A multi-scattering SAR imaging simulation method, system, device and medium based on physical consistency modeling

Abstract

The application discloses a kind of based on physical consistency modeling multiple scattering SAR imaging simulation method, system, equipment and medium, including the following steps: constructing the three-dimensional electromagnetic model of target;Geometric model under the condition of transmitting-receiving co-located SAR operating mode is constructed by light ray tracing;Using high-frequency electromagnetic scattering algorithm based on ray tracing, considering first-order, second-order and higher order multiple scattering path, the superposition and amplitude modulation of each order scattering contribution are carried out, the scattering field distribution of target under far-field condition is calculated, and the far-field scattering field is obtained;Total far-field scattering field is mapped by space propagation, and the far-field scattering result is mapped as radar platform near-field echo signal;Echo signal amplitude is corrected, and two-dimensional SAR near-field echo matrix is obtained;SAR imaging processing is carried out, and SAR imaging processing includes range compression, range migration correction RCM and azimuth compression.The application improves the fidelity and accuracy of SAR imaging simulation under complex target scene.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging and electromagnetic scattering simulation, and particularly relates to a multi-scattering SAR imaging simulation method, system, device and medium based on physical consistency modeling. BACKGROUND

[0002] Synthetic Aperture Radar (SAR) is a high-resolution imaging radar system, which is widely used in target identification and remote sensing imaging fields. In target electromagnetic characteristic modeling and SAR imaging simulation, it is usually necessary to combine the electromagnetic scattering characteristics of the target and the radar imaging process to generate a simulation image with physical consistency. However, the existing technology generally separates electromagnetic scattering calculation and SAR imaging processing into two independent modules, and lacks effective coupling and unified modeling mechanism between the two, which affects the imaging accuracy and physical consistency.

[0003] In terms of electromagnetic scattering modeling, traditional methods often use physical optics (PO), geometric optics (GO) or ray tracing (Ray Tracing) to perform single scattering calculation on the target model. Such methods are generally based on high-frequency far-field assumption, and it is difficult to accurately describe the near-field scattering or complex effects such as occlusion and multiple reflections, especially when dealing with large and complex electrically large targets (such as ships and aircrafts).

[0004] In terms of SAR signal simulation, traditional methods often regard scattering points as point targets, and based on a preset radar platform trajectory and radar parameters, construct a slant range delay and a frequency modulation signal to generate echo data, and then use distance compression, range migration correction (RCMC), azimuth compression and other algorithms to form an image. Since the target scattering points are usually in the near field or the far field, the SAR signal modeling directly uses the far field simplification formula, and does not fully consider the scattering physical mechanism of the target, especially the modeling of scattering path, phase evolution and occlusion effect. The existing methods have physical inconsistency problems in simulating the image characteristics of real targets.

[0005] Therefore, the current SAR imaging simulation methods have obvious contradictions between precision and efficiency, i.e. high-precision methods have large computational load and are difficult to implement in engineering applications; fast methods have insufficient precision and are difficult to truly reflect the imaging characteristics of complex targets, especially in the presence of structural occlusion, material changes and multiple scattering. Traditional methods are difficult to meet the needs of high-fidelity imaging simulation. SUMMARY

[0006] The first object of the present application is to provide a multi-scattering SAR imaging simulation method based on physical consistency modeling, which improves the fidelity and precision of SAR imaging simulation in complex target scenarios.

[0007] The second object of the present application is to provide a multi-scattering SAR imaging simulation system based on physical consistency modeling.

[0008] The third object of the present application is to provide an electronic device.

[0009] The fourth object of the present application is to provide a computer storage medium.

[0010] Technical scheme: To achieve the above objects, the present application provides a multi-scattering SAR imaging simulation method based on physical consistency modeling,

[0011] (1) According to the actual geometric structure and material information of the target, a three-dimensional electromagnetic model of the target is constructed, the three-dimensional electromagnetic model is composed of multiple triangular facets, and is used to describe the surface shape and material parameters of the target;

[0012] (2) According to the SAR system parameters, a geometric model under the co-located SAR working mode assisted by ray tracing is constructed;

[0013] (3) Based on the geometric model, combined with the visibility judgment result, a high-frequency electromagnetic scattering algorithm based on ray tracing is adopted, the first-order, second-order and higher-order multi-scattering paths are considered, the contributions of each order scattering are superimposed, and an empirical attenuation coefficient related to the material characteristics of the target is introduced for amplitude modulation, the scattering field distribution of the target under far-field conditions is calculated, and the far-field scattering field is obtained;

[0014] (4) The total far-field scattering field is mapped in space, the wavefront propagation compensation or phase inversion method is adopted, the far-field scattering result is mapped into the near-field echo signal of the radar platform, the radar equation is introduced in the conversion process, the target distance, scattering cross section and spatial propagation loss between the radar and the target are calculated, the echo signal amplitude is corrected, and a two-dimensional SAR near-field echo matrix is obtained;

[0015] (5) The two-dimensional SAR near-field echo matrix is subjected to SAR imaging processing, and the SAR imaging processing includes range compression, range migration correction RCMC and azimuth compression.

[0016] Optionally, in the construction process of the three-dimensional electromagnetic model in step (1), the target is disassembled into multiple sub-blocks, and the corresponding material parameters are assigned to each sub-block.

[0017] Optionally, step (2) specifically comprises the following steps:

[0018] (2.1) Obtain the SAR system parameters, the SAR system parameters including working frequency, bandwidth, pulse width, polarization mode, incidence angle, slant range resolution, azimuth resolution, platform height, flight speed and pulse repetition frequency;

[0019] (2.2) Establishing a coordinate system of the SAR platform and the target scene according to the SAR system parameters, and determining the spatial position of the radar antenna under the condition of transmitting and receiving in the same place, wherein the X axis is the direction of the radar platform motion, i.e. the X axis is the range direction, the Y axis is the horizontal direction orthogonal to the direction of the platform motion, i.e. the Y axis is the azimuth direction, and the Z axis is the height direction perpendicular to the ground, i.e. the Z axis is the height direction, the platform height is set as H, the oblique angle is the included angle between the line of sight of the platform and the reference azimuth direction, and the oblique distance is the spatial distance of the radar antenna relative to the center point of the target;

[0020] (2.3) According to the SAR imaging geometry, a virtual aperture plane is constructed in the radar observation direction, and the virtual aperture plane is discretized according to the set spatial sampling interval to form a set composed of multiple ray tubes; each ray tube represents a ray for light tracing, and is used to describe the propagation and scattering process of the radar wave in the target scene;

[0021] (2.4) Based on the ray set, a light tracing assisted geometric model is formed, which is used to describe the propagation and scattering characteristics of the electromagnetic wave under the condition of transmitting and receiving in the same place.

[0022] Optionally, the step (3) specifically comprises the following steps:

[0023] (3.1) Based on the spatial relationship between the triangular facets of the target surface in the geometric model, whether the facets have a line-of-sight condition is determined through double-pass visibility judgment, so as to determine whether there is an effective reflection path;

[0024] Let the radar platform position be , and the target surface scattering point position be , is a visibility indication function, and the value 1 indicates no occlusion, and the value 0 indicates that the path is occluded; the visibility judgment function of the scattering point is defined as:

[0025] ,

[0026] wherein, represents the visibility indication function on the transmitting path, represents the visibility indication function on the receiving path;

[0027] Only when , i.e. the transmitting and receiving paths between the radar platform and the target scattering point are both unoccluded, the corresponding scattering point is considered as an effective point contributing to the backscattering;

[0028] (3.2) Based on the condition of line of sight, starting from the radar, the next reflection point that meets the line of sight condition is searched step by step to form a tree-like search structure; at each candidate point, the reflection direction is calculated using the incident direction and the surface element normal vector, and line of sight is determined until the radar is returned or the preset number of scattering is reached, thus obtaining all possible first, second and third or higher scattering paths.

[0029] (3.3) For each obtained scattering path, calculate the propagation distance of each segment in turn and sum them to obtain the total propagation distance of the path; according to the propagation relationship of electromagnetic waves in free space, divide the total path length by the phase delay corresponding to the wavelength to determine the phase change of the path, and at the same time, superimpose the phase factor introduced by each reflection in the phase calculation to obtain the propagation distance and total phase information of the path.

[0030] (3.4) In each scattering process, an empirical attenuation coefficient related to the material type is introduced, wherein the attenuation coefficient for metallic materials is 0.9~0.98, and the attenuation coefficient for absorbing materials is 0.05~0.2;

[0031] (3.5) Based on the propagation distance, phase change and attenuation coefficient, construct the complex electric field vector representation of each scattering path;

[0032] Consider the incident wave as a far-field plane wave, assuming it returns to the receiver after N reflections, with each reflection covering a distance of... Then its complex electric field Represented as:

[0033] ,

[0034] in, The initial electric field; For the first The energy attenuation coefficient of secondary scattering , It is the relative attenuation of each reflection; For the first The Fresnel reflection coefficient of the order; j is an imaginary number, k is the wavenumber. For the first The length of the segment propagation path;

[0035] (3.6) After obtaining the complex electric field at the surface element for each scattering path, an equivalent surface current is constructed on the surface element using the physical optics approximation, and the far-field integral of the surface current is performed to obtain the far-field scattering field of the target at the radar receiving point, expressed as:

[0036] ,

[0037] In the formula, For the target position vector Far-field scattering field at that location; Represents the total electric field; For free space intrinsic impedance; This represents the real-time slant distance between the observation point and the target. The unit vector for scattering direction. It is the unit normal vector; For the target surface micro-element Position vector;

[0038] (3.7) Superimpose the far-field scattering vectors corresponding to all multiple scattering paths in complex form to obtain the total far-field scattering field of the target at the radar receiving point.

[0039] Optionally, step (4) specifically includes the following steps:

[0040] Assume the radar platform is at time... The spatial location is The target scattering center is located at Its instantaneous slant distance is:

[0041] ,

[0042] Corresponding global phase correction factor for:

[0043] ,in It is an imaginary number. Wavelength;

[0044] Through phase compensation and radar equation correction, a physically consistent conversion from far-field scattering to near-field echo from the platform was achieved, yielding a two-dimensional SAR near-field echo matrix. The expression is:

[0045] ,

[0046] in At the speed of light, For the constant terms of the radar equation, For the first Global phase correction factor for azimuth pulse. This represents the slant range of the radar reaching the center point of the target. This represents the distance that ray m travels multiple times within the target. Represents the RCS value. Let be the envelope function of the transmitted signal waveform. Indicates the azimuth pulse number. This indicates the distance to the sampling point.

[0047] Optionally, step (5) includes the following specific steps:

[0048] (5.1) Distance direction matched filtering is performed by using a linear frequency modulation template, and the matched filter is in the form of:

[0049] ,

[0050] wherein, is a distance frequency, is a distance direction linear frequency;

[0051] (5.2) Distance direction offset is corrected by distance migration correction;

[0052] (5.3) Azimuth direction matched filtering is performed based on the Doppler characteristics of target echoes, and the matched filter is in the form of:

[0053] ,

[0054] wherein, is an azimuth Doppler frequency, is an azimuth direction frequency;

[0055] (5.4) A final SAR image is obtained by two-dimensional FFT, RCMC and modulo operation:

[0056] ,

[0057] wherein, and represent the matched filter forms in the distance direction and the azimuth direction, and represent Fourier transform and inverse transform operations; represents a distance migration operation, represents a modulo value operation; is a two-dimensional SAR near-field echo matrix.

[0058] Based on the same inventive concept, the application discloses a multi-scattering SAR imaging simulation system based on physical consistency modeling, comprising:

[0059] An electromagnetic model construction module is configured to construct a three-dimensional electromagnetic model of a target according to actual geometric structure and material information of the target, the three-dimensional electromagnetic model being composed of multiple triangular facets and used for describing target surface shape and material parameters;

[0060] A geometric model construction module is configured to construct a geometric model in a light-tracing assisted co-location SAR working mode according to SAR system parameters;

[0061] The scattering field calculation module is configured to calculate a scattering field distribution of the target in a far field condition based on a geometric model, combined with a line-of-sight judgment result, by using a high-frequency electromagnetic scattering algorithm based on ray tracing, considering first-order, second-order and higher-order multiple scattering paths, superimposing the scattering contributions of each order, and introducing an empirical attenuation coefficient related to the material properties of the target to modulate the amplitude.

[0062] The echo matrix calculation module is configured to map the total far field scattering field in space propagation, and map the far field scattering result into a near field echo signal of the radar platform by using a wave front propagation compensation or phase inversion method. In the conversion process, the radar equation is introduced to correct the echo signal amplitude according to the target distance between the radar and the target, the scattering cross section and the spatial propagation loss, and a two-dimensional SAR near field echo matrix is obtained.

[0063] The SAR imaging processing module is configured to perform SAR imaging processing on the two-dimensional SAR near field echo matrix, and the SAR imaging processing includes range compression, range migration correction RCMC and azimuth compression.

[0064] Optionally, in the scattering field calculation module, the spatial relationship between the triangular facets of the target surface in the geometric model is determined by two-way line-of-sight judgment to determine whether there is a line-of-sight condition between the facets, so as to determine whether there is an effective reflection path.

[0065] Let the radar platform position be , and the target surface scattering point position be , is a line-of-sight indication function, and a value of 1 indicates no obstruction, and a value of 0 indicates that the path is obstructed; the scattering point is defined as a line-of-sight judgment function:

[0066] ,

[0067] wherein represents a line-of-sight indication function on the transmission path, represents a line-of-sight indication function on the receiving path;

[0068] Only when , that is, the transmission and receiving paths between the radar platform and the target scattering point are both unobstructed, the corresponding scattering point is considered as an effective point contributing to the backscattering;

[0069] On the basis of meeting the line-of-sight condition, the next reflection point meeting the line-of-sight condition is found from the radar, forming a tree-like search structure; the reflection direction is calculated by using the incident direction and the facet normal vector at each candidate point, and the line-of-sight is determined, until it returns to the radar or reaches the preset scattering number, that is, all possible first-order, second-order and more than third-order scattering paths are obtained.

[0070] For each scattering path, the propagation distance of each segment is calculated and summed to obtain the total propagation distance of the path; according to the propagation relationship of electromagnetic wave in free space, the phase change of the path is determined by dividing the total length of the path by the wavelength corresponding phase delay, and the phase factor introduced by each reflection is superimposed in the phase calculation, so as to obtain the propagation distance and total phase information of the path;

[0071] An empirical attenuation coefficient related to the type of material is introduced in each scattering process, wherein the attenuation coefficient corresponding to the metal material is 0.9-0.98, and the attenuation coefficient corresponding to the wave-absorbing material is 0.05-0.2;

[0072] Based on the propagation distance, phase change and attenuation coefficient, the complex electric field vector representation of each scattering path is constructed;

[0073] Considering that the incident wave is a far-field plane wave, it is assumed that the incident wave returns to the receiving end after N times of reflection, and the propagation distance of each time is Then the complex electric field is represented as:

[0074] ,

[0075] wherein, is the initial electric field; is the energy attenuation coefficient of the n-th scattering, , is the relative attenuation of each reflection; is the Fresnel reflection coefficient of the n-th; j is an imaginary number, k is a wave number, is the length of the n-th propagation path; After obtaining the complex electric field of each scattering path at the surface element, the equivalent surface current is constructed on the surface element by using the physical optics approximation, and the far-field integral is performed on the surface current to obtain the far-field scattering field of the target at the radar receiving point, and the expression is:

[0076]

[0077] ,

[0078] wherein, is the far-field scattering field of the target at the position vector ; represents the total electric field; is the intrinsic impedance of free space; is the real-time slant range of the observation point and the target; is the unit vector of the scattering direction, is the unit normal vector; is the position vector of the surface element of the target.​​

[0079] Superpose the far-field scattering field vectors corresponding to all multiple scattering paths in complex form to obtain the total far-field scattering field of the target at the radar receiving point.

[0080] Based on the same inventive concept, the application discloses an electronic device, comprising a processor and a storage medium;

[0081] The storage medium is used for storing instructions;

[0082] The processor is used for operating according to the instructions to perform the steps of the above method.

[0083] Based on the same inventive concept, the application discloses a computer readable storage medium, which stores a computer program, characterized in that the program is executed by a processor to realize the steps of the above method.

[0084] Advantages: compared with the prior art, the application has the following remarkable advantages: the application provides a complex electric large target-oriented, high-precision, physically consistent integrated SAR imaging simulation method, which can effectively fuse electromagnetic scattering calculation and imaging processing procedures, and take into account multiple scattering, visibility judgment and far-field mapping and other key physical mechanisms, thereby improving the authenticity and engineering practicability of SAR imaging simulation; the application aims to solve the problem of insufficient precision in the existing SAR simulation technology due to modeling simplification in multiple scattering effect, far-field and near-field propagation conversion and echo signal generation, and improve the authenticity and precision of imaging simulation; the application has remarkable advantages in electromagnetic modeling precision, multiple scattering modeling, far-field and near-field conversion and SAR imaging physical consistency, etc., and breaks through the complete process from electromagnetic scattering analysis to SAR image generation, realizes the high integration of electromagnetic scattering analysis and SAR imaging; the application is suitable for engineering needs considering multiple scattering effects, effectively supplements the traditional single scattering model, and is suitable for complex target recognition, high-resolution imaging simulation, radar system design verification and other engineering applications, and has wide practical value. BRIEF DESCRIPTION OF DRAWINGS

[0085] Figure 1 The flowchart of the application is shown in the figure;

[0086] Figure 2 The target three-dimensional modeling model splitting diagram in the application is shown in the figure;

[0087] Figure 3 The geometric model diagram in the light ray tracing auxiliary co-site SAR working mode in the application is shown in the figure;

[0088] Figure 4 The ray propagation diagram of multiple scattering in the application is shown in the figure;

[0089] Figure 5 Figure 1 is a ship model diagram in an embodiment of the present application;

[0090] Figure 6 Figure 2 is a ship multi-angle SAR imaging simulation result diagram in an embodiment of the present application;

[0091] Figure 7 Figure 3 is a comparison diagram of SAR imaging simulation results and RaySAR software simulation results in an embodiment of the present application. DETAILED DESCRIPTION

[0092] The technical solutions of the present application will be further described below with reference to the accompanying drawings.

[0093] Embodiment 1: As shown in the present application, a multi-scattering SAR imaging simulation method based on physical consistency modeling is disclosed, comprising the following steps: Figure 1

[0094] (1) According to the actual geometric structure and material information of the target, a three-dimensional electromagnetic model of the target is constructed, the three-dimensional electromagnetic model is composed of a plurality of triangular facets, and is used to describe the target surface shape and material parameters;

[0095] As shown in the present application, in the construction process of the three-dimensional electromagnetic model in step (1), the target is disassembled into a plurality of sub-blocks, and corresponding material parameters are assigned to each sub-block. Figure 2

[0096] (2) According to the SAR system parameters, a geometric model under the condition of light tracking auxiliary transmission and reception co-location SAR working mode is constructed.

[0097] As shown in the present application, the step (2) specifically comprises the following steps: Figure 3

[0098] (2.1) Obtain the SAR system parameters, the SAR system parameters include working frequency, bandwidth, pulse width, polarization mode, incidence angle, slant range resolution, azimuth resolution, platform height, flight speed and pulse repetition frequency;

[0099] (2.2) According to the SAR system parameters, the coordinate system of the SAR platform and the target scene is established, and the spatial position of the radar antenna under the condition of transmission and reception co-location is determined, wherein the X axis is the radar platform motion direction, that is, the X axis is the range direction, the Y axis is the horizontal direction perpendicular to the platform motion direction, that is, the Y axis is the azimuth direction, the Z axis is the height direction perpendicular to the ground, that is, the Z axis is the height direction, the platform height is set as H, the oblique angle is the included angle between the platform line of sight and the reference azimuth direction, and the slant range is the spatial distance of the radar antenna relative to the target center point;

[0100] ​​​(2.3) Based on the geometric relationship of SAR imaging, a virtual aperture surface is constructed in the radar observation direction, and the virtual aperture surface is discretized according to the set spatial sampling interval to form a set of multiple ray tubes; each ray tube represents a ray used for ray tracing to describe the propagation and scattering process of radar waves in the target scene;

[0101] (2.4) Based on the ray set, a ray tracing-assisted geometric model is formed to describe the propagation and scattering characteristics of electromagnetic waves under the condition of simultaneous transmission and reception.

[0102] (3) Based on the geometric model and combined with the line-of-sight judgment results, a high-frequency electromagnetic scattering algorithm based on ray tracing is adopted to consider the first-order, second-order and higher-order multiple scattering paths, and the scattering contributions of each order are superimposed. An empirical attenuation coefficient related to the target material properties is introduced for amplitude modulation. The attenuation coefficient corresponding to the metal surface is in the range of 0.9~0.98, and the attenuation coefficient corresponding to the absorbing material surface is in the range of 0.05~0.2, so as to enhance the real characterization of energy loss and multiple scattering contribution. The scattering field distribution of the target under far-field conditions is calculated to obtain the far-field scattering field.

[0103] Step (3) specifically includes the following steps:

[0104] (3.1) Based on the spatial relationship between the triangular facets of the target surface in the geometric model, the two-way visibility judgment is used to determine whether there is visibility between the facets, thereby determining whether there is an effective reflection path;

[0105] Let the location of the radar platform be... The location of the scattering point on the target surface is , This is a line-of-sight indicator function; a value of 1 indicates no obstruction, and a value of 0 indicates the path is obstructed; it defines the scattering point. The visibility judgment function is:

[0106] ,

[0107] in, This represents the line-of-sight indication function on the transmission path. This indicates the line-of-sight indication function on the receive path;

[0108] Only when This means that the transmission and reception paths between the radar platform and the target scattering point are unobstructed, and the corresponding scattering point Only then are they considered effective points contributing to backscattering;

[0109] (3.2) Based on the condition of line-of-sight, starting from the radar, the next reflection point that satisfies the line-of-sight condition is searched step by step, forming a tree-like search structure; at each candidate point, the reflection direction is calculated using the incident direction and the surface element normal vector, and line-of-sight determination is performed, until the radar is returned or the preset number of scattering is reached, thus obtaining all possible first, second, and higher scattering paths, such as... Figure 4 As shown;

[0110] (3.3) For each obtained scattering path, calculate the propagation distance of each segment in turn and sum them to obtain the total propagation distance of the path; according to the propagation relationship of electromagnetic waves in free space, divide the total path length by the phase delay corresponding to the wavelength to determine the phase change of the path, and at the same time, superimpose the phase factor introduced by each reflection in the phase calculation to obtain the propagation distance and total phase information of the path.

[0111] (3.4) In each scattering process, an empirical attenuation coefficient related to the material type is introduced, wherein the attenuation coefficient for metallic materials is 0.9~0.98, and the attenuation coefficient for absorbing materials is 0.05~0.2;

[0112] (3.5) Based on the propagation distance, phase change and attenuation coefficient, construct the complex electric field vector representation of each scattering path;

[0113] Consider the incident wave as a far-field plane wave, assuming it returns to the receiver after N reflections, with each reflection covering a distance of... Then its complex electric field Represented as:

[0114] ,

[0115] in, The initial electric field; For the first The energy attenuation coefficient of secondary scattering , It is the relative attenuation of each reflection; For the first The Fresnel reflection coefficient of the order; j is an imaginary number, k is the wavenumber. For the first The length of the segment propagation path;

[0116] (3.6) After obtaining the complex electric field at the surface element for each scattering path, an equivalent surface current is constructed on the surface element using the physical optics approximation, and the far-field integral of the surface current is performed to obtain the far-field scattering field of the target at the radar receiving point, expressed as:

[0117] ,

[0118] In the formula, For the target position vector far field scattering field at the radar receiving point; denotes the total electric field; is the intrinsic impedance of free space; is the real-time slant range between the observation point and the target; is the unit vector of the scattering direction, is the unit normal vector; is the position vector of the target surface element

[0119] (3.7) The far field scattering field vectors corresponding to all multiple scattering paths are superimposed in complex form to obtain the total far field scattering field of the target at the radar receiving point.

[0120] (4) The total far field scattering field is mapped in space propagation, and the wave front propagation compensation or phase inversion method is used to map the far field scattering result to the radar platform near field echo signal; In the conversion process, the radar equation is introduced, and according to the target distance, scattering cross section and space propagation loss between the radar and the target, the echo signal amplitude is corrected, the accurate mapping of the space field is realized and the physical authenticity of the echo simulation is improved;

[0121] Let the spatial position of the radar platform at time is , and the scattering center position of the target is , and its instantaneous slant range is:

[0122] ,

[0123] The corresponding global phase correction factor is:

[0124] , where is a complex number, is the wavelength;

[0125] Through phase compensation and radar equation correction, the physical consistent conversion of far field scattering to platform near field echo is realized, and the two-dimensional SAR near field echo matrix is obtained, and the expression is:

[0126] ,

[0127] , where is the speed of light, is the constant term of the radar equation, is the global phase correction factor, denotes the slant range from the radar to the target center point, denotes the distance of the ray m in the target multiple propagation, denotes the RCS value, is the envelope function of the transmitted signal waveform, ​represents the azimuth pulse number, represents the range sampling point.

[0128] (5) SAR imaging processing is performed on the two-dimensional SAR near-field echo matrix, and the SAR imaging processing includes range compression, range migration correction RCMC and azimuth compression, so as to obtain a high-resolution SAR image.

[0129] The step (5) includes the following specific steps:

[0130] (5.1) Range matching filtering is performed by using a linear frequency modulation template, and the matching filter is in the form of:

[0131] ,

[0132] wherein, is a range frequency, is a range linear frequency;

[0133] (5.2) The range offset is corrected by range migration correction, so as to ensure that each echo is focused on a correct range unit;

[0134] (5.3) Azimuth matching filtering is performed based on the Doppler characteristics of target echoes, so as to realize azimuth focusing, and the matching filter is in the form of:

[0135] ,

[0136] wherein, is an azimuth Doppler frequency, is an azimuth frequency;

[0137] (5.4) The final SAR image is obtained by two-dimensional FFT, RCMC and modulo operation:

[0138] ,

[0139] wherein, and represent the matching filter forms in the range direction and the azimuth direction, and represent Fourier transform and inverse transform operations; represents a range migration operation, represents a modulo value operation; is a two-dimensional SAR near-field echo matrix.

[0140] As Figure 5As shown, a 1:1 ship model is given, and the size of the model is 347m x 87m x 75m. The ship structure can be roughly divided into a command tower, a flight deck, and the flight deck has sporadic flame arresters and catapults. The incident wave frequency is 15GHz, the polarization mode is HH polarization, the sampling interval is 1.2m x 0.75m, the theoretical resolution is 1.5m, and the results of four different angles are simulated, which are , , , The simulation results are shown in Figure 6 , and the CPU of the simulation results is i5-12600KF@3.70GHz, and the GPU is NVIDIA GeForce RTX 3080.

[0141] Multiple scattering is analyzed from material properties and geometric structure: the deck and hull of the ship are usually made of high-strength steel or aluminum alloy, and such metal materials have very high electrical conductivity, and electromagnetic waves are almost completely reflected on their surface, forming strong single scattering, but the edges of the deck and the junctions of the ship structure are prone to angular reflection, which can further enhance the SAR echo signal; the command tower usually adopts a design combining composite materials and metal frames, and the structure is complex and usually presents a stepped layout, including a large number of vertical and near-vertical metal surfaces, these characteristics cause radar waves to reflect multiple times between the tower bodies, resulting in strong multiple scattering, which appears as a high-brightness area in SAR imaging, and forms a unique echo feature; the flame arresters and catapults are key components on the deck of the ship, made of high-conductivity metal materials, and contain a large number of dihedral and trihedral structures, the geometric and material properties of which jointly cause strong scattering phenomena, forming obvious high-brightness areas at specific angles, and Table 1 is the similarity index results of multi-angle simulation.

[0142] Table 1 Multi-angle simulation similarity index results

[0143]

[0144] As shown in Figure 7 , the simulation results of the present application and the RaySAR software simulation results are compared, Figure 7 The left column is the simulation result of the present application, Figure 7The right column of the RaySAR software simulation result is given in Table 1, and the structure similarity index and the cosine similarity quantitative comparison results of the corresponding angle diagram are given in Table 1. The structure similarity index values of four typical angles are all higher than 0.91, and the highest reaches 0.9526 (180°). The cosine similarity is between 0.78-0.83. From the overall average, the structure similarity index is 0.9295 on average, and the cosine similarity is 0.8080 on average. Through qualitative analysis and quantitative comparison, it can be concluded that the multi-angle simulation image of the method has good consistency in structure and feature dimensions, and can effectively capture the main scattering distribution characteristics of the target. RaySAR is not based on the simulation of the characteristics of the SAR full-coherent system, and belongs to the mapping imaging. The simulation result does not contain typical interference stripes (such as cross-silk structure), and the target structure is simplified to a certain extent in the simulation process.

[0145] The SAR imaging simulation method provided in the application fully integrates the electromagnetic characteristics of the complex structure and heterogeneous materials of the ship, models the first to multiple scattering to obtain the far-field scattering field of the target, and ensures the consistency of the scattering modeling and the imaging reconstruction process in the physical mechanism through the joint processing of the far-field propagation phase correction and the near-field reconstruction. At the same time, the radar equation is introduced to physically modulate the echo amplitude, which effectively reflects the transmission and reception characteristics of the system. The simulation results show that the scattering response of each part of the target is accurately reproduced, especially in the multiple scattering strong response areas such as the island and the deck edge, which shows high matching and physical rationality, verifying the innovation and effectiveness of the method in the key links of multiple scattering modeling, far-field to near-field, and radar equation correction, and fully embodying the precision and reliability advantages of the method in the high-resolution SAR imaging of complex electrically large targets.

[0146] Embodiment 2: The application discloses a multiple scattering SAR imaging simulation system based on physical consistency modeling, comprising:

[0147] An electromagnetic model construction module is configured to construct a three-dimensional electromagnetic model of a target according to actual geometric structure and material information of the target, the three-dimensional electromagnetic model being composed of multiple triangular facets and used for describing a target surface shape and material parameters; in the construction process of the three-dimensional electromagnetic model, the target is disassembled into multiple sub-blocks, and the sub-blocks are endowed with corresponding material parameters.

[0148] A geometric model construction module is configured to construct a geometric model in a monostatic SAR working mode assisted by light tracing according to SAR system parameters.

[0149] The SAR system parameters are acquired in the geometric model construction module, and the SAR system parameters include working frequency, bandwidth, pulse width, polarization mode, incidence angle, slant range resolution, azimuth resolution, platform height, flight speed and pulse repetition frequency.

[0150] A coordinate system of a SAR platform and a target scene is established according to SAR system parameters, and a spatial position of a radar antenna under a condition of transmitting and receiving in the same position is determined, wherein an X axis is a direction of platform motion, that is, the X axis is a range direction, a Y axis is a horizontal direction orthogonal to the direction of platform motion, that is, the Y axis is an azimuth direction, and a Z axis is a height direction perpendicular to the ground, that is, the Z axis is an elevation direction, a platform height is set as H, an oblique angle is an included angle between a platform line of sight and a reference azimuth direction, and an oblique distance is a spatial distance of the radar antenna relative to a target center point;

[0151] According to a SAR imaging geometric relationship, a virtual aperture plane is constructed in a radar observation direction, and the virtual aperture plane is discretized according to a set spatial sampling interval to form a set composed of multiple ray tubes; each ray tube represents a ray for light tracing, and is used to describe a propagation and scattering process of a radar wave in a target scene.

[0152] Based on the ray set, a light tracing assisted geometric model is formed, and is used to describe propagation and scattering characteristics of an electromagnetic wave under a condition of transmitting and receiving in the same position.

[0153] A scattering field calculation module is configured to, based on the geometric model and in combination with a line-of-sight judgment result, use a high-frequency electromagnetic scattering algorithm based on ray tracing, consider first-order, second-order and higher-order multiple scattering paths, superimpose contributions of each order of scattering, and introduce an empirical attenuation coefficient related to a target material property to perform amplitude modulation, calculate a scattering field distribution of the target under a far-field condition, and obtain a far-field scattering field.

[0154] In the scattering field calculation module, a spatial relationship between triangular facets of a target surface in the geometric model is used to determine, through double-path line-of-sight judgment, whether the facets have a line-of-sight condition, so as to determine whether an effective reflection path exists.

[0155] Let a radar platform position be , and a target surface scattering point position be , is a line-of-sight indication function, and a value of 1 indicates no occlusion, and a value of 0 indicates that a path is occluded; a line-of-sight judgment function of the scattering point is defined as:

[0156] ,

[0157] wherein represents a line-of-sight indication function on a transmitting path, represents a line-of-sight indication function on a receiving path;

[0158] Only when , that is, both a transmitting path and a receiving path between the radar platform and the target scattering point are not occluded, the corresponding scattering point is considered as an effective point contributing to backscattering.

[0159] On the basis of satisfying the visibility condition, the next reflection point satisfying the visibility condition is found from the radar, and a tree-like search structure is formed; the reflection direction is calculated by using the incident direction and the normal vector of the surface element at each candidate point, and the visibility is determined, until it returns to the radar or reaches the preset scattering number, that is, all possible one-time, two-time and three-time or more scattering paths are obtained, as shown in Figure 4 .

[0160] For each obtained scattering path, the propagation distance of each segment is calculated in turn and summed to obtain the total propagation distance of the path; according to the propagation relationship of electromagnetic waves in free space, the phase change of the path is determined by dividing the total length of the path by the wavelength, and the phase factor introduced by each reflection is superimposed in the phase calculation, so as to obtain the propagation distance and total phase information of the path.

[0161] An empirical attenuation coefficient related to the type of material is introduced in each scattering process, wherein the attenuation coefficient corresponding to the metal material is 0.9-0.98, and the attenuation coefficient corresponding to the wave-absorbing material is 0.05-0.2.

[0162] Based on the propagation distance, the phase change and the attenuation coefficient, a complex electric field vector representation of each scattering path is constructed;

[0163] Considering that the incident wave is a far-field plane wave, it is assumed that it returns to the receiving end after N times of reflection, and the propagation distance of each time is , then the complex electric field is expressed as:

[0164] ,

[0165] wherein, is the initial electric field; is the energy attenuation coefficient of the n-th scattering, , is the relative attenuation of each reflection; is the Fresnel reflection coefficient of the n-th; j is an imaginary number, k is a wave number, is the length of the n-th propagation path. After obtaining the complex electric field of each scattering path at the surface element, an equivalent surface current is constructed on the surface element by using the physical optics approximation, and the far-field integral is performed on the surface current to obtain the far-field scattering field of the target at the radar receiving point, and the expression is:

[0166]

[0167] ,

[0168] wherein, is the target to the position vector ​​The far-field scattering field of the target at the radar receiving point is obtained by superimposing the far-field scattering field vectors corresponding to all multiple scattering paths in complex form. represents the total electric field; is the free-space intrinsic impedance; is the real-time slant range between the observation point and the target; is the unit vector of the scattering direction, is the unit normal vector; is the position vector of the target surface element .

[0169] The far-field scattering field vectors corresponding to all multiple scattering paths are superimposed in complex form to obtain the total far-field scattering field of the target at the radar receiving point.

[0170] The echo matrix calculation module is used to perform spatial propagation mapping on the total far-field scattering field, and the far-field scattering result is mapped into a radar platform near-field echo signal by using a wavefront propagation compensation or a phase inversion method. In the conversion process, the radar equation is introduced, the echo signal amplitude is corrected according to the target distance between the radar and the target, the scattering cross section and the spatial propagation loss, and a two-dimensional SAR near-field echo matrix is obtained.

[0171] In the echo matrix calculation module, the spatial position of the radar platform at time is , the target scattering center position is , and the instantaneous slant range is:

[0172] ,

[0173] The corresponding global phase correction factor is:

[0174] wherein is an imaginary number, is a wavelength;

[0175] By phase compensation and radar equation correction, the physical consistency conversion from the far-field scattering to the platform near-field echo is realized, and a two-dimensional SAR near-field echo matrix is obtained, and the expression is:

[0176] ,

[0177] wherein is the speed of light, is a radar equation constant term, is a global phase correction factor, represents the slant range of the radar to the target center point, represents the distance of the ray m in the target multiple propagation, represents the RCS value, is an envelope function of the transmitted signal waveform, represents the azimuth pulse number, represents the sampling point in range direction.

[0178] a SAR imaging processing module, configured to perform SAR imaging processing on the two-dimensional SAR near-field echo matrix, the SAR imaging processing including range compression, range cell migration correction (RCMC) and azimuth compression.

[0179] The linear frequency modulation template is used for range direction matching filtering in the SAR imaging processing module, and the matching filter has the form of:

[0180] ,

[0181] wherein, is a range frequency, is a range direction linear frequency.

[0182] The range direction offset is corrected by the range cell migration correction to ensure that each echo is focused on a correct range cell.

[0183] Azimuth direction matching filtering is performed based on the Doppler characteristics of target echoes to realize azimuth direction focusing, and the matching filter has the form of:

[0184] ,

[0185] wherein, is an azimuth Doppler frequency, is an azimuth direction frequency.

[0186] The final SAR image is obtained through two-dimensional FFT, RCMC and modulo operation:

[0187] ,

[0188] wherein, and represent the matching filter forms in range direction and azimuth direction, and represent Fourier transform and inverse transform operations; represents a range cell migration operation, represents a modulo value operation; is a two-dimensional SAR near-field echo matrix.

[0189] Embodiment 3: An electronic device in this embodiment includes a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to perform the steps of the method as described above.

[0190] Embodiment 4: A computer readable storage medium in this embodiment has a computer program stored thereon, and the program is executed by a processor to realize the steps of the method as described above.

Claims

1. A simulation method for multiple scattering SAR imaging based on physical consistency modeling, characterized in that, Includes the following steps: (1) Based on the actual geometric structure and material information of the target, construct a three-dimensional electromagnetic model of the target. The three-dimensional electromagnetic model is composed of multiple triangular facets, which are used to describe the surface shape and material parameters of the target. (2) Construct a geometric model of the SAR working mode with ray tracing assisted transceiver based on the SAR system parameters; (3) Based on the geometric model and combined with the line-of-sight judgment results, a high-frequency electromagnetic scattering algorithm based on ray tracing is adopted. Considering the first-order, second-order and higher-order multiple scattering paths, the scattering contributions of each order are superimposed, and an empirical attenuation coefficient related to the target material properties is introduced for amplitude modulation. The scattering field distribution of the target under far-field conditions is calculated to obtain the far-field scattering field. The specific steps of step (3) include the following steps: (3.1) Based on the spatial relationship between the triangular facets of the target surface in the geometric model, the two-way visibility judgment is used to determine whether there is visibility between the facets, thereby determining whether there is an effective reflection path; Let the location of the radar platform be... The location of the scattering point on the target surface is , This is a line-of-sight indicator function; a value of 1 indicates no obstruction, and a value of 0 indicates the path is obstructed; it defines the scattering point. The visibility judgment function is: ， in, This represents the line-of-sight indication function on the transmission path. This indicates the line-of-sight indication function on the receive path; Only when This means that the transmission and reception paths between the radar platform and the target scattering point are unobstructed, and the corresponding scattering point Only then are they considered effective points contributing to backscattering; (3.2) Based on the condition of line of sight, starting from the radar, the next reflection point that meets the line of sight condition is searched step by step to form a tree-like search structure; at each candidate point, the reflection direction is calculated using the incident direction and the surface element normal vector, and line of sight is determined until the radar is returned or the preset number of scattering is reached, thus obtaining all possible first, second and third or higher scattering paths. (3.3) For each obtained scattering path, calculate the propagation distance of each segment in turn and sum them to obtain the total propagation distance of the path; according to the propagation relationship of electromagnetic waves in free space, divide the total path length by the phase delay corresponding to the wavelength to determine the phase change of the path, and at the same time, superimpose the phase factor introduced by each reflection in the phase calculation to obtain the propagation distance and total phase information of the path. (3.4) In each scattering process, an empirical attenuation coefficient related to the material type is introduced, wherein the attenuation coefficient for metallic materials is 0.9~0.98, and the attenuation coefficient for absorbing materials is 0.05~0.2; (3.5) Based on the propagation distance, phase change and attenuation coefficient, construct the complex electric field vector representation of each scattering path; Consider the incident wave as a far-field plane wave, assuming it returns to the receiver after N reflections, with each reflection covering a distance of... Then its complex electric field Represented as: ， in, The initial electric field; For the first The energy attenuation coefficient of secondary scattering , It is the relative attenuation of each reflection; For the first The Fresnel reflection coefficient of the order; j is an imaginary number, k is the wavenumber. For the first The length of the segment propagation path; (3.6) After obtaining the complex electric field at the surface element for each scattering path, an equivalent surface current is constructed on the surface element using the physical optics approximation, and the far-field integral of the surface current is performed to obtain the far-field scattering field of the target at the radar receiving point, expressed as: ， In the formula, For the target position vector Far-field scattering field at that location; Represents the total electric field; For free space intrinsic impedance; This represents the real-time slant distance between the observation point and the target. The unit vector for scattering direction. It is the unit normal vector; For the target surface micro-element Position vector; (3.7) Superimpose the far-field scattering vectors corresponding to all multiple scattering paths in complex form to obtain the total far-field scattering field of the target at the radar receiving point; (4) Perform spatial propagation mapping on the total far-field scattered field, and use wavefront propagation compensation or phase inversion method to map the far-field scattering result into the radar platform near-field echo signal; introduce the radar equation in the conversion process, and correct the echo signal amplitude according to the target distance between the radar and the target, the scattering cross section and the spatial propagation loss to obtain the two-dimensional SAR near-field echo matrix. (5) Perform SAR imaging processing on the two-dimensional SAR near-field echo matrix. SAR imaging processing includes range compression, range migration correction (RCMC), and azimuth compression.

2. The multiple scattering SAR imaging simulation method based on physical consistency modeling according to claim 1, characterized in that: In the process of constructing the three-dimensional electromagnetic model in step (1), the target is decomposed into multiple sub-blocks, and each sub-block is assigned corresponding material parameters.

3. The multiple scattering SAR imaging simulation method based on physical consistency modeling according to claim 1, characterized in that: Step (2) specifically includes the following steps: (2.1) Obtain SAR system parameters, including operating frequency, bandwidth, pulse width, polarization mode, incident angle, slant range resolution, azimuth resolution, platform height, flight speed and pulse repetition frequency; (2.2) Establish a coordinate system between the SAR platform and the target scene based on the SAR system parameters, and determine the spatial position of the radar antenna under the condition of transmitting and receiving in the same location. The X-axis is the direction of movement of the radar platform, i.e., the X-axis is the range direction, the Y-axis is the horizontal direction orthogonal to the direction of movement of the platform, i.e., the Y-axis is the azimuth direction, and the Z-axis is the height direction perpendicular to the ground, i.e., the Z-axis is the height direction. Set the platform height as H, the slant angle is the angle between the platform line of sight and the reference azimuth direction, and the slant range is the spatial distance of the radar antenna relative to the center point of the target. (2.3) Based on the geometric relationship of SAR imaging, a virtual aperture surface is constructed in the radar observation direction, and the virtual aperture surface is discretized according to the set spatial sampling interval to form a set of multiple ray tubes; each ray tube represents a ray used for ray tracing to describe the propagation and scattering process of radar waves in the target scene; (2.4) Based on the ray set, a ray tracing-assisted geometric model is formed to describe the propagation and scattering characteristics of electromagnetic waves under the condition of simultaneous transmission and reception.

4. The multiple scattering SAR imaging simulation method based on physical consistency modeling according to claim 1, characterized in that: Step (4) specifically includes the following steps: Assume the radar platform is at time... The spatial location is The target scattering center is located at Its instantaneous slant distance is: ， Corresponding global phase correction factor for: ,in It is an imaginary number. Wavelength; Through phase compensation and radar equation correction, a physically consistent conversion from far-field scattering to near-field echo from the platform was achieved, yielding a two-dimensional SAR near-field echo matrix. The expression is: ， in At the speed of light, For the constant terms of the radar equation, For the first Global phase correction factor for azimuth pulse. This represents the slant range of the radar reaching the center point of the target. This represents the distance that ray m travels multiple times within the target. Represents the RCS value. Let be the envelope function of the transmitted signal waveform. Indicates the azimuth pulse number. This indicates the distance to the sampling point.

5. The multiple scattering SAR imaging simulation method based on physical consistency modeling according to claim 1, characterized in that: Step (5) includes the following specific steps: (5.1) Range-direction matched filtering is performed using a linear frequency modulated template. The matched filter has the following form: ， in, For distance frequency, For distance-directed linear frequency modulation; (5.2) Correct the range offset by range migration correction; (5.3) Based on the Doppler characteristics of the target echo, azimuth matched filtering is performed. The matched filter has the following form: ， in, The azimuth Doppler frequency, For azimuth frequency tuning; (5.4) The final SAR image is obtained through two-dimensional FFT, RCMC, and modulus operations: ， in, and This represents the form of the matched filter in the range and azimuth directions. and This represents the Fourier transform and inverse transform operations; Indicates distance migration operation. This indicates a modulo operation; This is the near-field echo matrix of a two-dimensional SAR.

6. A multiple scattering SAR imaging simulation system based on physical consistency modeling, characterized in that, include: The electromagnetic model building module is used to build a three-dimensional electromagnetic model of the target based on the target's actual geometric structure and material information. The three-dimensional electromagnetic model is composed of multiple triangular facets, which are used to describe the target's surface shape and material parameters. The geometric model building module is used to build a geometric model for ray-traced assisted transceiver co-location SAR working mode based on SAR system parameters; The scattering field calculation module is used to calculate the scattering field distribution of the target under far-field conditions based on the geometric model and the line-of-sight judgment result, using a high-frequency electromagnetic scattering algorithm based on ray tracing, considering first-order, second-order and higher-order multiple scattering paths, superimposing the scattering contributions of each order, and introducing an empirical attenuation coefficient related to the target material properties for amplitude modulation, thus obtaining the far-field scattering field. The scattering field calculation module determines whether there is a valid reflection path by using two-way visibility judgment based on the spatial relationship between the triangular facets of the target surface in the geometric model. Let the location of the radar platform be... The location of the scattering point on the target surface is , This is a line-of-sight indicator function; a value of 1 indicates no obstruction, and a value of 0 indicates the path is obstructed; it defines the scattering point. The visibility judgment function is: ， in, This represents the line-of-sight indication function on the transmission path. This indicates the line-of-sight indication function on the receive path; Only when This means that the transmission and reception paths between the radar platform and the target scattering point are unobstructed, and the corresponding scattering point Only then are they considered effective points contributing to backscattering; Based on the condition of line of sight, starting from the radar, the next reflection point that meets the line of sight condition is searched step by step to form a tree-like search structure; at each candidate point, the reflection direction is calculated using the incident direction and the surface element normal vector, and line of sight is determined, until the radar is returned or the preset number of scattering is reached, that is, all possible first, second and third or higher scattering paths are obtained. For each obtained scattering path, the propagation distance of each segment is calculated in sequence and summed to obtain the total propagation distance of the path; according to the propagation relationship of electromagnetic waves in free space, the phase change of the path is determined by dividing the total path length by the phase delay corresponding to the wavelength, and the phase factor introduced by each reflection is superimposed in the phase calculation to obtain the propagation distance and total phase information of the path. An empirical attenuation coefficient related to the material type is introduced in each scattering process, with an attenuation coefficient of 0.9~0.98 for metallic materials and 0.05~0.2 for absorbing materials; Based on the propagation distance, phase change, and attenuation coefficient, a complex electric field vector representation is constructed for each scattering path; Consider the incident wave as a far-field plane wave, assuming it returns to the receiver after N reflections, with each reflection covering a distance of... Then its complex electric field Represented as: ， in, The initial electric field; For the first The energy attenuation coefficient of secondary scattering , It is the relative attenuation of each reflection; For the first The Fresnel reflection coefficient of the order; j is an imaginary number, k is the wavenumber. For the first The length of the segment propagation path; After obtaining the complex electric field at each scattering path at the surface element, an equivalent surface current is constructed on the surface element using the physical optics approximation. The far-field integral of this surface current is then performed to obtain the far-field scattered field of the target at the radar receiver point, expressed as: ， In the formula, For the target position vector Far-field scattering field at that location; Represents the total electric field; For free space intrinsic impedance; This represents the real-time slant distance between the observation point and the target. The unit vector for scattering direction. It is the unit normal vector; For the target surface micro-element Position vector; The total far-field scattered field vectors corresponding to all multiple scattering paths are superimposed in complex form to obtain the total far-field scattered field of the target at the radar receiving point. The echo matrix calculation module is used to perform spatial propagation mapping on the total far-field scattered field. It uses wavefront propagation compensation or phase inversion methods to map the far-field scattering results into the near-field echo signal of the radar platform. During the conversion process, the radar equation is introduced, and the amplitude of the echo signal is corrected according to the target distance between the radar and the target, the scattering cross section and the spatial propagation loss to obtain the two-dimensional SAR near-field echo matrix. The SAR imaging processing module is used to perform SAR imaging processing on the two-dimensional SAR near-field echo matrix. SAR imaging processing includes range compression, range migration correction (RCMC), and azimuth compression.

7. An electronic device, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 5.

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