Method and equipment for estimating the internal dielectric constant of an asteroid based on a single-station orbital radar

Abstract

The present invention discloses a method and device for estimating the internal dielectric constant of an asteroid based on a single-station orbital radar, relating to the field of planetary exploration. The method primarily comprises: separating diffraction waves from single-station orbital radar recordings, determining the number of diffraction points within the asteroid and the range of values ​​for the scanned dielectric constant; setting a diffraction point and a scanned dielectric constant value within the asteroid, solving the eikonal equation to obtain the travel time of the diffraction wave, and calculating the superposition energy of the diffraction waves within a fixed time window starting from the travel time; repeating the previous steps until all positions within the asteroid and the range of values ​​for the scanned dielectric constant are traversed; selecting several local maxima from all the superposition energies, determining the diffraction point positions and scanned dielectric constant values ​​corresponding to all the maxima; and interpolating the results to obtain the dielectric constant distribution within the asteroid. Implementing the method and device for estimating the internal dielectric constant of an asteroid based on a single-station orbital radar provided by the present invention can quickly and accurately obtain the internal dielectric constant distribution of the asteroid.

Description

Technical Field

[0001] The present invention relates to the field of planetary exploration, and more specifically, to a method and device for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar. Background Art

[0002] In recent years, deep space exploration of the solar system has been booming, with asteroid exploration becoming a major development focus. Asteroid exploration missions include determining physical parameters such as an asteroid's orbital parameters, rotation parameters, shape, size, and thermal radiation; investigating its morphology, surface material composition, and internal structure; and conducting laboratory analysis of returned samples to determine their physical properties, chemical and mineralogical composition, isotopic composition, and internal structure. Measuring the dielectric constant of an asteroid's surface and subsurface layers not only provides a deeper understanding of its internal structure and composition, but also sheds new light on the origin and evolution of asteroids and, ultimately, the solar system.

[0003] my country reportedly plans to launch its first small-body exploration mission, the Tianwen-2 mission, in the first half of 2025. This mission aims to conduct a flyby and sample-return mission to the near-Earth asteroid 2016 HO3. The Tianwen-2 probe's onboard single-station orbiter radar will conduct scientific research on the internal composition of 2016 HO3. Therefore, using the Tianwen-2 single-station orbiter radar data to invert the asteroid's interior dielectric constant remains a pressing technical challenge. Currently, full waveform inversion and tomographic inversion techniques used in ground-penetrating radar (GPR) have the potential to invert the asteroid's interior dielectric constant distribution using Tianwen-2 single-station orbiter radar data. However, both inversion methods rely heavily on initial models (dielectric constant and conductivity models). Inaccurate initial models can lead to inversion failures. Furthermore, both methods suffer from high computational requirements and low efficiency, making them crucial.

[0004] In the field of planetary vehicle-borne radar (Mars rover detection radar and lunar rover detection radar), the existing methods for estimating the dielectric constant of the interior of the planet mainly include hyperbola fitting method, three-dimensional velocity spectrum analysis method, optimized hyperbola fitting method, etc. However, these methods have two main problems: (1) Most of these methods assume that the antenna is close to the surface of the moon or Mars, and do not take into account the height of the planetary vehicle-borne radar antenna to the ground and the distance between the transmitting and receiving antennas. In actual observations by the Tianwen-2 orbital radar, the distance between the orbital radar antenna and the asteroid surface is relatively far, and there is also a certain distance between the transmitting and receiving antennas. These two factors cannot be ignored when estimating the dielectric constant of the asteroid interior; (2) Conventional methods for estimating the dielectric constant of the interior of the planet are all for ground single-line observation systems, while the Tianwen-2 single-station orbital radar is in an orbiting observation mode when detecting asteroids. There are obvious differences in the radar records obtained by the two different observation methods, and the difference in the morphological characteristics of the diffraction waves is even more significant. Therefore, the conventional dielectric constant estimation methods in the field of planetary vehicle-borne radar detection are not applicable to the dielectric constant estimation task of the Tianwen-2 single-station orbital radar records. In order to better serve the Tianwen-2 asteroid exploration mission, it is very necessary to study a set of methods suitable for single-station orbital radar that can quickly and accurately obtain the internal dielectric constant distribution of asteroids. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and device for estimating the internal dielectric constant of an asteroid based on a single-station orbital radar, which can quickly and accurately obtain the internal dielectric constant distribution of an asteroid.

[0006] The present invention provides a method for estimating the internal dielectric constant of an asteroid based on a single-station orbital radar, comprising the following steps: A1: pre-processing the single-station orbital radar record to obtain the single-station orbital radar record containing only diffraction waves, the number of diffraction points, and a fixed time window; A2: obtaining, based on the asteroid shape information, the orbital radar observation system, and the antenna center frequency, a spatial grid spacing, a numerical simulation calculation area, a grid number, and a grid number range where the asteroid's internal area is located; A3: dividing the range of the asteroid's internal dielectric constant value according to a preset dielectric constant scanning interval number to obtain a scanning dielectric constant sequence; A4: selecting a grid from the grid number range where the asteroid's internal area is located in ascending order according to the numerical simulation calculation area, the grid number, the asteroid shape information, and the orbital radar observation system as the diffraction point position and calculating the diffraction point position according to the numerical simulation calculation area, the grid number, the asteroid shape information, and the orbital radar observation system. A scanning dielectric constant value is selected from the scanning dielectric constant sequence in ascending order as the asteroid's interior dielectric constant, the eikonal equation is solved to obtain the diffraction wave travel time, the superposition energy of the diffraction waves in a fixed time window starting from the diffraction wave travel time in the single-station orbit radar record containing only the diffraction waves is calculated, and the diffraction wave superposition energy, diffraction point position and scanning dielectric constant value at this time are saved; A5: return to step A4 until the grid number range where the asteroid's interior region is located and the entire scanning dielectric constant sequence are traversed, and local maxima are selected from all the diffraction wave superposition energies. The number of local maxima is the number of diffraction points, and the diffraction point positions and scanning dielectric constant values ​​corresponding to each local maximum are selected; A6: spatially interpolate the diffraction point positions and scanning dielectric constant values ​​corresponding to each local maximum to obtain the asteroid's interior dielectric constant distribution.

[0007] Furthermore, step A1 specifically includes: A11: cutting out the direct wave in the single-station orbit radar record to obtain the single-station orbit radar record after the direct wave is cut out; A12: separating the reflected wave in the single-station orbit radar record after the direct wave is cut out to obtain a separated single-station orbit radar record; A13: separating the multiple waves in the separated single-station orbit radar record to obtain a single-station orbit radar record containing only diffraction waves and the diffraction waves; A14: obtaining the number of diffraction points and the maximum duration of the diffraction waves according to the waveform characteristics of the diffraction waves; and obtaining a fixed time window according to the maximum duration of the diffraction waves and the time sampling interval.

[0008] Furthermore, step A2 specifically includes: calculating the spatial grid spacing, such as the formula:

[0009]

[0010] in, represents the spatial grid spacing in the X direction, represents the speed of electromagnetic waves in vacuum, represents the dielectric constant of the asteroid's interior, represents the center frequency of the orbital radar antenna; similarly, the spatial grid spacing in other directions is also calculated using the above formula; the numerical simulation calculation area is obtained according to the asteroid shape information, the orbital radar observation system and the spatial grid spacing; according to the spatial grid spacing, the numerical simulation calculation area is divided into a series of discrete orthogonal regular grids and numbered in sequence to obtain the grid number, and the number range of the grid where the asteroid's interior area is located is further obtained according to the asteroid shape information.

[0011] Furthermore, step A4 specifically includes: A41: selecting a grid point in the grid number range of the asteroid interior region in ascending order according to the number range of the grids where the numerical simulation calculation area and the asteroid interior region are located as the diffraction point; A42: selecting a scanning dielectric constant value from the scanning dielectric constant sequence in ascending order according to the asteroid shape information, the orbital radar observation system and the diffraction point, solving the eikonal equation to obtain the diffraction wave traveltime; A43: obtaining the superposition energy of the diffraction waves in the fixed time window starting from the diffraction wave traveltime according to the diffraction wave traveltime, the fixed time window and the single-station orbital radar record containing only the diffraction waves; A44: returning to step A42 until the superposition energy of the diffraction waves in the fixed time window starting from the diffraction wave traveltime corresponding to all the scanning dielectric constant values ​​in the scanning dielectric constant sequence is calculated, and the corresponding diffraction wave superposition energy, diffraction point position and scanning dielectric constant value are saved.

[0012] Furthermore, step A43 specifically includes: obtaining the superposition energy of the diffraction waves in the fixed time window starting from the diffraction wave travel time based on the diffraction wave travel time, the fixed time window, and the single-station track radar record containing only the diffraction waves, and the calculation formula is as follows:

[0013]

[0014] in, Indicates the The position of the hypothetical diffraction point and the The superposition energy of the diffraction waves corresponding to the scanning dielectric constant values, Indicates the energy amplification factor, Indicates the number of radar channels in a single-station track radar record, Indicates that from step A42 based on The position of the hypothetical diffraction point and the The first one is selected from the diffraction wave travel time obtained by scanning the dielectric constant value When the diffraction wave of the road travels, is the length of the fixed time window, The first recorded by a single-station orbital radar containing only diffraction waves The diffraction wave data The diffraction wave amplitude at each time sampling point.

[0015] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar.

[0016] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar are implemented.

[0017] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar.

[0018] The implementation of the asteroid interior dielectric constant estimation method and device based on single-station orbital radar provided by the present invention has the following beneficial effects:

[0019] The present invention separates diffraction waves from single-station orbital radar records to determine the possible number of diffraction points and the scanning dielectric constant range. Based on the observation system and asteroid shape information, a point is selected from the asteroid's interior as the diffraction point and a scanning dielectric constant value is given. The eikonal equation is solved to obtain the travel time of the diffraction wave, and the superposition energy of the diffraction waves within a fixed time window starting from the travel time is calculated. The previous step is repeated until the dielectric constant scanning range and all positions inside the asteroid are traversed. A number of local maxima (equal to the number of diffraction points) are selected from all superposition energies, and the scanning dielectric constants and diffraction point positions corresponding to each of the maxima are determined. The result is interpolated to obtain the dielectric constant distribution inside the asteroid. The present invention can quickly and accurately obtain the dielectric constant distribution inside the asteroid, facilitating rapid analysis of the asteroid's internal structure and material composition. In addition, using the obtained dielectric constant distribution as an initial model for migration imaging and full waveform inversion can significantly improve the migration imaging and full waveform inversion effects, thereby providing a more reliable scientific basis for analyzing the asteroid's internal structure and material composition. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0021] Figure 1 This is a flow chart of the method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar provided by the present invention;

[0022] Figure 2 This is a schematic diagram of a two-dimensional uniform asteroid model with three diffraction points and a single-station orbit radar observation system provided by the present invention;

[0023] Figure 3This is the 10MHz Ricker wavelet and its amplitude spectrum used in the numerical simulation of single-station orbit radar recording provided by the present invention;

[0024] Figure 4 This is an example diagram of a simulated single-station orbit radar record obtained based on a two-dimensional uniform asteroid model containing three diffraction points, as provided by the present invention;

[0025] Figure 5 This is a diffraction wave superposition energy result diagram obtained by performing dielectric constant scanning on single-channel diffraction wave data provided by the present invention;

[0026] Figure 6 This is a graph of the diffraction wave superposition energy results obtained by scanning all diffraction waves based on 101 scanning dielectric constants and the interior area of ​​the asteroid, as provided by the present invention;

[0027] Figure 7 The present invention provides a method for obtaining a diffraction wave superposition energy level slice including a diffraction point position using the present invention;

[0028] Figure 8 is the real and estimated dielectric constant distribution diagram of the two-dimensional uniform asteroid model with three diffraction points provided by the present invention;

[0029] Figure 9 It is a structural block diagram of the computer device provided by the present invention. DETAILED DESCRIPTION

[0030] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0031] Figure 1 A schematic diagram of a method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar according to this embodiment is shown. In this embodiment, the method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar comprises the following steps:

[0032] A1: Preprocess the single-station orbit radar record to obtain the single-station orbit radar record containing only diffraction waves, the number of diffraction points and the fixed time window;

[0033] As an exemplary embodiment, in step A1, the single-station orbital radar record is preprocessed and the direct wave is removed. The diffracted wave is separated from the single-station orbital radar record based on the difference in propagation characteristics between the reflected wave and the diffracted wave. The number of diffraction points, the number of diffracted waves, and the maximum duration are determined. The length of the fixed time window should be slightly longer than the maximum duration.

[0034] As an exemplary embodiment, step A1 specifically includes: A11: removing the direct wave in the single-station orbit radar record to obtain the single-station orbit radar record after the direct wave is removed; A12: separating the reflected waves in the single-station orbit radar record after the direct wave is removed to obtain a separated single-station orbit radar record; A13: separating the multiple waves in the separated single-station orbit radar record to obtain a single-station orbit radar record containing only diffracted waves and the diffracted waves; A14: obtaining the number of diffraction points and the maximum duration of the diffracted waves based on the waveform characteristics of the diffracted waves; and obtaining a fixed time window based on the maximum duration of the diffracted waves and the time sampling interval.

[0035] It should be noted that the single-station orbit radar record referred to in step A1 is a simulated or actual radar record obtained by orbiting or hovering an asteroid using an asteroid single-station detection radar with a fixed spacing between the transmitting and receiving antennas placed on an asteroid orbiter.

[0036] A2: Based on the asteroid's shape information, the orbital radar observation system, and the antenna center frequency, the spatial grid spacing, the numerical simulation calculation area, the grid number, and the grid number range of the asteroid's interior area are obtained;

[0037] As an exemplary embodiment, in step A2, the asteroid shape information is obtained as follows: first, basic asteroid shape data is obtained using photogrammetry (or laser point cloud ranging, photometry), then a low-precision asteroid shape model is constructed based on image registration technology, and finally, a final high-precision asteroid shape model is generated using an iterative calculation method;

[0038] As an exemplary embodiment, step A2 specifically includes: calculating the spatial grid spacing, such as the formula:

[0039]

[0040] in, represents the spatial grid spacing in the X direction, represents the speed of electromagnetic waves in vacuum, represents the dielectric constant of the asteroid's interior, represents the center frequency of the orbital radar antenna; similarly, the spatial grid spacing in other directions is calculated using the above formula; the numerical simulation calculation area is obtained based on the asteroid shape information, the orbital radar observation system, and the grid spacing; according to the spatial grid spacing, the numerical simulation calculation area is divided into a series of discrete orthogonal regular grids and numbered in sequence to obtain the grid number; based on the asteroid shape information, the grid number range of the asteroid interior area is further obtained;

[0041] It should be noted that the calculation area of ​​the numerical simulation is set to be 10–20 spatial grid spacings larger than the orbital altitude of the orbital radar;

[0042] As an exemplary embodiment, in step A2, an appropriate numerical simulation calculation region and spatial grid spacing are selected based on the orbital radar antenna center frequency, time sampling interval, observation system, and asteroid shape information. The calculation region is divided into a series of discrete orthogonal regular grids and numbered sequentially. The grid number range corresponding to the asteroid interior region and the observation system (transmitting antenna and receiving antenna positions) is determined.

[0043] A3: Divide the dielectric constant value range of the asteroid's interior according to the preset dielectric constant scanning interval number to obtain a scanning dielectric constant sequence;

[0044] As an exemplary embodiment, the preset number of dielectric constant scanning intervals is 100;

[0045] It should be noted that the above-mentioned range of the asteroid interior dielectric constant is obtained based on the travel time information of the reflected wave, the asteroid shape information and the observation system;

[0046] A4: Based on the numerical simulation calculation area, grid number, asteroid shape information, and orbital radar observation system, select a grid from the grid number range of the asteroid's interior region in ascending order as the diffraction point location and select a scanning dielectric constant value from the scanning dielectric constant sequence as the asteroid's interior dielectric constant. Solve the eikonal equation to obtain the diffraction wave travel time. Calculate the superposition energy of the diffraction waves within a fixed time window starting from the diffraction wave travel time in the single-station orbital radar record containing only the diffraction waves. Save the diffraction wave superposition energy, diffraction point location, and scanning dielectric constant value at this time.

[0047] As an exemplary embodiment, in step A4, a discrete grid is selected from the discrete grid number range of the asteroid interior region obtained in step A2 as a diffraction point. The dielectric constants of the asteroid interior regions other than the diffraction point are set to the scanned dielectric constant values ​​in step A3. Based on the observation system and asteroid shape information, the diffraction wave traveltimes corresponding to all the scanned dielectric constant values ​​are obtained by solving the eikonal equation. The superposition energy of the diffraction waves within a fixed time window starting from the diffraction wave traveltime is calculated.

[0048] As an exemplary embodiment, the detailed steps of step A4 include:

[0049] A41: Based on the numerical simulation calculation area and the grid number range of the asteroid's interior area, a grid point is selected from the asteroid's interior area grid number range in ascending order as the diffraction point;

[0050] A42: Based on the asteroid's shape information, orbital radar observation system, and diffraction point, select a scanning dielectric constant value from the scanning dielectric constant sequence in ascending order, solve the eikonal equation, and obtain the diffraction wave travel time;

[0051] As an exemplary embodiment, in step A42, the dielectric constants of the region inside the asteroid excluding the diffraction point are sequentially set to the scanning dielectric constant values ​​of the scanning dielectric constant value series in step A3, based on the observation system information, such as Figure 2 The coordinate positions of "o" and "×" in the figure, and the asteroid's shape information are as follows: Figure 2 The asteroid ellipse equation shown above is used to solve the Eikonal equation to obtain the diffraction wave travel time corresponding to all the scanned dielectric constant values;

[0052] A43: Based on the diffraction wave travel time, a fixed time window and a single-station track radar record containing only diffraction waves, the superposition energy of the diffraction waves within the fixed time window starting from the diffraction wave travel time is obtained;

[0053] As an exemplary embodiment, step A43 specifically includes: obtaining the superposition energy of the diffraction waves within the fixed time window starting from the diffraction wave travel time based on the diffraction wave travel time, the fixed time window, and the single-station track radar record containing only the diffraction waves, using the following calculation formula:

[0054]

[0055] in, Indicates the The position of the hypothetical diffraction point and the The superposition energy of the diffraction waves corresponding to the scanning dielectric constant values, Indicates the energy amplification factor, Indicates the number of radar channels in a single-station track radar record, Indicates that from step A42 based on The position of the hypothetical diffraction point and the The first one is selected from the diffraction wave travel time obtained by scanning the dielectric constant value When the diffraction wave of the road travels, is the length of the fixed time window, The first recorded by a single-station orbital radar containing only diffraction waves The diffraction wave data The diffraction wave amplitude at each time sampling point;

[0056] It should be noted that in order to overcome the problem of small superposition energy change due to small amplitude of diffraction waves, The specific value of the energy amplification factor is flexibly set according to the amplitude of the diffraction wave;

[0057] A44: Return to step A42 until the superposition energy of the diffraction waves within the fixed time window starting from the travel time of the diffraction waves corresponding to all the scanning dielectric constant values ​​in the scanning dielectric constant sequence is calculated, and the corresponding diffraction wave superposition energy, diffraction point position and scanning dielectric constant value are saved;

[0058] As an exemplary embodiment, in step A44, steps A42 to A43 are repeated until the diffraction wave superposition energy corresponding to all grid points inside the asteroid and the entire scanning dielectric constant sequence is obtained. , ,…, save the diffraction point positions and scanning dielectric constant values ​​corresponding to all diffraction wave superposition energies;

[0059] A5: Return to step A4 until the grid number range of the asteroid's interior region and the entire scanning dielectric constant sequence are traversed. Local maxima are selected from the superposition energy of all diffraction waves. The number of local maxima is the number of diffraction points. The diffraction point positions and scanning dielectric constant values ​​corresponding to each local maximum are selected.

[0060] As an exemplary embodiment, in step A5, step A4 is repeated until the discrete grid number range of the asteroid interior region is traversed, a certain number (equal to the number of diffraction points) of local maxima are selected from all the obtained superposition energies, and the diffraction point positions and scanning dielectric constant values ​​corresponding to each local maximum are saved.

[0061] A6: Perform spatial interpolation on the diffraction point positions and scanned dielectric constant values ​​corresponding to the local maxima to obtain the dielectric constant distribution inside the asteroid.

[0062] As an exemplary embodiment, in step A6, spatial interpolation is performed based on the diffraction point positions and scanning dielectric constant values ​​corresponding to all local maxima obtained in step A5 to obtain the dielectric constant distribution inside the asteroid.

[0063] In some embodiments, the above-mentioned method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar is implemented in the following manner.

[0064] In an exemplary embodiment, a method for estimating the dielectric constant of an asteroid's interior based on a single-station orbital radar includes the following steps: S1: separating diffraction waves from single-station orbital radar records to determine the possible number of diffraction points and the scanning dielectric constant range; S2: based on the observation system and asteroid shape information, selecting a point from the asteroid's interior as the diffraction point and assigning a scanning dielectric constant value, solving the eikonal equation to obtain the travel time of the diffraction wave, and calculating the superposition energy of the diffraction waves within a fixed time window starting from the travel time; S3: repeating the previous step until the dielectric constant scanning range and all positions within the asteroid's interior are traversed; S4: selecting a number of local maxima (equal to the number of diffraction points) from all superposition energies, and determining the scanning dielectric constants and diffraction point positions corresponding to all local maxima; and S5: interpolating the results to obtain the dielectric constant distribution within the asteroid's interior.

[0065] In an exemplary embodiment, a flowchart of a method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar specifically includes the following steps:

[0066] In the first step, the single-station orbital radar records are preprocessed to remove direct waves. The diffracted waves are then separated from the single-station orbital radar records based on the differences in propagation characteristics between the reflected and diffracted waves. The number and maximum duration of the diffracted waves are determined, and the fixed time window length is set to be slightly larger than the maximum duration.

[0067] The asteroid single-station orbit radar record used in this embodiment is a simulated single-station orbit radar record obtained based on a two-dimensional asteroid model containing three diffraction points (representing a lone rock asteroid); Figure 2 (a) and (b) show the dielectric constant and conductivity distribution of a uniform asteroid model with three diffraction points, respectively; Figure 2 As shown in (a), the asteroid model is a two-dimensional uniform asteroid model with three diffraction points inside. Its shape is elliptical, with the lengths of the major and minor axes being 60 meters and 40 meters respectively, and the grid spacing between the horizontal and vertical directions is 1 meter. The dielectric constant inside the asteroid is 4, and the conductivity is 1×10 −5 S / m; the area outside the asteroid is a vacuum with a dielectric constant of 1 and a conductivity of 0; the dielectric constant at the diffraction point is 6 and the conductivity is also 1×10 −5 S / m; Transmitting antenna ( Figure 2 "o") and the receiving antenna ( Figure 2 The "×") was placed sequentially at 30 positions in a circular orbit at an altitude of 90 meters from the center of the asteroid for radar observation; Figure 3 The 10 MHz Ricker wavelet and its amplitude spectrum used in the numerical simulation of the single-station orbit radar are recorded using Figure 3The Ricker wavelet with a main frequency of 10 MHz is used as the excitation source, the time sampling interval is 1.5 ns, the recording time length is 1800 ns, and the fourth-order spatial and second-order temporal finite-difference time-domain algorithm is used to obtain the simulated single-station orbit radar record;

[0068] like Figure 4 Shown are simulated single-station orbit radar records obtained based on a two-dimensional uniform asteroid model containing three diffraction points. Figure 4 (a) shows the simulated single-station orbit radar record obtained by numerical simulation; (b) is the simulated single-station orbit radar record after cutting off the direct wave, (c) is the simulated single-station orbit radar record after cutting off the direct wave and reflected wave, and (d) is the simulated single-station orbit radar record including only a single diffraction wave; Figure 4 The direct wave event axis in the simulated single-station orbital radar record shown in (a) is not horizontal. This is because the model grid spacing is large, and the distance between the receiving and transmitting points is not strictly equal. In addition, due to the strong amplitude of the direct wave, the reflected and diffracted waves are not clear enough, which is not convenient for the next step of dielectric constant estimation. To highlight the reflected and diffracted waves, the direct wave in the simulated single-station orbital radar record is first removed. Figure 4 (b) shows the simulated single-station orbital radar record after removing the direct wave. From the figure, we can see that there are two reflection wave events with strong amplitudes (located at 400ns and 1200ns, respectively, indicating the reflection waves from the asteroid surface closer and farther away from the observation point), while the diffraction wave events are still not clear enough. Therefore, according to the difference in propagation characteristics of diffraction waves and reflection waves, Figure 4 The diffraction wave and the reflected wave in the simulated single-station orbit radar record in (b) are separated to obtain Figure 4 (c) shows the simulated single-station track radar record after removing the direct wave and the reflected wave; Figure 4 In (c), we can find that there are three diffraction waves with different shapes in the time window from 600ns to 1200ns. Multiple waves begin to appear after 1200ns, and the amplitude of the multiple waves is relatively strong. In order to eliminate the influence of the multiple waves on the estimation of the internal dielectric constant of the asteroid, Figure 4 In the simulated single-station orbital radar record shown in (c), the amplitude of the echo signal with a recording time greater than 1200ns is set to zero, that is, the synthetic orbital radar record contains only a single diffraction wave. The result is as follows Figure 4 As shown in (d), the number of diffraction points can be determined to be 3;

[0069] according to Figure 4 The diffraction wave waveform characteristics shown in FIG. 1 are as follows. The maximum duration of the diffraction wave is about 208 ns. The time sampling interval used in the simulation is 1.5 ns. Therefore, the fixed time window length of this embodiment is 210 ns.

[0070] The second step is to select an appropriate numerical simulation calculation area and spatial grid spacing based on the orbital radar antenna center frequency, time sampling interval, observation system, and asteroid shape information. The calculation area is divided into a series of discrete orthogonal regular grids and numbered sequentially. The grid number range corresponding to the asteroid's internal area and the observation system (transmitting antenna and receiving antenna positions) is determined.

[0071] The third step is to use the travel time information of the reflected waves in the single-station orbital radar records to preliminarily estimate the range of the asteroid's internal dielectric constant based on the observation system and the asteroid's shape information. The dielectric constant range is then divided into a series of equally spaced scanning dielectric constant values ​​at appropriate intervals.

[0072] In this embodiment, the center frequency of the monostatic orbital radar antenna is 10 MHz, the shape of the two-dimensional asteroid model is elliptical (with the major and minor axes being 40 and 28 meters, respectively), and the circular orbit altitude of the monostatic orbital radar is 90 meters above the asteroid model. Therefore, the maximum horizontal and vertical dimensions of the entire calculation interval are both set to 200 meters.

[0073] In this embodiment, the center frequency of the single-station orbital radar antenna and the two-dimensional asteroid model shape information are provided. The discrete grid spacing of the asteroid model is 1, and the entire asteroid model occupies a total of 3681 grids, which are numbered 1, 2, ..., 3680, and 3681 in sequence.

[0074] according to Figure 4 The time position of the reflected wave event axis shown in (b) is combined with the observation system information and the asteroid shape information. The relationship between the distance between the transmitting and receiving antennas and the asteroid surface, the internal dielectric constant and the electromagnetic wave propagation time is used to preliminarily estimate the distribution range of the asteroid's internal dielectric constant. , the number of intervals of scanning dielectric constant is set to 100, then the interval is 0.078, and a total of 101 scanning dielectric constant values ​​are obtained, which are 1.2, 1.278, …, 8.922, and 9 respectively;

[0075] The fourth step is to select a discrete grid from the discrete grid number range of the asteroid interior region in the first step as the diffraction point, set the dielectric constants of the asteroid interior region excluding the diffraction point to be the scanning dielectric constant values ​​in the third step, and solve the eikonal equation based on the observation system and the asteroid shape information to obtain the diffraction wave traveltimes corresponding to all the scanning dielectric constant values, and calculate the superposition energy of the diffraction waves within a fixed time window corresponding to all the traveltimes. The specific steps include:

[0076] Step (1): Select a discrete grid from the discrete grid number range where the interior region of the asteroid is located (for example, the grid point numbered 1 in the third step, i.e. Figure 2 The leftmost grid point in the inner region of the asteroid model is used as the diffraction point;

[0077] Step (2): Let the dielectric constant of the area inside the asteroid except the diffraction point be the scanning dielectric constant value in the third step, based on the observation system information ( Figure 2 The coordinate positions of "o" and "×" in the image), the asteroid's shape information ( Figure 2 The asteroid ellipse equation shown in Figure 2 is obtained by solving the Eikonal equation to obtain the diffraction wave travel time corresponding to all the scanned dielectric constant values; Figure 4 For the waveform data of the seventh track (i.e., the seventh observation point) recorded by the single-station orbit radar with only diffraction waves shown in (a), a total of 101 different travel times are obtained based on 101 scanning dielectric constant values, see Figure 5 (a) middle square; Figure 5 The figure shows the velocity scan and stacking energy results of a single-channel diffraction wave data. In this case, the diffraction point position is set to the grid point in the inner region of the asteroid numbered 1. The relevant results of 101 scanning dielectric constant calculations for the seventh observation point of the diffraction wave data are shown. (a) is the diffraction wave travel time obtained based on the 101 scanning dielectric constants, (b) is the seventh waveform of the first diffraction wave, marked with the diffraction wave travel time and fixed time window position, and (c) is the diffraction wave stacking energy result obtained based on the 101 scanning dielectric constants.

[0078] Step (3): Based on the diffraction wave traveltimes corresponding to all the scanning dielectric constant values ​​obtained in step 2, calculate the radar signal superposition energy within a fixed time window starting from the traveltime on the orbital radar profile corresponding to all the scanning dielectric constant values. The calculation formula is as follows:

[0079]

[0080] in, Indicates the The position of the hypothetical diffraction point and the The superposition energy of the diffraction waves corresponding to the scanning dielectric constant values, Indicates the energy amplification factor (in order to overcome the problem of small superposition energy change due to small diffraction wave amplitude, the specific value is flexibly set according to the diffraction wave amplitude). Indicates the number of radar channels in a single-station track radar record, Indicates that based on The position of the hypothetical diffraction point and the The first one is selected from the diffraction wave travel time obtained by scanning the dielectric constant value The travel time of the diffracted wave is is the length of the fixed time window, For the The diffraction wave data The diffraction wave amplitude at each time sampling point;

[0081] Step 4: Repeat steps 2 to 3 until the diffraction wave superposition energy corresponding to all scanned dielectric constant values ​​is obtained. 、 , ..., save the diffraction point positions and scanned dielectric constant values ​​corresponding to the superposition energy of all diffraction waves;

[0082] like Figure 5 As shown in (b), the curve is Figure 4 In the single-channel waveform diagram of the diffraction wave data shown in (d), the rectangle represents a fixed time window, and the dots represent the travel time of the diffraction wave calculated based on the first scan dielectric constant value. The diffraction wave superposition energy is calculated using the formula shown in step 1, that is, Figure 5 The first point of the square line in (c) corresponds to an energy value of 0.7641; similarly, the diffraction wave superposition energy corresponding to the remaining 100 scanning dielectric constant values ​​can be obtained ( Figure 5 (c) Points 2 to 101), the five-pointed star indicates the maximum value at that time;

[0083] Step 5: Repeat step 4 until all 3681 grids inside the asteroid model are traversed. Three local maxima are selected from the superposition energy values ​​of the obtained diffraction waves. The corresponding diffraction point positions and scanned dielectric constant values ​​are saved. That is, the diffraction point positions corresponding to the three diffraction waves and the equivalent dielectric constant of the asteroid interior are saved.

[0084] For this example, a total of 3681 grid points with 101 different scanning velocity values ​​are obtained. In order to display the results more intuitively and accurately, the 3681 grid points in the asteroid's interior are sequentially placed at the corresponding positions in the 200×200 grid of the simulation area. The superposition energy corresponding to the different scanning dielectric constant values ​​at each grid point is taken as the value on the Z axis. Figure 6 The three-dimensional graph of the diffraction wave superposition energy at these 3681 different points is shown. It is the diffraction wave superposition energy result obtained by scanning all diffraction waves based on 101 scanning dielectric constants and the interior area of ​​the asteroid, where (a) is the front view and (b) is the oblique view. Figure 1 , (c) is bevel cutting Figure 2 ; Figure 6 (a) shows a 3D plot of the complete result. Figure 6 (b) and (c) show the three-dimensional images of the resected parts;

[0085] from Figure 6Three local maxima are extracted from the three-dimensional data volume of the diffraction wave superposition energy shown in (a). The coordinates corresponding to the local maxima are (86, 96, 4.476), (101, 109, 4.008), and (112, 102, 3.54), respectively. The position information of these three points is the estimated position of the three diffraction points inside the asteroid and the corresponding dielectric constant; Figure 7 The horizontal slice of the diffraction wave superposition energy including the diffraction point position is obtained by the method of the present invention; (a) is the result of diffraction point 1, and the corresponding scanning dielectric constant is 4.476; (b) is the result of diffraction point 2, and the corresponding scanning dielectric constant is 4.008; (c) is the result of diffraction point 3, and the corresponding scanning dielectric constant is 3.540; the two "+"s represent the actual position and estimated position of the diffraction point, respectively; "×" and "o" represent the position of the receiving antenna and the position of the transmitting antenna, respectively; Figure 7 (a), (b), and (c) show horizontal slices of diffraction wave superposition energy with relative permittivities of 4.476, 4.008, and 3.54, respectively, taken from the diffraction wave superposition energy three-dimensional data volume; Figure 7 The estimated position of the diffraction point is close to the true position, and both are located at the local maximum of the superposition energy, indicating that the method is correct;

[0086] The sixth step is to obtain the internal dielectric constant distribution of the asteroid by spatial interpolation based on the diffraction point positions corresponding to all diffraction waves and the equivalent dielectric constant value of the asteroid. The results are as follows: Figure 8 As shown in (b); Figure 8 The true and estimated permittivity distributions of a two-dimensional uniform asteroid model with three diffraction points. (a) is the true permittivity distribution, and (b) is the estimated permittivity distribution. The two "+"s indicate the true and estimated positions of the diffraction points, respectively. "×" and "o" denote the positions of the receiving and transmitting antennas, respectively. Table 1 shows the comparison between the estimated and true values ​​of the diffraction point positions and the asteroid's interior permittivity.

[0087] Table 1: Comparison of the diffraction point positions and the estimated and true values ​​of the dielectric constant of the asteroid interior in the two-dimensional asteroid model dielectric constant estimation example

[0088]

[0089] from Figure 8 As can be seen from Table 1, the estimated positions of the three diffraction points are relatively close to the actual positions, and the estimated results of the dielectric constant distribution inside the asteroid ( Figure 8 (b)) and the real situation ( Figure 8The maximum absolute error of the dielectric constant estimation result is about 0.5, the average relative error of the estimation result is only 14.2%, and the structural similarity (SSIM) coefficient of the image quality of the estimation result is 0.81, indicating that the method of the present invention can obtain a relatively accurate distribution of the dielectric constant inside the asteroid. The method is effective and reliable, and is expected to provide methodological support for the actual asteroid single-station orbit radar data processing and inversion.

[0090] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method for estimating the interior dielectric constant of an asteroid using a single-station orbital radar. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD); the storage medium may also include a combination of the aforementioned types of memory.

[0091] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar are implemented.

[0092] like Figure 9As shown, the computer device may include: at least one processor 121, such as a central processing unit (CPU), at least one communication interface 123, a memory 124, and at least one communication bus 122. The communication bus 122 is used to enable communication between these components. The communication interface 123 may include a display and a keyboard. Optionally, the communication interface 123 may also include a standard wired interface or a wireless interface. The memory 124 may be a high-speed random access memory (RAM) or a non-volatile memory, such as at least one disk drive. The memory 124 may optionally be at least one storage device located remote from the processor 121. The memory 124 stores application programs, and the processor 121 invokes program code stored in the memory 124 to execute any of the aforementioned method steps. The communication bus 122 may be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, for example. The communication bus 122 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 9The use of only one line in the figure does not imply that there is only one bus or only one type of bus. Memory 124 may include volatile memory, such as random-access memory (RAM); it may also include non-volatile memory, such as flash memory, a hard disk drive (HDD), or a solid-state drive (SSD); or it may include a combination of these types of memory. Processor 121 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP. Processor 121 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof. Optionally, the memory 124 is further configured to store program instructions. The processor 121 may call the program instructions to implement the asteroid interior dielectric constant estimation method based on a single-station orbital radar as described in this embodiment.

[0093] This embodiment provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar.

[0094] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar, characterized in that: The following steps are involved: A1: Preprocess the single-station orbit radar record to obtain the single-station orbit radar record containing only diffraction waves, the number of diffraction points and the fixed time window; A2: Based on the asteroid's shape information, the orbital radar observation system, and the antenna center frequency, the spatial grid spacing, the numerical simulation calculation area, the grid number, and the grid number range of the asteroid's interior area are obtained; A3: Divide the dielectric constant value range of the asteroid's interior according to the preset dielectric constant scanning interval number to obtain a scanning dielectric constant sequence; A4: Based on the numerical simulation calculation area, grid number, asteroid shape information, and orbital radar observation system, a grid is selected from the grid number range where the asteroid's interior region is located in ascending order as the diffraction point position, and a scanning dielectric constant value is selected from the scanning dielectric constant sequence in ascending order as the asteroid's interior dielectric constant. The eikonal equation is solved to obtain the diffraction wave travel time. The superposition energy of the diffraction waves within a fixed time window starting from the diffraction wave travel time is calculated in the single-station orbital radar record containing only the diffraction waves, and the diffraction wave superposition energy, diffraction point position, and scanning dielectric constant value at this time are saved. A5: Return to step A4 until the grid number range of the asteroid's interior region and the entire scanning dielectric constant sequence are traversed, and local maxima are selected from all diffraction wave superposition energies. The number of local maxima is the number of diffraction points, and the diffraction point positions and scanning dielectric constant values ​​corresponding to each local maximum are selected. A6: Perform spatial interpolation on the diffraction point positions and scanning dielectric constant values ​​corresponding to the local maxima to obtain the dielectric constant distribution inside the asteroid.

2. The method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar according to claim 1, characterized in that: Step A1 specifically includes: A11: Remove the direct wave from the single-station orbit radar record to obtain the single-station orbit radar record after removing the direct wave; A12: separating the reflected waves in the single-station track radar record after the direct wave is removed to obtain a separated single-station track radar record; A13: separating the multiple waves in the separated single-station orbit radar record to obtain a single-station orbit radar record containing only diffraction waves and the diffraction waves; A14: According to the waveform characteristics of the diffraction wave, the number of diffraction points and the maximum duration of the diffraction wave are obtained; according to the maximum duration of the diffraction wave and the time sampling interval, a fixed time window is obtained.

3. The method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar according to claim 1, characterized in that: Step A2 specifically includes: calculating the spatial grid spacing, the formula is as follows: in, represents the spatial grid spacing in the X direction, represents the speed of electromagnetic waves in vacuum, represents the dielectric constant of the asteroid's interior, represents the center frequency of the orbital radar antenna. Similarly, the spatial grid spacing in other directions is also calculated using the above formula; A numerical simulation calculation area is obtained according to the asteroid shape information, the orbital radar observation system and the spatial grid spacing; According to the spatial grid spacing, the numerical simulation calculation area is divided into a series of discrete orthogonal regular grids and numbered in sequence to obtain grid numbers. According to the asteroid shape information, the number range of the grid where the internal area of ​​the asteroid is located is further obtained.

4. The method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar according to claim 1, wherein: Step A4 specifically includes: A41: Based on the numerical simulation calculation area and the grid number range of the asteroid's interior region, a grid point is selected from the asteroid's interior region grid number range in ascending order as the diffraction point; A42: Based on the asteroid's shape information, the orbital radar observation system, and the diffraction point, select a scanning dielectric constant value from the scanning dielectric constant sequence in ascending order, solve the eikonal equation, and obtain the diffraction wave travel time; A43: obtaining the superposition energy of the diffraction waves within the fixed time window starting from the diffraction wave travel time based on the diffraction wave travel time, the fixed time window, and the single-station track radar record containing only the diffraction waves; A44: Return to step A42 until the superposition energy of the diffraction waves within the fixed time window starting from the diffraction wave travel time corresponding to all the scanning dielectric constant values ​​in the scanning dielectric constant sequence is calculated, and the corresponding diffraction wave superposition energy, diffraction point position and scanning dielectric constant value are saved.

5. The method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar according to claim 4, characterized in that: Step A43 specifically includes: obtaining the superposition energy of the diffraction waves within the fixed time window starting from the diffraction wave travel time based on the diffraction wave travel time, the fixed time window, and the single-station track radar record containing only the diffraction waves, and the calculation formula is as follows: in, Indicates the The position of the hypothetical diffraction point and the The superposition energy of the diffraction waves corresponding to the scanning dielectric constant values, Indicates the energy amplification factor, Indicates the number of radar channels in a single-station track radar record, Indicates that from step A42 based on The position of the hypothetical diffraction point and the The first one is selected from the diffraction wave travel time obtained by scanning the dielectric constant value When the diffraction wave of the road travels, is the length of the fixed time window, The first recorded by a single-station orbital radar containing only diffraction waves The diffraction wave data The diffraction wave amplitude at each time sampling point.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for estimating the interior dielectric constant of an asteroid based on a single-station orbit radar as described in any one of claims 1 to 5 are implemented.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar are implemented as described in any one of claims 1 to 5.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method for estimating the interior dielectric constant of an asteroid based on a single-station orbital radar according to any one of claims 1 to 5 are implemented.

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