Second-order curved wave integral surface clutter simulation method for planetary exploration radar

Abstract

The application provides a second-order curved surface wave integral surface clutter simulation method of a planetary exploration radar, and can be applied to the technical field of radar signal processing. The method comprises the following steps: performing triangular facet division on a surface model of a target planet to obtain a plurality of triangular facets; obtaining relative distances from a radar observation point to points of each triangular facet except the center of gravity, wherein the relative distance is in a function form; based on a physical optics method, establishing a scattering electric field integral expression of each triangular facet containing the relative distance, and performing second-order Taylor expansion on the relative distance to retain a first-order term and a second-order term; based on an analytical solution of the first-order term and the second-order term, obtaining an analytical solution of second-order curved surface wave integral of the scattering electric field of each triangular facet, and calculating a corresponding scattering electric field; and accumulating the scattering electric fields of the plurality of triangular facets to obtain surface clutter of the target planet. In this way, high-precision and high-efficiency radar surface clutter simulation can be realized.

Description

Technical Field

[0001] This application relates to the field of radar signal processing technology, and specifically to a second-order surface wave integral surface clutter simulation method for planetary exploration radar. Background Technology

[0002] Radar plays a crucial role as a core payload in planetary exploration missions. It transmits electromagnetic signals to planets and receives echo signals to analyze and acquire various key planetary data. However, during radar echo reception, interference from surface clutter generated by the complex terrain of planets is inevitable. At the same time, due to the significant amplitude attenuation effect of electromagnetic waves propagating in the lossy medium of planets, weak echo signals from the planet's interior and strong surface clutter signals are severely mixed in the time and frequency domains, which seriously restricts the effective extraction and analysis of internal echoes.

[0003] In order to achieve effective separation of internal echoes and surface clutter from planets, it is necessary to generate surface clutter through high-precision simulation. However, in related technologies, there are still many problems in clutter simulation under complex terrain and time-varying scattering detection scenarios: (1) large phase error and low simulation accuracy make it difficult to accurately simulate the real characteristics of surface clutter, resulting in inaccurate results of subsequent internal echo extraction and analysis; (2) excessive consumption of computing resources and demanding requirements for hardware equipment make it impossible to achieve efficient application in actual engineering, which seriously restricts the efficiency of radar data processing in planetary exploration.

[0004] In summary, there is an urgent need for a clutter simulation method that can balance computational accuracy and efficiency to meet the practical needs of radar data processing in planetary exploration. Summary of the Invention

[0005] In view of the above problems, embodiments of this application provide a second-order surface wave integral surface clutter simulation method for planetary exploration radar.

[0006] According to a first aspect of this application, a second-order surface wave integral surface clutter simulation method for planetary exploration radar is provided, comprising: dividing the surface model of the target planet into triangular facets to obtain multiple triangular facets, wherein the surface model is a surface model characterizing the elevation distribution characteristics of the target planet's surface; obtaining the relative distances from the radar observation point to each triangular facet point except for the centroid, wherein the relative distances are in functional form; establishing an integral expression for the scattered electric field containing the relative distance for each triangular facet point based on physical optics, and performing a second-order Taylor expansion on the relative distances, retaining the first-order and second-order terms; obtaining the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular facet point based on the analytical solutions of the first-order and second-order terms, and calculating the corresponding scattered electric field; and accumulating the scattered electric fields of multiple triangular facet points to obtain the surface clutter of the target planet.

[0007] According to an embodiment of this application, obtaining the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element based on the analytical solutions of the first-order and second-order terms includes: obtaining the vertex coordinates and surface element normal vector of each triangular surface element; solving the first-order and second-order terms respectively based on the vertex coordinates and surface element normal vector to obtain the corresponding analytical solutions of the first-order and second-order terms; and multiplying the analytical solutions of the first-order and second-order terms to obtain the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element.

[0008] According to an embodiment of this application, the analytical solution of the first-order term is obtained in the following manner: a first vector is obtained based on the wave number of the radar incident wave and the centroid position vector of the triangular surface element. The first vector is used to characterize the phase accumulation effect of the radar incident wave after reflection by the triangular surface element; a second vector is obtained based on the first vector and the surface element normal vector. The second vector is used to characterize the projection component of the first vector within the triangular surface element; the scattered electric field vector of the triangular surface element is obtained based on the second vector, vertex coordinates, and surface element normal vector, and the scattered electric field vector is used as the analytical solution of the first-order term.

[0009] According to an embodiment of this application, the analytical solution of the second-order term is obtained as follows: two orthogonal basis vectors are established on a plane perpendicular to the radar illumination direction; the vectors within the triangular element are projected onto the plane to obtain the projected vectors, and the decomposition coefficients of the projected vectors on the two orthogonal basis vectors are used as local coordinates; based on the local coordinates, the Fresnel integral variables of each vertex within the triangular element are obtained; based on the Fresnel integral variables of each vertex, the corresponding complex Fresnel integral values ​​are calculated respectively; the product of the weighting coefficients corresponding to each vertex and the complex Fresnel integral values ​​is summed to obtain the analytical solution of the second-order term.

[0010] According to an embodiment of this application, the second-order Taylor expansion uses the centroid of the triangular facet as a reference point.

[0011] According to an embodiment of this application, the surface model is constructed based on a digital elevation model, which is a stereolithography engineering file generated based on triangular facet division.

[0012] According to a second aspect of this application, a second-order surface wave integral surface clutter simulation device for planetary exploration radar is provided, comprising: a triangular element partitioning module for partitioning the surface model of a target planet into multiple triangular elements, wherein the surface model is a surface model characterizing the elevation distribution of the target planet's surface; a distance acquisition module for acquiring the relative distance from the radar observation point to each triangular element except for the centroid, wherein the relative distance is in functional form; a Taylor expansion module for establishing a scattering electric field integral expression containing the relative distance for each triangular element based on physical optics, and performing a second-order Taylor expansion on the relative distance, retaining the first-order and second-order terms; a scattering electric field determination module for obtaining the analytical solution of the second-order surface wave integral of the scattering electric field of each triangular element based on the analytical solutions of the first-order and second-order terms, and calculating the corresponding scattering electric field; and a surface clutter determination module for accumulating the scattering electric fields of multiple triangular elements to obtain the surface clutter of the target planet.

[0013] According to a third aspect of this application, an electronic device is provided, comprising: one or more processors; and a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method described above.

[0014] According to a fourth aspect of this application, a computer-readable storage medium is also provided, on which a computer program or instructions are stored, wherein the computer program or instructions, when executed by a processor, implement the steps of the above-described method.

[0015] According to a fifth aspect of this application, a computer program product is also provided, comprising a computer program or instructions that, when executed by a processor, implement the steps of the above-described method.

[0016] According to the embodiments of this application, by performing a second-order Taylor expansion on the relative distance between the radar and the target surface element, the phase error caused by the second-order electromagnetic wave curvature term, which is approximately ignored in traditional plane waves, can be compensated, and high-precision radar surface clutter simulation can be achieved. By using the second-order surface wave integral analytical solution derived based on the analytical integration scheme, compared with the traditional numerical integration method, the analytical solution significantly improves the computational efficiency and accelerates the convergence speed, while effectively eliminating the truncation error and rounding error caused by discretization, thereby greatly reducing the demand for computing power while ensuring computational accuracy. Attached Figure Description

[0017] The above-mentioned contents, other objects, features and advantages of this application will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0018] Figure 1This diagram schematically illustrates an application scenario of the second-order surface wave integral surface clutter simulation method for planetary exploration radar according to an embodiment of this application.

[0019] Figure 2 A flowchart illustrating a second-order surface wave integral surface clutter simulation method for planetary exploration radar according to an embodiment of this application is shown schematically.

[0020] Figure 3A A schematic diagram of a planetary simulation model according to an embodiment of this application is shown.

[0021] Figure 3B The illustration schematically shows a three-dimensional visualization of the digital elevation model corresponding to the planetary simulation model according to an embodiment of this application;

[0022] Figure 4A The illustration shows a schematic diagram of the imaging result of the numerical integration method according to an embodiment of this application;

[0023] Figure 4B The schematic diagram illustrates the imaging results of the plane wave integral method according to an embodiment of this application;

[0024] Figure 4C The diagram illustrates the imaging results of the second-order surface wave integral method according to an embodiment of this application.

[0025] Figure 4D This illustration schematically shows a high-frequency back projection imaging result of the numerical integration method according to an embodiment of this application;

[0026] Figure 4E This illustration schematically shows a high-frequency back projection imaging result of the plane wave integral method according to an embodiment of this application;

[0027] Figure 4F This schematic diagram illustrates the high-frequency back projection imaging results of the second-order surface wave integral method according to an embodiment of this application.

[0028] Figure 5 The schematic diagram illustrates the structural block diagram of a second-order curved surface wave integral surface clutter simulation device for a planetary exploration radar according to an embodiment of this application;

[0029] Figure 6 A block diagram of an electronic device suitable for implementing a second-order surface clutter simulation method for planetary exploration radar, according to an embodiment of this application, is shown schematically. Detailed Implementation

[0030] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0031] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0032] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0033] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0034] Before disclosing the embodiments of this application in detail, the key technical terms used in the embodiments of this application will be explained one by one, as follows:

[0035] Scattered electric fields are secondary electromagnetic fields generated after electromagnetic waves are incident on the surface of an object and undergo reflection, diffraction, and secondary radiation. They contain key physical information such as the target's geometry and the electromagnetic properties of the medium.

[0036] Clutter is a useless scattered signal. It is a useless background echo formed by the scattering of radar electromagnetic waves on the surface of a planet due to the undulation of the surface, the inhomogeneity of the rock and soil medium, the local rough landforms and geological textures. It can obscure the scattered electric field signal of the planetary target itself and interfere with the accuracy of ground feature identification and electromagnetic parameter inversion.

[0037] Physical Optics (PO) is a high-frequency approximation calculation method based on the physical mechanisms of electromagnetic wave radiation and scattering. This method calculates the induced current distribution in different regions of a planet's surface under the physical optics approximation, then calculates the scattered electric field generated by its secondary radiation, and finally performs vector superposition of the scattered electric fields from each region to quickly estimate the intensity of surface clutter received by radar.

[0038] During radar echo reception, interference from surface clutter generated by irregular planetary terrain is inevitable. Simultaneously, electromagnetic waves experience amplitude attenuation when propagating in lossy media, causing weak internal target echoes to overlap with strong surface clutter, severely hindering the effective extraction and analysis of internal echoes. Therefore, generating surface clutter through high-precision simulation to achieve effective separation of internal echoes from surface clutter has become a key technical requirement in planetary radar detection.

[0039] Physical optics is the mainstream method for simulating surface clutter in planetary radar. Faced with the immense computational pressure from massive terrain data in planetary exploration, analytical integration schemes are typically preferred in engineering practice for physical optics to reduce computational load and improve integration efficiency. Among these, the plane wave integration method is the most widely used. Mars orbital radar operates at extremely high orbital altitudes, and Mars, as the target, has a large radius. In this scenario, spherical electromagnetic waves can be approximated as plane electromagnetic waves to obtain analytical solutions. The phase error resulting from this approximation is negligible and does not affect the accuracy of clutter simulation. However, the detection scenario for asteroid exploration radar differs fundamentally from that of Mars orbital radar: asteroid exploration radar typically operates in low-altitude orbits (e.g., at an altitude of 600m), where the curvature effect of electromagnetic waves is significant and cannot be ignored. Simultaneously, asteroid targets are small in size and rotate extremely rapidly (e.g., asteroid 2016HO3, with a radius of only 40m~100m and a rotation period of only 0.467h), requiring the radar beam to cover the entire asteroid surface and necessitating continuous illumination of the continuously rotating target. The above factors make the radar scattering conditions of asteroids more complex and give them significant time-varying characteristics.

[0040] Traditional plane wave integration methods only perform a first-order Taylor expansion on the relative distance between the radar and the planetary target, completely ignoring the second-order term of electromagnetic wave curvature. This results in significant phase errors in high-frequency, large-area-scale, and close-range detection scenarios for asteroid exploration radar, failing to meet accuracy requirements. While high-precision numerical integration methods offer controllable errors, they suffer from extremely high computational demands, memory consumption, and time consumption, making them unsuitable for the computationally intensive engineering applications of asteroid exploration radar. Therefore, there is an urgent need for a clutter simulation method that balances computational accuracy and efficiency, adaptable to the unique scenarios of close-range planetary radar detection.

[0041] Figure 1The diagram schematically illustrates an application scenario of the second-order surface wave integral surface clutter simulation method for planetary exploration radar according to an embodiment of this application. For example... Figure 1 As shown, the application scenario 100 according to the embodiments of this application may include a planetary exploration radar 110, a target object 120, and a terminal device 130.

[0042] Planetary exploration radar 110 can be an asteroid core scanning radar, which can employ synthetic aperture radar technology. The flight trajectory of the planetary exploration radar can be a circular trajectory around the target object 120. Planetary exploration radar 110 can transmit signals to the target object 120 and receive the echo signals reflected by the target object 120. The target object 120 can be an asteroid, planet, or moon, etc.

[0043] Terminal device 130 can be various electronic devices with a display screen, including but not limited to laptops and desktop computers. Terminal device 130 can perform imaging based on echo signals to obtain the characteristics of the asteroid.

[0044] It should be noted that the second-order surface clutter simulation method for planetary exploration radar provided in this application embodiment can generally be executed by the terminal device 130. Accordingly, the second-order surface clutter simulation device for planetary exploration radar provided in this application embodiment can generally be installed in the terminal device 130.

[0045] It should be understood that Figure 1 The number of planetary exploration radars, targets, and terminal equipment shown is merely illustrative. Depending on implementation needs, any number of planetary exploration radars, targets, and terminal equipment can be included.

[0046] Figure 2 A flowchart illustrating a second-order surface clutter simulation method for a planetary exploration radar according to an embodiment of this application is shown. Figure 2 As shown, the second-order curved surface wave integral surface clutter simulation method 200 for planetary exploration radar according to an embodiment of this application may include steps S210 to S250.

[0047] In step S210, the surface model of the target planet is divided into triangular facets to obtain multiple triangular facets.

[0048] In the embodiments of this application, the surface model is a surface model characterizing the elevation distribution features of the target planet's surface. This model is generated by radar after detecting the surface terrain of the target planet, and includes image data with location information. It can accurately describe the undulations, spatial coordinates, and terrain details of the target planet's surface. Dividing the surface model of the target planet into triangular facets is essentially the process of discretizing a continuous and complex planetary geometric surface into a large number of tiny triangular planar units.

[0049] After dividing the triangle into triangular elements, the centroid of each triangular element can be obtained by averaging the coordinates of its three vertices.

[0050] In step S220, the relative distance from the radar observation point to each point of each triangular element except for the centroid is obtained.

[0051] In the embodiments of this application, the relative distance between the radar observation point and each point of each triangular element other than the centroid is in the form of a function.

[0052] Specifically, since the centroid of a triangular facet is a fixed spatial point uniquely determined by the facet's geometric contour, the relative distance between the two points (denoted as ) can be directly calculated using a distance function (such as Euclidean distance) based on the relative positional relationship between the centroid and the radar observation point. This relative distance can be characterized in a definite numerical form. For any point of a triangular element other than its centroid, the relative distance between it and the radar observation point (denoted as ) The relative distance changes with the position of the point within the surface cell, and therefore can be represented as a distance function.

[0053] In step S230, based on the physical optics method, an integral expression of the scattering electric field containing the relative distance is established for each triangular surface element, and a second-order Taylor expansion is performed on the relative distance, retaining the first-order and second-order terms.

[0054] In the embodiments of this application, based on physical optics, a system containing relative distances can be established for each triangular element. The integral expression for the scattered electric field can be expressed as:

[0055] ;

[0056] ;

[0057] ;

[0058]

[0059] in, Represents the scattered electric field vector. This represents the frequency of the nth pulse; Indicates the starting frequency; Indicates the sequence number of the transmitted pulse; Indicates the step frequency; Indicates the frequency step number; Wave number represents the amount of phase change per unit distance when an electromagnetic wave propagates in a medium; Represents the speed of light; Represents the imaginary unit; The electric field strength is the emission field strength. It is the normal vector of a triangular facet (or simply facet normal vector). It is the wave vector of the incident wave; , Indicates the angle of incidence; S represents the relative distance from the radar observation point to all points of the triangular element except for the centroid; S is the integration region of the triangular element.

[0060] The traditional plane wave integral method decomposes a complex spatial wave field into a series of simple plane waves with different propagation directions and amplitudes. Utilizing the simple propagation form of plane waves in a homogeneous medium (only phase changes), the problem is transformed from the spatial domain to the plane wave domain for solution. Finally, the original wave field is obtained by superimposing these waves through an inverse transformation. Specifically, this method uses the relative distance R in the integral expression of the scattered electric field at the reference point... Perform a first-order Taylor expansion at (usually at the center of the surface element):

[0061] ;

[0062] in, This represents the relative distance from the radar observation point to all points on the triangular facet except for the centroid. Indicates to At the reference point The approximate expression after first-order Taylor expansion at the point; Represents the position vector of any point within a triangular element; Indicates that the radar has reached the reference point. The relative distance (i.e.) ), which is a zero-order Taylor term; Indicates reference point Position vector; Indicates in The gradient calculated at the location; Indicates from the reference point A position difference vector pointing to any point; It is a first-order Taylor term.

[0063] However, when using planetary radar to detect asteroids, the high frequency (short wavelength), large surface area, and close range characteristics significantly increase the linear approximation error based on first-order Taylor expansion in the traditional plane wave integral method. High-frequency electromagnetic waves are extremely sensitive to phase errors; even small path deviations can lead to significant phase distortion. Large surface area discretization means that the wavefront curvature within a single surface element cannot be ignored, violating the assumption of a local plane. Furthermore, close-range detection further amplifies the wavefront curvature effect. These factors combined cause the neglected second-order term of electromagnetic wave curvature to accumulate rapidly during integration, resulting in severe distortion of the amplitude and phase characteristics of the radar echo signal and affecting the final clutter simulation results.

[0064] In the embodiments of this application, the spatial wave field is decomposed into a second-order surface wave, that is, the relative distance R in the integral expression of the scattered electric field at the reference point. Perform a second-order Taylor expansion at this point, retaining both first-order and second-order terms:

[0065] ;

[0066] in, Indicates to At the reference point The approximate expression after second-order Taylor expansion at the point; Indicates from the reference point Transpose the position difference vector pointing to any point; It is a second-order Taylor term; Distance function The Hessian matrix describes the second-order partial derivative properties of the function, and its component form is:

[0067] ;

[0068] in, This represents the relative distance from point i to point j.

[0069] In the embodiments of this application, a second-order Taylor expansion is performed on the relative distance R at the reference point, and the resulting expansion terms are substituted into the integral expression of the scattered electric field. This expression can be called the second-order surface wave integral of the scattered electric field. After separating the integral expression of the scattered electric field, the first-order term expression (referred to as the first-order term) corresponding to the first-order Taylor term and the second-order term expression (referred to as the second-order term) corresponding to the second-order Taylor term can be obtained.

[0070] In step S240, based on the analytical solutions of the first-order and second-order terms, the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element is obtained, and the corresponding scattered electric field is calculated.

[0071] In the embodiments of this application, the first and second-order terms in the second-order surface wave integral of the scattered electric field can be solved using an analytical integration scheme to obtain analytical solutions for the first and second-order terms. Then, the analytical solutions for the first and second-order terms are integrated to obtain an analytical solution for the second-order surface wave integral of the scattered electric field of a triangular surface element. Finally, by combining the actual data of each triangular surface element (such as normal vector, vertex coordinates, and incident angle) with the analytical solution, the scattered electric field of each triangular surface element can be calculated one by one.

[0072] In step S250, the scattered electric fields of multiple triangular elements are accumulated to obtain the surface clutter of the target planet.

[0073] In the embodiments of this application, by vector superposition and summation of the scattered electric fields generated by each triangular surface element, the total surface clutter formed by the complex terrain of the target planet under radar illumination can be determined.

[0074] According to embodiments of this application, by performing a second-order Taylor expansion on the relative distance between the radar and the target surface element, the phase error caused by the second-order electromagnetic wave curvature term, which is approximately ignored in traditional plane wave simulations, can be compensated, thus improving the accuracy of surface clutter simulation for the target planet. Furthermore, by deriving the analytical solution of the second-order surface wave integral based on an analytical integration scheme and obtaining the surface clutter accordingly, computational efficiency can be significantly improved, memory usage effectively reduced, and dependence on hardware resources greatly alleviated. This method provides a reliable and generalized technical solution for simulating surface clutter in radar detection of celestial bodies such as planets, asteroids, and comets.

[0075] In the embodiments of this application, obtaining the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element based on the analytical solutions of the first-order and second-order terms may include: obtaining the vertex coordinates and surface element normal vector of each triangular surface element; solving the first-order and second-order terms respectively based on the vertex coordinates and surface element normal vector to obtain the corresponding analytical solutions of the first-order and second-order terms; and multiplying the analytical solutions of the first-order and second-order terms to obtain the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element.

[0076] Specifically, for each triangular element after partitioning, the coordinates of its three corresponding vertices can be identified, such as... , , Then, using the three vertices of the triangular element, two edge vectors are determined, and the cross product of these vectors is performed to obtain the normal vector of the plane containing the triangular element. Afterwards, analytical solutions can be obtained by solving the first-order and second-order terms based on the vertex coordinates and the normal vector.

[0077] For example, the field expression within the integration region can be transformed into a function of local coordinate variables using the vertex coordinates and normal vectors of the triangular facet elements. By performing analytical integration on this function, the integration variables are eliminated, ultimately yielding a closed-form expression that depends only on the geometric and electromagnetic parameters of the triangular facet elements—this is the analytical solution for the first-order term. Next, based on the same vertex coordinates and normal vectors, the second-order term can be solved to obtain an analytical solution. Specifically, the second-order term is modeled as a functional relationship between the vertex coordinates and the normal vector, and analytical integration is performed term by term in the local coordinate system. After algebraic simplification, the analytical solution for the second-order term, which depends only on the surface geometry and the incident conditions, is finally obtained.

[0078] Finally, the analytical solutions of the first and second orders are multiplied to obtain the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular element. This result is the contribution of a single triangular element to the scattered electric field after considering the second-order approximation, and is used to calculate the total scattered field by superimposing the contributions of all triangular elements.

[0079] According to the embodiments of this application, by deriving the analytical solution of the second-order surface wave integral based on the analytical solutions of the first-order and second-order terms, the phase lead or lag error caused by neglecting the wave curvature can be effectively suppressed while preserving the main wave structure, thus achieving high-precision radar surface clutter simulation.

[0080] In the embodiments of this application, the analytical solution of the first-order term can be obtained in the following way: based on the wave number of the radar incident wave and the centroid position vector of the triangular surface element, a first vector is obtained, which is used to characterize the phase accumulation effect of the radar incident wave after reflection by the triangular surface element; based on the first vector and the surface element normal vector, a second vector is obtained, which is used to characterize the projection component of the first vector in the triangular surface element; based on the second vector, vertex coordinates and surface element normal vector, the scattered electric field vector of the triangular surface element is obtained, and the scattered electric field vector is used as the analytical solution of the first-order term.

[0081] Gordon's algorithm is an iterative method for solving convex feasibility problems. It approximates the intersection of multiple convex sets by alternately projecting onto them, thus finding a solution that satisfies all constraints. For first-order terms, Gordon's algorithm can be used to obtain analytical solutions. The expression for solving first-order terms using Gordon's algorithm is:

[0082] ;

[0083] ;

[0084] ;

[0085] in, Indicates that at wavenumber In this mode, the scattered electric field vector generated by the triangular facet element based on the first-order term, Indicates the first vector; Indicates the second vector; Indicates at the vertex of the triangular element The position vector at that location; Indicates at the vertex of the triangular element The position vector at that location; Indicates at the vertex of the triangular element The position vector at that location; Indicates at the vertex of the triangular element The position vector at that location; Indicates at the vertex of the triangular element The position vector at that location.

[0086] According to the embodiments of this application, by using the Gordon algorithm to analytically solve the first-order terms, the analytical solution of the first-order terms can be obtained, thereby avoiding the huge computational overhead brought about by the traditional numerical integration method and realizing the efficient calculation of the first-order terms.

[0087] In the embodiments of this application, the analytical solution of the second-order term can be obtained as follows: two orthogonal basis vectors are established on a plane perpendicular to the radar illumination direction; the vectors in the triangular element are projected onto the plane to obtain the projection vector, and the decomposition coefficients of the projection vector on the two orthogonal basis vectors are used as local coordinates; based on the local coordinates, the Fresnel integral variables of each vertex in the triangular element are obtained; based on the Fresnel integral variables of each vertex, the corresponding complex Fresnel integral values ​​are calculated respectively; the product of the weighting coefficients corresponding to each vertex and the complex Fresnel integral values ​​is summed to obtain the analytical solution of the second-order term.

[0088] The complex Fresnel integral function is a generalization of the Fresnel integral in the complex plane. By extending the integration variables and parameters to the complex domain, this function can effectively handle generalized diffraction problems such as complex wavenumber, aperture edge effects, and light wave propagation in lossy media. The second-order term can be solved using the complex Fresnel integral function, and the corresponding mathematical expression is:

[0089]

[0090]

[0091]

[0092] Where A represents the integration result. Within the plane of the triangular element, a plane perpendicular to the radar illumination direction can be constructed, and two orthogonal basis vectors can be established on this plane. Projecting any vector within the triangular element onto this plane yields the projected vector; its decomposition coefficients under this set of orthogonal basis vectors can be used as local coordinates, denoted as u and v respectively. In the expression for solving the second-order term using the complex Fresnel integral function, the Fresnel integration variables include: the first Fresnel phase integration variable along the basis vector direction corresponding to u (denoted as...). ) and the second Fresnel phase integral variable along the basis vector direction corresponding to v (denoted as ) ). Indicates at the vertex of the triangular element The first Fresnel phase integral variable; Indicates at the vertex of the triangular element The second Fresnel phase integral variable; Represents the Fresnel cosine integral; Represents the Fresnel sine integral; Represents vertices The corresponding complex Fresnel integral value; Indicates at the vertex The corresponding weighting coefficient.

[0093] According to the embodiments of this application, by using the complex Fresnel integral function to analyze the second-order terms, the second-order terms are expressed in a closed analytical form, which can not only significantly reduce the consumption of computing resources, but also maintain strict phase consistency over a large range of Fresnel approximation conditions.

[0094] In the embodiments of this application, the second-order Taylor expansion is referenced to the centroid of the triangular facet.

[0095] Since the centroid of a triangular facet is uniquely determined by the position of its vertices, it always lies inside the facet and is the center of its geometric area. Therefore, it can serve as a stable and unique reference point, and can be used as such. From radar observation point To reference point relative distance It is in numerical form; based on this, the reference point can be... As a coordinate reference, the relative distance from the radar observation point to any point inside the triangular element can be expressed as a spatial position function with the local coordinates of the element as the independent variable.

[0096] According to the embodiments of this application, when the centroid of the triangular facet is used as the reference point for Taylor expansion, the distances from each point within the facet to the reference point are more balanced, which helps to reduce the truncation error of Taylor expansion and make the error distribution more consistent, thus facilitating error control.

[0097] In the embodiments of this application, the surface model is constructed based on a digital elevation model, which is a stereolithography engineering file generated based on triangular facet division.

[0098] In the embodiments of this application, the digital elevation model is reconstructed into a stereolithography engineering file using a triangulation algorithm. This file uses triangles as constituent units, and through the tight splicing and topological connection of a massive number of spatial triangular facets, the continuous terrain surface is discretized into a structure defined by vertices, edges, and faces. The number of triangular facets determines the precision of the surface terrain fitting; the more triangular facets, the more accurately the complex undulations of the target planet's surface can be reproduced, avoiding distortion of clutter signals due to terrain simplification. The vertex coordinates of each triangular facet can accurately locate the position and contour of each facet in three-dimensional space, and based on this data, the centroid of each triangle can be determined. The facet normal vector reflects the spatial orientation of the facet, providing a basis for accurately calculating the incident angle, reflection path, and echo intensity of electromagnetic waves on the target surface.

[0099] According to embodiments of this application, the surface model is constructed based on a digital elevation model, which can provide a high-precision planetary terrain geometry and accurately reproduce key factors such as slope, occlusion, and scattering direction, thereby greatly improving the accuracy and reliability of surface clutter simulation.

[0100] Figure 3A A schematic diagram of a planetary simulation model according to an embodiment of this application is shown. Figure 3B A schematic diagram illustrates a three-dimensional visualization of the digital elevation model corresponding to a planetary simulation model according to an embodiment of this application. For example... Figure 3A As shown, this is an asteroid model used for simulation. The radar flies along an orbit around the asteroid, maintaining a relative distance of 600m from the asteroid's surface; the asteroid is 100m long and 40m wide. Figure 3B Showing based on Figure 3A The image shows a 3D visualization of the digital elevation model corresponding to the planetary simulation model. The X-axis represents the length of the asteroid, the Y-axis represents the width of the asteroid, and the Z-axis represents the relative height of the asteroid. All units are meters.

[0101] Figure 4A The diagram illustrates the imaging results of the numerical integration method according to an embodiment of this application. Figure 4B A schematic diagram illustrating the imaging results of the plane wave integral method according to an embodiment of this application is shown. Figure 4C The diagram illustrates the imaging results of the second-order surface wave integral method (i.e., the second-order surface wave integral surface clutter simulation method) according to an embodiment of this application. Figures 4A-4B For low-frequency backprojection imaging corresponding to numerical integration, plane wave integration, and second-order surface wave integration, with Figure 4AAs a standard, Figure 4B The localized area of ​​the asteroid exhibits an inflated reflection intensity, an error caused by multiple factors. First, the plane wave integral is expanded using a first-order Taylor series over the relative distance R, neglecting second-order and higher-order terms. However, the radar's relative distance to the asteroid is only 600m, a close-range detection scenario, where the second-order terms are large and cannot be ignored, directly leading to an underestimation of the relative distance R and consequently, an overestimation of the reflection intensity. Second, the model's surface element side lengths range from 0.08m to 0.15m, introducing approximately 10% calculation error into the plane wave approximate integral imaging. Third, near the asteroid's minor axis, radar waves are more frequently perpendicularly incident on the surface elements than near the major axis, further exacerbating the error in this region. Figure 4C and Figure 4A The similarity indicates that the relative error between the second-order surface wave integral method and the numerical integration method is small.

[0102] Figure 4D This illustration schematically shows a high-frequency back projection imaging result of the numerical integration method according to an embodiment of this application; Figure 4D (b) in the middle is Figure 4D (a) A magnified view of the boxed area in the image. Figure 4E This illustration schematically shows a high-frequency back projection imaging result of the plane wave integral method according to an embodiment of this application; Figure 4E (b) in the middle is Figure 4E (a) A magnified view of the boxed area in the image. Figure 4F This schematic diagram illustrates the high-frequency back projection imaging results of the second-order surface wave integral method according to an embodiment of this application. Figure 4F (b) in the middle is Figure 4F A magnified view of the boxed area in (a) of the image. The error patterns in high-frequency scenes are similar to those in low-frequency scenes. (Comparison) Figure 4D visible, Figure 4E The overall reflection intensity is relatively high, while Figure 4F There was no significant difference in overall intensity. The error of the plane wave integral method was much greater than that of the low-frequency scene, while the result of the second-order surface wave integral method was very close to that of the numerical integration method. The reason why the error was more significant in the high-frequency band is that, in addition to the common influencing factors mentioned above, the calculation error caused by the frequency itself cannot be ignored in high-frequency detection, further amplifying the overall imaging error.

[0103] Table 1

[0104]

[0105] Table 1 compares the computational resource usage of numerical integration, plane wave integration, and second-order surface wave integration in planetary surface clutter simulation tasks.

[0106] On a unified Intel Core Ultra7 265KF processor platform, the resource consumption of the three integration algorithms differed significantly. Numerical integration had the highest memory usage (24.67GB) and the longest computation time (22.67 hours). Plane wave integration had the lowest memory usage and computation time (8.63GB and 9.72 hours, respectively). Second-order surface wave integration had resource consumption between the two, with 10.23GB of memory and a computation time of 13.60 hours, approximately 60% of that of numerical integration, while its memory usage was only 41% of that of numerical integration.

[0107] Comparative analysis of comprehensive imaging results and resource usage shows that the second-order surface wave integration method effectively reduces the error of the plane wave integration method in radar close-range detection scenarios. Regardless of low-frequency or high-frequency scenarios, the results are in good agreement with the numerical integration method. At the same time, in terms of computational efficiency, its time consumption and memory usage are much lower than those of the numerical integration method, which significantly reduces the hardware resource requirements.

[0108] Based on the aforementioned second-order curved surface wave integral surface clutter simulation method for planetary exploration radar, embodiments of this application also provide a second-order curved surface wave integral surface clutter simulation device for planetary exploration radar. The following will combine... Figure 5 The device is described in detail.

[0109] Figure 5 The schematic diagram illustrates the structural block diagram of a second-order curved surface wave integral surface clutter simulation device for a planetary exploration radar according to an embodiment of this application.

[0110] like Figure 5 As shown, the second-order curved surface wave integral surface clutter simulation device 500 for planetary exploration radar in this embodiment includes a triangular surface element division module 510, a range acquisition module 520, a Taylor expansion module 530, a scattered electric field determination module 540, and a surface clutter determination module 550.

[0111] The triangular element division module 510 is used to divide the surface model of the target planet into triangular elements, resulting in multiple triangular elements. The surface model is a surface model representing the elevation distribution characteristics of the target planet's surface. In one embodiment, the triangular element division module 510 can be used to perform step S210 as described above, which will not be repeated here.

[0112] The distance acquisition module 520 is used to acquire the relative distance from the radar observation point to all points of each triangular element except the centroid, wherein the relative distance is in the form of a function. In one embodiment, the distance acquisition module 520 can be used to perform step S220 described above, which will not be repeated here.

[0113] The Taylor expansion module 530 is used to establish an integral expression for the scattered electric field, including the relative distance, for each triangular element based on physical optics, and to perform a second-order Taylor expansion on the relative distance, retaining the first-order and second-order terms. In one embodiment, the Taylor expansion module 530 can be used to perform step S230 described above, which will not be repeated here.

[0114] The scattering electric field determination module 540 is used to obtain the analytical solution of the second-order surface wave integral of the scattering electric field of each triangular surface element based on the analytical solutions of the first-order and second-order terms, and to calculate the corresponding scattering electric field. In one embodiment, the scattering electric field determination module 540 can be used to perform step S240 described above, which will not be repeated here.

[0115] The surface clutter determination module 550 is used to accumulate the scattered electric fields of multiple triangular elements to obtain the surface clutter of the target planet. In one embodiment, the surface clutter determination module 550 can be used to perform step S250 described above, which will not be repeated here.

[0116] According to an embodiment of this application, the scattered electric field determination module 540 is further configured to obtain the vertex coordinates and surface normal vector of each triangular surface element; based on the vertex coordinates and surface normal vector, solve the first-order term and the second-order term respectively to obtain the corresponding analytical solutions of the first-order term and the second-order term; multiply the analytical solutions of the first-order term and the second-order term to obtain the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element.

[0117] According to an embodiment of this application, the second-order surface wave integral surface clutter simulation device 500 further includes a first-order term analytical solution acquisition module and a second-order term analytical solution acquisition module.

[0118] The first-order analytical solution acquisition module is used to obtain a first vector based on the wave number of the radar incident wave and the centroid position vector of the triangular surface element. The first vector is used to characterize the phase accumulation effect of the radar incident wave after reflection by the triangular surface element. Based on the first vector and the surface element normal vector, a second vector is obtained. The second vector is used to characterize the projection component of the first vector in the triangular surface element. Based on the second vector, vertex coordinates and surface element normal vector, the scattered electric field vector of the triangular surface element is obtained, and the scattered electric field vector is used as the first-order analytical solution.

[0119] The second-order analytical solution acquisition module is used to establish two orthogonal basis vectors on a plane perpendicular to the radar illumination direction; project the vectors within the triangular element onto the plane to obtain the projected vectors, and use the decomposition coefficients of the projected vectors on the two orthogonal basis vectors as local coordinates; based on the local coordinates, obtain the Fresnel integral variables of each vertex within the triangular element; based on the Fresnel integral variables of each vertex, calculate the corresponding complex Fresnel integral values ​​respectively; sum the products of the weighting coefficients corresponding to each vertex and the complex Fresnel integral values ​​to obtain the second-order analytical solution.

[0120] According to embodiments of this application, any multiple modules among the triangulation module 510, distance acquisition module 520, Taylor expansion module 530, scattered electric field determination module 540, and surface clutter determination module 550 can be combined into one module, or any one of these modules can be split into multiple modules. Alternatively, at least some of the functions of one or more of these modules can be combined with at least some of the functions of other modules and implemented in one module. According to embodiments of this application, at least one of the triangulation module 510, distance acquisition module 520, Taylor expansion module 530, scattered electric field determination module 540, and surface clutter determination module 550 can be at least partially implemented as hardware circuits, such as field-programmable gate arrays, programmable logic arrays, systems-on-a-chip, systems-on-a-substrate, systems-on-package, application-specific integrated circuits, or any other reasonable means of integrating or packaging circuits, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the triangular element partitioning module 510, distance acquisition module 520, Taylor expansion module 530, scattered electric field determination module 540, and surface clutter determination module 550 can be at least partially implemented as a computer program module, which can perform the corresponding function when the computer program module is run.

[0121] Figure 6 A block diagram of an electronic device suitable for implementing a second-order surface clutter simulation method for planetary exploration radar, according to an embodiment of this application, is shown schematically.

[0122] like Figure 6 As shown, an electronic device 600 according to an embodiment of this application includes a processor 601, which can perform various appropriate actions and processes according to a program stored in a read-only memory 602 or a program loaded from a storage portion 608 into a random access memory 603. The processor 601 may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a dedicated microprocessor. The processor 601 may also include onboard memory for caching purposes. The processor 601 may include a single processing unit or multiple processing units for executing different steps of the method flow according to an embodiment of this application.

[0123] Random access memory 603 stores various programs and data required for the operation of electronic device 600. Processor 601, read-only memory 602, and random access memory 603 are interconnected via bus 604. Processor 601 executes various steps of the method flow according to embodiments of this application by executing programs in read-only memory 602 and / or random access memory 603. It should be noted that the programs may also be stored in one or more memories other than read-only memory 602 and random access memory 603. Processor 601 may also execute various steps of the method flow according to embodiments of this application by executing programs stored in said one or more memories.

[0124] According to embodiments of this application, the electronic device 600 may further include an input / output interface 605, which is also connected to a bus 604. The electronic device 600 may also include one or more of the following components connected to the input / output interface 605: an input section 606 including a keyboard, mouse, etc.; an output section 607 including a cathode ray tube, liquid crystal display, etc., and a speaker, etc.; a storage section 608 including a hard disk, etc.; and a communication section 609 including a network interface card, such as a local area network card, modem, etc. The communication section 609 performs communication processing via a network such as the Internet. A drive 610 is also connected to the input / output interface 605 as needed. A removable medium 611, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 610 as needed so that computer programs read from it can be installed into the storage section 608 as needed.

[0125] Embodiments of this application also provide a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0126] According to embodiments of this application, the computer-readable storage medium can be a non-volatile computer-readable storage medium, such as including but not limited to: portable computer disks, hard disks, random access memory, read-only memory, erasable programmable read-only memory, portable compact disk read-only memory, optical storage devices, magnetic storage devices, or any suitable combination thereof. In embodiments of this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of this application, the computer-readable storage medium may include the read-only memory 602 described above, and / or random access memory 603, and / or one or more memories other than read-only memory 602 and random access memory 603.

[0127] Embodiments of this application also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code is used to cause the computer system to implement the methods provided in the embodiments of this application.

[0128] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and downloaded and installed via the communication section 609, and / or installed from the removable medium 611. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0129] In embodiments of this application, the computer program can be downloaded and installed from a network via communication section 609, and / or installed from removable medium 611. When the computer program is executed by processor 601, it performs the functions defined in the system of embodiments of this application. According to embodiments of this application, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0130] According to embodiments of this application, program code for executing the computer programs provided in the embodiments of this application can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. The program code can be executed entirely on the user's computing device, partially on the user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0131] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0132] Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

Claims

1. A second-order surface clutter simulation method for planetary exploration radar using surface wave integration, characterized in that, The method includes: The surface model of the target planet is divided into triangular facets to obtain multiple triangular facets. The surface model is a surface model that characterizes the surface elevation distribution of the target planet. Obtain the relative distance from the radar observation point to each of the triangular facet elements except for the centroid, wherein the relative distance is in the form of a function; Based on the physical optics method, an integral expression for the scattered electric field containing the relative distance is established for each of the triangular facets, and a second-order Taylor expansion is performed on the relative distance, retaining the first-order and second-order terms; Based on the analytical solutions of the first-order and second-order terms, the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element is obtained, and the corresponding scattered electric field is calculated. The scattered electric fields of the multiple triangular facets are accumulated to obtain the surface clutter of the target planet.

2. The method according to claim 1, characterized in that, The analytical solution for obtaining the second-order surface wave integral of the scattered electric field of each triangular surface element based on the analytical solutions of the first-order and second-order terms includes: Obtain the vertex coordinates and face normal vector of each triangle element; Based on the vertex coordinates and surface element normal vectors, the first-order term and the second-order term are solved respectively to obtain the corresponding analytical solutions for the first-order term and the second-order term; By multiplying the analytical solutions of the first-order and second-order terms, we obtain the analytical solution of the second-order surface wave integral of the scattered electric field of each triangular surface element.

3. The method according to claim 2, characterized in that, The analytical solution of the first-order term is obtained using the following method: Based on the wave number of the radar incident wave and the centroid position vector of the triangular element, a first vector is obtained. The first vector is used to characterize the phase accumulation effect of the radar incident wave after being reflected by the triangular element. Based on the first vector and the surface element normal vector, a second vector is obtained, which is used to characterize the projection component of the first vector within the triangular surface element; Based on the second vector, the vertex coordinates, and the surface element normal vector, the scattered electric field vector of the triangular surface element is obtained, and the scattered electric field vector is used as an analytical solution of the first-order term.

4. The method according to claim 2, characterized in that, The analytical solution of the second-order term is obtained using the following method: Establish two orthogonal basis vectors on a plane perpendicular to the radar illumination direction; The vectors within the triangular element are projected onto the plane to obtain the projection vector, and the decomposition coefficients of the projection vector on the two orthogonal basis vectors are used as local coordinates. Based on the local coordinates, the Fresnel integral variables of each vertex within the triangular element are obtained; Based on the Fresnel integral variables of each vertex, calculate the corresponding complex Fresnel integral values ​​respectively; The analytical solution of the second-order term is obtained by summing the products of the weighting coefficients corresponding to each vertex and the complex Fresnel integral.

5. The method according to claim 1, characterized in that, The second-order Taylor expansion uses the centroid of the triangular facet as a reference point.

6. The method according to claim 1, characterized in that, The surface model is constructed based on a digital elevation model, which is a stereolithography engineering file generated based on triangular facet division.

7. A second-order curved surface wave integral surface clutter simulation device for planetary exploration radar, characterized in that, The device includes: The triangular surface division module is used to divide the surface model of the target planet into triangular surfaces to obtain multiple triangular surfaces. The surface model is a surface model that characterizes the surface elevation distribution features of the target planet. The distance acquisition module is used to acquire the relative distance from the radar observation point to each of the triangular elements except for the centroid, wherein the relative distance is in the form of a function; The Taylor expansion module is used to establish an integral expression of the scattered electric field containing the relative distance for each of the triangular facets based on physical optics, and to perform a second-order Taylor expansion on the relative distance, retaining the first-order and second-order terms; The scattered electric field determination module is used to obtain the analytical solution of the second-order surface wave integral of the scattered electric field of each of the triangular surface elements based on the analytical solutions of the first-order and second-order terms, and to calculate the corresponding scattered electric field; and The surface clutter determination module is used to accumulate the scattered electric fields of the multiple triangular elements to obtain the surface clutter of the target planet.

8. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs. The characteristic feature is that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 6.

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