A space domain perception constellation design method and system based on earth-moon periodic orbit

Abstract

The application relates to the technical field of deep space exploration, and particularly discloses a space domain perception constellation design method and system based on an earth-moon periodic orbit, wherein the method comprises the following steps: designing a periodic orbit based on an earth-moon circular restricted three-body problem model, generating a closed orbit by adjusting initial position and velocity parameters; uniformly deploying multiple sensor satellites on the periodic orbit to form a monitoring constellation; correcting the periodic orbit and the closed orbit by using a high-precision four-body model, calculating and implementing velocity increment correction through a state transition matrix and a differential correction method to cope with solar gravitational disturbance; and judging the visibility of a target satellite in real time based on a visual magnitude model and a repulsion angle constraint to realize continuous space situation awareness.

Description

Technical Field

[0001] This invention relates to the field of deep space exploration technology, specifically to a space domain sensing constellation design method and system based on the Earth-Moon periodic orbit. Background Technology

[0002] Current Space Domain Awareness (SDA) technologies primarily rely on ground-based observation stations or low Earth orbit (LEO) satellite networks, but these technologies face challenges in their application within the lunisolar space. The vast coverage area and complex gravitational environment of lunisolar space, coupled with the limitations of traditional sensors in terms of geometric visibility and signal strength, severely hinders their monitoring capabilities in critical regions (such as L1 / L2 halo orbits). For instance, ground-based sensors are affected by Earth's curvature and atmospheric interference, resulting in extremely short visibility windows for distant targets in lunisolar space; while LEO satellites, due to their orbital altitude limitations, struggle to continuously cover areas near the Moon. Existing research has utilized Earth-Moon resonance orbits (such as 2:1 resonance orbits) or Lyapunov orbits for SDA missions to optimize monitoring capabilities, but these approaches face significant challenges in multibody gravitational environments. Taking the 2:1 Earth-Moon resonance orbit as an example, although its periodic orbital characteristics allow for repeated coverage of specific regions, the introduction of solar gravitational perturbations significantly reduces orbital stability, necessitating frequent orbital corrections. This not only increases fuel consumption but also reduces system reliability. Similarly, while Lyapunov orbits are stable in simplified models, their practical application in high-precision dynamic models is costly and difficult to meet the requirements of long-term missions. For example, the AFRL's "Cislunar Highway Patrol Systems" (CHPS) aims to monitor Earth-Moon space targets through specific orbital designs, but still faces challenges in fuel efficiency and coverage.

[0003] Insufficiency of existing technology:

[0004] (1) Limited Coverage: The core problem of Earth-Moon space monitoring lies in the limitation of sensor perspective. The occlusion effect of the Earth and Moon results in extremely short direct observation time for L1 / L2 targets. For example, when the target is located on the far side of the Moon, ground sensors cannot capture the signal at all; while low-Earth orbit satellites suffer from severe signal attenuation due to the great distance (the average distance between the Earth and the Moon is about 380,000 kilometers), making it difficult for the signal-to-noise ratio to meet the requirements for target identification. In addition, sunlight reflected from the lunar surface will create strong background noise at certain phase angles, further reducing the effective detection capability of the sensors.

[0005] (2) High fuel costs: Existing orbital designs (such as the Lyapunov orbit) rely on periodic closure characteristics in simplified models (such as CR3BP), but in actual multibody gravitational environments (such as the BCR4BP model which includes solar gravity), orbital stability is significantly disturbed. To maintain the preset trajectory, differential correction techniques must be frequently used to correct velocity deviations, leading to a surge in fuel consumption. For example, the annual fuel demand of traditional schemes may increase several times after the introduction of solar gravity, severely restricting the sustainability of the mission.

[0006] (3) Unique constellation design: Existing research mostly focuses on single orbit types, lacking a systematic assessment of the synergistic effects of multiple orbits. Simulations show that multi-orbit combined deployment may lead to dispersed sensor perspectives, thereby reducing overall coverage. For example, when satellites are distributed in different orbits, some areas may have overlapping coverage, while key monitoring areas may have blind spots, resulting in wasted resources.

[0007] (4) Insufficient model accuracy: Most orbit designs are based on a simplified three-body model (CR3BP), which ignores the impact of solar gravitational perturbations on the long-term stability of the orbit. This simplification leads to a serious underestimation of fuel requirements in actual missions. For example, a closed orbit in CR3BP may deviate from the preset path by tens of kilometers after the introduction of solar gravity, requiring additional fuel for correction, and traditional models are unable to accurately predict such deviations.

[0008] Existing technologies for monitoring the Earth-Moon space suffer from core problems such as insufficient coverage, low fuel efficiency, insufficient model accuracy, and lack of collaborative design. The innovation of this patent lies in proposing an SDA solution with high coverage and low fuel consumption by optimizing the Earth-Moon periodic orbit characteristics and multibody model. Summary of the Invention

[0009] To achieve the objectives of this invention, this application provides a spatial domain-aware constellation design method based on the Earth-Moon periodic orbit, comprising:

[0010] Step S1: Design a periodic orbit based on the Earth-Moon circular restricted three-body problem model, and generate a closed orbit by adjusting the initial position and velocity parameters;

[0011] Step S2: Distribute multiple sensor satellites evenly in the periodic orbit to form a monitoring constellation;

[0012] Step S3: Correct the periodic orbit and closed orbit using a high-precision four-body model. Calculate and implement velocity increment correction using the state transition matrix and differential correction method to cope with solar gravitational disturbances.

[0013] Step S4: Based on the visual magnitude model and repulsion angle constraint, the visibility of the target satellite is judged in real time to achieve continuous space situational awareness.

[0014] In some specific embodiments, step S1 includes:

[0015] Step S11: Iteratively optimize the initial state using a differential correction algorithm so that the closed orbit satisfies the periodic closure condition under the Earth-Moon circular restricted three-body problem model;

[0016] Step S12: Obtain the orbital parameters of the periodic orbit and the closed orbit based on the Earth-Moon circular restricted three-body problem model;

[0017] Step S13: Using the orbital parameters as initial values, perform segmented target correction under the high-precision four-body model, and reclose the orbit.

[0018] In some specific embodiments, step S3 includes:

[0019] Step S31: Divide the closed orbit obtained under the Earth-Moon circular restricted three-body problem into segments and define multiple splicing points;

[0020] Step S32: Apply a velocity increment correction with an initial assumption of zero at each segment point;

[0021] Step S33: Integrate the dynamic equations for each segment and calculate the deviation between the final state of the orbit and the desired state;

[0022] Step S34: Backpropagation is achieved through chain multiplication of the state transition matrix, and the velocity increment of each segment point is dynamically adjusted so that the segmented track is reclosed under the high-precision four-body model.

[0023] In some specific embodiments, step S4 includes:

[0024] The angles between the target and the sun, earth, and moon are calculated in real time. When the angle between the target and the sun is less than 30°, the angle with the earth is less than 15°, or the angle with the moon is less than 6°, and the apparent magnitude of the target is higher than 35, the target is determined to be imperceptible.

[0025] In some specific embodiments, the calculation of the velocity increment correction is achieved through a single or multiple-shot differential correction method to obtain the minimum total velocity increment that maintains the quasi-periodicity of the orbit.

[0026] To achieve the same inventive objective, this application also provides a space-domain sensing constellation design system based on the Earth-Moon periodic orbit, comprising:

[0027] Periodic orbit design module: used to design periodic orbits based on the Earth-Moon circular restricted three-body problem model, generating closed orbits by adjusting the initial position and velocity parameters;

[0028] Monitoring constellation generation module: used to uniformly deploy multiple sensor satellites on the said periodic orbit to form a monitoring constellation;

[0029] Orbit correction module: used to correct the periodic orbit and closed orbit using a high-precision four-body model, and calculate and implement velocity increment correction through state transition matrix and differential correction method to cope with solar gravitational disturbances;

[0030] Space perception module: used to determine the visibility of target satellites in real time based on visual magnitude models and repulsion angle constraints, so as to realize continuous space situational awareness.

[0031] In some specific embodiments, the periodic orbit design module is used to perform the following steps:

[0032] Step S11: Iteratively optimize the initial state using a differential correction algorithm so that the closed orbit satisfies the periodic closure condition under the Earth-Moon circular restricted three-body problem model;

[0033] Step S12: Obtain the orbital parameters of the periodic orbit and the closed orbit based on the Earth-Moon circular restricted three-body problem model;

[0034] Step S13: Using the orbital parameters as initial values, perform segmented target correction under the high-precision four-body model, and reclose the orbit.

[0035] In some specific embodiments, the orbit correction module is used to perform the following steps:

[0036] Step S31: Divide the closed orbit obtained under the Earth-Moon circular restricted three-body problem into segments and define multiple splicing points;

[0037] Step S32: Apply a velocity increment correction with an initial assumption of zero at each segment point;

[0038] Step S33: Integrate the dynamic equations for each segment and calculate the deviation between the final state of the orbit and the desired state;

[0039] Step S34: Backpropagation is achieved through chain multiplication of the state transition matrix, and the velocity increment of each segment point is dynamically adjusted so that the segmented track is reclosed under the high-precision four-body model.

[0040] In some specific embodiments, the spatial sensing module is used for:

[0041] The angles between the target and the sun, earth, and moon are calculated in real time. When the angle between the target and the sun is less than 30°, the angle with the earth is less than 15°, or the angle with the moon is less than 6°, and the apparent magnitude of the target is higher than 35, the target is determined to be imperceptible.

[0042] In some specific embodiments, the calculation of the velocity increment correction is achieved through a single or multiple-shot differential correction method to obtain the minimum total velocity increment that maintains the quasi-periodicity of the orbit.

[0043] The beneficial effects of the above technical solution are as follows:

[0044] This application proposes a space-domain sensing constellation design method and system based on the Earth-Moon periodic orbit, which solves the problems of coverage, fuel efficiency and model accuracy through multi-dimensional technological innovation:

[0045] (1) Low-fuel periodic orbit design: Utilizing the natural periodicity in the Earth-Moon Three-Body Model (CR3BP), a closed orbit is designed to enable long-term operation without fuel when there are no external disturbances. By optimizing the initial position and velocity parameters, orbits with long dwell times (such as orbits close to the Moon) are generated to maximize the continuous monitoring window for L1 / L2 targets. In the high-precision four-body model (BCR4BP), differential correction techniques are used to dynamically correct solar gravitational disturbances, significantly reducing fuel consumption per unit time.

[0046] (2) Single-orbit high-density constellation deployment

[0047] Abandoning the complex architecture of traditional multi-orbit combinations, a high-density deployment strategy using a single orbit is adopted. By evenly distributing multiple satellites on a single-period orbit, the blind spots of multi-orbit deployment are eliminated, and the orbital geometry is utilized to achieve full-time coverage of the target. Combined with dynamic elimination of angular constraints (such as shielding from interference reflections from the Sun, Earth, and Moon), the effective observation time ratio is further optimized.

[0048] (3) Collaborative Validation of Multibody Gravitational Models: A high-precision orbit correction framework is constructed by combining the CR3BP and BCR4BP models. The influence of the initial solar phase on orbital deviation is quantified using the State Transition Matrix (STM), and the correction amount is dynamically adjusted to ensure the robustness of the orbit in complex gravitational environments. For example, the perturbation compensation amount is calculated in real time based on the solar position to keep fuel consumption fluctuations within an extremely low range.

[0049] (4) Dynamic visual magnitude model: Develop a visual magnitude calculation model based on phase angle and diffuse reflectance coefficient to assess target visibility in real time. Automatically shield interference areas by excluding angle thresholds, and dynamically optimize the monitoring strategy in combination with sensor performance parameters. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 A flowchart illustrating a space-domain sensing constellation design method based on the Earth-Moon periodic orbit, provided as an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of the structure of a space domain sensing constellation design system based on the Earth-Moon periodic orbit, provided as an embodiment of the present invention. Detailed Implementation

[0053] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0054] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0055] Example 1

[0056] One embodiment of the present invention provides a space-domain sensing constellation design method based on the Earth-Moon periodic orbit, comprising:

[0057] Step S1: Design a periodic orbit based on the Earth-Moon circular restricted three-body problem model, and generate a closed orbit by adjusting the initial position and velocity parameters;

[0058] In a specific embodiment of the present invention, step S1 includes:

[0059] Step S11: Iteratively optimize the initial state using a differential correction algorithm so that the closed orbit satisfies the periodic closure condition under the Earth-Moon circular restricted three-body problem model;

[0060] Step S12: Obtain the orbital parameters of the periodic orbit and the closed orbit based on the Earth-Moon circular restricted three-body problem model;

[0061] Step S13: Using the orbital parameters as initial values, perform segmented target correction under the high-precision four-body model, and reclose the orbit.

[0062] Specifically, the dimensionless equations of motion for the double-circle restricted four-body model (BCR4BP) in the Earth-Moon rendezvous coordinate system are expressed as follows:

[0063]

[0064] A1 represents the dimensionless distance parameter between the Sun and the inertial reference frame; A2 represents the dimensionless distance parameter between the inertial reference frame and the Earth-Moon synodic reference frame. μ represents the position of the center of mass of the Earth-Moon system, and x and y represent the position coordinates in the Earth-Moon synodic coordinate system. In the synodic reference frame, the scalar distances of the satellite relative to the Earth, Moon, and Sun are defined by the following formulas:

[0065]

[0066] Where, x S and y S These are the x and y coordinates of the Sun relative to the barycenter of the Earth-Moon composite reference frame:

[0067] x S =-(A1+A2)cos(θ) S -θ e )

[0068] y S =-(A1+A2)sin(θ) S -θ e )

[0069] Angle θ S With θ e It is given by the following formula:

[0070]

[0071] The dimensionless constants of BCR4BP are shown in the table below:

[0072]

[0073] Step S2: Distribute multiple sensor satellites evenly in the periodic orbit to form a monitoring constellation;

[0074] In order to determine whether a target in a ring orbit is visible, airspace sensing must calculate the apparent magnitude of the aircraft. The first step in calculating the apparent magnitude is to determine the phase (or solar angle) at each point in time. The phase angle is calculated using equations.

[0075]

[0076] in, The vector position of the target relative to the sensor-carrying satellite. This is the vector position of the target relative to the Sun. Assuming the target is modeled as a sphere, the phase function Ψ becomes:

[0077]

[0078] C d It is the diffuse reflectance coefficient, which is a function of the average wavelength.

[0079] Apparent magnitude is calculated using the following formula:

[0080]

[0081] Where A represents the surface area of ​​the target.

[0082] A target is considered visible when its visual magnitude is 18.5. The constants used in SDA analysis are the target area A and the diffuse reflectance coefficient C. d The values ​​are 2.25m. 2 And 0.86. When the angle between the satellite-target and satellite-gravitational body vectors is less than the solar repulsion angle, the target is assumed to be imperceptible because the sun is reflected onto the corresponding gravitational body.

[0083] When the apparent magnitude of the target is 35, and the solar repulsion angle of the satellite relative to the Sun, Earth, and Moon is less than the values ​​in the table below, the target is considered imperceptible.

[0084] sun 30° 35 Earth 15° 35 moon 6° 35

[0085] Six orbits are selected from the orbital families north of points L1 and L2, and their isophase distribution is used as the SDA constellation. Since they are symmetric about the xz plane in the CR3BP model, the initial values ​​of the orbits can be written as follows: The initial orbit values ​​are as follows:

[0086]

[0087]

[0088] Step S3: Correct the periodic orbit and closed orbit using a high-precision four-body model. Calculate and implement velocity increment correction using the state transition matrix and differential correction method to cope with solar gravitational disturbances.

[0089] In a specific embodiment of the present invention, step S3 includes:

[0090] Step S31: Divide the closed orbit obtained under the Earth-Moon circular restricted three-body problem into segments and define multiple splicing points;

[0091] Step S32: Apply a velocity increment correction with an initial assumption of zero at each segment point;

[0092] Step S33: Integrate the dynamic equations for each segment and calculate the deviation between the final state of the orbit and the desired state;

[0093] Step S34: Backpropagation is achieved through chain multiplication of the state transition matrix, and the velocity increment of each segment point is dynamically adjusted so that the segmented track is reclosed under the high-precision four-body model.

[0094] Specifically, a differential correction algorithm is used for trajectory design under the CR3BP model:

[0095] First, numerical integration is performed on the initial state for a period of time, allowing it to return to its initial position. Then, the position error of the orbit after one period is calculated.

[0096] ΔX=X(T)-X0

[0097] If ΔX is small enough, the orbit is considered to meet the periodicity requirement; otherwise, further correction is performed.

[0098] Calculate the state transition matrix Φ:

[0099]

[0100] Using linearized relations:

[0101] ΔX=ΦΔX0

[0102] Solve for ΔX, then update the initial iteration conditions:

[0103]

[0104] The process is iterated continuously until ΔX converges to an accuracy of 1e-6.

[0105] The above steps yielded the orbit under the CR3BP model. Using the obtained orbital parameters as initial values, the orbit was segmented, and the segment points were marked for targeting. By adjusting the velocity at each segment point, the orbit was reclosed under the new dynamic environment. The required velocity corrections were calculated, and these correction values ​​were accumulated to obtain the total correction over the entire orbital period. The calculation steps are as follows:

[0106] Divide the track into segments and define a set of splicing points. Initial velocity correction accumulation:

[0107]

[0108] Each dynamic equation satisfies:

[0109]

[0110] Error propagation model:

[0111] δX k =Φ(t) k ,t k-1 )δX k-1 +Bk ΔV k

[0112] Inverse correction is achieved through matrix chain multiplication:

[0113]

[0114] Where m represents the number of orbital segments and ΔV total This represents the total velocity correction, ΔV, over the entire orbital period. k Let X represent the velocity correction for the k-th segment, X represent the state vector containing position and velocity information, f(X,t) describe the change of the state vector X with time t, and Φ(t) represent the velocity correction for the k-th segment. k ,t k-1 Let A(t) represent the state transition matrix from time tk-1 to time t, and let A(t) represent the coefficient matrix of the state transition matrix. δX k Let δX represent the state correction amount for the k-th segment. k-1 B represents the state correction amount of the (k-1)th segment. k The coefficient matrix δr represents the coefficient matrix associated with the k-th segment. k This indicates the position correction of the k-th segment.

[0115] Step S4: Based on the visual magnitude model and repulsion angle constraint, the visibility of the target satellite is judged in real time to achieve continuous space situational awareness.

[0116] In a specific embodiment of the present invention, step S4 includes:

[0117] The angles between the target and the sun, earth, and moon are calculated in real time. When the angle between the target and the sun is less than 30°, the angle with the earth is less than 15°, or the angle with the moon is less than 6°, and the apparent magnitude of the target is higher than 35, the target is determined to be imperceptible.

[0118] In one specific embodiment of the present invention, the calculation of the velocity increment correction is achieved by a single or multiple target differential correction method to obtain the minimum total velocity increment that maintains the quasi-periodicity of the orbit.

[0119] This application utilizes the CR3BP model to generate periodic orbits, achieves orbit closure by adjusting initial conditions (such as adjusting the y-velocity at the x-axis starting point), and obtains high-precision periodic orbits using fine-tuning algorithms. The inherent repeatability of periodic orbits ensures that the satellite can cover a predetermined area within a fixed time, facilitating continuous surveillance. Under the ideal CR3BP model, no additional orbital correction fuel is required after orbit closure, reducing fuel consumption during long-term operation and extending mission life.

[0120] Due to external disturbances such as those caused by the sun in real-world environments, the BCR4BP model incorporates factors like solar gravity. By constructing a state transition matrix (STM) and implementing single / multiple-shot differential correction methods, orbital deviations are corrected in real time, and the necessary ΔV correction is calculated and executed. This effectively compensates for disturbances to the orbit caused by multibody gravity, allowing the orbit, which would have been closed under CR3BP, to maintain quasi-periodicity in a higher-fidelity model. A precise algorithm calculates the minimum ΔV correction, minimizing fuel consumption and ensuring high-precision orbit maintenance even under multi-perturbation environments.

[0121] Example 2

[0122] One embodiment of the present invention provides a space-domain-aware constellation design system based on the Earth-Moon periodic orbit, comprising:

[0123] Periodic orbit design module 10: Used to design periodic orbits based on the Earth-Moon circular restricted three-body problem model, generating closed orbits by adjusting the initial position and velocity parameters;

[0124] In one specific embodiment of the present invention, the periodic orbit design module 10 is used to perform the following steps:

[0125] Step S11: Iteratively optimize the initial state using a differential correction algorithm so that the closed orbit satisfies the periodic closure condition under the Earth-Moon circular restricted three-body problem model;

[0126] Step S12: Obtain the orbital parameters of the periodic orbit and the closed orbit based on the Earth-Moon circular restricted three-body problem model;

[0127] Step S13: Using the orbital parameters as initial values, perform segmented target correction under the high-precision four-body model, and reclose the orbit.

[0128] Monitoring constellation generation module 20: used to uniformly deploy multiple sensor satellites on the periodic orbit to form a monitoring constellation;

[0129] Orbit correction module 30: used to correct the periodic orbit and closed orbit using a high-precision four-body model, and to calculate and implement velocity increment correction through state transition matrix and differential correction method to cope with solar gravitational disturbances;

[0130] In one specific embodiment of the present invention, the track correction module 30 is used to perform the following steps:

[0131] Step S31: Divide the closed orbit obtained under the Earth-Moon circular restricted three-body problem into segments and define multiple splicing points;

[0132] Step S32: Apply a velocity increment correction with an initial assumption of zero at each segment point;

[0133] Step S33: Integrate the dynamic equations for each segment and calculate the deviation between the final state of the orbit and the desired state;

[0134] Step S34: Backpropagation is achieved through chain multiplication of the state transition matrix, and the velocity increment of each segment point is dynamically adjusted so that the segmented track is reclosed under the high-precision four-body model.

[0135] Space perception module 40: Used to determine the visibility of target satellites in real time based on visual magnitude model and repulsion angle constraints, so as to realize continuous space situational awareness.

[0136] In one specific embodiment of the present invention, the spatial sensing module 40 is used for:

[0137] The angles between the target and the sun, earth, and moon are calculated in real time. When the angle between the target and the sun is less than 30°, the angle with the earth is less than 15°, or the angle with the moon is less than 6°, and the apparent magnitude of the target is higher than 35, the target is determined to be imperceptible.

[0138] In one specific embodiment of the present invention, the calculation of the velocity increment correction is achieved by a single or multiple target differential correction method to obtain the minimum total velocity increment that maintains the quasi-periodicity of the orbit.

[0139] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0140] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the functions specified in one or more boxes. Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the invention. Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0141] The methods and apparatus provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

[0142] In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "a specific embodiment" or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A spatial domain-aware constellation design method based on the Earth-Moon periodic orbit, characterized in that, include: Step S1: Design a periodic orbit based on the Earth-Moon circular restricted three-body problem model, and generate a closed orbit by adjusting the initial position and velocity parameters; Step S2: Distribute multiple sensor satellites evenly in the periodic orbit to form a monitoring constellation; Step S3: Correct the periodic orbit and closed orbit using a high-precision four-body model. Calculate and implement velocity increment correction using the state transition matrix and differential correction method to cope with solar gravitational disturbances. Step S4: Based on the visual magnitude model and repulsion angle constraint, the visibility of the target satellite is judged in real time to achieve continuous space situational awareness.

2. The spatial domain sensing constellation design method based on the Earth-Moon periodic orbit as described in claim 1, characterized in that, Step S1 includes: Step S11: Iteratively optimize the initial state using a differential correction algorithm so that the closed orbit satisfies the periodic closure condition under the Earth-Moon circular restricted three-body problem model; Step S12: Obtain the orbital parameters of the periodic orbit and the closed orbit based on the Earth-Moon circular restricted three-body problem model; Step S13: Using the orbital parameters as initial values, perform segmented target correction under the high-precision four-body model, and reclose the orbit.

3. The spatial domain sensing constellation design method based on the Earth-Moon periodic orbit as described in claim 1, characterized in that, Step S3 includes: Step S31: Divide the closed track into segments and define multiple splicing points; Step S32: Apply a velocity increment correction with an initial assumption of zero at each segment point; Step S33: Integrate the dynamic equations for each segment and calculate the deviation between the final state of the orbit and the desired state; Step S34: Backpropagation is achieved through chain multiplication of the state transition matrix, and the velocity increment of each segment point is dynamically adjusted so that the segmented track is reclosed under the high-precision four-body model.

4. The spatial domain sensing constellation design method based on the Earth-Moon periodic orbit as described in claim 1, characterized in that, Step S4 includes: The angles between the target and the sun, earth, and moon are calculated in real time. When the angle between the target and the sun is less than 30°, the angle with the earth is less than 15°, or the angle with the moon is less than 6°, and the apparent magnitude of the target is higher than 35, the target is determined to be imperceptible.

5. The spatial domain sensing constellation design method based on the Earth-Moon periodic orbit according to claim 3, characterized in that, The calculation of the velocity increment correction is achieved through a single or multiple target differential correction method to obtain the minimum total velocity increment that maintains the quasi-periodicity of the orbit.

6. A space-domain sensing constellation design system based on the Earth-Moon periodic orbit, characterized in that, include: Periodic orbit design module: used to design periodic orbits based on the Earth-Moon circular restricted three-body problem model, generating closed orbits by adjusting the initial position and velocity parameters; Monitoring constellation generation module: used to uniformly deploy multiple sensor satellites on the said periodic orbit to form a monitoring constellation; Orbit correction module: used to correct the periodic orbit and closed orbit using a high-precision four-body model, and calculate and implement velocity increment correction through state transition matrix and differential correction method to cope with solar gravitational disturbances; Space perception module: used to determine the visibility of target satellites in real time based on visual magnitude models and repulsion angle constraints, so as to realize continuous space situational awareness.

7. The space-domain sensing constellation design system based on the Earth-Moon periodic orbit according to claim 6, characterized in that, The periodic orbit design module is used to perform the following steps: Step S11: Iteratively optimize the initial state using a differential correction algorithm so that the closed orbit satisfies the periodic closure condition under the Earth-Moon circular restricted three-body problem model; Step S12: Obtain the orbital parameters of the periodic orbit and the closed orbit based on the Earth-Moon circular restricted three-body problem model; Step S13: Using the orbital parameters as initial values, perform segmented target correction under the high-precision four-body model, and reclose the orbit.

8. The space-domain sensing constellation design system based on the Earth-Moon periodic orbit according to claim 6, characterized in that, The trajectory correction module is used to perform the following steps: Step S31: Divide the closed orbit obtained under the Earth-Moon circular restricted three-body problem into segments and define multiple splicing points; Step S32: Apply a velocity increment correction with an initial assumption of zero at each segment point; Step S33: Integrate the dynamic equations for each segment and calculate the deviation between the final state of the orbit and the desired state; Step S34: Backpropagation is achieved through chain multiplication of the state transition matrix, and the velocity increment of each segment point is dynamically adjusted so that the segmented track is reclosed under the high-precision four-body model.

9. The space-domain sensing constellation design system based on the Earth-Moon periodic orbit according to claim 6, characterized in that, The spatial sensing module is used for: The angles between the target and the sun, earth, and moon are calculated in real time. When the angle between the target and the sun is less than 30°, the angle with the earth is less than 15°, or the angle with the moon is less than 6°, and the apparent magnitude of the target is higher than 35, the target is determined to be imperceptible.

10. The space-domain sensing constellation design system based on the Earth-Moon periodic orbit according to claim 8, characterized in that, The calculation of the velocity increment correction is achieved through a single or multiple target differential correction method to obtain the minimum total velocity increment that maintains the quasi-periodicity of the orbit.

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