accurate the calculation results. When the bisection order does not satisfy formula (12) (α=0), the calculation cannot converge, so the calculation results are not shown in the figure. When the calculated box size is consistent, the farther the test distance, the more accurate the inversely derived bistatic RCS, and the less likely the calculation will fail to converge. When the bisection order reaches 4 and 5, the absolute error of the calculation results for the three test distances is less than 1dB, and the calculation results all meet the requirements. In summary, Figure 2 This demonstrates the effectiveness of the present invention in improving calculation accuracy by increasing the number of binary divisions and reducing the box size.

[0091] Figure 3 The following is given in D min The graph shows the trends in calculation error, total number of unknowns, and calculation time for a sample size of 70m as a function of the number of bisections. It can be seen that as the number of bisections increases, the calculation error decreases significantly, but at the same time, the number of unknowns increases significantly, leading to a decrease in calculation efficiency. This is because as the number of bisections increases, the total number of boxes increases. Although the number of plane spectra that need to be collected in each box decreases, the total number of plane spectra still increases significantly (as shown in the table below). Figure 3 It can be seen that the near-field extrapolation calculation for the flat cylinder shows a significant increase after three bisections, while the absolute error has already dropped below 1 dB. Therefore, for this problem, bisectioning two to three times can maintain high computational efficiency while ensuring the required accuracy, where α∈[0,2]. For other near-field measurement distances, the table below also gives the corresponding number of bisections (α=0). To ensure accuracy, the division can be refined by one more step, making α=2. In summary, Figure 3 The computational accuracy and efficiency of different binary search orders were compared in detail, and the range of α for balancing accuracy and efficiency was analyzed.

[0092]

[0093] Example 2: Model of the American B-2 stealth bomber

[0094] This invention establishes a model of the American stealth bomber B-2, such as Figure 4 As shown, the B-2 bomber has a wingspan of 30m and a height of 4.5m. The plane wave synthesis region is slightly larger than the aircraft's wingspan, forming a cylinder with a radius of 32m and a height of 4.5m. Its subdivision dimension is 0.4 times the free-space electromagnetic wavelength. The aircraft can rotate within this region for near-field measurements. The calculation frequency is 150MHz. The monostatic scattering over the angular range is calculated with an electrical dimension of 32 electrical wavelengths. The bistatic near-field measurement points required for near-field extrapolation are distributed on a sphere with a radius of 70m; therefore, the box segmentation of plane wave aggregation is as follows: Figure 4As shown by the dashed line, taking U=2, this region is divided into 16 sub-boxes, with a total of 172888 unknowns. The calculation results are as follows: Figure 5 As shown, the results of near-field extrapolation (NF2FF method) are in good agreement with the scattering calculations of the MLFMA method. The root mean square error of the 90° principal polarization is 1.44 dB. The error at a single point is calculated in dB as follows: Figure 5 The short dashed line represents the absolute error at a single point. It can be seen that the absolute error at a single point is no greater than 3dB, and most of them are below 0dB.

[0095] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A near-field RCS testing method for shortening the near-field sampling distance, characterized in that, Includes the following steps: Step 1: Use the plane wave synthesis algorithm to solve for the transmission coefficient of each transmitting antenna; Step 2: Determine the box size of the focused plane spectrum based on the target size, divide the box using the bisection method, and determine the total number N of non-empty boxes in the bounding box; Step 3: Using near-field test data, solve for the far-field values ​​using the fast irregular antenna field change algorithm of the multi-plane wave focusing center; Step 4: Multiply the transmission coefficient corresponding to each transmitting antenna by the far-field electric field corresponding to the target direction, and superimpose the results of all transmitting antennas to obtain the far-field electric field in the target direction and convert it into RCS; In step two, the box size must ensure that the distance of the transfer operation is greater than twice the size of the box itself, and ensure that the target fills the total range of multiple boxes. In the framework of multi-layer fast multipole, the bisection method is used to divide the maximum size of the target into U parts. The formula for calculating U is: ； in, The location of the nearest test site. For the maximum target radius, To calculate accuracy parameters, Take a value between 0 and 2; Step three specifically involves: After determining the bisection degree U, the number of non-empty boxes N under this division is obtained. The plane wave in each box is treated as an independent unknown, and the spectrum of each plane wave is calculated. The correlation with the near-field value is expressed as: Where N is the total number of non-empty boxes. Here, q represents the effective plane spectrum number within each box, and q is the label of the receiving antenna. express The unit vector of direction, express The unit vector of direction, It is the near-field electric field value Directional components, It is the near-field electric field value Directional components; using a near-field extrapolation algorithm, the correlation matrix between the plane wave spectrum and the near-field value is filled and solved, and the magnitude of each plane wave spectrum is solved simultaneously; finally, the plane wave spectra of multiple boxes in the same direction are phase-shifted and superimposed, and the electric field value in the target direction is obtained after interpolation calculation. The expression is: in, Let these be the center coordinates of each box. Using the origin coordinates, when superimposing the coefficients, the shift factor from the box to the origin needs to be considered. , plane spectrum or Unknown coefficients in the components.

2. The near-field RCS testing method for shortening the near-field sampling distance as described in claim 1, characterized in that, Box size Must meet: in, The location of the nearest test site. For the maximum target radius, To calculate accuracy parameters, Take a value between 0 and 2.

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