Fast near field extrapolation RCS calculation method based on back propagation method

Abstract

The invention discloses a fast near field extrapolation RCS calculation method based on a back propagation method. The method comprises the following steps: calculating an emission coefficient of each emission antenna; establishing a receiving antenna array for each transmitting antenna, and measuring an electric field value of each receiving antenna; establishing a tangential electric field equation based on the electric field value and position distribution of the receiving antenna as the input of near field extrapolation; solving the tangential electric field equation based on a back propagation method, and obtaining a far-field electric field value in the target direction; multiplying the emission coefficient of each emission antenna by the far-field electric field value of the target direction and then superposing to obtain a total far-field electric field value of the target direction; and calculating a far-field radar cross section according to the total far-field electric field value in the target direction, and completing near-field extrapolation RCS calculation. According to the method, the calculation speed of the whole single-station RCS near-field extrapolation is improved.

Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic measurement, and in particular to a fast near-field extrapolated RCS calculation method based on a back-propagation method. Background Art

[0002] Radar Cross Section (RCS) is used to measure the ability of radar detection objects such as aircraft, vehicles, and ships to scatter electromagnetic waves. Therefore, when designing stealth targets with important military value, the measurement and evaluation of RCS is very necessary. However, it is very difficult to measure the RCS of the target aircraft because the calculation of RCS requires plane wave incidence and requires the reception to meet the far field (FF) conditions. According to the different architectures of the RCS measurement system, the actual measurement of the target RCS characteristics can be divided into three types: far field measurement, compact field measurement, and near field measurement. The typical characteristics of each measurement method are as follows:

[0003] 1. Far-field measurement: Testing of electrically large targets requires a very long test site and high-power test equipment, and can only be performed off-site. Therefore, the measurement accuracy of far-field testing is easily affected by the ground test environment and weather, and the confidentiality is very poor, especially it cannot be used to test military targets that have not yet been made public.

[0004] 2. Compact field measurement uses a huge reflecting parabola and dielectric prism to generate plane waves for testing at a shorter distance. Therefore, compact field measurement can greatly shorten the test distance, but the parabola is expensive, and the equipment operation and maintenance costs are high. At the same time, for test targets that are too large, when the original compact field equipment cannot meet the requirements, the cycle of redesigning and building the equipment is relatively long.

[0005] 3. Near-field measurement The near-field (NF) information of the target is measured and assisted by the near-field-far-field transformation (NFFFT) algorithm to obtain the test results of the far-field RCS. The usual post-processing algorithms are divided into imaging approximation algorithms and full-wave algorithms. The imaging approximation algorithm uses the single-station measurement information of the near field to extrapolate the single-station information of the target in the far field. When it comes to multiple scattering and other complex coupling effects of some complex targets, the approximate method may not provide accurate calculation results. The full-wave method requires measuring the two-station results of the near field, and uses the plane-wave synthesis (PWS) method to make the field distribution in a certain area approximate to the state of plane wave incidence. Since the full-wave method starts from the spectrum expansion and there is no approximation in theory, the result of its extrapolation algorithm is more accurate. When there is a high accuracy requirement for the measurement results, the full-wave algorithm is usually used for near-far field conversion.

[0006] Although the full-wave method of dual-station measurement has higher accuracy, it has higher requirements on the distance, range and distribution form of antenna distribution. The method of using a specific wave function expansion to calculate the near-field extrapolation can effectively reduce the distribution range of the antenna. At the same time, the Fast Fourier Transform (FFT) can quickly solve the inverse problem and obtain the result of near-field extrapolation. However, the near-field sampling points of these methods can only be distributed on regular classical measurement surfaces, such as spheres, cylinders and planes. If there is a certain offset between the near-field measurement points and the classical measurement surface, it will significantly affect the calculation accuracy. The Fast-Irregular Antenna Field Transformation Algorithm (FIAFTA) uses equivalent current, plane wave spectrum or spherical wave spectrum as unknowns for calculation. Since the algorithm itself does not require special wave function expansion, the near-field sampling points can be arbitrarily distributed within the effective range of solving the single-direction plane wave spectrum, which reduces the difficulty of arranging the sampling points during the test process. At the same time, it has strong robustness to the truncation of the sampling area and can reduce the range of the near-field sampling area.

[0007] The near-field dual-station measurement technology can test the far-field RCS at a relatively close distance to the target, thereby reducing the size of the microwave darkroom and significantly reducing the construction cost. However, its advantage comes at the cost of a large number of dual-station tests. When performing near-field RCS measurement in a certain incident direction of the target, it is necessary to synthesize incident waves from multiple different incident directions within an angular space range around this incident direction into a plane wave in a single direction, and for each incident wave, it is necessary to measure the dual-station near field within an angular space range around it. Therefore, when the near field is extrapolated to the far-field RCS, N×M extrapolation calculations are required, where N is the number of single-station RCS calculations and M is the number of transmitting antennas required for plane wave synthesis.

[0008] When performing near-field extrapolation calculations, existing methods all use the least squares method to construct an equivalent positive definite equation of the original problem, and then solve the plane wave spectrum solution of the original problem by inverting the equation. The GMRES iterator is generally used for inversion, which is very time-consuming, especially when the equation converges slowly. At the same time, a complete RCS measurement requires a large amount of extrapolation inversion calculations, which means that most of the overall calculation time is spent on the iterative inversion process. Summary of the invention

[0009] In view of the above-mentioned deficiencies in the prior art, the fast near-field extrapolated RCS calculation method based on the back-propagation method provided by the present invention solves the problem that the existing near-field extrapolated RCS calculation method is time-consuming.

[0010] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0011] A fast near-field extrapolated RCS calculation method based on back propagation method is provided, which comprises the following steps:

[0012] S1. Determine the location distribution and number of transmitting antennas and calculate the transmission coefficient of each transmitting antenna;

[0013] S2. For each transmitting antenna, establish a receiving antenna array and measure the electric field value of each receiving antenna;

[0014] S3, establishing a tangential electric field equation based on the electric field value and position distribution of the receiving antenna as input for near-field extrapolation;

[0015] S4, solving the tangential electric field equation based on the back propagation method to obtain the far-field electric field value in the target direction;

[0016] S5, multiplying the emission coefficient of each transmitting antenna by the far-field electric field value in the target direction and superimposing them to obtain the total far-field electric field value in the target direction;

[0017] S6. Calculate the far-field radar cross section based on the total far-field electric field value in the target direction and complete the near-field extrapolated RCS calculation.

[0018] Furthermore, the specific method of determining the position distribution and number of transmitting antennas and calculating the transmission coefficient of each transmitting antenna in step S1 includes the following sub-steps:

[0019] S1-1. Determine the position distribution of M transmitting antennas according to the interval requirement of Nyquist sampling theorem and the range requirement of projection theorem;

[0020] S1-2. Calculate the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at field point r;

[0021] S1-3. Establish an equation expression for plane wave synthesis based on the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at the field point r;

[0022] S1-4. Solve the plane wave synthesis equation to obtain the transmission coefficient of each transmitting antenna.

[0023] Furthermore, in step S1-2, the unit radiation electric field E of the mth transmitting antenna at the field point r is m (r) and unit radiation magnetic field H m The calculation expressions of (r) are:

[0024]

[0025]

[0026] Where e is a natural constant; j is an imaginary unit; k is a wave number; is the unit vector of the plane wave expansion; r O is the center coordinate of the box where the target is located; D t is the distance from the center of the box where the target is located to each transmitting antenna; T L (.) represents the transfer function of the plane wave, The plane spectrum of the equivalent current source generated by the unit excitation at the mth antenna is formed by the aggregation of the equivalent current generated by the unit excitation at the mth transmitting antenna. The aggregation range is the box where the transmitting antennas are aggregated. Indicates a symmetric arrow; Represents the unit sphere Differentiation; L is the upper limit of the summation, It means rounding up, d is the maximum side length of the box where the transmitting antennas are gathered, d0 is the accuracy parameter; l is a constant; is the second kind of Hankel function; P l (.) is the Legendre function; D t The corresponding unit direction vector; Z0 is the free space wave impedance; ω represents the angular frequency corresponding to the incident frequency; μ represents the air magnetic permeability; represents the unit vector; r' is the integral point in the volume region where the equivalent current source generated by the unit excitation at the transmitting antenna is located, that is, the source point; J m (r') represents the equivalent surface current at the source point; r S is the coordinate of the center of the box where the transmitting antenna is gathered; ∫∫∫(·)dV' represents the integration of the volume area V' where the equivalent current source generated by unit excitation at the transmitting antenna is located; π is the pi.

[0027] Furthermore, the equation expression of the plane wave synthesis in step S1-3 is:

[0028]

[0029] where a m is the transmission coefficient of the mth transmitting antenna; E syn (r) is the electric field required for testing at the field point r; H syn (r) is the magnetic field required for testing at field point r.

[0030] Furthermore, the expression of the tangential electric field equation in step S3 is:

[0031]

[0032] in is the electric field component in the θ direction measured by the qth receiving antenna; is the value measured by the qth receiving antenna Directional electric field component; K is the effective plane wave spectrum number in the box; is the unit vector of the qth receiving antenna in the θ direction; is the qth receiving antenna at Unit vector of direction; The plane wave spectrum of the target is The near-field electric field value presented in the direction, The relationship between the plane wave spectrum and its corresponding coefficients is:

[0033]

[0034]

[0035] where b kθ and is the plane wave spectrum coefficient, is the parameter to be solved; is a plane wave spectrum; D r is the distance from the center of the box where the target is located to each receiving antenna; D r The corresponding unit direction vector.

[0036] Furthermore, in step S4, the specific method of solving the tangential electric field equation based on the back propagation method to obtain the far-field electric field value in the target direction includes the following sub-steps:

[0037] S4-1. Rewrite the tangential electric field equation into the following matrix form:

[0038] [G]{b}={E}

[0039] Where [G] is a K×Q dimensional linear matrix constructed by the tangential electric field equation; {b} is a column vector, which is composed of b kθ and Composition; {E} is Column vector of ;

[0040] S4-2. According to the principle of back propagation, an expression is constructed that the plane wave spectrum excited by the incident wave is approximately proportional to the near-field value back propagated to the target position:

[0041] {b}≈γ[G] H {E}

[0042] where γ is the ratio of the plane wave spectrum to the back propagation field value; [G] H is the conjugate transpose of [G];

[0043] S4-3, taking the second-order error of the scattered field as the cost function, solving γ with the minimum cost function, and then directly obtaining the plane wave spectrum coefficient b from the expression in step S4-2 kθ and

[0044] S4-4, the plane wave spectrum coefficient b kθ and Transfer to the center of the observation coordinate system and get the θ direction or The far-field electric field component in the direction;

[0045] S4-5. Perform Lagrangian linear interpolation on the plane wave spectrum of four points around the target direction to obtain the far-field electric field value in the target direction.

[0046] Furthermore, the expression of the cost function in step S4-3 is:

[0047] F(γ)=||{E}-[G]γ[G] H {E}|| 2

[0048] Where F(γ) is the cost function; ||.|| 2 represents the two-norm of a vector;

[0049] The solution expression of γ in step S4-3 is:

[0050]

[0051] Where <,> represents inner product calculation.

[0052] Further, the θ direction or The expression of the far-field electric field component in the direction is:

[0053]

[0054] in is the θ direction or The far-field electric field component in the direction of r c is the center coordinate of the target;

[0055]

[0056] Furthermore, the calculation expression of the far-field electric field value in the target direction in step S4-5 is:

[0057]

[0058] in is the far-field electric field value in the target direction; ω i is the Lagrange interpolation coefficient of point i; is the θ direction of point i or The far-field electric field component in the direction of

[0059] Furthermore, the calculation expression of the far-field radar cross section in step S6 is:

[0060]

[0061] in is the far-field radar cross section; is the total far-field electric field value in the target direction.

[0062] The beneficial effects of the present invention are as follows: based on the principle of back propagation (BP, Back Propagation), the method can quickly solve the approximate inverse of the near-field extrapolation problem, greatly reducing the time of each extrapolation calculation and greatly improving the overall single-station RCS near-field extrapolation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a schematic diagram of the process of this method;

[0064] Figure 2 This is the model schematic diagram of Example 1;

[0065] Figure 3 This is the RCS result diagram of a single station using different near-field extrapolation methods under the condition of a near-field test distance of 10m in Example 1;

[0066] Figure 4 is the root mean square error of the two near-field extrapolation methods at different near-field test distances in Example 1;

[0067] Figure 5 is the model schematic diagram of Example 2;

[0068] Figure 6 This is the RCS result diagram of a single station using different near-field extrapolation methods in Example 2 under the condition that the near-field test distance is 70m. DETAILED DESCRIPTION

[0069] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0070] like Figure 1 As shown, the fast near-field extrapolation RCS calculation method based on the back propagation method (BP-NFFFT method) includes the following steps:

[0071] S1. Determine the location distribution and number of transmitting antennas and calculate the transmission coefficient of each transmitting antenna;

[0072] S2. For each transmitting antenna, establish a receiving antenna array and measure the electric field value of each receiving antenna;

[0073] S3, establishing a tangential electric field equation based on the electric field value and position distribution of the receiving antenna as input for near-field extrapolation;

[0074] S4, solving the tangential electric field equation based on the back propagation method to obtain the far-field electric field value in the target direction;

[0075] S5, multiplying the emission coefficient of each transmitting antenna by the far-field electric field value in the target direction and superimposing them to obtain the total far-field electric field value in the target direction;

[0076] S6. Calculate the far-field radar cross section based on the total far-field electric field value in the target direction and complete the near-field extrapolated RCS calculation.

[0077] The specific method of determining the position distribution and number of transmitting antennas and calculating the transmission coefficient of each transmitting antenna in step S1 includes the following sub-steps:

[0078] S1-1. Determine the position distribution of M transmitting antennas according to the interval requirement of Nyquist sampling theorem and the range requirement of projection theorem;

[0079] S1-2. Calculate the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at field point r;

[0080] S1-3. Establish an equation expression for plane wave synthesis based on the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at the field point r;

[0081] S1-4. Solve the plane wave synthesis equation to obtain the transmission coefficient of each transmitting antenna.

[0082] The unit radiation electric field E of the mth transmitting antenna at the field point r in step S1-2 m (r) and unit radiation magnetic field H m The calculation expressions of (r) are:

[0083]

[0084]

[0085] Where e is a natural constant; j is an imaginary unit; k is a wave number; is the unit vector of the plane wave expansion; r O is the center coordinate of the box where the target is located; Dt is the distance from the center of the box where the target is located to each transmitting antenna; T L (.) represents the transfer function of the plane wave, The plane wave spectrum of the equivalent current source generated by the unit excitation at the mth antenna is formed by the aggregation of the equivalent current generated by the unit excitation at the mth transmitting antenna. The aggregation range is the box where the transmitting antennas are aggregated. Indicates a symmetric arrow; Represents the unit sphere Differentiation; L is the upper limit of the summation, It means rounding up, d is the maximum side length of the box where the transmitting antennas are gathered, d0 is the accuracy parameter; l is a constant; is the second kind of Hankel function; P l (.) is the Legendre function; D t The corresponding unit direction vector; Z0 is the free space wave impedance; ω represents the angular frequency corresponding to the incident frequency; μ represents the air magnetic permeability; represents the unit vector; r' is the integral point in the volume region where the equivalent current source generated by the unit excitation at the transmitting antenna is located, that is, the source point; J m (r') represents the equivalent surface current at the source point; r S is the coordinate of the center of the box where the transmitting antenna is gathered; ∫∫∫(·)dV' represents the integration of the volume area V' where the equivalent current source generated by unit excitation at the transmitting antenna is located; π is the pi.

[0086] In E m (r) and H m In the process of solving (r), the equivalent current generated by unit excitation at the transmitting antenna is known (which can be obtained through the radiation mode of the transmitting antenna when it is working). First, The gathering operation gathers the equivalent current generated by the unit excitation at the transmitting antenna into a center of r S The plane wave spectrum of the collection is generally called a box, which is a cubic range with a side length of d; T L (k,x) is generally called the transfer operation, which transfers the plane wave from the center to r S The box is transferred to the center r O Box; It is called the divergence operation, which takes the center as r O The plane wave is converted into the field value at the sampling point. Through the whole process, the unit radiation electric field or unit radiation magnetic field at any point in space can be obtained from the unit excitation at the transmitting antenna.

[0087] The equation expression of the plane wave synthesis in step S1-3 is:

[0088]

[0089] where a m is the transmission coefficient of the mth transmitting antenna; E syn (r) is the electric field required for testing at the field point r; H syn (r) is the magnetic field required for testing at field point r.

[0090] In the plane wave synthesis equation, the unit radiation electromagnetic field of each transmitting antenna on the test basis function is a known quantity, and the plane wave electromagnetic field expression that is ultimately desired to be synthesized is the right-hand term to solve the transmission coefficient of each transmitting antenna.

[0091] In order to solve the synthesis problem in numerical calculation, a test function can be established at the boundary of the test area and the boundary conditions can be tested. The expression is:

[0092]

[0093] Where M is the total number of transmitting antennas; β p (r) is the test function, which is defined on the envelope S of the plane wave synthesis area. Generally, the RWG basis function is used. The number of discrete basis functions of the envelope S of the plane wave synthesis area is P. This expression can establish an M×P dimensional linear matrix C for solution. However, since the matrix is ​​not a reversible matrix, an approximate solution method is required to minimize the root mean square error of the problem. The expression is:

[0094]

[0095] The C matrix is ​​the matrix formed by the left side of the test boundary condition expression; x is a m a is the column vector of the calculation result on the right side of the test boundary condition expression; b is the column vector of the calculation result on the right side of the test boundary condition expression; the expression of this approximate solution method can be equivalent to the solution equation:

[0096] C H Cx=C H b

[0097] Cx=b

[0098] The result of H is the conjugate transposed matrix of C. This equation can be solved using the GMRES iterator.

[0099] In the specific implementation process, the commercial CAD software CATIA can be used to establish the plane wave synthesis area covering the target and segment the regional envelope surface. The segmentation size is 0.4 times the wavelength of the incident wave. The envelope surface of the plane wave synthesis area is used to establish the electromagnetic field equation (E m(r) and H m The calculation expression of (r) is used to establish the test boundary conditions (the equation expression of plane wave synthesis is the equation constructed based on the boundary conditions).

[0100] When constructing the plane wave synthesis equation, the basis function initially discretized on the surface of the plane wave synthesis area is used as the test function. In the equation, the unit radiation electromagnetic field of each transmitting antenna on the test basis function is a known quantity, and the plane wave electromagnetic field expression that is ultimately desired to be synthesized is the right-hand term to solve the emission coefficient of each antenna. Based on the emission coefficient of each antenna and its unit radiation electromagnetic field at any field point, the equivalent plane wave excitation required for RCS testing can be synthesized.

[0101] The expression of the tangential electric field equation in step S3 is:

[0102]

[0103] in is the electric field component in the θ direction measured by the qth receiving antenna; is the value measured by the qth receiving antenna Directional electric field component; K is the effective plane wave spectrum number in the box; is the unit vector of the qth receiving antenna in the θ direction; is the qth receiving antenna at The unit vector of the direction and the field value test results of the receiving antenna 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 of the target is The near-field electric field value presented in the direction, The relationship between the plane wave spectrum and its corresponding coefficients is:

[0104]

[0105]

[0106] where b kθ and is the plane wave spectrum coefficient, is the parameter to be solved; is a plane wave spectrum; D r is the distance from the center of the box where the target is located to each receiving antenna; D r The corresponding unit direction vector.

[0107] In step S4, the specific method of solving the tangential electric field equation based on the back propagation method to obtain the far-field electric field value in the target direction includes the following sub-steps:

[0108] S4-1. Rewrite the tangential electric field equation into the following matrix form:

[0109] [G]{b}={E}

[0110] Where [G] is a K×Q dimensional linear matrix constructed by the tangential electric field equation; {b} is a column vector, which is composed of b kθ and Composition; {E} is Column vector of ;

[0111] S4-2. According to the principle of back propagation, an expression is constructed that the plane wave spectrum excited by the incident wave is approximately proportional to the near-field value back propagated to the target position:

[0112] {b}≈γ[G] H {E}

[0113] where γ is the ratio of the plane wave spectrum to the back propagation field value; [G] H is the conjugate transpose of [G], [G] H It means mapping the scattered field measured in the near field area to the plane wave spectrum of the target area;

[0114] S4-3, taking the second-order error of the scattered field as the cost function, solving γ with the minimum cost function (equivalent to setting the partial derivative of the cost function with respect to γ ​​to 0), and then directly obtaining the plane wave spectrum coefficient b from the expression in step S4-2 kθ and

[0115] S4-4, the plane wave spectrum coefficient b kθ and Transfer to the center of the observation coordinate system and get the θ direction or The far-field electric field component in the direction;

[0116] S4-5. Perform Lagrangian linear interpolation on the plane wave spectrum of four points around the target direction to obtain the far-field electric field value in the target direction.

[0117] The expression of the cost function in step S4-3 is:

[0118] F(γ)=||{E}-[G]γ[G] H {E}|| 2

[0119] Where F(γ) is the cost function; ||.|| 2 represents the two-norm of a vector;

[0120] The solution expression of γ in step S4-3 is:

[0121]

[0122] Where <,> represents inner product calculation.

[0123] S4-4 obtains the θ direction or The expression of the far-field electric field component in the direction is:

[0124]

[0125] in is the θ direction or The far-field electric field component in the direction of r c is the center coordinate of the target; Essentially, the θ direction or The far-field electric field component in the direction is the plane spectral coefficient Multiply by the phase shift factor The result after.

[0126] For the far-field electric field in the target direction, since the Green function is quite smooth in the far field, it is only necessary to perform Lagrange linear interpolation on the plane wave spectrum and consider the coefficients of the plane wave spectrum at four points around the target direction. Therefore, the calculation expression of the far-field electric field value in the target direction in step S4-5 is:

[0127]

[0128] in is the far-field electric field value in the target direction; ω i is the Lagrange interpolation coefficient of point i; is the θ direction of point i or The far-field electric field component in the direction of

[0129] The calculation expression of the far-field radar cross section in step S6 is:

[0130]

[0131] in is the far-field radar cross section; is the total far-field electric field value in the target direction.

[0132] In the prior art, when solving the far-field electric field in the target direction, the equation (C H Cx=C H b, Cx = b) constructs a positive definite matrix and uses the GMRES iterator to solve it, which takes a long time to calculate. This method uses the back propagation method to obtain an approximate solution to the original equation, without the need for an iterative inversion process, while retaining good accuracy.

[0133] In one embodiment of the present invention, the flying object model established is as follows: Figure 2As shown, the flying object is 2.2m long and is covered by an equivalent cylindrical surface with a diameter of 3m as the comprehensive test area. The distance between the target center and the near-field test area is D min This example mainly explores the influence of the near-field test distance on the accuracy of near-field to far-field conversion. The subdivision size of the comprehensive test area is 0.4 times the free space electrical wavelength. The frequency of the plane wave is 1GHz, and the horizontal incident angle range is θ=90°, The accuracy of the single-station test result is compared with the far-field scattering result of the missile model directly calculated at the corresponding angle in free space. The near-field measurement points of the dual-station are distributed in a circle with a radius of D and a center of the target. min On the sphere, the distribution range is θ∈[65°,115°], The measurement interval is 2.6°.

[0134] Figure 3 Given the near field test distance D min = 10m, the results of the classical near-far field extrapolation using the inversion method (Standard NFFFT method) and the results using this method are compared with the exact results of the forward calculation (SIE method). Figure 3 It can be seen that the two near-field and far-field conversion methods are relatively close to the exact results, but the calculation time of this method is 11.656s, while the calculation time of the standard NFFFT method is 62.657s, which is more than five times that of this method.

[0135] Then, this embodiment calculates the single-station root mean square error of the target at different near-field test distances as follows: Figure 4 The formula for calculating the root mean square error is:

[0136]

[0137] Where A is the root mean square error, N is the total number of sampling points at a single station; σ cal is the RCS result obtained by near-field extrapolation calculation of an infinite metal plate; σ ref This is the far-field RCS result directly calculated by the SIE method in free space. Figure 4 It can be found that as the test distance increases, the root mean square error of both methods decreases significantly. At the same time, the root mean square error of this method is slightly higher than that of the standard NFFFT method, because the accuracy of the approximate inverse is not as high as that of the direct inverse method. However, the root mean square error of both methods is less than 3dB, so both meet the accuracy requirements.

[0138] In the embodiment, it is also established that Figure 5The model of the US stealth bomber B2 is shown. The wingspan of the B2 bomber is 30m and the height is 4.5m. The plane wave integration area is slightly larger than the wingspan of the aircraft, which is a cylinder with a radius of 32m and a height of 4.5m. Its segmentation size is 0.4 times the free space electrical wavelength. The aircraft can rotate in this area for near-field measurement. The calculation frequency is 150MHz, and the calculation θ=90°, The single-station scattering of the angle range is calculated to be 32 electrical wavelengths. The near-field measurement points of the two-station near-field extrapolation are distributed on a spherical surface with a radius of 70m. When performing single-station RCS extrapolation, the angle of θ in the near-field sampling range is 25°. The angle of the direction is 35° and the sampling interval is 1.8°. The calculation results are as follows Figure 6 As shown in the figure, it can be seen that the results of this method and the standard NFFFT method are consistent with the results of the SIE method scattering calculation, which proves the reliability of this method in solving NFFFT in terms of accuracy. After calculating the root mean square error, the error of this method is 2.14dB, while the error of the standard NFFFT method is 2.12dB, and the errors of the two are very close. For this large-scale example, the standard NFFFT method takes 12 minutes and 2 seconds, while this method takes 1m37 seconds, which greatly improves efficiency. The standard NFFFT method requires 7 iterations for each extrapolation calculation, while the process of solving the approximate inverse by this method can be equivalent to the calculation amount of 1 iteration, which greatly reduces the calculation time.

[0139] In summary, this method greatly improves the calculation time without significantly decreasing the accuracy.

Claims

1. A fast near-field extrapolated RCS calculation method based on back propagation method, characterized in that: The following steps are involved: S1. Determine the location distribution and number of transmitting antennas and calculate the transmission coefficient of each transmitting antenna; S2. For each transmitting antenna, establish a receiving antenna array and measure the electric field value of each receiving antenna; S3, establishing a tangential electric field equation based on the electric field value and position distribution of the receiving antenna as input for near-field extrapolation; S4, solving the tangential electric field equation based on the back propagation method to obtain the far-field electric field value in the target direction; S5, multiplying the emission coefficient of each transmitting antenna by the far-field electric field value in the target direction and superimposing them to obtain the total far-field electric field value in the target direction; S6. Calculate the far-field radar cross section based on the total far-field electric field value in the target direction and complete the near-field extrapolated RCS calculation.

2. The fast near-field extrapolation RCS calculation method based on the back propagation method according to claim 1 is characterized in that: The specific method of determining the position distribution and number of transmitting antennas and calculating the transmission coefficient of each transmitting antenna in step S1 includes the following sub-steps: S1-1. Determine the position distribution of M transmitting antennas according to the interval requirement of Nyquist sampling theorem and the range requirement of projection theorem; S1-2. Calculate the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at field point r; S1-3. Establish an equation expression for plane wave synthesis based on the unit radiation electric field and unit radiation magnetic field of each transmitting antenna at the field point r; S1-4. Solve the plane wave synthesis equation to obtain the transmission coefficient of each transmitting antenna.

3. The fast near-field extrapolation RCS calculation method based on the back propagation method according to claim 2 is characterized in that: The unit radiation electric field E of the mth transmitting antenna at the field point r in step S1-2 m (r) and unit radiation magnetic field H m The calculation expressions of (r) are: Where e is a natural constant; j is an imaginary unit; k is a wave number; is the unit vector of the plane wave expansion; r O is the center coordinate of the box where the target is located; D t is the distance from the center of the box where the target is located to each transmitting antenna; T L (.) represents the transfer function of the plane wave, The plane spectrum of the equivalent current source generated by the unit excitation at the mth antenna is formed by the aggregation of the equivalent current generated by the unit excitation at the mth transmitting antenna. The aggregation range is the box where the transmitting antennas are aggregated. Indicates a symmetric arrow; Represents the unit sphere Differentiation; L is the upper limit of the summation, It means rounding up, d is the maximum side length of the box where the transmitting antennas are gathered, d0 is the accuracy parameter; l is a constant; is the second kind of Hankel function; P l (.) is the Legendre function; D t The corresponding unit direction vector; Z0 is the free space wave impedance; ω represents the angular frequency corresponding to the incident frequency; μ represents the air magnetic permeability; represents the unit vector; r' is the integral point in the volume region where the equivalent current source generated by the unit excitation at the transmitting antenna is located, that is, the source point; J m (r') represents the equivalent surface current at the source point; r S is the coordinate of the center of the box where the transmitting antenna is gathered; ∫∫∫(·)dV' represents the integration of the volume area V' where the equivalent current source generated by unit excitation at the transmitting antenna is located; π is the pi.

4. The fast near-field extrapolation RCS calculation method based on the back propagation method according to claim 3 is characterized in that: The equation expression of the plane wave synthesis in step S1-3 is: where a m is the transmission coefficient of the mth transmitting antenna; E syn (r) is the electric field required for testing at field point r; H syn (r) is the magnetic field required for testing at field point r.

5. The fast near-field extrapolation RCS calculation method based on back propagation method according to claim 3 is characterized in that: The expression of the tangential electric field equation in step S3 is: in is the electric field component in the θ direction measured by the qth receiving antenna; is the value measured by the qth receiving antenna Directional electric field component; K is the effective plane wave spectrum number in the box; is the unit vector of the qth receiving antenna in the θ direction; is the qth receiving antenna at Unit vector of direction; The plane wave spectrum of the target is The near-field electric field value presented in the direction, The relationship between the plane wave spectrum and its corresponding coefficients is: where b kθ and is the plane wave spectrum coefficient, is the parameter to be solved; is a plane wave spectrum; D r is the distance from the center of the box where the target is located to each receiving antenna; D r The corresponding unit direction vector.

6. The fast near-field extrapolation RCS calculation method based on back propagation method according to claim 5 is characterized in that: In step S4, the specific method of solving the tangential electric field equation based on the back propagation method to obtain the far-field electric field value in the target direction includes the following sub-steps: S4-1. Rewrite the tangential electric field equation into the following matrix form: [G]{b}={E} Where [G] is a K×Q dimensional linear matrix constructed by the tangential electric field equation; {b} is a column vector, which is composed of b kθ and Composition; {E} is Column vector of ; S4-2. According to the principle of back propagation, an expression is constructed that the plane wave spectrum excited by the incident wave is approximately proportional to the near-field value back propagated to the target position: {b}≈γ[G] H {E} where γ is the ratio of the plane wave spectrum to the back propagation field value; [G] H is the conjugate transpose of [G]; S4-3, taking the second-order error of the scattered field as the cost function, solving γ with the minimum cost function, and then directly obtaining the plane wave spectrum coefficient b from the expression in step S4-2 kθ and S4-4, the plane wave spectrum coefficient b kθ and Transfer to the center of the observation coordinate system and get the θ direction or The far-field electric field component in the direction; S4-5. Perform Lagrangian linear interpolation on the plane wave spectrum of four points around the target direction to obtain the far-field electric field value in the target direction.

7. The fast near-field extrapolation RCS calculation method based on back propagation method according to claim 6 is characterized in that: The expression of the cost function in step S4-3 is: F(γ)=||{E}-[G]γ[G] H {E}|| 2 Where F(γ) is the cost function; ||.|| 2 represents the two-norm of a vector; The solution expression of γ in step S4-3 is: Where <,> represents inner product calculation.

8. The fast near-field extrapolation RCS calculation method based on back propagation method according to claim 6 is characterized in that: S4-4 obtains the θ direction or The expression of the far-field electric field component in the direction is: in is the θ direction or The far-field electric field component in the direction of r c is the center coordinate of the target; 9. The fast near-field extrapolation RCS calculation method based on back propagation method according to claim 8 is characterized in that: The calculation expression of the far-field electric field value in the target direction in step S4-5 is: in is the far-field electric field value in the target direction; ω i is the Lagrange interpolation coefficient of point i; is the θ direction of point i or The far-field electric field component in the direction of 10. The fast near-field extrapolation RCS calculation method based on back propagation method according to claim 9 is characterized in that: The calculation expression of the far-field radar cross section in step S6 is: in is the far-field radar cross section; is the total far-field electric field value in the target direction.

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