Asteroid internal structure three-dimensional reverse time migration imaging method based on single-station radar

Abstract

The invention discloses an asteroid internal structure three-dimensional reverse time migration imaging method based on a single-station radar, and belongs to the technical field of planet detection, and the method comprises the steps: estimating wavelets from the observation data of the single-station radar; constructing an asteroid three-dimensional dielectric model based on a velocity analysis result and prior information; selecting a group of transmitting and receiving source positions, and performing forward modeling by taking wavelets as excitation sources to obtain forward transmission wave fields of electric field components at all moments; interchanging the positions of the transmitting source and the receiving source, and performing forward modeling by taking radar observation data as an excitation source to obtain a corresponding back propagation wave field; zero-delay cross-correlation is carried out on the forward and backward propagation wave fields, and an imaging result of a single source point is obtained; repeating the three steps until the imaging results of all the source points are obtained; and superposing imaging results of all source points, and suppressing low-frequency noise through Laplace filtering to obtain a high-resolution three-dimensional imaging result. By implementing the method provided by the invention, the three-dimensional internal structure of the asteroid can be quickly and accurately obtained, and then a reliable basis is provided for analyzing the origin and evolution of the asteroid.

Description

Technical Field

[0001] This invention relates to the field of planetary exploration technology, and more specifically, to a method for three-dimensional reverse time migration imaging of the internal structure of asteroids based on monostation radar. Background Technology

[0002] Exploring the internal structure of asteroids is not only crucial for understanding their origin and evolution, but also holds significant scientific value and practical applications in studying the early material composition of Earth and other planets, searching for resources, minerals, and water, and mitigating the potential risks of small celestial bodies impacting Earth. Since the 1990s, humanity has conducted a series of asteroid exploration missions. However, these missions have primarily relied on observations from scientific payloads (such as optical imagers and spectrometers) and limited surface samples to infer their internal structure. No scientific payloads have yet been deployed to directly observe the asteroid's interior. While these indirect inferences have greatly advanced our initial understanding of asteroid internal structures, they still fall short of comprehensively and accurately revealing the true state of an asteroid's interior.

[0003] Planetary subsurface radar is one of the best geophysical methods for probing the internal structure of planets. Depending on the system configuration, asteroid subsurface radars are mainly divided into two types: bistatic radar and monostatic radar. Bistatic radar generally consists of two radars, one located on the asteroid orbiter and the other on the lander (or orbiter), while monostatic radar consists of one radar located on the orbiter. To date, only the European Space Agency's Rosetta mission has successfully conducted scientific exploration of comet 67P using bistatic radar. On October 27, 2024, the European Space Agency's Hera asteroid probe was successfully launched, with plans to conduct scientific exploration of the binary asteroid system Didymos using monostatic radar by the end of 2026. On May 29, 2025, the Tianwen-2 probe was successfully launched, marking the official start of my country's first small celestial body exploration mission. The Tianwen-2 probe carries a single-station radar system. Its scientific mission is to acquire surface and subsurface radar echoes from asteroid 2016 HO3 and main-belt comet 311P, thereby studying their internal structure and material composition. The low-frequency channel of the single-station radar on Tianwen-2 will conduct scientific investigations into the internal structure and electrical parameters of asteroid 2016 HO3 based on a circularly polarized transmission and dual-polarized reception mode. To better serve the Tianwen-2 asteroid exploration mission, it is essential to conduct prior research on three-dimensional internal structure imaging methods for asteroids based on single-station radar.

[0004] In the field of single-station radar data imaging research, Sava and Asphaug proposed reverse-time migration imaging and tomographic imaging methods for the internal structure of three-dimensional asteroids based on a single-station spiral observation mode, and analyzed the influencing factors of the imaging effect of these two methods. Wang Yujun et al., based on single-station radar orbital exploration of asteroids, proposed a two-dimensional orbital scanning tomographic imaging method for subsurface exploration radar, realizing imaging of the internal structure of simple two-dimensional onion-shaped small celestial bodies. Eyraud's team, targeting quasi-single-station radar measurement data, successively proposed time-domain and frequency-domain imaging methods for the internal structure of asteroids based on induced current reconstruction theory, realizing the reconstruction of the internal structure of a three-dimensional asteroid 3D printed model. Hu Chaoran et al. proposed a fast three-dimensional imaging method for small celestial bodies based on a fast decomposition back projection algorithm, which can obtain imaging results of asteroid internal structures that are approximately the same as those obtained by the classical back projection algorithm, with a significant improvement in algorithm efficiency. However, previous imaging methods based on single-station radar data have two main problems: (1) most methods are based on linearly polarized transmission and linearly polarized reception modes without considering polarization characteristics; (2) most methods can only achieve good imaging results under high radar observation density, which limits their effectiveness in actual exploration work. Therefore, it is very necessary to study an imaging method that considers the polarization characteristics of single-station radar data and can quickly obtain relatively accurate images of the internal structure of asteroids.

[0005] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0006] The purpose of this invention is to provide a three-dimensional reverse time migration imaging method for the internal structure of asteroids based on monostatic radar, which can quickly and accurately acquire the three-dimensional internal structure of asteroids.

[0007] This invention provides a method for reverse time migration imaging of the three-dimensional internal structure of an asteroid based on monostatic radar, comprising the following steps: A1: Acquiring monostatic radar observation data and corresponding radar observation system information, and obtaining radar wavelet based on the monostatic radar observation data; A2: Performing velocity analysis on the monostatic radar observation data to obtain the relative permittivity result of the asteroid's interior, and constructing a three-dimensional dielectric model of the asteroid by combining it with prior information about the asteroid obtained from other scientific payloads; A3: Obtaining the transmitter position and receiver position corresponding to the radar observation point position based on the radar wavelet and the corresponding radar observation system information, and performing forward modeling based on the three-dimensional dielectric model of the asteroid to obtain the forward propagation wave field of the monostatic radar electric field component at different times; A4: ... The single-station radar observation data received at the receiving source location corresponding to the observation point location is used as the excitation source. The transmitting source location and receiving source location corresponding to the radar observation point location are interchanged. Forward modeling is performed using the three-dimensional dielectric model of the asteroid to obtain the backpropagation wave field of the single-station radar electric field component at different times; A5: The forward propagation wave field and the backpropagation wave field of the single-station radar electric field component at different times are cross-correlated with zero delay to obtain the imaging result of a single source point; A6: Steps A3 to A5 are repeated until all radar observation points are traversed to obtain the imaging results of all source points; A7: The imaging results of all source points are superimposed, and low-frequency noise is suppressed using Laplace filtering to obtain a high-resolution three-dimensional imaging result.

[0008] Furthermore, the aforementioned radar observation system information includes the type of radar observation orbit, the location of radar observation points, the number of radar observation points, and the radar antenna polarization method; the type of radar observation orbit is a circular orbit, an elliptical orbit, a spiral orbit, an irregular orbit, or an equivalent circular orbit that achieves orbital observation by hovering the orbital radar and utilizing the rotation of asteroids; the radar antenna polarization method is circular polarization transmission with dual-line polarization reception or linear polarization transmission with linear polarization reception.

[0009] Furthermore, the above-mentioned method of obtaining radar wavelets from single-station radar observation data specifically includes: preprocessing the single-station radar observation data, removing the direct wave to obtain single-station radar observation data after removing the direct wave, and estimating the radar wavelet using wavelet estimation methods based on the single-station radar observation data after removing the direct wave to obtain the radar wavelet.

[0010] Further, step A2 specifically includes: A21: performing velocity analysis on the single-station radar observation data after removing the direct wave to obtain the relative permittivity result inside the asteroid; A22: based on the relative permittivity result inside the asteroid and combined with the asteroid-related prior information obtained from other loads, constructing a three-dimensional dielectric model of the asteroid.

[0011] Further, step A3 specifically includes: A31: Using the radar wavelet as the excitation source, select a radar observation point location based on the corresponding radar observation system information, and determine the transmitting source location and receiving source location corresponding to the radar observation point location; A32: Combining the three-dimensional dielectric model of the asteroid, perform three-dimensional forward modeling using the forward modeling method to obtain the forward propagation wave field of the single-station radar electric field component at different times.

[0012] Furthermore, the aforementioned forward modeling method is a time-domain finite-difference method based on interleaved grids; the simulation method for circularly polarized transmission and dual-linearly polarized reception involves loading the excitation source onto the transmitting antenna. In this direction, the excitation source phase is delayed by 90° and then applied to the transmitting antenna. In direction, and through the receiving antenna direction and Simultaneous reception of electric field in both directions; the simulation method for linearly polarized transmission and linearly polarized reception involves loading the excitation source onto the transmitting antenna. direction or In direction, and through the receiving antenna direction or Directional electric field reception.

[0013] Furthermore, step A4 specifically includes: A41: The radar observation data received at the receiving source position corresponding to the radar observation point position is used as the excitation source, and the transmitting source position and receiving source position corresponding to the radar observation point position are used as the receiving source position and transmitting source position in the back-propagation process, respectively. A42: Combining the three-dimensional dielectric model of the asteroid, three-dimensional forward modeling was performed using the forward modeling method to obtain the back propagation wave field of the single-station radar electric field component at different times.

[0014] Further, step A5 specifically includes: performing zero-delay cross-correlation on the forward propagation wavefield of the monostatic radar electric field component obtained in step A3 at different times and the reverse propagation wavefield of the monostatic radar electric field component obtained in step A4 at different times to obtain the imaging result of a single source point. The zero-delay cross-correlation calculation formula is as follows: , in, , and These represent the positions of any point within the asteroid model in three-dimensional space. Indicates the receiving antenna direction and direction; Indicates the first The source point (i.e., the first source point) The reverse time migration imaging results corresponding to each radar observation point Indicates the first The source point (i.e., the first source point) The single-station radar electric field corresponding to each radar observation point direction or Directional components in the 1st The forward propagation wave field at any given moment, Indicates the first The source point (i.e., the first source point) The single-station radar electric field corresponding to each radar observation point direction or Directional components in the 1st The reverse propagation wave field at any moment, and These represent the time sampling interval and the total number of samples, respectively.

[0015] Furthermore, the cross-correlation calculation formula used in step A5 needs to be adjusted according to different antenna receiving methods, specifically including: when using a dual-polarization receiving method, the forward propagation wave field... A propagating wave field containing components of the electric field in both directions, i.e., the electric field. Directional components and The forward propagation wave field of the directional component, and similarly, the reverse propagation wave field. It also includes the forward propagating wave field containing components of the electric field in both directions, i.e., the electric field. Directional components and The inverse propagation wave field of the directional component; the forward propagation wave field when using linear polarization reception. A propagating wave field that contains only the component of the electric field in one direction, i.e., the electric field. Directional component or The forward propagation wave field of the directional component, and similarly, the reverse propagation wave field. It is also a back-propagating wave field that only contains the component of the electric field in one direction, i.e., the electric field. Directional component or The back propagation wave field of the directional component.

[0016] Furthermore, step A7 specifically includes: A71: The superimposed imaging results of all source points are obtained as shown in the formula: , in, This indicates the image result after superposition; This represents the total number of source points, corresponding to the total number of radar observation points. A72: Using Laplace filtering to suppress low-frequency noise after the superposition of imaging results from all source points, a high-resolution three-dimensional imaging result is finally obtained.

[0017] The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar provided by this invention has the following beneficial effects: This invention obtains radar wavelets from single-station radar observation data and corresponding radar observation system information; performs velocity analysis on the single-station radar observation data to obtain the relative permittivity of the asteroid's interior; combines this with prior information about the asteroid obtained from other scientific payloads to construct a three-dimensional dielectric model of the asteroid; uses the radar wavelet as an excitation source, selects a radar observation point from the corresponding radar observation system information, and determines its corresponding transmitter and receiver positions; combines this with the three-dimensional dielectric model of the asteroid and performs a three-dimensional forward modeling to obtain the forward propagation wavefield of the single-station radar electric field component at different times; and then uses the single-station radar wavelet received from the receiver position selected in the previous step to perform a three-dimensional forward modeling. Using the observation data as the excitation source, the selected transmitter and receiver positions from the previous step are used as the receiver and transmitter positions in the reverse propagation process, respectively. Combined with the asteroid's three-dimensional dielectric model, a three-dimensional forward modeling method is used to obtain the reverse propagation wavefield of the single-station radar electric field component at different times. The forward propagation wavefield and reverse propagation wavefield of the single-station radar electric field component obtained in the first two steps are cross-correlated with each other at different times with zero delay to obtain the imaging result of a single source point. The aforementioned three steps are repeated until all radar observation points are traversed, thereby obtaining the imaging results of all source points. The imaging results of all source points are superimposed and Laplace filtering is used to suppress low-frequency noise, finally obtaining a high-resolution three-dimensional imaging result. This invention, used in imaging tasks with single-station radar data, can quickly and accurately acquire the three-dimensional internal structure of asteroids, thus providing a reliable scientific basis for analyzing the origin and evolution of asteroids. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of the three-dimensional reverse time migration imaging method for the internal structure of asteroids based on monostation radar provided by the present invention; Figure 2 These are three-dimensional diagrams and two-dimensional slice diagrams of the relative permittivity of the three-dimensional rubble pile asteroid model provided by this invention; Figure 3 This is a schematic diagram of the propagation of the 100MHz Ricker wavelet and its Hilbert form, circularly polarized trajectory, used in the forward modeling of single-station radar data provided by this invention. Figure 4 The electric field Ex component is obtained from single-station radar simulation data (after removing the direct wave) using a three-dimensional rubble pile asteroid model, Ricker wavelet and its Hilbert form forward modeling provided by this invention. Figure 5 The electric field Ey component is obtained from single-station radar simulation data (after removing the direct wave) using a three-dimensional rubble pile asteroid model, Ricker wavelet and its Hilbert form forward modeling provided by this invention. Figure 6These are the three-dimensional structural diagram and two-dimensional slice diagram of the imaging result of the three-dimensional rubble pile asteroid model obtained by the reverse time migration imaging method provided by the present invention. Detailed Implementation

[0019] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0020] Figure 1 A schematic diagram of the three-dimensional reverse time migration imaging method for the internal structure of asteroids based on monostation radar in this embodiment is shown.

[0021] In this embodiment, the three-dimensional reverse-time migration imaging method for the internal structure of an asteroid based on monostatic radar includes the following steps: A1: Obtain single-station radar observation data and corresponding radar observation system information, and obtain radar wavelet based on single-station radar observation data; In one exemplary embodiment, the corresponding radar observation system information includes the type of radar observation track, the location of the radar observation point, the number of radar observation points, and the radar antenna polarization mode. As an exemplary embodiment, the type of radar observation orbit for the corresponding radar observation system information can be a circular orbit, an elliptical orbit, a spiral orbit, or an irregular orbit; it can also be an equivalent circular orbit achieved by hovering a single-station radar and utilizing the rotation of an asteroid to achieve orbital observation.

[0022] In one exemplary embodiment, the radar antenna polarization method includes two methods: circular polarization transmission with dual linear polarization reception or linear polarization transmission with linear polarization reception.

[0023] In one exemplary embodiment, obtaining the radar wavelet from single-station radar observation data specifically includes: preprocessing the single-station radar observation data and removing the direct wave to obtain single-station radar observation data after removing the direct wave; and estimating the radar wavelet using a wavelet estimation method based on the single-station radar observation data after removing the direct wave to obtain the radar wavelet. The preprocessing includes: 1. Data acquisition, inspection, and editing: checking whether the original data is missing or abnormal, and deleting abnormal channels; 2. Bandpass filtering: removing low-frequency and high-frequency noise from single-station radar observation data using a bandpass filter; 3. DC offset removal: removing DC offset from single-station radar observation data using a differential method or high-pass filtering.

[0024] As an exemplary embodiment, in step A1, a classical wavelet estimation method, such as the sparse pulse deconvolution method, is used to estimate the radar wavelet from the single-station radar observation data after the direct wave is removed; A2: Velocity analysis of single-station radar observation data yields the relative permittivity of the asteroid's interior. Combined with prior information about the asteroid obtained from other scientific payloads, a three-dimensional dielectric model of the asteroid is constructed. In one exemplary embodiment, step A2 specifically includes: A21: Velocity analysis was performed on single-station radar observation data after the direct wave was removed to obtain the relative permittivity inside the asteroid; A22: Based on the relative permittivity results inside the asteroid and combined with prior information about the asteroid obtained from other loads, a three-dimensional dielectric model of the asteroid is constructed. It should be noted that the three-dimensional dielectric model of the asteroid was established based on the velocity analysis results obtained in step A2 and the asteroid-related prior information, which includes the asteroid's three-dimensional shape and physical property parameters obtained from other scientific payloads. A3: Based on the radar wavelet and the corresponding radar observation system information, the transmitting source position and receiving source position corresponding to the radar observation point position are obtained. Combined with the three-dimensional dielectric model of the asteroid, forward modeling is performed to obtain the forward propagation wave field of the single-station radar electric field component at different times. In one exemplary embodiment, step A3 specifically includes: A31: Using radar wavelet as excitation source, select a radar observation point location based on the corresponding radar observation system information, and determine the corresponding transmitter and receiver locations. A32: Combining the three-dimensional dielectric model of the asteroid, the forward modeling method is used to perform three-dimensional forward modeling to obtain the forward propagation wave field of the single-station radar electric field component at different times.

[0025] In one exemplary embodiment, the forward modeling method is a time-domain finite-difference method based on interlaced grids; the simulation method for circularly polarized transmission and dual-linearly polarized reception involves loading an excitation source onto the transmitting antenna. In this direction, the excitation source phase is delayed by 90° and then applied to the transmitting antenna. In direction, and through the receiving antenna and Simultaneously receiving the electric field of a single-station radar; if simulating linearly polarized transmission and reception, the excitation source is applied to a specific direction of the transmitting antenna (i.e., direction or (direction), and through a receiving antenna in a specific direction (which can be) Direction can also be (Direction) Receives the electric field of a single-station radar.

[0026] It should be noted that in step A3, when obtaining the forward and reverse propagation wave fields of the single-station radar electric field component at different times based on the three-dimensional dielectric model of the asteroid, the three-dimensional forward modeling is performed using the time-domain finite difference method based on staggered grids. The time discretization accuracy and spatial discretization accuracy are set to the second order and the eighth order, respectively. The uniaxial anisotropic medium fully matched layer absorption boundary condition is used to absorb the outward propagating electromagnetic waves. The antenna polarization mode is circular polarization transmission and dual-line polarization reception. A4: Using the single-station radar observation data received at the receiving source position corresponding to the radar observation point position as the excitation source, the transmitting source position and receiving source position corresponding to the radar observation point position are interchanged, and forward modeling is performed in combination with the three-dimensional dielectric model of the asteroid to obtain the reverse propagation wave field of the single-station radar electric field component at different times. In one exemplary embodiment, step A4 specifically includes: A41: The single-station radar observation data received at the receiving source position corresponding to the radar observation point position is used as the excitation source, and the transmitting source position and receiving source position corresponding to the radar observation point position are used as the receiving source position and transmitting source position in the backpropagation process, respectively. A42: Combining the three-dimensional dielectric model of the asteroid, three-dimensional forward modeling was performed using the forward modeling method to obtain the back propagation wave field of the single-station radar electric field component at different times.

[0027] It should be noted that in step A4, a radar observation point should be selected from the observation system (which contains information on more than one radar observation point). The location of this radar observation point will have corresponding information on the location of the transmitting and receiving sources. The radar wavelet is used as the excitation source, and forward modeling is performed in combination with the three-dimensional dielectric model of the asteroid to obtain the forward propagation wave field of the single-station radar electric field component at different times.

[0028] A5: Perform zero-delay cross-correlation between the forward propagation wave field of the single-station radar electric field component at different times and the reverse propagation wave field of the single-station radar electric field component at different times to obtain the imaging result of a single source point. As an exemplary embodiment, in step A5, the forward propagation wave field and the reverse propagation wave field of the monostation radar electric field component obtained in steps A3 and A4 are cross-correlated at different times to obtain the imaging result of a single source point. The calculation formula is as follows: , in, , and These represent the positions of any point inside the asteroid model. Indicates the receiving antenna direction and direction; Indicates the first The source point (i.e., the first source point) The reverse time migration imaging results corresponding to each radar observation point Indicates the first The source point (i.e., the first source point) The single-station radar electric field corresponding to each radar observation point direction or Directional components in the 1st The forward propagation wave field at any given moment, Indicates the first The source point (i.e., the first source point) The single-station radar electric field corresponding to each radar observation point direction or Directional components in the 1st The reverse propagation wave field at any moment, and These represent the time sampling interval and the total number of samples, respectively. The cross-correlation calculation formula used in step A5 needs to be adjusted according to different antenna receiving methods, specifically including: when using a dual-polarization receiving method, the forward propagation wave field The forward propagation wave field should include components of the electric field in both directions, namely the electric field and the propagation wave field in the two directions. Forward propagation wave field of directional components and The forward propagation wave field of the directional component, and similarly, the reverse propagation wave field. The anti-propagating wave field should include components of the electric field in both directions, namely... Directional components and The inverse propagation wave field of the directional component; the forward propagation wave field when using linear polarization reception. A propagating wave field that contains only the component of the electric field in one direction, i.e., the electric field. direction or The forward propagation wave field of the directional component, and similarly, the reverse propagation wave field. A propagating wave field that contains only the component of the electric field in one direction, i.e., the electric field. Directional component or The back propagation wave field of the directional component.

[0029] It should be noted that in step A5, the positions of the transmitting source and the receiving source in the previous step should be interchanged first, and the observation radar data should be used as the excitation source. Then, forward modeling should be performed in combination with the three-dimensional dielectric model of the asteroid to obtain the backpropagation wave field of the single-station radar electric field component at different times.

[0030] A6: Repeat steps A3 to A5 until all radar observation points have been traversed to obtain the imaging results of all source points; As an exemplary embodiment, in step A6, different radar transceiver pairs are selected, and steps A3 to A6 are repeated until the imaging results of all radar transceiver pairs are obtained, that is, the imaging results of all source points. A7: Superimpose all source point imaging results and use Laplace filtering to suppress low-frequency noise to obtain high-resolution three-dimensional imaging results.

[0031] As an exemplary embodiment, step A7 specifically includes: A71: The superimposed imaging results of all source points are obtained as shown in the formula: , in, This indicates the image result after superposition; This represents the total number of source points, corresponding to the total number of radar observation points. A72: By using Laplace filtering to suppress low-frequency noise after the superposition of imaging results from all source points, a high-resolution three-dimensional imaging result is obtained, namely the three-dimensional reverse-time migration imaging result of the asteroid's internal structure, thus obtaining a more accurate internal structure of the asteroid.

[0032] In some embodiments, the above-described three-dimensional reverse-time migration imaging method for asteroid internal structure based on monostatic radar can also be implemented in the following manner. In this embodiment, the three-dimensional reverse-time migration imaging method for asteroid internal structure based on monostatic radar includes: The first step is to remove the direct waves from the single-station radar data to obtain the single-station radar data after removing the direct waves, and then estimate the radar wavelet from it. Based on the obtained single-station radar data, information about the radar observation system is obtained, such as the radar observation track type, the location of the radar observation point, the number of radar observation points, and the radar antenna polarization mode. Since it is temporarily impossible to obtain true single-station radar observation data, in this embodiment, single-station radar simulation data obtained based on a three-dimensional rubble pile asteroid model and a 100MHz main frequency Ricker wavelet forward model is used as "single-station radar observation data". Figure 2 The diagram shows a three-dimensional plot and a two-dimensional slice of the relative permittivity of a three-dimensional rubble-pile asteroid model. (See diagram for reference.) Figure 2 As shown in (a), the main body of the three-dimensional rubble-pile asteroid model is an ellipsoid (orange part), with a relative permittivity of It has a relative permittivity of 9.0; it contains three spherical fragments (blue parts) and its relative permittivity is... The conductivity is 4.0, and the electrical conductivity throughout the asteroid is uniformly distributed, with a value of 0 S / m. The asteroid model is approximately ellipsoidal in shape, with a major axis of 6 m and a minor axis of 2.8 m. The asteroid model contains three fragments with radii ranging from [missing value]. . Figure 2 Figures (b) to (d) show slices of the three-dimensional rubble pile asteroid model on the XOY, YOZ, and ZOX planes, respectively.

[0033] To simulate the radar observation system used by the Tianwen-2 single-station radar in asteroid exploration, both the transmitting and receiving antennas of the single-station radar are placed at the same location on the asteroid probe. The single-station radar then orbits the asteroid at a certain distance from its center, forming a circular orbit with a radius of 9.5 meters, and the orbital plane is parallel to the asteroid's orbital plane. Figure 2 The XOZ plane in (a). Figure 2 In the three orbital planes in (a), the middle orbital plane (Y=8m) coincides with the equatorial plane of the asteroid model, while the upper orbital plane (Y=6m) and the lower orbital plane (Y=10m) are both 2 meters away from the equatorial plane. Then, here... Figure 2 In section (a), 120 radar observation points are set up on each circular track (i.e., Figure 2 (a) Black dots on the circular orbit), the total number of radar observation points on the three orbits is 360. The antenna polarization mode of the Tianwen-2 single-station radar is circular polarization for transmission and dual-line polarization for reception, which will be handled accordingly during simulation.

[0034] To obtain "single-station radar observation data," the three-dimensional model of the asteroid was discretized with a spatial grid step size of 0.1m. The entire numerical simulation computation space was 22m × 22m × 16m, the time sampling interval was 0.1ns, and the total radar recording time was 200ns. To simulate the circular polarization transmission and dual-linear polarization reception observation mode of the Tianwen-2 probe radar, a 100MHz Ricker wavelet was selected as the main frequency. Figure 3 (a) is used as the excitation source and loaded onto Figure 2 The electric field component in the Y direction (i.e., the Ey component) is transformed into the Hilbert transform form of the wavelet. Figure 3 (b) is used as the excitation source and loaded onto Figure 2 The electric field component in the Z direction (i.e., the Ez component) and the received signals are respectively Figure 2 The electric field components in the Y and Z directions (i.e., the Ey and Ez components). It should be noted that the Ey and Ez components are used here, while the previous two sections mentioned using the Ex and Ey components. Although the electric field components used are different, they are essentially the same and can still achieve three-dimensional imaging of the asteroid's internal structure. For example... Figure 3 As shown in (c), the blue and red lines represent two components, while the solid green line indicates that the electric field vector of the circularly polarized wave in this simulation changes in a circular trajectory over time. Three-dimensional forward modeling was performed using an eighth-order spatial and fourth-order temporal finite-difference method based on staggered grids. A perfectly matched layer absorbing boundary condition in a uniaxial anisotropic medium was employed to absorb the outwardly propagating electromagnetic waves, ultimately yielding "single-station radar observation data" containing the direct wave.

[0035] Because the direct wave amplitude was relatively strong, the reflected and diffracted waves in the "single-station radar observation data" were not clear enough. To highlight the electromagnetic wave characteristics related to the asteroid's surface and interior, the direct wave in the "single-station radar observation data" was cropped. Figure 4 The Ey component profile of the "single-station radar observation data" after removing the direct wave is shown. Figure 4 (a) to (c) are Ey component profiles of "single-station radar observation data" after the direct wave has been removed from the middle, upper, and lower orbits, respectively. Figure 5 The diagram shows the Ez component profile of the "single-station radar observation data" after the direct wave was removed from the three orbits. Figure 5 Images (a) to (c) show the Ez component profiles of the "single-station radar observation data" after removing the direct wave on the intermediate, upper, and lower orbits, respectively. Figure 4 and Figure 5 A strong reflected wave phase axis can be seen, located between 30ns and 60ns, corresponding to the reflected wave from the outer surface of the asteroid. Multiple waves and diffraction waves can be seen after 80ns.

[0036] Three-dimensional reverse time migration imaging requires a reasonable radar wavelet. In practice, classical wavelet extraction methods (such as constrained sparse pulse deconvolution) can be used to estimate the wavelet from monostation radar data. For simplicity, we use the wavelet from the forward modeling simulation as the estimated radar wavelet. The second step involves performing velocity analysis on the single-station radar observation data after the direct wave is removed to obtain the relative permittivity inside the asteroid. Combined with prior information about the asteroid obtained from other payloads, such as three-dimensional shape information and inferred material composition, a three-dimensional dielectric model of the asteroid is constructed.

[0037] To establish an initial three-dimensional model of the asteroid, available prior information includes the asteroid's three-dimensional shape, which can be obtained through measurements taken by an optical camera mounted on the asteroid. Therefore, it is assumed here that the initial asteroid model's three-dimensional shape is exactly the same as that of the actual asteroid model. Information on the asteroid's internal structure and dielectric constant is generally difficult to obtain directly; however, for some asteroids with simple internal structures, the dielectric constant range can be preliminarily determined based on the velocity analysis characteristics of single-station radar data. For simplicity, we assume that the internal structure and physical properties of the asteroid's three-dimensional dielectric model are consistent with those of the actual asteroid model.

[0038] The third step involves selecting a radar observation point from the corresponding radar observation system information, determining the corresponding transmitter and receiver locations, and using the radar wavelet obtained in the first step and its Hilbert transform as excitation sources to apply an electric field to the transmitter location. Components and In terms of components, by combining the three-dimensional dielectric model of the asteroid and using the forward modeling method to perform three-dimensional forward modeling, the forward propagation wave field of the electric field component in the single-station radar simulation data at different times is obtained.

[0039] The fourth step involves using the transmitter and receiver positions determined in the third step as the receiver and transmitter positions in the backpropagation process, respectively. The electric field of the "monostationary radar observation data" obtained in the first step is then used at the transmitter position determined in the third step. Components and The components of the electric field applied at the source location during the reverse propagation process, respectively, are the excitation sources. Components and In terms of components, combining the three-dimensional dielectric model of the asteroid, a three-dimensional forward modeling method is used to obtain the electric field in the single-station radar simulation data. Components and The backpropagation wave field of the component at different times.

[0040] The fifth step involves cross-correlation calculations using the electric field components in the single-station radar simulation data at different times for the forward and reverse propagation wave fields. The calculation formula is as follows: , in, , and These represent the positions of any point inside the asteroid model. Indicates the receiving antenna direction and direction; Indicates the first The source point (i.e., the first source point) The reverse time migration imaging results corresponding to each radar observation point Indicates the first The source point (i.e., the first source point) The single-station radar electric field corresponding to each radar observation point direction or Directional components in the 1st The forward propagation wave field at any given moment, Indicates the first The source point (i.e., the first source point) The single-station radar electric field corresponding to each radar observation point direction or Directional components in the 1st The reverse propagation wave field at any moment, and These represent the time sampling interval and the total number of samples, respectively.

[0041] Step 6: Repeat steps 3 through 5 until all radar observation points in the radar observation system information have been traversed, thereby obtaining the imaging results of all source points.

[0042] Step 7: Superimpose the imaging results of all source points to obtain the imaging results of all source points. The superposition formula is as follows: , in, The total number of radar observation points is given; then, a Laplace filter is used to suppress the low-frequency noise after the imaging results of all source points are superimposed, and finally a high-resolution three-dimensional imaging result is obtained.

[0043] Figure 6 This paper presents a 3D structural diagram and a 2D slice diagram of the imaging results obtained from 3D reverse-time migration imaging based on asteroid model "single-station radar observation data". (Comparison) Figure 2 and Figure 6 It can be observed that the imaging method provided by this invention can obtain imaging results of a three-dimensional rubble pile-type asteroid model that are very close to the actual internal structure. The position and size of the rubble pile are accurately imaged, indicating that the method of this invention can obtain a relatively accurate internal structure of asteroids and is expected to provide a reliable and high-precision method for actual single-station radar data imaging of asteroids.

[0044] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for three-dimensional reverse-time migration imaging of the internal structure of an asteroid based on monostatic radar, characterized in that, Includes the following steps: A1: Obtain single-station radar observation data and corresponding radar observation system information, and obtain radar wavelet based on the single-station radar observation data; A2: The relative permittivity inside the asteroid is obtained by velocity analysis of the single-station radar observation data. Combined with prior information about the asteroid obtained from other scientific payloads, a three-dimensional dielectric model of the asteroid is constructed. A3: Based on the radar wavelet and the corresponding radar observation system information, the transmitting source position and receiving source position corresponding to the radar observation point position are obtained. Combined with the three-dimensional dielectric model of the asteroid, forward modeling is performed to obtain the forward propagation wave field of the single-station radar electric field component at different times. A4: Using the single-station radar observation data received at the receiving source position corresponding to the radar observation point position as the excitation source, the transmitting source position and receiving source position corresponding to the radar observation point position are interchanged, and forward modeling is performed in combination with the three-dimensional dielectric model of the asteroid to obtain the reverse propagation wave field of the single-station radar electric field component at different times. A5: Perform zero-delay cross-correlation between the forward propagation wave field of the single-station radar electric field component at different times and the reverse propagation wave field of the single-station radar electric field component at different times to obtain the imaging result of a single source point. A6: Repeat steps A3 to A5 until all radar observation points have been traversed to obtain the imaging results of all source points; A7: Superimpose the imaging results of all source points, use Laplace filtering to suppress low-frequency noise, and obtain high-resolution three-dimensional imaging results.

2. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, The corresponding radar observation system information includes the type of radar observation orbit, the location of radar observation points, the number of radar observation points, and the radar antenna polarization mode; the type of radar observation orbit is a circular orbit, an elliptical orbit, a spiral orbit, an irregular orbit, or an equivalent circular orbit that achieves orbital observation by hovering a single-station radar and utilizing the rotation of an asteroid; the radar antenna polarization mode is circular polarization transmission with dual-line polarization reception or linear polarization transmission with linear polarization reception.

3. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, The step of obtaining the radar wavelet based on the single-station radar observation data specifically includes: preprocessing the single-station radar observation data and removing the direct wave to obtain single-station radar observation data after removing the direct wave; and estimating the radar wavelet using a wavelet estimation method based on the single-station radar observation data after removing the direct wave to obtain the radar wavelet.

4. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 3, characterized in that, Step A2 specifically includes: A21: The relative permittivity inside the asteroid is obtained by velocity analysis of the single-station radar observation data after the direct wave is removed; A22: Based on the relative permittivity results inside the asteroid and combined with prior information about the asteroid obtained from other scientific payloads, a three-dimensional dielectric model of the asteroid is constructed.

5. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, Step A3 specifically includes: A31: Using the radar wavelet as the excitation source, select a radar observation point location based on the corresponding radar observation system information, and determine the transmitting source location and receiving source location corresponding to the radar observation point location. A32: Combining the aforementioned three-dimensional dielectric model of the asteroid, three-dimensional forward modeling was performed using the forward modeling method to obtain the forward propagation wave field of the single-station radar electric field component at different times.

6. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 5, characterized in that, The forward modeling method is a time-domain finite-difference method based on interlaced grids; during the forward modeling process, if simulating circularly polarized transmission and dual-linearly polarized reception, the excitation source is applied to the transmitting antenna. Direction, and its phase delayed by 90° before being loaded onto Direction, receiving antennas are respectively in direction and Simultaneously receiving the monostatic radar electric field in the same direction; if simulating linearly polarized transmission and reception, the excitation source is applied to a specific direction of the transmitting antenna, and the monostatic radar electric field is received through a specific direction of the receiving antenna. These two specific directions correspond to the transmitting and receiving antennas, respectively. direction or The directions can be the same or different.

7. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, Step A4 specifically includes: A41: The single-station radar observation data received at the receiving source position corresponding to the radar observation point position is used as the excitation source, and the transmitting source position and receiving source position corresponding to the radar observation point position are used as the receiving source position and transmitting source position in the back-propagation process, respectively. A42: Combining the three-dimensional dielectric model of the asteroid, three-dimensional forward modeling was performed using the forward modeling method to obtain the back propagation wave field of the single-station radar electric field component at different times.

8. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, Step A5 specifically includes: performing cross-correlation calculations on the forward and reverse propagation wave fields of the single-station radar electric field components at different times to obtain the imaging result of a single source point, as shown in the formula: ， in, , and These represent the positions of any point within the asteroid model in three-dimensional space. Indicates the receiving antenna direction and direction; Indicates the first The source point, that is, the first source point. Each radar observation point corresponds to the reverse time-shift imaging results; Indicates the first The source point, that is, the first source point. Each radar observation point corresponds to a single-station radar electric field. Directional component or Directional components in the 1st The forward propagation wave field at any given moment; Indicates the first The source point, that is, the first source point. Each radar observation point corresponds to a single-station radar electric field. Directional component or Directional components in the 1st The reverse propagation wave field at any given moment; and These represent the time sampling interval and the total number of samples, respectively.

9. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, The cross-correlation calculation formula used in step A5 needs to be adjusted according to different antenna receiving methods, specifically including: when using a dual-polarization receiving method, the forward propagation wave field A propagating wave field containing components of the electric field in two directions, namely the electric field and the propagating wave field. Forward propagation wave field of directional components and Forward propagation wave field and backward propagation wave field of directional components It also includes the anti-propagating wave field containing the components of the electric field in two directions, namely... Directional components and The inverse propagation wave field of the directional component; the forward propagation wave field when using linear polarization reception. A propagating wave field that contains only the component of the electric field in one direction, i.e., the electric field. direction or Forward propagation wave field and backward propagation wave field of directional components It is also a propagating wave field that only contains the component of the electric field in one direction, i.e., the electric field. Directional component or The backpropagating wave field of the directional component.

10. The three-dimensional reverse-time migration imaging method for the internal structure of asteroids based on monostatic radar according to claim 1, characterized in that, Step A7 specifically includes: A71: The superimposed imaging results of all source points are obtained as shown in the formula: ， in, This indicates the image result after superposition; This represents the total number of source points, corresponding to the total number of radar observation points. A72: Using Laplace filtering to suppress low-frequency noise after the superposition of imaging results from all source points, a high-resolution three-dimensional imaging result is obtained.

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