SAR image simulation method under distance Doppler imaging geometric mapping

Abstract

The invention relates to the field of synthetic aperture radar simulation, in particular to an SAR image simulation method under distance Doppler imaging geometric mapping. According to the method, firstly, an SAR mode ray tracing framework is designed on the basis of RD imaging geometric characteristics and in combination with a ray tracing algorithm, and then a micro-surface element scattered field integral is equivalently converted into scattered field vector summation of discrete electromagnetic waves in an SAR beam reference scanning mode; the method comprises the following steps: dynamically recording the amplitude and the real-time slope distance when each discrete electromagnetic wave is scattered for multiple times by adopting an SAR mode ray tracing architecture, finally distributing the backscattering amplitude into a corresponding range gate according to a range Doppler condition equation, and directly mapping a 3D target to generate an SAR target simulation image; according to the method, the relation between the simulation fidelity and the simulation efficiency of the SAR image is effectively balanced, echo signal generation and focusing imaging processes are not involved, and a typical target SAR image data set can be quickly generated.

Description

Technical Field

[0001] The invention relates to the field of synthetic aperture radar simulation, and in particular to a SAR image simulation method under range Doppler imaging geometric mapping. Background Art

[0002] Synthetic Aperture Radar (SAR) is an active microwave imaging sensor. Satellite-borne and airborne SAR remote sensing systems are not restricted by weather and imaging time, and have extremely high application value in military and civilian fields. At present, the SAR images of typical targets obtained by actual measurement are still faced with limitations such as high hardware investment costs, diverse environmental conditions, and access rights management of specific typical targets. In particular, non-cooperative targets (such as military facilities, disaster scenes, etc.) further increase the complexity of actual measurement. However, SAR image simulation technology can generate SAR simulation images of typical targets under various conditions efficiently and at low cost in a computer virtual controllable environment according to different imaging parameters set by users (such as radar frequency, polarization mode, incident angle, flight altitude, speed, etc.), target characteristics (such as shape, material, roughness, etc.) and environmental factors (such as atmospheric propagation effects, terrain undulations, etc.). SAR image simulation technology provides researchers with an experimental platform that is not restricted by time and space, especially in the expansion of typical target SAR image data sets, SAR image interpretation, and reliability verification of some SAR system parameters. At the same time, SAR image simulation technology has been a research hotspot in the international radar field in recent years. my country's SAR technology is in a stage of vigorous development. Continuous investment and in-depth research on SAR image simulation technology will help improve my country's independent innovation capabilities in this field and help maintain its competitive advantage globally.

[0003] At present, how to effectively balance the relationship between the fidelity and efficiency of SAR image simulation is an urgent problem to be solved. The feature-based SAR image simulation method adopts the range Doppler (RD) geometric imaging model that strictly expresses the object-image relationship during SAR imaging, and brings the amplitude and slant range of each scattering of electromagnetic waves into the RD geometric imaging model. According to the real-time slant range, the amplitude of each scattering is mapped to each corresponding range gate. Without involving the echo signal generation and focusing imaging process, the SAR simulation image can be directly and quickly mapped and generated, effectively reproducing the geometric and radiation characteristics of the SAR image, and playing a great role in quickly generating typical target SAR image data sets and assisting SAR image interpretation.

[0004] Defects and shortcomings of the existing technology:

[0005] Most existing SAR image simulation methods use the surface integral method of microfacet scattering intensity to calculate the target backscattering field, which is convenient for docking with existing high-frequency electromagnetic scattering algorithms based on the plane wave assumption. They have achieved good simulation results in many application scenarios, but are also limited by the fixed simulation architecture of commercial electromagnetic scattering software. This type of simulation method usually assumes that the current intensity at each microfacet is equal to the current intensity at the center of the facet, while the current intensity and phase generated by the actual incident electromagnetic wave at different positions on the target surface are different. In order to take into account the fidelity of the simulation results, it is necessary to reduce the cross-section of the ray tube and the facet size, which makes the number of emitted electromagnetic waves surge. At the same time, the facet size of the target model is controlled at the wavelength level, which causes the distributed complex targets to be over-divided inevitably, generating a large number of facets. Even with the support of a high-configuration hardware acceleration platform, its computational efficiency is still not ideal, making it difficult to effectively carry out SAR image simulation research on complex distributed targets, which is not conducive to giving full play to the practical application efficiency of SAR image simulation technology. In summary, the method of calculating the target backscattering field by surface integral of the micro-facet scattering intensity has great limitations and poor scalability. It is difficult to improve the traditional SAR image simulation architecture and it is difficult to balance the relationship between simulation fidelity and efficiency. Summary of the invention

[0006] In view of the above problems, the present invention provides a SAR image simulation method under range Doppler imaging geometric mapping. Through the SAR image simulation method under RD imaging geometric mapping, the method first designs a SAR mode ray tracing architecture and a SAR mode physical illumination model according to the actual physical working characteristics of SAR, and performs electromagnetic wave backscattering multiple simulation. Then, using the SAR beam reference scanning method, while maintaining the original non-uniform dual-scale facet size of the distributed target model, electromagnetic waves are emitted toward the SAR beam radiation area, and the target facets in the radiation area are converted into discrete electromagnetic waves corresponding thereto, and the micro-facet scattering field integral is equivalently converted into the scattering field vector summation of discrete electromagnetic waves. Since the cosine value of the local incident angle at each location on the target surface is proportional to the backscattering intensity, this conversion operation can further refine the local incident angle. In the process of calculating the local scattering intensity of the facet, the various scattering mechanisms and the material properties of the surfaces of the components of the distributed target are fully considered. The SAR mode ray tracing architecture is used to dynamically record the amplitude and real-time slant range of each discrete electromagnetic wave during multiple scattering to ensure the correct matching relationship between the two. While recording its propagation path, it can effectively take into account the multiple coupling scattering mechanisms between the components, so that the backscattering sub-fields between the components of the distributed target are associated. Finally, according to the range Doppler condition equation, the backscattering amplitude is allocated to the corresponding range gate, and the 3D target is directly mapped to generate a SAR target simulation image, effectively balancing the relationship between the fidelity and efficiency of SAR image simulation.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A SAR image simulation method under range Doppler imaging geometric mapping comprises the following steps:

[0009] S1: Backward multiple scattering simulation based on SAR mode ray tracing; Based on the RD imaging geometric characteristics and combined with the ray tracing algorithm, the SAR mode ray tracing architecture is designed, taking into account various scattering mechanisms and target surface material properties, and integrating the bidirectional reflectance distribution function and radar equation to complete the backward multiple scattering simulation;

[0010] S1.1: SAR mode ray tracing design, considering the comprehensive influence of the energy of the SAR sensor's own active electromagnetic wave emission and the continuous attenuation process of multiple scattered energy on the backscattering field. The sampling time interval of the sensor along the azimuth direction is in the second level, while the sampling time interval in the range direction is in the microsecond level. The two are defined as the azimuth slow time and the range fast time respectively. In the process of SAR image simulation of local small scenes, the above two-dimensional sampling time magnitude difference conditions are generally met;

[0011] The purpose of the SAR mode ray tracing architecture is to determine the main axis direction of the forward scattering lobe of the electromagnetic wave after each scattering;

[0012] S1.2: Simulation of multiple backscattering of electromagnetic waves; SAR beam reference scanning is used to emit discrete electromagnetic waves toward the radiation area corresponding to the distributed target, and the amplitude and real-time slant range of each electromagnetic wave when multiple scattering occurs are recorded in sequence using the ray tracing algorithm, and the amplitude and real-time slant range are substituted into the RD condition equation to directly project the 3D target mapping into the SAR slant range coordinate system; the amplitude of each scattering is mapped to each corresponding range gate according to the real-time slant range, and the backscattering amplitude values ​​in the same range gate are superimposed to obtain the SAR simulation image;

[0013] S2: SAR image simulation taking into account multiple backscattering; the SAR mode ray tracing architecture is used to dynamically record the amplitude and real-time slant range of each discrete electromagnetic wave during multiple scattering, which can effectively take into account the multiple coupling scattering mechanism between components while recording its propagation path; finally, according to the range Doppler condition equation, the backscattering amplitude is allocated to the corresponding range gate, and the 3D target is directly mapped to generate a SAR target simulation image.

[0014] In the SAR image simulation method under the range Doppler imaging geometric mapping, when the sensor moves sequentially according to the pre-set sampling interval in azimuth and emits electromagnetic waves, and receives the echo signal at the same position, the intersection coordinates of each discrete electromagnetic wave where the kth scattering occurs and the real-time slant range are two key quantities for calculating the target backscattering field; the specific steps are as follows:

[0015] S1.1.1: The SAR beam reference scanning method is adopted, that is, the beam center section is used as the reference scanning surface, and the corresponding relationship between the real-time incident angle of the electromagnetic wave and the change of the slant range sampling interval is determined in combination with the RD imaging geometric relationship. The electromagnetic wave emission density is set according to the Nyquist sampling theorem, and then the discrete electromagnetic wave is incident on the radar beam radiation area, which can be specifically expressed as:

[0016]

[0017] Where M is the number of sampling points in azimuth, N is the number of range gates in slant range; x max and x min is the scene's orientation coordinate, R min and R max are close distance and far distance respectively; ρ r is the slant range sampling interval; R J is the slant distance in the zero Doppler plane; θ j is the angle of incidence; is the incident direction; x i is the sensor azimuth coordinate; ρ a is the azimuth sampling space; θ is the incident angle; EM is the simulated incident electromagnetic wave; P is the coordinate of any point on the target surface; H is the platform height; S0 is the platform sensor coordinate;

[0018] S1.1.2: After the simulated emitted electromagnetic wave interacts with the target surface, the macroscopic mirror reflection direction at the intersection of the electromagnetic wave and the target surface is calculated according to the Fresnel reflection law, that is, the forward propagation direction of the electromagnetic wave. The forward propagation of the electromagnetic wave satisfies the Fresnel reflection law, which can be specifically expressed as:

[0019]

[0020] in, is the mirror reflection direction when the electromagnetic wave is scattered for the kth time, and the electromagnetic wave continues to propagate forward along the mirror reflection direction of the energy axis; is the incident direction of the electromagnetic wave when the kth scattering occurs; the process of simulating multiple scattering of electromagnetic waves is essentially a recursive iterative process of recursively taking the mirror reflection direction of the energy axis of the electromagnetic wave when the k-1th scattering occurs as the incident direction when the kth scattering occurs; P k is the real-time slant distance when the kth scattering occurs; S k-1 is the coordinate of the intersection point of the k-1th scattering;

[0021] S1.1.3: In the design process of the SAR mode physical illumination model, the macroscopic mirror reflection direction is used as the main energy axis, and part of the diffuse reflection energy continues to propagate forward around the main energy axis; the SAR mode physical illumination model divides the target backscatter energy into diffuse reflection energy and mirror reflection energy, and sets a macroscopic energy attenuation coefficient for each component face element of the distributed target to quantify the energy loss value of the electromagnetic wave after each scattering, and uses its remaining energy value as the main energy for forward propagation; the intersection of the electromagnetic wave and the target surface face element is used as the starting point of the electromagnetic wave forward propagation, and the mirror reflection direction is used as the new incident direction of the electromagnetic wave, and the multiple scattering simulation of the electromagnetic wave is recursively completed; the energy threshold is set to effectively prevent the electromagnetic wave from encountering the cavity structure and entering an infinite loop, and the complex multiple scattering path of each discrete electromagnetic wave can be judged and terminated by itself; the energy attenuation process of the electromagnetic wave after multiple scattering can be expressed as:

[0022]

[0023] Among them, I in(1) =I T(1) It represents the initial incident energy of electromagnetic wave, which is set to 1 in the experiment; I in(k) K is the residual energy value of the electromagnetic wave when it is scattered for the Kth time; los is the energy attenuation coefficient. During the multiple scattering process of electromagnetic waves, they will intersect with different plane elements. This coefficient is a variable. end is the energy attenuation threshold, which is set to 0.1 in the experiment. The attenuation ratio of each scattering is quantified by the attenuation coefficients of different intersecting facets. When it is lower than the energy attenuation threshold, the multiple scattering recursive process will be stopped.

[0024] In the process of multiple scattering of electromagnetic waves and target surfaces, electromagnetic waves always intersect with target surface elements with different material properties; the surface element normal vector is divided into macro normal vector and micro normal vector. When calculating the coordinates of the intersection of the k-th scattering of discrete electromagnetic waves and the target surface, the normal vector and index number of the intersecting surface element are recorded at the same time, and the corresponding material parameters are determined by referring to the index number; the ray tracing method is used to track the propagation path of each discrete electromagnetic wave. In the design process of the SAR mode physical illumination model, the energy loss caused by the propagation path of the radar receiving and transmitting electromagnetic waves must also be considered. Specifically, combined with the radar equation P r =P t G t G r λ 2 σ / (4π) 3 R 4 It can be seen that the radar receiving echo power P r The fourth power of the propagation distance R 4 Inversely proportional, by setting the shortest slant distance D0 of the scene center as the reference slant distance, the propagation distance attenuation factor is expressed as D0 4 / R4 ; Assuming that the recursive depth of the path tracing of discrete electromagnetic waves is k, the amplitude value of the kth backscattering coefficient can be expressed as:

[0025]

[0026] In the formula, I s is the backscattered energy; I in is the incident energy; is the surface element normal vector; K d is the diffuse reflectance, K d / π represents the diffuse reflection scattering mechanism; K f is the specular reflection coefficient; K s is the specular reflectance index, K los is the energy attenuation coefficient; is the incident direction of electromagnetic wave, is the mirror reflection direction of electromagnetic waves; is the receiving direction of backscattered energy;

[0027] S1.1.4: In the simulation process of multiple scatterings of electromagnetic waves with the target surface, the coordinates of the intersection points of the kth scatterings of the electromagnetic waves with the target surface are obtained in sequence, and the instantaneous slant distance of the kth scattering is calculated by the following formula;

[0028]

[0029] Among them, R k is the instantaneous slant distance of the kth scattering, which is equivalent to half of the sum of the distances from the instantaneous position S′ of the sensor to the intersection of the kth scattering and then to S′; P′ is the coordinate of the intersection of each scattering; S′ is the instantaneous position of the sensor; R″ is the coordinate of the intersection of the kth scattering on the target; P k The distance from ′ to S′.

[0030] The SAR image simulation method under range Doppler imaging geometric mapping, step 2 also includes the following steps:

[0031] S2.1: Assign parameters to target functional components;

[0032] Considering the correspondence between the functions of each component of the distributed target and its surface material, each component is disassembled according to its function, and the parameters of the surface material are assigned to it before assembly; the OBJ model files of several disassembled main components are read in sequence, and different material parameter files are assigned; the material Txt text records the diffuse reflection coefficient, specular reflection coefficient, highlight index, and energy attenuation coefficient in sequence;

[0033] Finally, the disassembled component OBJ models are read in sequence to complete the splicing. The facets of different components have different attribute parameters, which are saved in the form of facet lists. The above target functional component reading and parameter assignment processes are set as independent modules, and independent interfaces are reserved for the continuous iteration and improvement of the backscattering model.

[0034] S2.2: Range gate position determination and mapping imaging;

[0035] The number of azimuth sampling points and the number of range gates are determined according to the boundary range outside the buffer zone, and the discrete electromagnetic waves emitted can be determined in each zero Doppler plane. The amplitude and real-time slant range of each electromagnetic wave when the kth scattering occurs can be calculated by referring to formulas (4) and (5):

[0036]

[0037] In the formula, It means that when the electromagnetic wave is scattered for the kth time, the real-time slant range and the backscattering amplitude value maintain a corresponding relationship;

[0038] Combining the range Doppler condition equation and the electromagnetic wave scattering slant range history, the following formula is obtained:

[0039]

[0040] In the formula, ρ r is the slant range sampling interval of the SAR system; y is the range gate position; (X S Y S Z S ) corresponds to the coordinates of the radiation area of ​​the dot matrix; f dc is the Doppler frequency; λ is the wavelength; R is the slant distance when the first scattering occurs; R near It is the short-range delay and the slant range reference for SAR image simulation. By bringing the real-time slant range of the transmitted electromagnetic wave into the distance condition equation when multiple scattering occurs, the target backscattering amplitude information can be accurately allocated to the corresponding range gate. It can be specifically expressed as:

[0041]

[0042] In the formula, y k is the coordinate value of the corresponding range gate position, i.e. the slant range direction of the SAR simulation image; Indicates rounding up; Indicates the corresponding relationship between the coordinate values ​​of the slant range direction of the SAR image and the backscatter amplitude value; R near For close-range delay, the scene center side angle θ and the scene close-range end coordinate y minand the platform height H is determined; the zero Doppler surface scanning process is regarded as the process of the sensor emitting M pulse trains by PRT. The electromagnetic waves emitted in the mth scanning surface will be sequentially scattered k times when the real-time slant range is substituted into formula (8), and the corresponding backscattering amplitude value is Divide into corresponding range gates By performing vector superposition on the backscatter amplitude within the same range gate, a two-dimensional SAR simulation image in the SAR slant range coordinate system can be obtained. Specifically, it can be expressed as:

[0043]

[0044] Where [σ] represents the two-dimensional SAR simulation image; It represents the backscattering amplitude value when the electromagnetic wave emitted in the mth scanning surface is scattered for the kth time; M represents the total number of pulse trains, which corresponds to the number of scanning surfaces; K represents the total number of electromagnetic wave scattering.

[0045] Compared with the prior art, the invention has the following beneficial effects: the present invention mainly proposes a SAR image simulation method under RD imaging geometric mapping, which effectively balances the relationship between SAR image simulation fidelity and efficiency, does not involve echo signal generation and focused imaging process, and can quickly generate a typical target SAR image data set. The method first designs a SAR mode ray tracing architecture based on RD imaging geometric characteristics and in combination with a ray tracing algorithm, takes into account a variety of scattering mechanisms and target surface material properties, and integrates the bidirectional reflectance distribution function and the radar equation to complete the backscattering simulation. Then, the SAR beam reference scanning method is adopted, and under the condition of maintaining the original non-uniform dual-scale facet size of the distributed target model, electromagnetic waves are emitted toward the SAR beam radiation area, and the target facets in the radiation area are converted into corresponding discrete electromagnetic waves, and the micro-facet scattering field integral is equivalently converted into the scattering field vector summation of discrete electromagnetic waves. Since the cosine value of the local incident angle at each location on the target surface is proportional to the backscattering intensity, this conversion operation can further refine the local incident angle. In the process of calculating the local scattering amplitude of the facet, a variety of scattering mechanisms and the material properties of the surfaces of each component of the distributed target are taken into account. The SAR mode ray tracing architecture is used to dynamically record the amplitude and real-time slant range of each discrete electromagnetic wave during multiple scattering, which can effectively take into account the multiple coupling scattering mechanism between components while recording its propagation path. Finally, according to the range Doppler condition equation, the backscattering amplitude is allocated to the corresponding range gate, and the 3D target is directly mapped to generate a SAR target simulation image. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Other features, objectives and advantages of the present invention will become more apparent from a reading of the detailed description of non-limiting embodiments made with reference to the following accompanying drawings.

[0047] Figure 1 It is a specific flow chart of the SAR image simulation method under range Doppler imaging geometric mapping of the present invention;

[0048] Figure 2 It is a diagram of the backscattered subfield vector superposition process under the range Doppler imaging geometric mapping of the present invention;

[0049] Figure 3 It is a three-dimensional model diagram in the present invention;

[0050] Figure 4 This is a multiple scattering decomposition result diagram during the simulation process of the present invention;

[0051] Figure 5 This is a comprehensive comparison chart of the Eiffel Tower SAR image simulation and actual measurement, and RaySAR simulation results.

[0052] in Figure 3 The 3D model of the Eiffel Tower is in OBJ format. The base width of the model is 120m, the total height is 324m, and the number of facets is 220,202.

[0053] Figure 4 This is the multiple scattering decomposition result during the Eiffel Tower simulation;

[0054] Figure 5 This is a comprehensive comparison between the Eiffel Tower SAR image simulation and actual measurement, as well as RaySAR simulation results. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below by examples, which are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0056] The present invention proposes a SAR image simulation method under range Doppler imaging geometric mapping. Specific technical solution description: (1) First, considering the RD imaging geometric characteristics, that is, the SAR sensor is an active and unique radiation source, the transmitted electromagnetic wave and the received echo are located at the same position, that is, the transmission and reception are co-located, so there is no need to consider the contribution of the environment and its own radiation energy to the backscattering field, only the comprehensive influence of the SAR sensor's own energy of actively transmitting electromagnetic waves and its continuous attenuation process of multiple scattered energy on the backscattering field is considered, and then the SAR mode ray tracing architecture design is completed in combination with the ray tracing algorithm; considering that the radar echo caused by the surface reflection of the distributed target of electrical large size or above is very strong, it is the main source of the target backscattering field, considering a variety of surface scattering mechanisms and target surface material properties, the backscattering multiple scattering simulation can be completed by integrating the bidirectional reflection distribution function and the radar equation.

[0057] (2) Then, the SAR beam reference scanning method is adopted to determine the relationship between the real-time incident angle of the electromagnetic wave and the slant range sampling interval while maintaining the original non-uniform dual-scale surface element size of the distributed target model. Then, a discrete electromagnetic wave is constructed to be incident on the radar beam radiation area, and the target surface elements in the radiation area are converted into corresponding discrete electromagnetic waves. The micro-surface scattering field integral is equivalently converted into the scattering field vector summation of the discrete electromagnetic wave. The cosine value of the local incident angle at each location on the target surface is fully considered to be proportional to the backscattering intensity, and the local incident angle is further refined.

[0058] (3) Finally, the designed SAR mode ray tracing architecture is used to dynamically record the amplitude and real-time slant range of each discrete electromagnetic wave during multiple scattering, taking into account the multiple coupling scattering mechanism between components while recording its propagation path. According to the classic range Doppler condition equation, the nearest slant range is used as the reference slant range, the backscattering amplitude is allocated to the corresponding range gate, and the 3D target is directly mapped to generate a SAR target simulation image.

[0059] The specific implementation process of the present invention is as follows:

[0060] Step 1: Backward multiple scattering simulation based on SAR mode ray tracing. Based on the RD imaging geometric characteristics and combined with the ray tracing algorithm, the SAR mode ray tracing architecture is designed, taking into account various scattering mechanisms and target surface material properties, and integrating the bidirectional reflectance distribution function and radar equation to complete the backward multiple scattering simulation.

[0061] Specifically:

[0062] 1) SAR mode ray tracing design. In the field of SAR image simulation, the ray tracing algorithm is combined with electromagnetic scattering theory or physical illumination model to simulate the complex process of multiple backscattering of the target. Unlike the light rendering in the field of computer graphics, the single-station mode SAR sensor is an active and only radiation source. The electromagnetic wave emitted and the echo received are located at the same position, that is, the transmission and reception are co-located. Therefore, there is no need to consider the contribution of the environment and its own radiation energy to the backscattering field. Only the comprehensive influence of the SAR sensor's own energy of actively emitting electromagnetic waves and its continuous attenuation process of multiple scattered energy on the backscattering field is considered. Usually, the sampling time interval of the sensor along the azimuth direction is in seconds, while the sampling time interval in the range direction is in microseconds. The two can be defined as slow time in azimuth and fast time in range, respectively. In the process of SAR image simulation of local small scenes, the above two-dimensional sampling time magnitude difference conditions are generally met, and the stop-go mode can be adopted.

[0063] The main function of the SAR mode ray tracing architecture is to determine the main axis direction of the forward scattering lobe after each scattering of the electromagnetic wave. The electromagnetic wave is incident on the target surface and is reflected in a certain direction. The main axis direction of the forward scattering lobe of the electromagnetic wave can be determined by the Fresnel mirror reflection law. The macroscopic surface element normal vector of the target surface, the incident direction of the electromagnetic wave, and the mirror reflection direction are coplanar. In actual application, the mirror reflection direction calculated by the macroscopic surface element normal vector at the intersection of the electromagnetic wave is the main axis direction of the forward scattering lobe.

[0064] 2) Simulation of multiple backscattering of electromagnetic waves. Based on the design of the SAR mode ray tracing architecture, the present invention takes into account that the traditional physical illumination model belongs to a local scattering model, and the coupled scattering mechanism between the components of the distributed target is not effectively reflected. The SAR model physical illumination model is designed according to the actual working characteristics of the SAR, and combined with the SAR mode ray tracing architecture, multiple backscattering simulation of electromagnetic waves can be performed. The SAR beam reference scanning method is adopted to emit discrete electromagnetic waves toward the radiation area corresponding to the distributed target, and the ray tracing algorithm is used to record the amplitude and real-time slant range of each electromagnetic wave when multiple scattering occurs in turn, and it is brought into the RD condition equation to directly project the 3D target mapping into the SAR slant range coordinate system. The essence of this method is to map the amplitude of each scattering to each corresponding range gate according to the real-time slant range, and the backscattering amplitude values ​​in the same range gate are superimposed to obtain a SAR simulation image.

[0065] When the sensor moves and emits electromagnetic waves in sequence according to the pre-set sampling interval in azimuth, and receives the echo signal at the same position, the intersection coordinates of each discrete electromagnetic wave where the kth scattering occurs and the real-time slant range are two key quantities for calculating the target's backscattering field. The specific steps are as follows:

[0066] ① The SAR beam reference scanning method is adopted, that is, the beam center section is used as the reference scanning surface, and the corresponding relationship between the real-time incident angle of the electromagnetic wave and the change of the slant range sampling interval is determined in combination with the RD imaging geometric relationship. The electromagnetic wave emission density is set according to the Nyquist sampling theorem, and then the discrete electromagnetic wave is incident on the radar beam radiation area, which can be specifically expressed as:

[0067]

[0068] Where M is the number of sampling points in azimuth, N is the number of range gates in slant range; x max and x min is the scene's orientation coordinate, R min and R max are close distance and far distance respectively; ρ r is the slant range sampling interval; R J is the slant distance in the zero Doppler plane; θ j is the angle of incidence; is the incident direction; x i is the sensor azimuth coordinate; ρ a is the azimuth sampling space; θ is the incident angle; EM is the simulated incident electromagnetic wave; P is the coordinate of any point on the target surface; H is the platform height; S0 is the platform sensor coordinate;

[0069] ② After the simulated emitted electromagnetic wave interacts with the target surface, the macroscopic mirror reflection direction at the intersection of the electromagnetic wave and the target surface is calculated according to the Fresnel reflection law, that is, the forward propagation direction of the electromagnetic wave. The forward propagation of the electromagnetic wave satisfies the Fresnel reflection law, that is, in the plane where the incident electromagnetic wave, the reflected electromagnetic wave and the normal vector at the intersection are located, the reflection angle is equal to the incident angle. It can be specifically expressed as:

[0070]

[0071] in, is the mirror reflection direction when the electromagnetic wave is scattered for the kth time, and the electromagnetic wave continues to propagate forward along the mirror reflection direction of the energy axis; is the incident direction of the electromagnetic wave when it is scattered for the kth time; the process of simulating multiple scattering of electromagnetic waves is essentially a recursive iterative process of recursively taking the mirror reflection direction of the energy axis of the electromagnetic wave when it is scattered for the k-1th time as the incident direction for the kth scattering. k is the real-time slant distance when the kth scattering occurs; S k-1 + is the intersection coordinate of the k-1th scattering.

[0072] ③ In the design process of the SAR mode physical illumination model, considering that the target surface material has a certain glossiness and roughness at the same time, it is easy to have directional scattering dominated by the mirror reflection mechanism, with the macroscopic mirror reflection direction as the main energy axis, and part of the diffuse reflection (including subsurface scattering) energy continues to propagate forward around the main energy axis. The SAR mode physical illumination model designed by the present invention divides the target backscattering energy into diffuse reflection energy and mirror reflection energy. Since diffuse reflection and absorption energy are not easy to quantify and calculate, in order to facilitate the calculation of the forward propagation energy of the electromagnetic wave after each scattering, a macroscopic energy attenuation coefficient is set for each component face element of the distributed target to quantify the energy loss value of the electromagnetic wave after each scattering, and its energy remaining value is used as the main energy of forward propagation. The electromagnetic wave intersects with different component positions on the target surface, and the material properties of each component face element are different, which has different effects on the attenuation of the propagation energy. The intersection of the electromagnetic wave and the target surface face element is used as the starting point of the forward propagation of the electromagnetic wave, and the mirror reflection direction is used as the new incident direction of the electromagnetic wave, and the multiple scattering simulation of the electromagnetic wave is recursively completed. During the multiple scattering process, electromagnetic waves follow the law of conservation of energy. Specifically, the macroscopic manifestation is that the outgoing energy is not higher than the incident energy. As multiple scattering occurs, the propagation energy will continue to decay. Therefore, the recursive depth of multiple scattering is determined by the actual propagation path of the electromagnetic wave and the energy attenuation. In the experiment, the present invention sets an energy threshold to effectively prevent the electromagnetic wave from entering a dead loop when encountering a cavity structure, and can automatically determine and terminate the tracking of the complex multiple scattering path of each discrete electromagnetic wave. The energy attenuation process of multiple scattering of electromagnetic waves can be expressed as

[0073]

[0074] Among them, I in(1) =I T(1) It represents the initial incident energy of electromagnetic wave, which is set to 1 in the experiment; I in(k) K is the residual energy value of the electromagnetic wave when it is scattered for the Kth time; los is the energy attenuation coefficient. During the multiple scattering process of electromagnetic waves, they will intersect with different plane elements. This coefficient is a variable. end is the energy attenuation threshold, which is set to 0.1 in the experiment. The attenuation ratio of each scattering is quantified by the attenuation coefficients of different intersecting face elements. When it is lower than the energy attenuation threshold, the multiple scattering recursive process will be stopped.

[0075] In the process of multiple scattering between electromagnetic waves and target surfaces, electromagnetic waves always intersect with target surface elements with different material properties. The surface element normal vector is divided into macroscopic normal vector and microscopic normal vector. The macroscopic surface element normal vector is an important variable for recursively determining the forward tracking direction of electromagnetic waves, and is also a key factor in calculating the surface element backscattering field. The micro-surface element normal vector is a reasonable correction to the backscattering amplitude value from the perspective of the micro-surface element. According to the regularity of the distribution of the tiny surface element normal vector, the index of the quantified target surface material gloss and roughness is set. The material parameter type in the physical illumination model is used to set the specular reflection coefficient, diffuse reflection coefficient, highlight index, and energy attenuation coefficient. When calculating the intersection coordinates of the kth scattering of the discrete electromagnetic wave and the target surface, the normal vector and index number of the intersecting surface element are recorded at the same time, and the corresponding material parameters are determined by referring to the index number. The ray tracing method is used to track the propagation path of each discrete electromagnetic wave. When the selected distributed target geometry is relatively regular, the termination condition of multiple scattering is mainly that there is no collision point to end the recursion. In addition, in the design process of the SAR mode physical illumination model, the energy loss caused by the propagation path of the radar receiving and transmitting electromagnetic waves must also be considered. r =P t G t G r λ 2 σ / (4π) 3 R 4 It can be seen that the radar receiving echo power P r The fourth power of the propagation distance R 4 Inversely proportional, by setting the shortest slant distance D0 of the scene center as the reference slant distance, the propagation distance attenuation factor is expressed as D0 4 / R 4 Assuming that the recursive depth of the path tracing of discrete electromagnetic waves is k, the amplitude value of the kth backscattering coefficient can be expressed as:

[0076]

[0077] In the formula, I s is the backscattered energy; I in is the incident energy; is the surface element normal vector; K d is the diffuse reflectance, K d / π represents the diffuse reflection scattering mechanism; K f is the specular reflection coefficient; K s is the specular reflectance index, K los is the energy attenuation coefficient; is the incident direction of electromagnetic wave, is the direction of mirror reflection of electromagnetic waves; is the receiving direction of backscattered energy.

[0078] ④ In the simulation process of multiple scatterings between the electromagnetic wave and the target surface, the coordinates of the intersection points of the k-th scatterings between the electromagnetic wave and the target surface are obtained in sequence, and the instantaneous slant distance of the k-th scattering is calculated by the following formula.

[0079]

[0080] Among them, R k is the instantaneous slant distance of the kth scattering, which is equivalent to half of the sum of the distances from the instantaneous position S' of the sensor to the intersection of the kth scattering and then to S'. P' is the coordinate of the intersection of each scattering. S' is the instantaneous position of the sensor. R" is the coordinate of the intersection of the kth scattering on the target. k The distance from ′ to S′.

[0081] In summary, the research on the simulation of electromagnetic wave backscattering based on the SAR mode ray tracing architecture is an important part of the SAR image simulation process, which directly affects the quality of SAR simulation images. First, the distributed targets in the beam radiation area are converted into discrete electromagnetic waves using the SAR beam scanning method. Combined with the SAR mode ray tracing architecture and the SAR mode physical illumination model, the amplitude and real-time slant range of each electromagnetic wave when multiple scattering occurs are recorded. Both are necessary parameters for the calculation of the target backscattering field. Then, the amplitude and slant range during multiple scattering are brought into the distance condition equation, and the amplitude information is directly mapped to the two-dimensional SAR slant range image to generate a SAR target simulation image.

[0082] Step 2: SAR image simulation taking into account multiple backscattering. The SAR mode ray tracing architecture is used to dynamically record the amplitude and real-time slant range of each discrete electromagnetic wave during multiple scattering. While recording its propagation path, it can effectively take into account the multiple coupling scattering mechanism between each component. Finally, according to the range Doppler condition equation, the backscattering amplitude is allocated to the corresponding range gate, and the 3D target is directly mapped to generate a SAR target simulation image.

[0083] Specifically:

[0084] 1) Assign parameters to the target functional component.

[0085] Considering the corresponding relationship between the functions of each component of the distributed target and its surface material, each component is disassembled according to its function, and the parameters of the surface material are assigned to it before assembly. The OBJ model files of several disassembled main components are read in sequence, and different material parameter text files are assigned. For example, component 1 (OBJ-1) corresponds to material parameter 1 (Txt-1), and a structure for storing facet information is established, including geometric coordinate elements and material parameter elements. In the actual simulation process, its geometric data (vertex coordinates v and facet number f) is mainly used, and the index number of the corresponding construction facet vertex coordinates is found according to the facet number f data, and the corresponding vertex coordinates v are read cyclically to complete the construction of the complete scene and read the material Txt-1 text format parameters corresponding to each target. Each parameter is separated by a space, and the number of parameters needs to be specifically determined in combination with the scattering model used. According to the designed SAR mode physical illumination model, the material Txt text records the diffuse reflection coefficient, specular reflection coefficient, highlight index, and energy attenuation coefficient in sequence.

[0086] Finally, the disassembled component OBJ models are read in sequence to complete the splicing. The facets of different components have different attribute parameters, which are saved in the form of facet lists. In the process of program design, the process of reading and assigning parameters of the above target functional components is set as an independent module, and an independent interface is reserved for the continuously iterative and improved backscattering model. In the process of continuous improvement of the backscattering model, the material parameters considered are more comprehensive, and the material Txt text matches the material parameter content considered by the backscattering model at any time.

[0087] 2) Determine the range gate position and map the image.

[0088] The number of azimuth sampling points and the number of range gates are determined according to the boundary range outside the buffer zone, and the discrete electromagnetic waves emitted can be determined in each zero Doppler plane. Referring to formulas (4) and (5), the amplitude and real-time slant range of each electromagnetic wave when the kth scattering occurs can be calculated as:

[0089]

[0090] In the formula, It means that when the electromagnetic wave is scattered for the kth time, the real-time slant range and the backscattering amplitude value maintain a corresponding relationship;

[0091] Combining the range Doppler condition equation and the electromagnetic wave scattering slant range history, the following formula is obtained:

[0092]

[0093] In the formula, ρ r is the slant range sampling interval of the SAR system; y is the range gate position; (X S Y S ZS ) corresponds to the coordinates of the radiation area of ​​the dot matrix; f dc is the Doppler frequency; λ is the wavelength; R is the slant distance when the first scattering occurs; R near It is the short-range delay and the slant range reference for SAR image simulation. By bringing the real-time slant range of the transmitted electromagnetic wave into the distance condition equation when multiple scattering occurs, the target backscattering amplitude information can be accurately allocated to the corresponding range gate. It can be specifically expressed as:

[0094]

[0095] In the formula, y k is the coordinate value of the corresponding range gate position, i.e. the slant range direction of the SAR simulation image; Indicates rounding up; Indicates the corresponding relationship between the coordinate values ​​of the slant range direction of the SAR image and the backscatter amplitude value; R near For close-range delay, the scene center side angle θ and the scene close-range end coordinate y min The platform height H is determined. The zero Doppler scanning process is regarded as the process of the sensor transmitting M pulse trains by PRT. The electromagnetic waves emitted in the mth scanning surface will be sequentially scattered k times when the real-time slant range is substituted into formula (8), and the corresponding backscattering amplitude value is Divide into corresponding range gates By performing vector superposition on the backscatter amplitude within the same range gate, a two-dimensional SAR simulation image in the SAR slant range coordinate system can be obtained, which can be specifically expressed as:

[0096]

[0097] Where [σ] represents the two-dimensional SAR simulation image; It represents the backscattering amplitude value when the electromagnetic wave emitted in the mth scanning surface is scattered for the kth time; M represents the total number of pulse trains, corresponding to the number of scanning surfaces; K represents the total number of electromagnetic wave scattering;

[0098] In the actual operation, the specific steps are as follows: first, the SAR mode ray tracing architecture is used to calculate the amplitude and real-time slant range of the electromagnetic waves emitted in each real-time scanning plane when they are scattered multiple times, and the two are stored in two matrices respectively. The real-time slant range matrix is ​​substituted into the distance condition equation to generate the slant range coordinate matrix, such as Figure 2 As shown in the figure, taking the 4×4 grid recorded when a local scene scatters, each element value of the slant range coordinate matrix is ​​an integer and unordered, but has a definite matching relationship with the position of the amplitude matrix element σ. Each real-time scanning surface corresponds to an azimuth line, and the range gate coordinate y is converted to the same azimuth line of the two matrices. kThe same amplitude values ​​are superimposed. Along the first row of azimuth lines, there are two amplitude values ​​located in the third range gate, namely σ2 and σ3. Fill the result of σ2+σ3 into the third range gate in the first row of azimuth lines. If there is no corresponding range gate coordinate in the slant range coordinate matrix, for example, there is no amplitude value located in the second range gate in the first row of azimuth lines, then the amplitude value in the final two-dimensional simulation image matrix is ​​0, and it is displayed in black. Refer to the above operation steps for different azimuth lines, and fill different amplitude results into the SAR slant range coordinate system prefabricated according to the two-dimensional boundary of the buffer zone to generate a SAR target simulation image.

[0099] Table 1 shows the main parameters of the SAR system;

[0100] Table 2 shows the computer configuration parameters used in the experiment;

[0101] Table 3 shows the quantitative evaluation of the simulation results;

[0102] Table 4 shows the test time statistics.

[0103] Table 1

[0104]

[0105] Table 2

[0106]

[0107] Table 3

[0108]

[0109] Table 4

[0110]

[0111] Although the specific embodiments of the present invention are described above, it should be understood by those skilled in the art that this is only for illustration and the protection scope of the present invention is defined by the appended claims. Those skilled in the art may make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but these changes and modifications all fall within the protection scope of the present invention.

Claims

1. A SAR image simulation method under range Doppler imaging geometric mapping, characterized in that: The steps include: S1: Backward multiple scattering simulation based on SAR mode ray tracing; Based on the RD imaging geometric characteristics and combined with the ray tracing algorithm, the SAR mode ray tracing architecture is designed, taking into account various scattering mechanisms and target surface material properties, and integrating the bidirectional reflectance distribution function and radar equation to complete the backward multiple scattering simulation; S1.1: SAR mode ray tracing design, considering the comprehensive influence of the energy of the SAR sensor's own active electromagnetic wave emission and the continuous attenuation process of multiple scattered energy on the backscattering field. The sampling time interval of the sensor along the azimuth direction is in the second level, while the sampling time interval in the range direction is in the microsecond level. The two are defined as the azimuth slow time and the range fast time respectively. In the process of SAR image simulation of local small scenes, the above two-dimensional sampling time magnitude difference conditions are met; The purpose of the SAR mode ray tracing architecture is to determine the main axis direction of the forward scattering lobe of the electromagnetic wave after each scattering; S1.2: Simulation of multiple backscattering of electromagnetic waves; SAR beam reference scanning is used to emit discrete electromagnetic waves toward the radiation area corresponding to the distributed target, and the amplitude and real-time slant range of each electromagnetic wave when multiple scattering occurs are recorded in sequence using the ray tracing algorithm, and the amplitude and real-time slant range are substituted into the RD condition equation to directly project the 3D target mapping into the SAR slant range coordinate system; the amplitude of each scattering is mapped to each corresponding range gate according to the real-time slant range, and the backscattering amplitude values ​​in the same range gate are superimposed to obtain the SAR simulation image; S2: SAR image simulation taking into account multiple backscattering; the SAR mode ray tracing architecture is used to dynamically record the amplitude and real-time slant range of each discrete electromagnetic wave during multiple scattering, which can effectively take into account the multiple coupling scattering mechanism between components while recording its propagation path; finally, according to the range Doppler condition equation, the backscattering amplitude is allocated to the corresponding range gate, and the 3D target is directly mapped to generate a SAR target simulation image.

2. The SAR image simulation method under range Doppler imaging geometric mapping according to claim 1, characterized in that: When the sensor moves in sequence according to the pre-set sampling interval in azimuth and emits electromagnetic waves, and receives the echo signal at the same position, the intersection coordinates and real-time slant range of each discrete electromagnetic wave where the kth scattering occurs are two key quantities for calculating the target's backscattering field; the specific steps are as follows: S1.1.1: The SAR beam reference scanning method is adopted, that is, the beam center section is used as the reference scanning surface, and the corresponding relationship between the real-time incident angle of the electromagnetic wave and the change of the slant range sampling interval is determined in combination with the RD imaging geometric relationship. The electromagnetic wave emission density is set according to the Nyquist sampling theorem, and then the discrete electromagnetic wave is incident on the radar beam radiation area, which can be specifically expressed as: Where M is the number of sampling points in azimuth, N is the number of range gates in slant range; x max and x min is the scene's orientation coordinate, R min and R max are close distance and far distance respectively; ρ r is the slant range sampling interval; R J is the slant distance in the zero Doppler plane; θ j is the angle of incidence; is the incident direction; x i is the sensor azimuth coordinate; ρ a is the azimuth sampling space; θ is the incident angle; EM is the simulated incident electromagnetic wave; P is the coordinate of any point on the target surface; H is the platform height; S 0 is the platform sensor coordinate; S1.1.2: After the simulated emitted electromagnetic wave interacts with the target surface, the macroscopic mirror reflection direction at the intersection of the electromagnetic wave and the target surface is calculated according to the Fresnel reflection law, that is, the forward propagation direction of the electromagnetic wave. The forward propagation of the electromagnetic wave satisfies the Fresnel reflection law, which can be specifically expressed as: in, is the mirror reflection direction when the electromagnetic wave is scattered for the kth time, and the electromagnetic wave continues to propagate forward along the mirror reflection direction of the energy axis; is the incident direction of the electromagnetic wave when the kth scattering occurs; the process of simulating multiple scattering of electromagnetic waves is essentially a recursive iterative process of recursively taking the mirror reflection direction of the energy axis of the electromagnetic wave when the k-1th scattering occurs as the incident direction when the kth scattering occurs; P k is the real-time slant distance when the kth scattering occurs; S k-1 is the coordinate of the intersection point of the k-1th scattering; S1.1.3: In the design process of the SAR mode physical illumination model, the macroscopic mirror reflection direction is used as the main energy axis, and part of the diffuse reflection energy continues to propagate forward around the main energy axis; the SAR mode physical illumination model divides the target backscatter energy into diffuse reflection energy and mirror reflection energy, and sets a macroscopic energy attenuation coefficient for each component face element of the distributed target to quantify the energy loss value of the electromagnetic wave after each scattering, and uses its remaining energy value as the main energy for forward propagation; the intersection of the electromagnetic wave and the target surface face element is used as the starting point of the electromagnetic wave forward propagation, and the mirror reflection direction is used as the new incident direction of the electromagnetic wave, and the multiple scattering simulation of the electromagnetic wave is recursively completed; the energy threshold is set to effectively prevent the electromagnetic wave from encountering the cavity structure and entering an infinite loop, and the complex multiple scattering path of each discrete electromagnetic wave can be judged and terminated by itself; the energy attenuation process of the electromagnetic wave after multiple scattering can be expressed as: Among them, I in(1) =I T(1) It represents the initial incident energy of electromagnetic wave, which is set to 1 in the experiment; I in(k) K is the residual energy value of the electromagnetic wave when it is scattered for the kth time; los is the energy attenuation coefficient. During the multiple scattering process of electromagnetic waves, they will intersect with different plane elements. This coefficient is a variable. end is the energy attenuation threshold, which is set to 0.1 in the experiment. The attenuation ratio of each scattering is quantified by the attenuation coefficients of different intersecting facets. When it is lower than the energy attenuation threshold, the multiple scattering recursive process will be stopped. In the process of multiple scattering of electromagnetic waves and target surfaces, electromagnetic waves always intersect with target surface elements with different material properties; the surface element normal vector is divided into macro normal vector and micro normal vector. When calculating the coordinates of the intersection of the k-th scattering of discrete electromagnetic waves and the target surface, the normal vector and index number of the intersecting surface element are recorded at the same time, and the corresponding material parameters are determined by referring to the index number; the ray tracing method is used to track the propagation path of each discrete electromagnetic wave. In the design process of the SAR mode physical illumination model, the energy loss caused by the propagation path of the radar receiving and transmitting electromagnetic waves must also be considered. Specifically, combined with the radar equation P r =P t G t G r λ 2 σ / (4π) 3 R 4 It can be seen that the radar receiving echo power P r It is inversely proportional to the fourth power of the propagation distance R4. By setting the shortest slant distance D0 of the scene center as the reference slant distance, the propagation distance attenuation factor is expressed as D0 4 / R 4 ; Assuming that the recursive depth of the path tracing of discrete electromagnetic waves is k, the amplitude value of the kth backscattering coefficient can be expressed as: In the formula, I s is the backscattered energy; I in is the incident energy; N is the surface element normal vector; K d is the diffuse reflectance, K d / π represents the diffuse scattering mechanism in all directions; K f is the specular reflection coefficient; K s is the specular reflectance index, K los is the energy attenuation coefficient; is the incident direction of electromagnetic wave, is the direction of mirror reflection of electromagnetic waves; is the receiving direction of backscattered energy; S1.1.4: In the simulation process of multiple scatterings of electromagnetic waves with the target surface, the coordinates of the intersection points of the kth scatterings of the electromagnetic waves with the target surface are obtained in sequence, and the instantaneous slant distance of the kth scattering is calculated by the following formula; in, R k is the instantaneous slant distance of the kth scattering, which is equivalent to half of the sum of the distances from the instantaneous position S′ of the sensor to the intersection of the kth scattering and then to S′; P′ is the coordinate of the intersection of each scattering; S′ is the instantaneous position of the sensor; R″ is the coordinate of the intersection of the kth scattering on the target; P k ′ The distance to S'.

3. The SAR image simulation method under range Doppler imaging geometric mapping according to claim 2, characterized in that: Step 2 also includes the following steps: S2.1: Assign parameters to target functional components; Considering the correspondence between the functions of each component of the distributed target and its surface material, each component is disassembled according to its function, and the parameters of the surface material are assigned to it before assembly; the OBJ model files of several disassembled main components are read in sequence, and different material parameter files are assigned; the material Txt text records the diffuse reflection coefficient, specular reflection coefficient, highlight index, and energy attenuation coefficient in sequence; Finally, the disassembled component OBJ models are read in sequence to complete the splicing. The facets of different components have different attribute parameters, which are saved in the form of facet lists. The above target functional component reading and parameter assignment processes are set as independent modules, and independent interfaces are reserved for the continuous iteration and improvement of the backscattering model. S2.2: Range gate position determination and mapping imaging; The number of azimuth sampling points and the number of range gates are determined according to the boundary range outside the buffer zone, and the discrete electromagnetic waves emitted can be determined in each zero Doppler plane. Referring to formulas (4) and (5), the amplitude and real-time slant range of each electromagnetic wave when the kth scattering occurs can be calculated as follows: In the formula, It means that when the electromagnetic wave is scattered for the kth time, the real-time slant range and the backscattering amplitude value maintain a corresponding relationship; Combining the range Doppler condition equation and the electromagnetic wave scattering slant range history, the following formula is obtained: In the formula, ρ r is the slant range sampling interval of the SAR system; y is the range gate position; (X S Y S Z S ) corresponds to the coordinates of the radiation area of ​​the dot matrix; f dc is the Doppler frequency; λ is the wavelength; R is the slant distance when the first scattering occurs; R near It is the short-range delay and the slant range reference for SAR image simulation. By bringing the real-time slant range of the emitted electromagnetic wave into the distance condition equation when multiple scattering occurs, the target backscatter amplitude information can be accurately allocated to the corresponding range gate. It can be specifically expressed as: In the formula, y k is the coordinate value of the slant range direction of the corresponding range gate position, i.e., the SAR simulation image. Indicates rounding up; Indicates the corresponding relationship between the coordinate values ​​of the slant range direction of the SAR image and the backscatter amplitude value; R near For close-range delay, the scene center side angle θ and the scene close-range end coordinate y min and the platform height H is determined; the zero Doppler surface scanning process is regarded as the process of the sensor transmitting M pulse trains by PRT. The electromagnetic wave emitted in the mth scanning surface will be substituted into the real-time slant range when the kth scattering occurs in turn into formula (8), and the corresponding backscattering amplitude value is Divide into corresponding range gates By performing vector superposition on the backscatter amplitude within the same range gate, a two-dimensional SAR simulation image in the SAR slant range coordinate system can be obtained, which can be specifically expressed as: Where, [σ] represents the two-dimensional SAR simulation image; It represents the backscattering amplitude value when the electromagnetic wave emitted in the mth scanning surface is scattered for the kth time; M represents the total number of pulse trains, which corresponds to the number of scanning surfaces; K Indicates the total number of times electromagnetic waves are scattered.

Images