Modeling method of parameterized model for calculating chaff cloud and target composite electromagnetic scattering

Abstract

The invention discloses a modeling method of a parameterized model for calculating chaff cloud and target composite electromagnetic scattering, which comprises the following steps: S1, acquiring chaff cloud geometric parameters including the bottom radius, length, position coordinate, orientation angle and space density distribution of chaff and a parameterized scattering center model of a target; s2, based on chaff cloud geometric parameters and a target parameterized scattering center model, calculating a chaff cloud forward scattering electric field, a chaff cloud back scattering electric field and a target back scattering field through vector superposition; s3, based on the forward scattering electric field, the backward scattering electric field and the target backward scattering field of the chaff cloud cluster test model, the transmittance, the forward scattering coefficient and the backward scattering coefficient of chaff cloud are determined through genetic algorithm fitting; s4, on the basis of the transmittance, the forward scattering coefficient, the backward scattering coefficient and the relative distance between the target and the chaff cloud, the echo electric field intensity of each path is calculated according to a nine-scattering-path mechanism; and S5, based on the echo electric field intensity of each path, obtaining a composite scattering total field through complex field vector superposition.

Description

Technical Field

[0001] This invention relates to the field of parametric modeling technology, and in particular to a parametric modeling method for calculating the combined electromagnetic scattering of chaff clouds and targets. Background Technology

[0002] Deploying chaff in aerial combat is one of the effective means for targets to provide self-protection. In modern air combat, the complex multipath scattering of chaff and targets is a key technology in electronic warfare. Through multiple reflections, refractions, and diffractions of electromagnetic waves between the chaff, the target, and the environment, complex signal propagation paths are formed, significantly enhancing the jamming effect or confusing enemy radar. In the initial stages of chaff deployment, to achieve effective jamming, the chaff and the target must be within the same radar field of view. In this situation, an electromagnetic coupling effect exists between the target and the chaff.

[0003] The composite scattering of a target and a chaff cloud requires consideration of the obstruction effect between multiple targets. For example, when the chaff cloud is in front of the target, its scattered signal may be obstructed by the target's fuselage; conversely, if the chaff cloud is to the side, it may enhance composite scattering. The contribution of the obstruction region to composite scattering can be accurately calculated using the ray tracing (SBR) algorithm combined with geometrical optics (GO) methods. Existing techniques have statistically rewritten the ray tracing method to align with vector radiative transfer (VRT) theory, discretizing the incident wave into a series of particles carrying the frequency, polarization, and phase information of the incident wave. These particles interact electromagnetically with the target based on the principle of ray independence and Fresnel's law of reflection. The movement of particles between the chaff cloud and the target can be accounted for, as the particle's movement, attenuation, and electromagnetic interactions with the chaff or target will affect the information carried by the particles.

[0004] In the SBR algorithm, accurate determination of the occlusion relationship between rays, targets, and chaff is crucial. However, the accuracy and efficiency of occlusion determination are affected by multiple occlusions and mutual occlusions in complex scenes. The electromagnetic coupling effect between chaff and targets is difficult to handle precisely in the SBR-VRT method. This coupling effect can lead to deviations in scattering results, especially when the chaff cloud is close to the target. While the SBR algorithm is efficient in handling scattering from electrically large targets, it involves complex ray tracing and patch partitioning. For targets with complex geometries, the algorithm's implementation and computational complexity increase significantly. Vector radiative transfer theory needs to consider multiple scattering and coupling effects between chaff, requiring the establishment of complex scattering field equations and solving them using Monte Carlo methods, further increasing the algorithm's complexity. To handle scattering calculations from large-scale chaff clouds, parallel computing techniques are required. However, the parallelization process itself increases the difficulty of programming and debugging and requires high-performance computing resources.

[0005] Therefore, there is an urgent need for a parameterized modeling method to calculate the combined electromagnetic scattering of chaff clouds and targets. Summary of the Invention

[0006] This invention provides a parameterized modeling method for calculating the combined electromagnetic scattering of chaff clouds and targets, in order to solve the aforementioned problems existing in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A parameterized modeling method for calculating the combined electromagnetic scattering between chaff clouds and a target includes:

[0009] S1: Obtain the geometric parameters of the chaff cloud, including the bottom radius, length, position coordinates, orientation angle and spatial density distribution of the chaff, as well as the parameterized scattering center model of the target;

[0010] S2: Based on the geometric parameters of the chaff cloud and the parameterized scattering center model of the target, the forward scattering electric field, the backscattering electric field of the chaff cloud and the backscattering field of the target are calculated by vector superposition;

[0011] S3: Based on the forward scattering electric field, backscattering electric field, and target backscattering field of the chaff cloud test model, the transmittance, forward scattering coefficient, and backscattering coefficient of the chaff cloud are determined by fitting using a genetic algorithm.

[0012] S4: Based on transmittance, forward scattering coefficient, back scattering coefficient and the relative distance between the target and the chaff cloud, calculate the echo electric field intensity of each path according to the nine scattering path mechanism;

[0013] S5: Based on the electric field intensity of the echoes from each path, the total composite scattering field is obtained by superimposing vectors in the complex domain.

[0014] Step S1 includes:

[0015] S11: Obtain the bottom radius a, length L, geometric center coordinates, pitch angle, and azimuth angle parameters of a single foil strip;

[0016] S12: Based on the parameters of a single foil strip, determine the spatial distribution of the foil cloud according to the spatial distribution function and the number of foil strips per unit volume;

[0017] S13: Based on the target's geometric structure characteristics, the target is decomposed into a combination of distributed scattering centers, localized scattering centers, and sliding scattering centers.

[0018] Step S2 includes:

[0019] S21: Based on the geometric parameters and orientation angle of each foil strip, calculate the forward-scattered electric field component of a single foil strip using the forward scattering formula for a cylinder;

[0020] S22: Based on the forward scattering electric field components of a single foil strip, the total forward scattering electric field of the foil cloud is obtained by vector summation in the complex domain;

[0021] S23: Calculate the backscattered electric field components of a single foil strip using the cylindrical backscattering formula and perform vector summation to obtain the total backscattered electric field of the foil cloud;

[0022] S24: Based on the three types of scattering center parameters of the target, calculate the scattering electric field of each scattering center and superimpose them to obtain the total backscattering electric field of the target.

[0023] Step S3 includes:

[0024] S31: Construct a test model of a small-sized foil cloud with the same density and orientation distribution as the target;

[0025] S32: Based on the forward scattering electric field, backscattering electric field, and target backscattering field of the test model, transmittance, forward scattering coefficient, and backscattering coefficient are set as variables to be optimized;

[0026] S33: Using the root mean square error of radar cross section and the correlation coefficient of inverse synthetic aperture radar image as fitness functions, the optimal parameter values ​​are determined through iterative optimization using a genetic algorithm.

[0027] Step S4 includes:

[0028] S41: Determine the propagation distance of the nine scattering paths based on the relative distance between the chaff cloud and the target and the radar distance;

[0029] S42: Based on the propagation distance, transmittance, forward scattering coefficient, backscattering coefficient, chaff forward radar cross section, chaff back radar cross section, and target back radar cross section, calculate the electric field intensity according to the formula for each path;

[0030] S43: Based on wavenumber and radar line-of-sight vector, phase delay and range attenuation corrections are applied to the electric field intensity of each path.

[0031] The nine scattering paths include:

[0032] Path 1: The single-station echo of the chaff cloud. The expression for the electric field intensity of the radar echo generated by this path is:

[0033] ;

[0034] Path 2: The target's single-station echo. The expression for the electric field intensity of the radar echo generated by this path is:

[0035] ;

[0036] Path 3: Source foil cloud Target The electric field intensity expression for the radar echo generated by this path is:

[0037] ;

[0038] Path 4: Source foil cloud Target foil cloud The electric field intensity expression for the radar echo generated by this path is:

[0039] ;

[0040] Path 5: Source Target foil cloud The electric field intensity expression for the radar echo generated by this path is:

[0041] ;

[0042] Path 6: Source foil cloud Target foil cloud Target The electric field intensity expression for the radar echo generated by this path is:

[0043] ;

[0044] Path 7: Source foil cloud Target foil cloud Target foil cloud The electric field intensity expression for the radar echo generated by this path is:

[0045] ;

[0046] Path 8: Source Target foil cloud Target The electric field intensity expression for the radar echo generated by this path is:

[0047] ;

[0048] Path 9: Source-Target-Chaff Cloud-Target-Chaff Cloud-Source. The electric field intensity expression for the radar echo generated by this path is:

[0049] ;

[0050] Where τ is the forward scattering coefficient and δ is the backscattering coefficient. Forward RCS of the foil strip, For the target's backward RCS, The rearward RCS of chaff refers to the rearward radar cross-section of a single chaff strip or the entire chaff cloud. The distance between the foil cloud and the plane of the electromagnetic source is [missing information]. The distance between the chaff cloud and the geometric center of the target. For radar line-of-sight vector, The imaginary unit, For wave number.

[0051] After determining the relevant parameters of the chaff cloud, the forward scattering electric field and the backscattering electric field of the chaff cloud are calculated.

[0052] Forward scattering formula for chaff clouds:

[0053] ,

[0054] Where j is the imaginary unit, k is the wave number, a is the radius of the cylinder's base, and L is the length of the cylinder. For the launch elevation angle, It is a unit vector in the direction of pitch angle. Directional factor;

[0055] Backscattering formula for foil clouds:

[0056]

[0057] Where j is the imaginary unit, k is the wave number, a is the radius of the cylinder's base, and L is the length of the cylinder's generatrix. The pitch angle, It is a unit vector in the direction of the pitch angle. Directional factor;

[0058] The forward and backward scattering fields of each foil strip are calculated based on the forward scattering formula and the backward scattering formula of the foil cloud. The calculated results are then vector-superimposed to obtain the overall forward and backward scattering fields of the foil cloud.

[0059] The calculation of the three types of scattering centers includes:

[0060] Distributed scattering center electric field DSC:

[0061] ;

[0062] Where j is the imaginary unit and k is the wave number. The pitch angle, Let be the normal vector of the surface element. For radar line-of-sight vector, The horizontal component of the radar line of sight on the target plane. This represents the vertical component of the radar line of sight on the target plane.

[0063] Localized scattering center electric field LSC: ;

[0064] Where j is the imaginary unit, k is the wave number, ξ represents the radar observation angle, including elevation and azimuth angles; f is the radar frequency; f c The radar center frequency; A0 represents the amplitude at the scattering center, which is a constant. These are usually unknown parameters, which can be estimated using optimization methods. This is the radar line-of-sight vector in the local coordinate system;

[0065] Sliding scattering center electric field SSC: ;

[0066] Where j is the imaginary unit and k is the wave number. This indicates the radar incident angle ξ. The radar observation angle is a comprehensive angle parameter that includes elevation and azimuth angles, representing the curvature of the two surfaces in the orthogonal direction at the effective reflection point of the hyperboloid; A0 is a constant term representing the amplitude, which can be obtained through parameter estimation, but has a definite value for typical geometries such as spheres or ellipsoids; for hyperboloid reflection, the frequency dependence factor α=0.

[0067] Step S5 includes:

[0068] S51: Obtain the corrected electric field strengths E1 to E9 for the nine paths;

[0069] S52: Calculate the total electric field of composite scattering based on the principle of electromagnetic field superposition. .

[0070] Compared with the prior art, the present invention has the following advantages:

[0071] A parameterized modeling method for calculating the combined electromagnetic scattering of chaff clouds and targets includes: S1: obtaining the geometric parameters of the chaff cloud, including the base radius, length, position coordinates, orientation angle, and spatial density distribution of the chaff, as well as the parameterized scattering center model of the target; S2: calculating the forward scattering electric field, backscattering electric field, and target backscattering field of the chaff cloud by vector superposition based on the geometric parameters of the chaff cloud and the parameterized scattering center model of the target; S3: determining the transmittance, forward scattering coefficient, and backscattering coefficient of the chaff cloud by fitting the forward scattering electric field, backscattering electric field, and target backscattering field of the chaff cloud test model using a genetic algorithm; S4: calculating the echo electric field intensity of each path according to the nine scattering path mechanisms based on the transmittance, forward scattering coefficient, backscattering coefficient, and the relative distance between the target and the chaff cloud; S5: obtaining the total combined scattering field by vector superposition in the complex domain based on the echo electric field intensity of each path. This paper elucidates the mechanism of composite scattering from the perspective of radar echoes, analyzes the echo paths between chaff clouds and targets, and constructs a parameterized model of composite scattering based on the parameterized models of targets and chaff clouds, thereby reducing the computational complexity.

[0072] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention.

[0073] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0074] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0075] Figure 1 This is a schematic diagram of the composite scattering of the target and the foil cloud in an embodiment of the present invention;

[0076] Figure 2 This is a schematic diagram of the composite scattered echo components in an embodiment of the present invention;

[0077] Figure 3 This is a flowchart of the composite scattering calculation in an embodiment of the present invention. Detailed Implementation

[0078] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0079] This invention provides a parameterized modeling method for calculating the combined electromagnetic scattering of chaff clouds and targets, comprising:

[0080] S1: Obtain the geometric parameters of the chaff cloud, including the bottom radius, length, position coordinates, orientation angle and spatial density distribution of the chaff, as well as the parameterized scattering center model of the target;

[0081] S2: Based on the geometric parameters of the chaff cloud and the parameterized scattering center model of the target, the forward scattering electric field, the backscattering electric field of the chaff cloud and the backscattering field of the target are calculated by vector superposition;

[0082] S3: Based on the forward scattering electric field, backscattering electric field and target backscattering field of the chaff cloud test model, the transmittance, forward scattering coefficient and backscattering coefficient of the chaff cloud are determined by fitting with a genetic algorithm.

[0083] S4: Based on transmittance, forward scattering coefficient, back scattering coefficient and the relative distance between the target and the chaff cloud, calculate the echo electric field intensity of each path according to the nine scattering path mechanism;

[0084] S5: Based on the electric field intensity of the echoes from each path, the total composite scattering field is obtained by superimposing vectors in the complex domain.

[0085] The working principle and beneficial effects of the above technical solution are as follows: The transmission process of electromagnetic waves through the chaff cloud is described by the following four core physical processes:

[0086] Direct penetration—without interacting with any chaff: The electromagnetic wave passes directly through the gaps in the cloud without encountering any chaff in its propagation path, illuminating the target behind it.

[0087] Scattered Penetration—Transmission after Interaction with Foil Strips: After electromagnetic waves enter a cloud, they are scattered by one or more foil strips, such as forward scattering. The energy is redistributed to other directions, but some energy still propagates along the original direction or approximately the original direction, eventually penetrating out of the cloud.

[0088] Reflection-scattering back to the original space: After the electromagnetic wave interacts with the chaff, the energy is scattered in the opposite direction of the incident direction, forming a radar echo, i.e., an interference signal.

[0089] Absorption—Energy converted into heat: When electromagnetic waves interact with the foil, the surface current of the foil generates ohmic losses, and some of the energy is converted into heat and dissipated.

[0090] The report idealizes the chaff as a perfect electrical conductor, thus neglecting the thermal loss of electromagnetic energy. Based on the above physical processes, the composite scattering of the target coupled with the chaff cloud is as follows: Figure 1 As shown.

[0091] Transmittance of foil clouds The forward scattering coefficient represents the probability that an electromagnetic wave penetrates a chaff cloud without interacting with any of the chaff; its value ranges from 0 to 1. and backscattering coefficient It characterizes the ratio of transmission to reflection of electromagnetic waves when they strike a cloud of foil. and All are complex numbers, and the phase change occurring on the chaff cloud illuminated by the electromagnetic wave can be represented by the phase of the complex number. The transmittance P and forward scattering coefficient of chaff clouds with different densities and distributions vary. Backscattering coefficient Unlike other methods, determining specific values ​​requires parameter fitting.

[0092] When the chaff cloud completely obscures the target, the radar echo consists of... As shown.

[0093] The radar echo components shown contain nine paths, and the electric field intensity expressions for the radar echoes generated by each path are as follows, where, The forward RCS (in square meters) of the foil strip. The backward RCS (in square meters) of the target. The forward RCS (in square meters) of the foil strip.

[0094] Path 1: Single-station echo of chaff clouds

[0095] (1)

[0096] Path 2: Single-station echo of the target

[0097] (2)

[0098] Path 3: Source foil cloud Target source

[0099] (3)

[0100] Path 4: Source foil cloud Target foil cloud source

[0101] (4)

[0102] Path 5: Source Target foil cloud source

[0103] (5)

[0104] Path 6: Source foil cloud Target foil cloud Target source

[0105] (6)

[0106] Path 7: Source foil cloud Target foil cloud Target foil cloud source

[0107] (7)

[0108] Path 8: Source Target foil cloud Target source

[0109] (8)

[0110] Path 9: Source Target foil cloud Target foil cloud source

[0111] (9)

[0112] The physical meaning of the parameters in Formulas 1-9 is explained as follows: The forward RCS (in square meters) of the foil strip. The backward RCS (in square meters) of the target. The forward RCS (in square meters) of the foil strip. The distance from the foil cloud to the plane of the electromagnetic source (unit: meters). Distance between the chaff cloud and the geometric center of the target (unit: meters) This is the radar line-of-sight vector. The imaginary unit, For wave number.

[0113] Forward scattering coefficients in the above equations Backscattering coefficient All scenarios require consideration of the transmission probability P of the chaff cloud, i.e., forward and backscattering occurring when the electromagnetic wave is not transmitted. In each coupling path, phase delay and range attenuation due to distance must also be considered. The phase delay and range attenuation terms are expressed using a directionality factor. To correct this, after determining each echo path, the backscattering field of the chaff cloud, the backscattering field of the target, and the forward scattering field of the chaff cloud are calculated separately, followed by subsequent coupling calculations. The total field of the composite scattering is obtained by superimposing the electric fields of the scattered echoes from each path.

[0114] (2) Implementation process:

[0115] The implementation process of the above technical principles is as follows:

[0116] like Figure 3 As shown, step one: First, the geometric parameters of the foil cloud should be determined, including the geometric shape of the foil cloud and the density distribution of the foil strips in the cloud.

[0117] Taking cylindrical chaff as an example, the geometric parameters of a chaff cloud include: 1. The base radius *a* and length *L* of the chaff. 2. The position of the chaff in a specific distribution space (the distribution shape of the chaff cloud can be set according to actual needs, such as spherical, cuboid, or fan-shaped distribution). The coordinates of the geometric center of the chaff can be considered as its position. 3. The orientation angle (pitch angle, azimuth angle) of the chaff. 4. The density of chaff in the cloud, which is the number of chaff strips per unit volume.

[0118] Step 2: After determining the relevant parameters of the chaff cloud, calculate the forward scattering electric field and the backscattering electric field of the chaff cloud.

[0119] Forward scattering formula for chaff clouds:

[0120]

[0121] Parameter meanings: j is the imaginary unit, k is the wave number, a is the radius of the cylinder's base, and L is the length of the cylinder. For the launch elevation angle, It is a unit vector in the direction of pitch angle. It is a directional factor.

[0122] Backscattering formula for foil clouds:

[0123]

[0124] Parameter meaning explanation: j is the imaginary unit, k is the wave number, a is the radius of the cylinder's base, and L is the length of the cylinder's generatrix. The pitch angle, It is a unit vector in the direction of the pitch angle. It is a directional factor.

[0125] The forward and backward scattering fields of each foil strip are calculated according to the above formula. The calculated results are then vector-superimposed to obtain the overall forward and backward scattering fields of the foil cloud.

[0126] Meanwhile, the target's parameterized model is used as input to calculate the target's backscattered field.

[0127] Scattering centers of complex targets are mainly classified into three types: 1. Distributed Scattering Centers (DSCs): The scattering mechanisms described by DCS mainly include plane reflection, single-curved surface reflection (cylindrical reflection), and straight-edge diffraction. 2. Localized Scattering Centers (LSCs): The formation mechanism of LSCs is mainly sharp-point diffraction. 3. Sliding Scattering Centers (SSCs): SSCs are mainly formed by hyperboloid reflection.

[0128] The expression for DSC is:

[0129]

[0130] Explanation of parameters: j is the imaginary unit, k is the wave number. The pitch angle, Let be the normal vector of the surface element. For radar line-of-sight vector, The horizontal component of the radar line of sight on the target plane. This represents the vertical component of the radar line of sight on the target plane.

[0131] The expression for LSC is:

[0132]

[0133] Parameter meaning explanation: j is the imaginary unit, k is the wave number, ξ represents the radar observation angle, including elevation and azimuth angles; f is the radar frequency; f c The radar center frequency; A0 represents the amplitude at the scattering center, which is a constant. These are usually unknown parameters, which can be estimated using optimization methods. This is the radar line-of-sight vector in the local coordinate system.

[0134] Sliding scattering center electric field SSC: ;

[0135] Where j is the imaginary unit and k is the wave number. This indicates the radar incident angle ξ. The radar observation angle is a comprehensive angle parameter that includes elevation and azimuth angles, representing the curvature of the two surfaces in the orthogonal direction at the effective reflection point of the hyperboloid; A0 is a constant term representing the amplitude, which can be obtained through parameter estimation, but has a definite value for typical geometries such as spheres or ellipsoids; for hyperboloid reflection, the frequency dependence factor α=0.

[0136] The target's geometry is divided into the three types of scattering center models mentioned above according to its geometric characteristics, and the target's scattering field is calculated according to the corresponding expressions.

[0137] Step 3: Establish a chaff cloud test model. Based on the method used in Step 2 to calculate the forward scattering electric field and backscattering electric field of the chaff cloud, as well as the backscattering field of the target, calculate the forward scattering electric field and backscattering electric field of the test model and the test target, and determine the forward scattering coefficient, backscattering coefficient, transmittance, etc., of the chaff cloud. The determination of these parameters needs to be achieved through parameter fitting.

[0138] Calculating the composite scattering of electrically large targets and chaff clouds using the full-wave method is extremely difficult. For a chaff cloud with a fixed density and uniformly random orientation of the chaff within it, the values ​​of transmittance, forward scattering coefficient, and backscattering coefficient can be considered inherent parameters of the chaff cloud, and are definite values. Therefore, an electrically small target and a small chaff cloud (maintaining the same density and random uniform orientation) are used as test models, and parameters are estimated according to the above technical scheme and the composite scattering results calculated by the full-wave method. The transmittance P and forward scattering coefficient are... Backscattering coefficient Parameter optimization is performed using a genetic algorithm (GA). A genetic algorithm (GA) is a search heuristic algorithm that simulates the mechanisms of natural selection and genetics in Darwin's theory of evolution. Its core idea is to iteratively optimize the potential solutions to a problem by simulating mechanisms such as heredity, crossover (hybridization), and mutation in biological evolution, gradually approaching the optimal or near-optimal solution. When using the GA algorithm, transmittance P and forward scattering coefficient are used as parameters. Backscattering coefficient The parameters to be estimated are set, and the optimal solution is obtained based on criteria such as the lowest root mean square error of the radar cross-section (RCS) and the highest similarity to the inverse synthetic aperture radar (ISAR) image. These determined optimal parameters are then used as the transmittance P and forward scattering coefficient of the chaff cloud required for subsequent calculations. Backscattering coefficient .

[0139] Step 4: Based on the forward scattering coefficient, backscattering coefficient, transmittance, etc. obtained in Step 3, calculate the relative distance between the chaff cloud and the target (i.e., the distance between the target and the target) as needed. ),according to Figure 2 The nine paths in the equation are calculated based on the scattering field of each path provided by equations (1) to (9).

[0140] Step 5: Directly superimpose the electric fields generated by the echoes from each path calculated in Step 4 to obtain the total field of composite scattering.

[0141]

[0142] Among them, the forward scattering coefficient and backscattering coefficient These represent the ratio of transmission and reflection of electromagnetic waves onto the foil cloud, respectively; transmittance This represents the probability that an electromagnetic wave penetrates a chaff cloud without interacting with any of the chaff, and its value ranges from 0 to 1. Multiple reflections, refractions, and diffractions of electromagnetic waves between the chaff cloud, the target, and the environment create complex signal propagation paths. The parameterized scattering center model of a radar target is related to the target's physical structure and geometric parameters, and can accurately represent the target's scattering characteristics. The application of the scattering center method in practical electromagnetic calculations requires three steps: determining the mathematical expression for the scattering center; modeling the scattering center of the target; and applying the model to the radar signal processing process.

[0143] In another embodiment, step S1 includes:

[0144] S11: Obtain the bottom radius a, length L, geometric center coordinates, pitch angle, and azimuth angle parameters of a single foil strip;

[0145] S12: Based on the parameters of a single foil strip, determine the spatial distribution of the foil cloud according to the spatial distribution function and the number of foil strips per unit volume;

[0146] S13: Based on the target's geometric structure characteristics, the target is decomposed into a combination of distributed scattering centers, localized scattering centers, and sliding scattering centers.

[0147] The working principle and beneficial effects of the above technical solution are as follows: In step S11, the system collects the geometric characteristic parameters of each foil strip. Each foil strip is modeled as an ideal cylinder, and the base radius a (usually on the order of micrometers), axial length L (on the order of centimeters), three-dimensional coordinates (x, y, z) of the geometric center, and the pitch and azimuth angles of the spatial orientation are recorded. These parameters determine the electromagnetic scattering characteristics of a single foil strip.

[0148] In step S12, the spatial distribution function of the foil cloud is set according to the actual application scenario, and a spherical, cuboid, or fan-shaped distribution pattern can be adopted. Combining the foil strip density parameter per unit volume, the spatial position and orientation distribution of each foil strip in the entire cloud are generated using the Monte Carlo method or a deterministic placement algorithm to ensure that the statistical characteristics conform to the actual deployment situation.

[0149] In step S13, the scattering centers of the target are decomposed. Distributed scattering centers mainly originate from plane reflection, cylindrical reflection, and straight-edge diffraction; localized scattering centers correspond to the apex diffraction mechanism; and sliding scattering centers are formed by hyperboloid reflection. Based on the target's CAD model or measurement data, the position, size, and orientation parameters of various scattering sources are identified, and a complete parametric characterization is established.

[0150] In another embodiment, step S2 includes:

[0151] S21: Based on the geometric parameters and orientation angle of each foil strip, calculate the forward-scattered electric field component of a single foil strip using the forward scattering formula for a cylinder;

[0152] S22: Based on the forward scattering electric field components of a single foil strip, the total forward scattering electric field of the foil cloud is obtained by vector summation in the complex domain;

[0153] S23: Calculate the backscattered electric field components of a single foil strip using the cylindrical backscattering formula and perform vector summation to obtain the total backscattered electric field of the foil cloud;

[0154] S24: Based on the three types of scattering center parameters of the target, calculate the scattering electric field of each scattering center and superimpose them to obtain the total backscattering electric field of the target.

[0155] The working principle and beneficial effects of the above technical solution are as follows: The forward scattering contribution of each foil strip within the cloud is calculated individually. Based on the electromagnetic scattering theory of cylinders, the forward scattered electric field component is expressed as... The elevation angle θ is determined by the angle between the incident direction and the chaff axis. The forward-scattered electric fields of all chaff strips are coherently superimposed. Backscattering is calculated using a cylindrical scattering formula similar to that for forward scattering, but with the scattering direction reversed. The backscattered electric field of a single chaff strip is calculated using the same physical model, and then vector superimposed to obtain the overall backscattered field of the cloud. This field constitutes the main component of the radar echo from the chaff cloud.

[0156] In step S24, the target scattering field is calculated based on the three types of scattering centers.

[0157] In another embodiment, step S3 includes:

[0158] S31: Construct a test model of a small-sized foil cloud with the same density and orientation distribution as the target;

[0159] S32: Based on the forward scattering electric field, backscattering electric field, and target backscattering field of the test model, transmittance, forward scattering coefficient, and backscattering coefficient are set as variables to be optimized;

[0160] S33: Using the root mean square error of radar cross section and the correlation coefficient of inverse synthetic aperture radar image as fitness functions, the optimal parameter values ​​are determined through iterative optimization using a genetic algorithm.

[0161] The working principle and beneficial effects of the above technical solution are as follows: A scaled-down test model for parameter calibration is constructed. The statistical characteristics of the foil density and orientation distribution are maintained consistent with actual applications, but the cloud size and target size are scaled down proportionally, allowing for the use of full-wave electromagnetic calculation methods to obtain accurate composite scattering reference values. This model provides standard data for subsequent parameter fitting.

[0162] In step S32, the transmittance P is set in the interval [0,1] to characterize the probability that electromagnetic waves directly penetrate the cloud; the forward scattering coefficient τ and the backscattering coefficient δ are set as complex variables, with their amplitudes representing the scattering intensity and their phases representing the phase shift caused by scattering. These three parameters constitute the parameter space to be optimized, and their values ​​are adjusted to match the scattering characteristics of the test model.

[0163] In step S33, the comprehensive fitness function is defined. The root mean square error term of the radar cross section ensures the accuracy of the scattering intensity; the correlation coefficient term of the inverse synthetic aperture radar image ensures the similarity of the scattering distribution. The genetic algorithm searches the parameter space through selection, crossover, and mutation operations, iteratively optimizing until the fitness function reaches its optimum. The obtained parameter values ​​can then be used for actual calculations.

[0164] In another embodiment, step S4 includes:

[0165] S41: Determine the propagation distance of the nine scattering paths based on the relative distance between the chaff cloud and the target and the radar distance;

[0166] S42: Based on the propagation distance, transmittance, forward scattering coefficient, backscattering coefficient, chaff forward radar cross section, chaff back radar cross section, and target back radar cross section, calculate the electric field intensity according to the formula for each path;

[0167] S43: Based on wavenumber and radar line-of-sight vector, phase delay and range attenuation corrections are applied to the electric field intensity of each path.

[0168] The working principle and beneficial effects of the above technical solution are as follows: forward scattering coefficient Backscattering coefficient All scenarios require consideration of the transmission probability P of the chaff cloud, i.e., forward and backscattering occurring when the electromagnetic wave is not transmitted. In each coupling path, phase delay and range attenuation due to distance must also be considered. The phase delay and range attenuation terms are expressed using a directionality factor. To correct this, after determining each echo path, the backscattering field of the chaff cloud, the backscattering field of the target, and the forward scattering field of the chaff cloud are calculated separately, followed by subsequent coupling calculations. The total field of the composite scattering is obtained by superimposing the electric fields of the scattered echoes from each path.

[0169] In another embodiment, the nine scattering paths include:

[0170] Path 1: The single-station echo of the chaff cloud. The expression for the electric field intensity of the radar echo generated by this path is:

[0171] ;

[0172] Path 2: The target's single-station echo. The expression for the electric field intensity of the radar echo generated by this path is:

[0173] ;

[0174] Path 3: Source foil cloud Target The electric field intensity expression for the radar echo generated by this path is:

[0175] ;

[0176] Path 4: Source foil cloud Target foil cloud The electric field intensity expression for the radar echo generated by this path is:

[0177] ;

[0178] Path 5: Source Target foil cloud The electric field intensity expression for the radar echo generated by this path is:

[0179] ;

[0180] Path 6: Source foil cloud Target foil cloud Target The electric field intensity expression for the radar echo generated by this path is:

[0181] ;

[0182] Path 7: Source foil cloud Target foil cloud Target foil cloud The electric field intensity expression for the radar echo generated by this path is:

[0183] ;

[0184] Path 8: Source Target foil cloud Target The electric field intensity expression for the radar echo generated by this path is:

[0185] ;

[0186] Path 9: Source-Target-Chaff Cloud-Target-Chaff Cloud-Source. The electric field intensity expression for the radar echo generated by this path is:

[0187] ;

[0188] Where τ is the forward scattering coefficient and δ is the backscattering coefficient. Forward RCS of the foil strip, For the target's backward RCS, The rearward RCS of chaff refers to the rearward radar cross-section of a single chaff strip or the entire chaff cloud. The distance between the foil cloud and the plane of the electromagnetic source is [missing information]. The distance between the chaff cloud and the geometric center of the target. For radar line-of-sight vector, The imaginary unit, For wave number.

[0189] The working principle and beneficial effects of the above technical solutions are as follows: Path 1 represents the direct backscattering of the chaff cloud, which is the main source of interference signals. After electromagnetic waves illuminate the chaff cloud, some energy is reflected back to the radar. Path 2 is the single-station scattering of the target, and the effect of the electromagnetic waves penetrating the chaff cloud twice needs to be considered. Paths 3 and 5 involve a coupling effect. In Path 3, the electromagnetic wave is first forward-scattered by the chaff cloud and then back-reflected by the target; Path 4 adds forward scattering of the chaff cloud upon return; Path 5 arrives at the target first, is reflected, and then forward-scattered by the chaff cloud. Paths 6 to 9 are higher-order coupling paths. Paths 6 and 7 involve multiple ping-pong reflections of electromagnetic waves between the chaff cloud and the target; paths 8 and 9 are target-dominated multiple reflection paths. Although the contribution of higher-order paths is usually small, it can have a significant impact under certain geometric configurations.

[0190] In another embodiment, after determining the relevant parameters of the foil cloud, the forward scattering electric field and the backscattering electric field of the foil cloud are calculated.

[0191] Forward scattering formula for chaff clouds:

[0192] ,

[0193] Where j is the imaginary unit, k is the wave number, a is the radius of the cylinder's base, and L is the length of the cylinder. For the launch elevation angle, It is a unit vector in the direction of pitch angle. Directional factor;

[0194] Backscattering formula for foil clouds:

[0195]

[0196] Where j is the imaginary unit, k is the wave number, a is the radius of the cylinder's base, and L is the length of the cylinder's generatrix. The pitch angle, It is a unit vector in the direction of the pitch angle. Directional factor;

[0197] The forward and backward scattering fields of each foil strip are calculated based on the forward scattering formula and the backward scattering formula of the foil cloud. The calculated results are then vector-superimposed to obtain the overall forward and backward scattering fields of the foil cloud.

[0198] The working principle and beneficial effects of the above technical solutions are as follows: While the backscattering formulas have the same form, their physical meanings differ. Backscattering corresponds to the reverse propagation of electromagnetic waves along the incident direction, primarily contributed by specular reflection from the cylindrical surface and edge diffraction. In randomly oriented chaff clouds, the superposition of scattering from numerous chaff strips produces isotropic scattering characteristics, which is the physical basis for chaff clouds' ability to effectively interfere with radar.

[0199] In another embodiment, the calculation of the three types of scattering centers includes:

[0200] Distributed scattering center electric field DSC:

[0201] ;

[0202] Where j is the imaginary unit and k is the wave number. The pitch angle, Let be the normal vector of the surface element. For radar line-of-sight vector, The horizontal component of the radar line of sight on the target plane. This represents the vertical component of the radar line of sight on the target plane.

[0203] Localized scattering center electric field LSC: ;

[0204] Where j is the imaginary unit, k is the wave number, ξ represents the radar observation angle, including elevation and azimuth angles; f is the radar frequency; f c The radar center frequency; A0 represents the amplitude at the scattering center, which is a constant. These are usually unknown parameters, which can be estimated using optimization methods. This is the radar line-of-sight vector in the local coordinate system;

[0205] Sliding scattering center electric field SSC: ;

[0206] Where j is the imaginary unit and k is the wave number. This indicates the radar incident angle ξ. The radar observation angle is a comprehensive angle parameter that includes elevation and azimuth angles, representing the curvature of the two surfaces in the orthogonal direction at the effective reflection point of the hyperboloid; A0 is a constant term representing the amplitude, which can be obtained through parameter estimation, but has a definite value for typical geometries such as spheres or ellipsoids; for hyperboloid reflection, the frequency dependence factor α=0.

[0207] The working principle and beneficial effects of the above technical solution are as follows: the combined use of the three types of models realizes accurate electromagnetic modeling of any complex target, and provides a reliable target scattering field input for composite scattering calculation.

[0208] In another embodiment, step S5 includes:

[0209] S51: Obtain the corrected electric field strengths E1 to E9 for the nine paths;

[0210] S52: Calculate the total electric field of composite scattering based on the principle of electromagnetic field superposition. .

[0211] The working principle and beneficial effects of the above technical solution are as follows: the electric fields generated by the echoes from each path are directly superimposed to obtain the total field of composite scattering.

[0212] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from the spirit and scope of this invention.

Claims

1. A parameterized modeling method for calculating the combined electromagnetic scattering of chaff clouds and targets, characterized in that, Comprise: S1: Obtain foil cloud geometric parameters, including the bottom radius of the foil, the length, the position coordinates, the orientation angle and the spatial density distribution, and the parameterized scattering center model of the target; S2: Based on the geometric parameters of the foil cloud and the parameterized scattering center model of the target, the forward scattering electric field, the backscattering electric field of the foil cloud and the backscattering field of the target are calculated by vector superposition; S3: Based on the forward scattering electric field, the backscattering electric field of the test model of the foil cloud group and the backscattering field of the target, the transmittance, the forward scattering coefficient and the backscattering coefficient of the foil cloud are determined by genetic algorithm fitting; S4: Based on the transmittance, the forward scattering coefficient, the backscattering coefficient and the relative distance between the target and the foil cloud, the echo electric field intensity of each path is calculated according to the nine scattering path mechanism; S5: Based on the echo electric field intensity of each path, the complex scattering total field is obtained by complex domain vector superposition.

2. The method of claim 1, wherein, S1 step includes: S11: Obtain the bottom radius a, length L, geometric center coordinates and pitch angle, azimuth angle parameters of single foil; S12: Based on the parameters of single foil, the spatial distribution of foil cloud group is determined according to the spatial distribution function and the number of foil roots per unit volume; S13: Based on the geometric structure characteristics of the target, the target is decomposed into the combination of distributed scattering center, local scattering center and sliding scattering center.

3. The parametric model modeling method of computing chaff cloud and target composite electromagnetic scattering according to claim 1, characterized in that, S2 step includes: S21: Based on the geometric parameters and orientation angle of each foil, the forward scattering electric field component of single foil is calculated by using the forward scattering formula of cylinder; S22: Based on the forward scattering electric field component of single foil, the total forward scattering electric field of foil cloud is obtained by complex domain vector summation; S23: The backscattering electric field component of single foil is calculated by using the backscattering formula of cylinder and vector summation, and the total backscattering electric field of foil cloud is obtained; S24: Based on the parameters of three types of scattering centers of the target, the scattering electric field of each scattering center is calculated and superimposed to obtain the total backscattering electric field of the target.

4. The parametric model modeling method of computing chaff cloud and target composite electromagnetic scattering according to claim 1, characterized in that, S3 step includes: S31: Construct small size foil cloud with same density and orientation distribution and target test model; S32: Based on the forward scattering electric field, the backscattering electric field of the test model and the backscattering field of the target, set the transmittance, the forward scattering coefficient and the backscattering coefficient as the to-be-optimized variables; S33: Take the root mean square error of radar scattering cross section and the correlation coefficient of inverse synthetic aperture radar image as the fitness function, and determine the optimal parameter value by genetic algorithm iteration optimization.

5. The parametric model modeling method of computing chaff cloud and target composite electromagnetic scattering according to claim 1, characterized in that, S4 step includes: S41: Based on the relative distance between the foil cloud and the target and the radar distance, the propagation distance of the nine scattering paths is determined; S42: Based on the propagation distance, the transmittance, the forward scattering coefficient, the backscattering coefficient, the forward radar scattering cross section of foil, the backscattering radar scattering cross section of foil and the backscattering radar scattering cross section of target, the electric field intensity is calculated according to the formula of each path; S43: Based on the wave number and radar line of sight vector, the phase delay and distance attenuation correction are made to the electric field intensity of each path.

6. The method of claim 5, wherein: The nine scattering paths include: Path 1: Single station echo of foil cloud, the electric field intensity expression of radar echo produced by this path is: ； Path 2: Single station echo of target, the electric field intensity expression of radar echo produced by this path is: ； Path 3: Source Foil cloud Target Source, the expression of the electric field intensity of the radar echo generated by this path is: ； Path 4: Source Chaff cloud Target Chaff cloud Source, the expression of the electric field intensity of the radar echo generated by this path is: ； Path 5: Source Target Chaff cloud Source, the expression of the electric field intensity of the radar echo generated by this path is: ； Path 6: Source Chaff cloud Target Chaff cloud Target Source, the expression of the electric field intensity of the radar echo generated by this path is: ； Path 7: Source Chaff cloud Target Chaff cloud Target Chaff cloud Source, the electric field intensity expression of the radar echo generated by this path is: ； Path 8: Source Target Foil cloud Target Source, the expression of the electric field intensity of the radar echo generated by this path is: ； Path 9: source-target-foil strip cloud-target-foil strip cloud-source, the expression of the electric field intensity of the radar echo generated by the path is: ； where τ is the forward scattering coefficient, δ is the backscattering coefficient, is the forward RCS of the foil strip, is the backscattering RCS of the target, is the backscattering RCS of the foil strip, indicating the backscattering radar cross section of a single foil strip or the whole foil cloud; is the distance of the foil cloud from the electromagnetic source plane, is the distance between the foil cloud and the geometric center of the target, is the radar line of sight vector, is the imaginary unit, is the wave number.

7. The parameterized model modeling method for calculating the electromagnetic scattering of foil strip clouds and targets according to claim 3, characterized in that: After the relevant parameters of the foil strip cloud cluster are determined, the forward scattering electric field and the backscattering electric field of the foil strip cloud are calculated; Forward scattering formula of foil strip cloud: ， where j is the imaginary unit, k is the wave number, a is the radius of the cylinder base, L is the cylinder length, is the exit elevation angle, is the unit vector in the direction of the elevation angle, is the directivity factor; Backscattering formula of foil strip cloud: ， where j is the imaginary unit, k is the wave number, a is the radius of the cylinder base, L is the cylinder generatrix length, is the pitch angle, is the unit vector in the pitch angle direction, is the directivity factor; The forward scattering field and the backscattering field of each foil strip are calculated according to the forward scattering formula of the foil strip cloud and the backscattering formula of the foil strip cloud, and the calculated results are vector superimposed to obtain the forward scattering field and the backscattering field of the entire foil strip cloud cluster.

8. The method of claim 3, wherein: The calculation of the three types of scattering centers includes: Distributed scattering center electric field DSC: ； where j is the imaginary unit and k is the wave number is the pitch angle, is the normal vector of the facet, is the radar line of sight vector, is the horizontal component of the radar line of sight in the target plane, is the vertical component of the radar line of sight in the target plane. Localised scattering centre electric field LSC: ; where j is the imaginary unit, k is the wave number, ξ represents the radar observation angle, including the pitch angle and azimuth angle; f is the radar frequency; f c is the radar center frequency; A0represents the amplitude of the scattering center, which is a constant term; is usually an unknown parameter, which can be obtained by parameter estimation through optimization method, is the radar line-of-sight vector in the local coordinate system; Sliding-type scattering center electric field SSC: ; where j is the imaginary unit and k is the wave number, represents the radar observation angle at the radar incidence angle ξ, represents the radar observation angle, which is a comprehensive angle parameter containing the pitch angle and the azimuth angle, the two surface curvatures in the orthogonal directions at the hyperboloid effective reflection point; A0is a constant term representing the amplitude, which can be obtained by parameter estimation, but for typical geometric bodies such as spheres or ellipsoids, it has a clear value; for hyperboloid reflection, the frequency-dependent factor α = 0.

9. The parametric model modeling method of computing chaff cloud and target composite electromagnetic scattering according to claim 1, characterized in that, The S5 step includes: S51: obtaining the modified electric field intensities E1 to E9 of the nine paths; S52: Calculate the total composite scattering electric field based on the electromagnetic field superposition principle .

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