A near-field extrapolation RCS test method with reduced measurement clutter

Abstract

The present application is directed to a near-field extrapolation RCS testing method for reducing measurement clutter in far-field measurement of complex targets. In the near-field testing, the present application uses a metal ground testing environment to measure the near-field of the target, reduces the influence of the uncertainty of the testing environment and unknown scattering sources; then, in the fast irregular antenna field variation algorithm, the equivalent mirror source brought by the metal ground is considered for the transfer calculation of the near-field field value, and in the extrapolation far-field calculation link, the influence of the mirror source on the far-field field value is eliminated, and finally the approximate RCS result under the condition of no metal plane is obtained.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic measurement technology. It relates to efficient near-field extrapolation calculations for electrically large and complex targets, and can be used for far-field RCS measurement in confined indoor environments. 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 divided into three types: far-field measurement, compressed-field measurement, and near-field measurement. The typical characteristics of each measurement method are as follows:

[0003] 1. Far-field measurements for testing electrical targets require very long test sites and high-power test equipment, and can only be conducted off-site. Therefore, the measurement accuracy of far-field tests is easily affected by the ground test environment and weather, and the confidentiality is very poor, especially for testing military targets that have not yet been disclosed.

[0004] 2. Compact field measurement uses a large reflecting parabolic surface and a dielectric prism to generate plane waves for testing over a shorter distance. Therefore, compact field measurement can significantly shorten the testing distance, but the parabolic surface is expensive, and the equipment operation and maintenance costs are high. Furthermore, for excessively large testing targets, when existing compact field equipment cannot meet the requirements, the cycle of redesigning and building new equipment is relatively long.

[0005] 3. Near-field measurement utilizes 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, for complex targets with multiple scattering and other complex coupling effects, approximation methods may not provide accurate calculation results. Full-wave methods require bistational measurements of the near field and use plane-wave synthesis (PWS) to approximate the field distribution within a certain region to the state of plane wave incidence. Since the full-wave method starts from wave pattern expansion and theoretically has no approximations, its extrapolation algorithm yields more accurate results. When high accuracy of the measurement results is required, the full-wave algorithm is typically used for near-field–far-field transformation.

[0006] While the full-wave method of bistatic measurements offers higher accuracy, it places high demands on the distance, size, and distribution of antennas. Methods 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 the near-field measurement points deviate from the classical measurement surface, the calculation accuracy will be significantly affected. The Fast-Irregular Antenna Field Transformation Algorithm (FIAFTA) uses equivalent current, plane spectrum, or spherical spectrum as unknowns for calculation. Since the algorithm itself does not require special wavefunction expansion, near-field sampling points can be arbitrarily distributed within the effective range for solving a single-direction plane spectrum, reducing the difficulty of sampling point placement during testing. It also exhibits strong robustness to sampling region truncation, reducing the size of the near-field sampling area.

[0007] Near-field extrapolation RCS testing technology faces challenges during near-field sampling. The presence of numerous surrounding structures and the difficulty of covering rotating structures with ground-based absorbing materials, or the ineffectiveness of absorbing materials due to low test frequencies, lead to unwanted scattering sources and multipath propagation of electromagnetic waves, negatively impacting the accuracy of near-field sampling results. Besides maximizing the absorption capacity of the test environment, clutter cancellation technology is a key method for improving the accuracy of near-field sampling results. This technology is primarily divided into two categories: time-domain and frequency-domain techniques. Time-domain techniques mainly use time windows to avoid receiving results after multiple reflections from the target and other elements. Frequency-domain techniques primarily use fast Fourier transforms to eliminate impossible frequency signals, thus eliminating clutter. However, frequency-domain techniques cannot eliminate the influence of excitation currents generated by the interaction between the target and other elements, while time-domain techniques have requirements for the bandwidth of the test frequency and the resolution of multipath propagation distance. Therefore, neither method can completely remove the influence of clutter on the test.

[0008] Instead of employing complex methods to eliminate clutter, it's more efficient to directly remove the absorbing material from the ground and replace it with a large area of ​​metal. In this case, only the deterministic reflection results between the metal ground and the target need to be considered. Subsequently, the basic algorithm for near-field extrapolation RCS technology is adjusted to eliminate the reflection effect of the metal ground. This improves both the accuracy of near-field measurements and the repeatability of the tests. Summary of the Invention

[0009] In view of this, the present invention proposes a near-field extrapolation RCS testing method to reduce measurement clutter. In the near-field test, the present invention uses a metal ground test environment to measure the near-field of the target, reducing the uncertainty of the test environment and the influence of unknown scattering sources. Then, in the fast irregular antenna field change algorithm, the transfer calculation of the near-field field value caused by the equivalent image source brought by the metal ground is considered. In the extrapolation far-field calculation stage, the influence of the image source on the far-field field value is eliminated, and finally the approximate RCS result under the condition of no metal plane is obtained.

[0010] The specific technical solution described in this invention is as follows:

[0011] A near-field extrapolation RCS testing method to reduce measurement clutter includes four steps.

[0012] Step 1: Plane wave synthesis, used to obtain plane wave excitation composed of the radiation fields of multiple transmitting antennas Tx in the indoor near-field region;

[0013] Step 2: Determine the box size and number of non-empty boxes for the near-field extrapolation plane spectrum. This is used to determine the parameters required for the near-field extrapolation calculation and to prepare for the near-field extrapolation calculation.

[0014] Step 3: Near-field extrapolation calculation on an infinitely large metal plane containing a mirror source, used to solve for the far-field electric field value that is not affected by the metal plane;

[0015] Step 4: Remove the near-field extrapolation RCS synthesis of the mirror source, which is used to convert the far-field electric field value into an approximate RCS result under the condition of a metal-free plane.

[0016] Furthermore, the formula for calculating the side length d of the near-field extrapolation planar spectral box in step 2 is as follows:

[0017]

[0018] in,

[0019] D min R represents the location of the test site closest to the target. max The maximum target measurement radius is α, and the calculation accuracy parameter is α.

[0020] The method for determining the number of non-empty boxes is as follows: after determining the side length of the near-field extrapolation plane spectrum box, the plane wave synthesis region is divided by the near-field extrapolation plane spectrum box, and the boxes with discrete basis functions of the envelope surface are defined as non-empty boxes, thereby determining the total number of non-empty boxes N.

[0021] Furthermore, step 3 comprises three sub-steps.

[0022] Step 3.1: For each Tx antenna, establish a receiving antenna Rx array and measure the near-field electric field value at each receiving antenna;

[0023] Step 3.2: Based on the measured results, the plane spectral coefficient b corresponding to the target considering the influence of the metal plane is obtained through the tangential electric field equation. nkθ and

[0024] Step 3.3: For the portion that does not require superimposing the mirror source, based on the plane spectral coefficient b... nkθ and Interpolation yields the far-field scattered electric field value corresponding to the target direction.

[0025] Furthermore, the tangential electric field equation in step 3.2 is as follows:

[0026]

[0027] in,

[0028] Let be the component of the near-field electric field measured in the θ direction for the q-th Rx.

[0029] The near-field electric field measured for the q-th Rx is in directional components,

[0030] N is the total number of near-field extrapolation planar spectral boxes.

[0031] K n The number of effective plane spectra within each box,

[0032] k is the wave number.

[0033] Let be the unit vector of the plane wave expansion.

[0034] q is the label of Rx, and a total of Q Rx points are used to receive the electric field.

[0035] Let q be the unit vector of the q-th Rx in the θ direction.

[0036] For the q-th Rx in The unit vector of direction,

[0037] Furthermore,

[0038]

[0039]

[0040] in,

[0041] T L (*,*) denotes the transfer function of a plane wave.

[0042] D T Let Rx be the distance from the center of the target source box to each Rx.

[0043] The corresponding distance direction unit vector,

[0044] For the target plane spectrum,

[0045] for Decomposed into the θ direction and Unit component of direction,

[0046] b nkθ For the target plane spectrum Decomposed into θ direction component Plane spectral coefficients on

[0047] For the target plane k-wave spectrum Decomposed into of Directional components Plane spectral coefficients on

[0048] Furthermore,

[0049]

[0050]

[0051] in,

[0052] For the plane wave spectrum in the nth mirror box The near-field electric field value, which is oriented in one direction, can also be decomposed into components in two directions.

[0053] D M This represents the distance from the center of the mirror source box to each Rx.

[0054] The corresponding distance direction unit vector,

[0055] According to the mirror principle, the equivalent currents of the mirror source and the target source are opposite in the horizontal direction but the same in the vertical direction, and the plane spectrum at the mirror source is... Decomposed into θ direction component The plane wave spectral coefficients on the target plane wave spectrum, and the π-θ in the target plane wave spectrum kThe plane wave spectral coefficients are consistent in the direction, therefore they are represented as b. nk(π-θ) Planar spectrum at the mirror source Decomposed into of Directional components The plane spectral coefficients on the target plane spectrum, and the plane spectral coefficients in the target plane spectrum The plane wave spectral coefficients are consistent in the direction, therefore they are represented as

[0056] Furthermore, in the near-field extrapolation calculation of the metal-containing plane in step 3, the solution of the tangential electric field equation differs from the solution obtained in free space. The two solutions are physically different due to the influence of the coupling between the target and the metal plane. However, this influence varies with the height of the target and the incident angle of the plane wave synthesis. Under specific height and angle constraints, it can be ignored. The specific height and angle constraints are as follows: for a test target with a size of 1 air wavelength, the horizontal incident angle is within ±15° in the horizontal direction, and the target is higher than 2 times the air wavelength above the metal ground; or, the horizontal incident angle is within ±45° in the horizontal direction, and the target is higher than 4 times the air wavelength above the metal ground; or, the target is higher than 6 times the air wavelength above the metal ground, and the incident angle is ignored.

[0057] Furthermore, step 4 includes: using the emission coefficient corresponding to each Tx antenna and the far-field scattered electric field value corresponding to the target direction. Multiplying and superimposing the results from all Tx antennas yields the final far-field electric field in that direction. Reuse formula: The far-field RCS is obtained.

[0058] Furthermore, the plane wave synthesis comprises three sub-steps.

[0059] Step 1.1: Establish the plane wave synthesis region according to the test requirements and perform necessary subdivisions so that the surface can represent discrete basis functions;

[0060] Step 1.2: Based on the position distribution of transmitting antenna Tx and the expression of the unit radiated electromagnetic field corresponding to each transmitting antenna, obtain the unit radiated electromagnetic field generated at any field point by the unit excitation at each transmitting antenna Tx;

[0061] Step 1.3: By solving the equation expression of plane wave synthesis, the emission coefficient of each transmitting antenna Tx is obtained; based on the emission coefficient of each transmitting antenna and the unit radiated electromagnetic field of each transmitting antenna at any field point, the equivalent plane wave excitation required for RCS testing is obtained.

[0062] Furthermore, step 1.2 includes: determining the positional distribution of the M transmitting antennas Tx according to the interval requirements of the Nyquist sampling theorem and the range requirements of the projection theorem; in the process of constructing the expression for the unit radiated electromagnetic field corresponding to each transmitting antenna Tx, the equivalent current source generated by the unit excitation of each antenna Tx is a known quantity, each equivalent current source is gathered into a plane wave spectrum within the source field box, and then the plane wave spectrum is transferred to the field point box, and then the plane wave spectrum is uniformly diverged and converted into the field value of each field point, so as to obtain the magnitude of the unit radiated electromagnetic field of each transmitting antenna at any field point.

[0063] Beneficial effects

[0064] 1. This invention addresses the problem of far-field measurement of complex targets by proposing a near-field extrapolation RCS testing technique to reduce measurement clutter. Specifically, it proposes a testing scheme for near-field measurements on a metallic surface, which can mitigate the impact of uncertain scattering sources on the accuracy and repeatability of near-field measurements.

[0065] 2. This invention considers the transfer calculation of near-field values ​​caused by the equivalent mirror source of the metal ground;

[0066] 3. In the final extrapolation far-field calculation stage, this invention eliminates the influence of the mirror source on the far-field value, and obtains the approximate RCS result under the condition of a metal-free plane.

[0067] 4. This invention explores the correlation between target height, plane wave incident angle, and the accuracy of near-field extrapolation RCS results: the near-field extrapolation algorithm on an infinitely large metal plane cannot eliminate the influence of the coupling between the target and the metal plane, but this influence varies with the target height and the incident angle. Tests show that the coupling between the metal plane and the target is negligible under near-horizontal incident conditions, and increasing the target height can further reduce the influence of coupling. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating the near-field extrapolation RCS testing technique for reducing measurement clutter according to the present invention.

[0069] Figure 2 This is a schematic diagram of the model for example one;

[0070] Figure 3 The following are the near-field extrapolation bistatic RCS results of Example 1 at different heights from the metal plane under incident angles of (a) θ = 90° and (b) θ = 45°.

[0071] Figure 4 The root mean square error of the near-field extrapolation bi-station RCS under different incident angles and heights in Example 1;

[0072] Figure 5 This is a schematic diagram of the model for example two;

[0073] Figure 6 This is the near-field extrapolation single-station RCS result diagram of Example 2 under the conditions of incident angles of (a) θ = 75° and (b) θ = 90°, with the target distance from the metal being 30m above the ground. Detailed Implementation

[0074] The present invention will be described in detail with reference to the accompanying drawings and inventive steps:

[0075] This invention mainly consists of four main implementation steps: plane wave synthesis, determining the box size and number of non-empty boxes for the focused plane wave spectrum, near-field extrapolation calculation on an infinitely large metallic plane containing a mirror source, and near-field extrapolation RCS synthesis without the mirror source. Plane wave synthesis is used to obtain a plane wave excitation composed of the radiation fields from multiple transmitting antennas Tx in the indoor near-field region (RCS testing requires ① excitation ② measurement, this is the first step). Determining the box size and number of non-empty boxes for the focused plane wave spectrum is used to determine the parameter settings for the near-field extrapolation calculation, preparing for the calculation. Near-field extrapolation calculation on an infinitely large metallic plane containing a mirror source is used to solve for the far-field electric field value unaffected by the metallic plane. Near-field extrapolation RCS synthesis without the mirror source is used to convert the far-field electric field value into an approximate RCS result under conditions without a metallic plane. The steps are described below in sequence:

[0076] Step 1: Plane wave synthesis

[0077] This process mainly consists of three sub-steps: First, a plane wave synthesis region is established according to the test requirements and necessary subdivisions are performed so that the surface can represent discrete basis functions. Second, the location distribution of transmitting antennas Tx and the expression for the unit radiated electromagnetic field corresponding to each transmitting antenna are determined. During the expression construction, the equivalent current source generated by the unit excitation at antenna Tx is taken as a known quantity, aggregated into a plane wave spectrum within the source field box, then transferred to the field point box, and then uniformly diverged to each field point, converting it into the field value at each field point, thus obtaining the magnitude of the unit radiated electromagnetic field of each transmitting antenna at any field point. Finally, the equation expression for plane wave synthesis is established, and the emission coefficient of each transmitting antenna Tx is obtained by solving the equation. When constructing the equation, the basis functions initially discrete on the surface of the plane wave synthesis region are used as test functions. In the equation, the unit radiated electromagnetic field of each transmitting antenna on the test basis function is a known quantity, and the final plane wave electromagnetic field expression to be synthesized is the right-hand side term to solve for the emission coefficient of each antenna. Based on the emission coefficient of each antenna and its unit radiated electromagnetic field at any field point, the equivalent plane wave excitation required for RCS testing can be synthesized.

[0078] Step 1.1: Use the commercial CAD software CATIA to establish the plane wave synthesis region covering the target and divide the region's envelope surface. The division size is 0.4 times the incident wave wavelength. The envelope surface of the plane wave synthesis region is used to establish the electromagnetic field equation (1) based on the uniqueness theorem. The discrete basis functions formed after division are used to establish the test boundary conditions (formula (6) in step 1.3 is an equation constructed based on the boundary conditions).

[0079] Step 1.2: Based on the interval requirements of the Nyquist sampling theorem and the range requirements of the projection theorem, determine the positional distribution of the M transmitting antennas Tx. Then, calculate the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at the field point r. Wherein, the unit radiation electric field E of the m-th transmitting antenna at the field point r... m (r) and the unit radiation magnetic field H of the m-th transmitting antenna at field point r. m The formula for calculating (r) is as follows:

[0080]

[0081]

[0082] Where j is the imaginary unit, Let k be the unit vector of the plane wave expansion, k be the wave number, 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 distance. Z0 is the unit direction vector corresponding to the transfer distance, and Z0 is the free space wave impedance. Let Tx represent the plane wave spectrum of the equivalent current source generated by the unit excitation at the m-th antenna. It is formed by the aggregation of the equivalent current generated by the unit excitation at Tx. The aggregation range is generally called the box, and the expression is shown in (3).

[0083]

[0084] Where ω represents the angular frequency corresponding to the incident frequency, and μ represents the air permeability. Let V' represent the unit dyadic vector, V' represent the volume region where the equivalent current source generated by the unit excitation at Tx is located, and r' is the integration point within the volume region, or simply the source point. S J represents the center coordinates of the box containing the source point. m The equivalent surface current at the source point can be determined by the radiation mode of the transmitting antenna.

[0085] T L (*,*) denotes the transfer function of a plane wave, expressed as (4).

[0086]

[0087] in, For the second type of Hankel function, P l Let L be the Legendre function. The upper limit of the summation L takes the value of (5).

[0088]

[0089] Where d p The side length of the aggregation box for planar synthesis is typically 0.3 times the electrical wavelength, and d0 is the precision parameter, typically between 3 and 4.

[0090] In solving formulas (1) and (2), the equivalent current generated by the unit excitation at antenna Tx is known (which can be obtained through the radiation mode when the antenna is working). First, through... The focusing operation concentrates the equivalent current generated by the unit excitation at antenna Tx into a point centered at r. S The plane spectrum, the area of ​​which is concentrated is generally called the box, which is a cubic area with a side length of d; T L (k,x) is generally called a transfer operation, which transfers the plane 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. Through this entire process, the unit radiation electric field or unit radiation magnetic field at any point in space can be obtained from the unit excitation at Tx.

[0091] Step 1.3: Establish the equation for plane wave synthesis, and then obtain the emission coefficient of each transmitting antenna Tx by solving the equation. In the equation, the unit radiated electromagnetic field of each transmitting antenna on the test basis function is a known quantity, and the final expression for the plane wave electromagnetic field to be synthesized is the right-hand side term. The specific equation is expressed as follows:

[0092]

[0093] Where M is the total number of transmitting antennas, E syn To test the required electric field, H syn To test the required magnetic field, a m The emission coefficient for each Tx.

[0094] 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 (7).

[0095]

[0096] Where, β p(r) is the test function, defined on the envelope surface S of the plane wave synthesis region. Generally, RWG basis functions are used, and there are a total of P discrete basis functions on the envelope surface of the plane wave synthesis region. Formula (7) 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 (8).

[0097]

[0098] Where C matrix is ​​the matrix spanned by the left side of formula (7), and x is a m Zhang Cheng's column vector, b is Zhang Cheng's column vector calculated from the right side of formula (7). Formula (8) can be equivalent to solving equation (9).

[0099] C H Cx = C H b Cx=b (9)

[0100] Where C H Let C be the conjugate transpose of matrix C. This equation is solved using the GMRES iterator.

[0101] Step 2: Determine the box size and number of non-empty boxes for the focused plane spectrum.

[0102] To satisfy the accuracy of the superposition theorem in formula (4), the transfer distance should be more than twice the size of the box itself. Therefore, the formula that the side length d of the box needs to satisfy is (10).

[0103]

[0104] Where D min R represents the location of the test site closest to the target. max Let α be the maximum target measurement radius, and α be the calculation accuracy parameter. When α is 0, it exactly satisfies twice the box size, but the calculation accuracy is not high at this time. Therefore, α, as the ratio increment, is generally taken between 0 and 2. After determining the box side length, it is divided according to the maximum size of the plane wave synthesis region. Boxes with discrete basis functions of the envelope surface are defined as non-empty boxes, and the total number N of non-empty boxes is determined according to the actual distribution of the envelope surface.

[0105] Step 3: Near-field extrapolation algorithm for multi-plane spectral convergence centers

[0106] This process mainly consists of three sub-steps: First, for each Tx antenna, a receiving antenna (Rx) array is established, and the near-field electric field value at that point is measured. Second, based on the measured results, a tangential electric field equation is established, and the plane spectrum corresponding to the target considering the influence of the metallic plane is solved. In the process of establishing the equation, the near-field electric field value at the receiving antenna (Rx) measured in the previous step is the right-hand side, and the transfer relationship from the unknown coefficients of the plane spectrum to the near-field field value is known, so the unknown coefficients of the plane spectrum can be obtained by solving the equation. Finally, based on the plane spectrum coefficients, the far-field scattered electric field value of the target is interpolated.

[0107] Step 3.1: For each Tx antenna, establish a receiving antenna array consisting of Q receiving antennas and measure the electric field value of Rx for each receiving antenna. Use the distribution location of the Rx antennas and the measured field strength as inputs to establish the tangential electric field equation required by the near-field extrapolation algorithm in Step 3.2.

[0108] Step 3.2: Construct the tangential electric field equations and solve for the spectral coefficients corresponding to each plane spectrum using these equations. The influence of the metal plane will be considered in the near-field extrapolation algorithm. Taking the vertical projection point of the target's centroid on the metal plane as the origin and the direction of gravity as the negative z-axis, an absolute rectangular coordinate system and a spherical coordinate system are established respectively. Let the plane z = 0 and the plane θ = 90° coincide. Assuming that the metal plane is the plane z = 0 in the absolute rectangular coordinate system and the approximate metal plane is a theoretically infinite metal plane, the induced current on the target will generate a virtual mirror current with the same vertical direction and opposite horizontal direction below the metal plane, which will affect the electric field value at Rx. Therefore, the field distribution at Rx can be calculated by superimposing the plane spectrum of the target current and the plane spectrum of the mirror current source. Thus, the tangential electric field equation can be constructed, and the expression is shown in (11).

[0109]

[0110] in The electric field component in the θ direction measured by the qth Rx. The q-th Rx was measured Directional electric field components, N is the total number of boxes obtained in step two, K n Let q be the effective plane spectrum number within each box, and let q be the label of Rx. A total of Q Rx points are used to receive the electric field. Let q be the unit vector of the q-th Rx in the θ direction. For the q-th Rx in The direction is a unit vector. At this time, the field value test results of the Rx point are all scalars, so there is no need to use the test function to calculate the inner product for scalarization. The plane wave spectrum in the nth box as the target is The near-field electric field value presented in the direction, and the relationship between this field value and the plane wave spectrum and its corresponding coefficients are as follows:

[0111]

[0112] Where D T Let Rx be the distance from the center of the target source box to each Rx. This is the corresponding distance direction unit vector. As a plane spectrum, it can be decomposed into θ direction component The unknown coefficient b nkθ ,and Directional components Unknown coefficients Therefore, solving for the plane wave spectrum is equivalent to solving for b. nkθ and These two unknown coefficients.

[0113] For the plane wave spectrum in the nth mirror box The near-field electric field value is presented in the direction. Since the distribution range of the mirror source and the target current source are exactly the same, and the size and segmentation of the mirror source's box are exactly the same as those of the target, it also has N mirror boxes. The current magnitudes of the mirror source and the target source are the same but their directions are different, and the coefficients corresponding to the plane wave spectrum are also the same, only the directions have changed. Therefore, Near-field electric field value in the direction The relationship between the plane spectrum and its corresponding coefficients is as follows:

[0114]

[0115] Where D M This represents the distance from the center of the mirror source box to each Rx. This represents the corresponding distance direction unit vector. The mirror box is also symmetric to the target box about the z=0 plane, so the distances from the center of the mirror box to each Rx can also be quickly obtained through symmetry. The plane wave spectrum at the mirror source is decomposed into the near-field to far-field conversion algorithm. θ direction component Unknown coefficients and Directional components The unknown coefficients. According to the principle of mirror images, the equivalent currents on the source and target are opposite in horizontal direction but the same in vertical direction. Therefore, The unknown coefficient in the direction is b nk(π-θ) , The unknown coefficients in the direction are

[0116] As can be seen, the calculation formulas for the mirror source and the target source differ mainly in the following ways:

[0117] First, the transfer distance changed from the center of the target box to Rx to the center of the corresponding mirror box Rx, where the centers of the target box and the mirror box are symmetrical about the z-plane;

[0118] Secondly, the θ component of the mirrored plane spectrum is symmetrical with respect to the target plane spectrum at an angle of θ = π, while The component sizes are opposite.

[0119] Finally, Equation (11) will form an NK×Q dimensional linear matrix, where the right-hand side represents the near-field electric field value at the receiving antenna (Rx), and the unknowns are the unknown coefficients of the plane wave spectrum. The solution method is similar to that of Equation (9), and will not be repeated here.

[0120] It should be emphasized that the solution obtained by formula (11) is not the same as the solution obtained in free space. The two solutions differ physically in the influence of the coupling between the target and the metal plane. However, this influence varies with the height of the target and the incident angle of the plane wave synthesis. Under certain height and angle constraints, the influence of coupling can be considered negligible. For a test target with a size of 1 air wavelength, if the horizontal incident angle is within ±15° in the horizontal direction, the influence of coupling can be ignored by raising the target by 2 times the air wavelength. If the horizontal incident angle is within ±45° in the horizontal direction, the influence of coupling can be ignored by raising the target by approximately 4 times the air wavelength. For targets more than six times the height of the ground, the influence of coupling can be ignored for any incident angle.

[0121] Step 3.3: Use the solved plane wave spectral coefficients to interpolate and obtain the far-field scattered electric field value in the target direction.

[0122] First, the planar wave spectra of multiple target boxes in the same direction need to be superimposed. Note that the far-field electric field in free space is being solved here, so there is no need to superimpose the portion of the mirror source. The superposition formula is (14).

[0123]

[0124] Where r c Let r be the center coordinates of each target 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. For θ or The far-field electric field component in the direction is obtained by formula (14) and the unknown coefficient b. nkθ or (collective) (This is obtained by superimposing.)

[0125] For the far-field electric field in the target direction at θ or For the components in the direction, since the Green's function behaves quite smoothly in the far field, it is only necessary to consider the far-field electric field components at four points around the target direction using Lagrange linear interpolation, as shown in expression (15).

[0126]

[0127] Where ω i These are the Lagrange interpolation coefficients. The coefficients for the four surrounding points are at θ or... Far-field electric field components in the direction It can be obtained from formula (14).

[0128] Step 4: RCS Synthesis

[0129] 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.

[0130] Step 4.2: Calculate the far-field RCS. The calculation formula is shown in (16).

[0131]

[0132] in Through θ or Far-field electric field components in the direction The total far-field value of the synthesis.

[0133] Step three involves identifying key points and points to be protected.

[0134] The simulation results are as follows:

[0135] Example 1: Standard Cylinder Model

[0136] This invention establishes a standard cylindrical model, as follows: Figure 2 As shown internally, the cylinder is 1m high and 0.8m in diameter, with its center at a distance D from the ideal infinitely large metal plane. Example 1 primarily investigates the influence of the target's height above the metal plane and the angle of incidence of the plane wave on the accuracy of near-field to far-field conversion. The integrated test area is consistent with the model, with a subdivision size of 0.1 times the free-space electrical wavelength. The plane wave frequency is 300MHz, and the incident angle ranges from horizontal incidence (θ=90°, ), gradually changing to perpendicular incidence (θ=0°, The polarization direction is θ. Example 1 uses θ = 90°. The accuracy of the bistatic results was compared with the far-field scattering results of a standard cylinder at the corresponding angle in free space. Therefore, the required bistatic near-field measurement points are distributed on a sphere with a radius of 4m centered at the cylinder's center, within the range θ∈[60°,120°]. The measurement interval was 4°, totaling 1456 sampling points. The target was enclosed in a box with a side length of one air wavelength during the calculation, with 454 plane spectral unknowns.

[0137] Figure 3 The comparison of near-field extrapolation accuracy as the target distance and height from the metal plane are presented, demonstrating that when the incident plane wave is horizontal to the metal plane (θ=90°, The results were obtained when the target was two, four, and six times the air wavelength at its distance from the metal plane. Figure 3 This indicates that when the incident wave is horizontally incident, the near-field extrapolation result is more accurate, and increasing the distance between the target and the metal plane can effectively reduce the influence of coupling, thereby improving accuracy.

[0138] Subsequently, the root mean square error of the bistatic results for targets at different altitudes under different incident angles was calculated, as follows: Figure 4 As shown in the figure, seven different incident angles were tested at three different distances from the metal plane (2 times, 4 times, and 6 times the air wavelength), gradually changing from vertical to horizontal incidence. The formula for calculating the root mean square error is:

[0139]

[0140] Where N is the total number of dual-station sampling points, σ cal The RCS result is obtained by near-field extrapolation calculation for an infinitely large metal plate, σ ref The far-field RCS result is obtained directly in free space using the MLFMA method. (Comparison) Figure 4 It can be observed that as the incident angle gradually becomes more perpendicular to the metal plane, the error in the calculation results at the same height gradually increases. For a test target with a size of 1 air wavelength, if the horizontal incident angle is within ±15° in the horizontal direction, the coupling effect can be ignored by raising the target by 2 times the air wavelength; if the horizontal incident angle is within ±45° in the horizontal direction, the coupling effect can be ignored by raising the target by approximately 4 times the air wavelength; for targets more than six times the height of the ground, the coupling effect can be ignored for any incident angle. In summary, Figure 4 The study quantitatively demonstrates the impact of target height and incident angle on the accuracy of bistatic RCS near-field extrapolation results for a standard cylinder, and provides the approximate target height required from the metal plane for the range of measured angles.

[0141] Example 2: Stealth Machine Model

[0142] This invention establishes a stealth machine model as follows: Figure 5 As shown, the model has a wingspan of 30m and a height of 4.5m. The plane wave synthesis region is slightly larger than the stealth aircraft's wingspan, and is a cylinder with a radius of 32m and a height of 4.5m. Its mesh size is 0.4 times the free-space electromagnetic wavelength, allowing the aircraft to rotate within this region for near-field measurements. The target is placed on an ideal, infinitely large plane, with its center 30m above the ground. The calculation frequency is 150MHz, and θ = 75° and 90° are calculated. 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. When performing monostatic RCS extrapolation, the near-field sampling range θ... The angle of each sample is 35°, with a total of 2840 sampling points. The calculation results are as follows: Figure 6 As shown, where Figure 6 'a' represents the near-field extrapolation result when the incident angle is 75° at a distance of 30m from the metal plane. Figure 6 b represents the near-field extrapolation result when the incident angle is 90° at a distance of 30m from the metal plane. Both results are consistent with the scattering calculation results of the MLFMA method, proving that within the required angle of the aircraft, the coupling between the metal plane and the target will not affect the near-field extrapolation result of the target, and will also have a positive effect on the suppression of clutter at the test site.

Claims

1. A near-field extrapolation RCS testing method for reducing measurement clutter, characterized in that: It includes four steps, Step 1: Plane wave synthesis, used to obtain plane wave excitation composed of the radiation fields of multiple transmitting antennas Tx in the indoor near-field region; Step 2: Determine the box size and number of non-empty boxes for the near-field extrapolation plane spectrum. This is used to determine the parameters required for the near-field extrapolation calculation and to prepare for the near-field extrapolation calculation. Step 3: Near-field extrapolation calculation on an infinitely large metal plane containing a mirror source, used to solve for the far-field electric field value unaffected by the metal plane; Step 4: Remove the near-field extrapolated RCS synthesis of the mirror source, which is used to convert the far-field electric field value into an approximate RCS result under the condition of a metal-free plane. Step 3 consists of 3 sub-steps: Step 3.1: For each Tx antenna, establish a receiving antenna Rx array and measure the near-field electric field value at each receiving antenna; Step 3.2: Based on the measured results, the plane wave spectrum coefficients of the target considering the influence of the metal plane are obtained through the tangential electric field equation. and ; Step 3.3: For the portion that does not require superimposing the mirror source, based on the plane spectral coefficients... and Interpolation yields the far-field scattered electric field value corresponding to the target direction. ; The tangential electric field equation in step 3.2 is as follows: in, For the plane wave spectrum in the nth mirror box The near-field electric field value presented in the direction, The near-field electric field measured for the q-th Rx is... directional components, The near-field electric field measured for the q-th Rx is... directional components, N represents the total number of near-field extrapolation planar spectral boxes. K n The number of effective plane spectra within each box, k is the wave number. Let be the unit vector of the plane wave expansion. q is the label of Rx, and a total of Q Rx points are used to receive the electric field. For the q-th Rx in The unit vector of direction, For the q-th Rx in The unit vector of direction, in, T L (*,*) denotes the transfer function of a plane wave. D T Let Rx be the distance from the center of the target source box to each Rx. The corresponding distance direction unit vector, For the target plane spectrum, , for Decomposed into direction and Unit component of direction, For the target plane spectrum Decomposed into of Directional components Plane spectral coefficients on For the target plane spectrum Decomposed into of Directional components Plane spectral coefficients on in, For the plane wave spectrum in the nth mirror box The near-field electric field value, presented in the direction, can also be decomposed into components in two directions. This represents the distance from the center of the mirror source box to each Rx. The corresponding distance direction unit vector, According to the principle of mirrors, the equivalent currents of the mirror source and the target source are opposite in the horizontal direction but the same in the vertical direction. Planar spectrum at mirror source Decomposed into of Directional components The plane spectral coefficients on the target plane spectrum, and the plane spectral coefficients in the target plane spectrum The plane wave spectral coefficients are consistent in the direction, therefore they are represented as , Planar spectrum at mirror source Decomposed into of Directional components The plane spectral coefficients on the target plane spectrum, and the plane spectral coefficients in the target plane spectrum The plane wave spectral coefficients are consistent in the direction, therefore they are expressed as... .

2. The near-field extrapolation RCS testing method for reducing measurement clutter according to claim 1, characterized in that, The formula for calculating the side length d of the near-field extrapolation planar spectral box in step 2 is as follows: in, D min R represents the location of the test site closest to the target. max For the maximum target measurement radius, For calculating accuracy parameters; The method for determining the number of non-empty boxes is as follows: after determining the side length of the near-field extrapolation plane spectrum box, the plane wave synthesis region is divided by the near-field extrapolation plane spectrum box, and the boxes with discrete basis functions of the envelope surface are defined as non-empty boxes, thereby determining the total number of non-empty boxes N.

3. The near-field extrapolation RCS testing method for reducing measurement clutter according to claim 1, characterized in that: In step 3, the near-field extrapolation calculation of the metal-containing plane results in a solution to the tangential electric field equation that differs from the solution obtained in free space. The two solutions are physically related to the coupling effect between the target and the metal plane. However, this effect varies with the target's height and the incident angle of the plane wave synthesis. Under specific height and angle constraints, this effect is negligible. These specific height and angle constraints are: for a test target with a size of 1 air wavelength, the horizontal incident angle is within ±15° in the horizontal direction, and the target is more than twice the air wavelength above the metal ground; or, the horizontal incident angle is within ±45° in the horizontal direction, and the target is more than four times the air wavelength above the metal ground; or, the target is more than six times the air wavelength above the metal ground, and the incident angle is negligible.

4. The near-field extrapolation RCS testing method for reducing measurement clutter according to claim 3, characterized in that: Step 4 specifically includes: using the emission coefficient corresponding to each Tx antenna and the far-field scattered electric field value corresponding to the target direction. Multiplying and superimposing the results from all Tx antennas yields the final far-field electric field in that direction. Then use the formula: The far-field RCS is obtained.

5. The near-field extrapolation RCS testing method for reducing measurement clutter according to claim 4, characterized in that: The plane wave synthesis comprises three sub-steps. Step 1.1: Establish the plane wave synthesis region according to the test requirements and perform subdivision so that the surface represents discrete basis functions; Step 1.2: Based on the position distribution of transmitting antenna Tx and the expression of the unit radiated electromagnetic field corresponding to each transmitting antenna, obtain the unit radiated electromagnetic field generated by the unit excitation at each transmitting antenna Tx at any field point; Step 1.3: By solving the equation for plane wave synthesis, the transmission coefficient of each transmitting antenna Tx is obtained; Based on the emission coefficient of each transmitting antenna and the unit radiated electromagnetic field of each transmitting antenna at any field point, the equivalent plane wave excitation required for RCS testing is obtained.

6. The near-field extrapolation RCS testing method for reducing measurement clutter according to claim 5, characterized in that: Step 1.2 includes: determining the positional distribution of the M transmitting antennas Tx according to the interval requirements of the Nyquist sampling theorem and the range requirements of the projection theorem; in the process of constructing the unit radiated electromagnetic field expression for each transmitting antenna Tx, the equivalent current source generated by the unit excitation of each antenna Tx is a known quantity, each equivalent current source is gathered into a plane wave spectrum within the source field box, then the plane wave spectrum is transferred to the field point box, and then the plane wave spectrum is uniformly diverged and converted into the field value of each field point, so as to obtain the magnitude of the unit radiated electromagnetic field of each transmitting antenna at any field point.

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