Multifunctional satellite constellation configuration design optimization method based on large language model

Abstract

The invention discloses a multifunctional satellite constellation configuration design optimization method based on a large language model, and belongs to the technical field of spacecraft system design, and the method comprises the steps: setting design variables and fixed variables, and the design variables comprise the orbit inclination angle and orbit height of a satellite in a satellite constellation; constructing an evaluation function based on the coverage percentage, the ground pixel resolution, the average visible star number and the geometric accuracy factor; and based on the design variables and the fixed variables, generating a solution through large language model iteration, evaluating the solution through an evaluation function, and based on an evaluation result, obtaining an optimal satellite constellation configuration design scheme. According to the technical scheme, the satellite constellation configuration design optimization method considering various optimization aspects can be provided.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft system design, and in particular relates to a multifunctional satellite constellation configuration design optimization method based on a large language model. Background Art

[0002] A multi-satellite multi-function constellation refers to a group of small satellites that use distributed cooperative control and wireless communication technologies to move in a specific configuration in orbit or deep space in response to different work requirements, and jointly perform tasks that are difficult for traditional large single satellites to complete alone. However, since the large-scale multi-function constellation configuration design increases exponentially with the increase of its satellite scale, and the constraints are often complex, it is a typical NP-hard problem and it is difficult to find the optimal solution within a limited time. Therefore, the difficulty of design lies in how to find high-quality feasible solutions and suboptimal solutions within a limited time. In the constellation concept design stage, traditional constellation configuration design algorithms mainly include simulation comparison method, geometric analysis method, and design method based on manually designed optimization algorithm, but traditional algorithms are prone to fall into local optimality. In addition, large-scale constellation configurations are usually large and have high deployment costs. Traditional algorithms are often designed for a single function, resulting in low satellite utilization. In order to improve resource utilization and save orbital resources and deployment costs, it is necessary to explore multi-function constellation configuration design methods to achieve multiple uses of one satellite. Therefore, in order to overcome the limitations of traditional algorithms for constellations, it is necessary to develop an intelligent search optimization algorithm that can explore the existence of optimization space and has generalization capabilities, so that the design and autonomous optimization of satellite constellation configuration schemes can be realized in the overall design stage, providing a scientific basis and reference for the overall design of satellite constellation systems. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a multi-functional satellite constellation configuration design optimization method based on a large language model to solve the problems existing in the above-mentioned prior art.

[0004] To achieve the above object, the present invention provides a multifunctional satellite constellation configuration design optimization method based on a large language model, comprising:

[0005] Setting design variables and fixed variables, wherein the design variables include orbital inclinations and orbital altitudes of satellites in the satellite constellation;

[0006] An evaluation function is constructed based on coverage percentage, ground pixel resolution, average number of visible stars and geometric precision factor;

[0007] Based on the design variables and fixed variables, solutions are iteratively generated through a large language model, and the solutions are evaluated through an evaluation function. Based on the evaluation results, the optimal satellite constellation configuration design solution is obtained.

[0008] Optionally, the objective optimization function is

[0009] find x=[h,i]

[0010]

[0011] st i min ≤i≤i max ,h min ≤h≤h max ,C r =100

[0012] Among them, w1, w2, w3, and w4 are the weights of the corresponding targets, F(x) is the evaluation function, and C r is the coverage percentage, is the dimensionless ground pixel resolution after normalization, N is the average number of visible stars, GDOP is the geometric dilution of precision, x is the design variable, h is the orbit altitude, i is the orbit inclination, and the subscripts min and max represent the corresponding minimum and maximum values.

[0013] Optionally, the process of obtaining the coverage percentage includes:

[0014] The coverage angle, the center angle and the coverage bandwidth are calculated according to the orbital height of a single satellite and the corresponding sub-satellite point; the longitude and latitude of the ground target and the longitude and latitude of the sub-satellite point of the satellite are obtained according to the coverage angle, the center angle and the coverage bandwidth; the geocentric angle is calculated according to the longitude and latitude of the ground target and the longitude and latitude of the sub-satellite point of the satellite, and the geocentric angle and the coverage angle are judged. If the geocentric angle is less than or equal to the coverage angle, the ground target is included in the coverage range of the current satellite;

[0015] Make a grid map of the observation area, use the grid points as feature points, and use the feature points as ground targets to determine whether the ground targets are included in the coverage of the current satellite. Obtain the total time that all feature points in the observation area are covered by one or more satellites, and divide the total time by the total simulation time to get the coverage percentage.

[0016] Optionally, the process of obtaining the ground pixel resolution includes:

[0017] The ground pixel resolution of the payload is calculated according to the orbital altitude, the pixel size of the satellite payload and the focal length of the satellite's optical system, and the ground pixel resolution of the payload is normalized to obtain a normalized dimensionless ground pixel resolution.

[0018] Optionally, the process of obtaining the average number of visible stars includes:

[0019] Taking the geocentric space rectangular coordinate system as the reference system, the coordinates of the ground observation station and the satellite are obtained. According to the coordinates of the ground observation station and the satellite, the observation vector from the ground observation station to the satellite is obtained. The observation vector is converted from the geocentric space rectangular coordinate system to the station-centered coordinate system based on the ground observation station. According to the converted observation vector, calculation is performed to obtain the satellite altitude angle. When the preset altitude cutoff angle is less than the satellite altitude angle, the satellite is visible to the ground observation station.

[0020] Make a grid map of the observation area, use the grid points as feature points, and use the feature points as ground observation stations to determine whether the satellite is visible to the ground observation station. Get the sum of the number of visible stars at all feature points at each moment, and divide the sum of the number of visible stars by the total simulation time to get the average number of visible stars.

[0021] Optionally, the process of obtaining the geometric precision factor includes:

[0022] According to the satellite elevation angle and satellite azimuth angle, a coefficient matrix is ​​obtained. According to the coefficient matrix, the mean square error of the three-dimensional position and clock deviation is obtained. According to the mean square error of the three-dimensional position and clock deviation, the geometric precision factor is calculated.

[0023] Optionally, fixed parameters include the total number of satellites, the number of orbital planes, phase parameters, and the longitude and latitude range of the observation area.

[0024] The process of obtaining the optional optimal satellite constellation configuration design solution includes:

[0025] Initializing design variables, optimizing the design variables by using a large language model as an optimizer, and obtaining a solution, wherein the solution is a new constellation configuration scheme;

[0026] Evaluate the solution through the evaluation function to obtain the evaluation score;

[0027] According to the evaluation scores, the solutions are screened to obtain the better solutions. Meta-prompts are generated based on the better solutions and task descriptions. The meta-prompts are predicted and optimized through the large language model to generate new solutions.

[0028] Repeat the solution generation, evaluation and screening steps until the maximum number of iterations is reached, and then obtain the solution with the best evaluation score as the optimal satellite constellation configuration design solution.

[0029] Compared with the prior art, the present invention has the following advantages and technical effects:

[0030] In view of the problem that the traditional algorithm of large-scale multi-function constellation configuration design is prone to local optimality due to the exponential increase of parameters and complex constraints, this paper proposes a constellation configuration design optimization algorithm based on a large language model, which can generate and autonomously find the optimal solution to the problem under zero sample number. Compared with the traditional design method, the optimization effect is better and the algorithm has stronger generalization ability. In view of the fact that large-scale constellations are usually large in size and have high deployment costs, and the traditional single-function constellation configuration design method leads to low satellite utilization, a multi-function constellation configuration design method is proposed to improve satellite utilization and save orbital resources and deployment costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0032] Figure 1 A schematic diagram of a satellite ground coverage model according to an embodiment of the present invention;

[0033] Figure 2 A schematic diagram of a satellite visibility analysis model according to an embodiment of the present invention;

[0034] Figure 3 A schematic diagram of the distribution of satellites involved in the positioning solution when calculating the GDOP according to an embodiment of the present invention;

[0035] Figure 4 This is an overview diagram of the large language model optimization algorithm framework of an embodiment of the present invention;

[0036] Figure 5 is an optimization flow chart of an embodiment of the present invention;

[0037] Figure 6 It is a schematic diagram of optimization results of the large language model optimization method according to an embodiment of the present invention;

[0038] Figure 7 It is a schematic diagram of optimization results of the improved genetic algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0040] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0041] In order to overcome the problem that traditional algorithms are prone to fall into local optimality due to the exponential increase of parameters and complex constraints in the design of large-scale multifunctional satellite constellation configurations, the present invention discloses a multifunctional satellite constellation configuration design optimization method based on a large language model, which is an efficient constellation configuration design method. The problem to be solved is to explore the existence of optimization space and construct an intelligent search optimization algorithm with generalization ability to realize the constellation configuration design integrating navigation enhancement and remote sensing, so that the coverage percentage of the target observation area is as high as possible, the pixel resolution of the payload and the GDOP of navigation are as small as possible, the average number of visible stars in the target area is as large as possible, and the cost of satellite constellation design is reduced, orbital resources are saved, and resource utilization is improved.

[0042] The present invention is achieved through the following technical solutions.

[0043] The invention discloses a multifunctional satellite constellation configuration design optimization method based on a large language model. Based on the Walker-δ constellation configuration, the initial conditions of the satellite constellation optimization design problem are determined, and a satellite constellation ground coverage analysis model, a satellite constellation ground observation resolution model, a visibility analysis model and a GDOP model are established. The large language model optimization algorithm is used for autonomous optimization, and the orbital height and orbital inclination are optimized with coverage percentage, ground pixel resolution, number of visible satellites and GDOP as objective functions. In addition, a linear weighted method is used to convert the multi-objective problem into a single-objective problem, so as to efficiently obtain a set of optimal configuration solutions that meet engineering requirements.

[0044] Specifically, the present invention discloses an efficient constellation configuration design method, comprising the following steps.

[0045] 1. Optimize model building

[0046] (1) Design variables: Set the design variables to the satellite's orbital height h = [h1,h2,…,h n ], orbital inclination i=[i1,i2,…,i n ], n is the total number of satellites in the constellation. Since the Walker-δ constellation configuration is adopted in the present invention, the orbital height h and orbital inclination i in the constellation are unified, which is abbreviated as x=[h,i].

[0047] (2) Constraints: Track height constraint h∈[h min ,h max ], orbital inclination constraint i∈[i min ,i max ], the target area has no leakage coverage constraint, that is, the cumulative coverage percentage should be 100%.

[0048] (3) Optimization objectives: Among them C r(x) is the cumulative coverage percentage of the satellite to the target area within 24 hours, R p (x) is the ground pixel resolution of satellite earth observation, N(x) is the average number of visible stars in the target area, and GDOP(x) is the geometric precision factor that measures the navigation performance in the target area.

[0049] The above optimization target calculation method is as follows.

[0050] a. Coverage percentage calculation method

[0051] First, establish a satellite coverage analysis model. The satellite constellation coverage model is as follows: Figure 1 As shown. According to the satellite orbit height h and the minimum observation angle σ, the coverage angle d of a single satellite is calculated σ , center angle α σ and coverage bandwidth S wσ On this basis, the geocentric angle θ corresponding to the ground target and the satellite is obtained to determine whether the point is within the coverage of the satellite.

[0052] Assume that the orbital height of satellite S at a certain time is h, and the corresponding sub-satellite point is G. According to formula (1), the coverage angle d under the minimum observation angle σ is calculated respectively: σ , center angle α σ and coverage bandwidth S wσ .

[0053]

[0054] S wσ =2a E ·d σ

[0055] Among them, a E represents the radius of the earth, and P represents a point on the earth.

[0056] The intersection of the line connecting the spacecraft and the Earth's center of mass and the Earth's surface is called the sub-satellite point. The curve formed by a series of sub-satellite points formed by the spacecraft in orbit is called the sub-satellite point trajectory. The sub-satellite point is usually represented by longitude and latitude, and can be calculated by the orbital elements of the satellite. If the orbital elements of the satellite at the current moment are known, the longitude and latitude of the sub-satellite point can be expressed as

[0057]

[0058] Among them, λ S is the satellite subsatellite point longitude, is the latitude of the satellite sub-satellite point; i is the orbital inclination, u=ω+f is the latitude argument, ω is the perigee argument, f is the true anomaly; Ω is the right ascension of the orbital ascending node, α G It is the Greenwich mean sidereal hour angle, which is affected by the rotation of the Earth.

[0059] The Julian date starts at noon Greenwich on July 1, 4713 BC. From this epoch, the Julian date increases by 1 for each mean solar day. The Julian date can be used to easily calculate the length of time between two dates. Given the Coordinated Universal Time (year (yr), month (mon), day (day), hour (hr), minute (min), second (sec)), the corresponding Julian date JD can be obtained as

[0060]

[0061] The corresponding calculation method of Greenwich mean sidereal time is defined as

[0062] α G =67310.54841+(876600+8640184.812866)T UTI +0.093104T 2 UTI -6.2×10 -6 T 3 UTI

[0063] Where T UTI is the Julian century relative to 12:00 UT1 on January 1, 2000, calculated as

[0064]

[0065] Where JD is the corresponding Julian day.

[0066] Based on the above coverage angle, center angle, coverage bandwidth and longitude and latitude of the sub-satellite point, assume that the longitude of the current ground target is λ w , latitude is According to formula (3), calculate the geocentric angle θ between the ground target and the satellite; if θ≤d σ , it means that the ground target is included in the coverage of satellite S.

[0067]

[0068] A grid map is drawn at preset latitude and longitude intervals in the observation area, and the obtained grid points are used as feature points; the coverage percentage C is used r As an indicator of the constellation's earth observation coverage performance, it is equal to the total time that all feature points in the observation area are covered by one or more satellites divided by the total simulation time. The present invention uses simulation software to calculate the cumulative coverage percentage, that is, the percentage of the target area covered by satellite sensors within a specified time.

[0069] b. Calculation method of ground pixel resolution

[0070] According to the satellite orbit height h, the payload pixel size d and the optical system focal length f, the ground pixel resolution R of the payload is obtained according to formula (4): p As an indicator of the constellation's Earth observation resolution performance:

[0071]

[0072] According to formula (5), R p Normalize it to get the dimensionless ground pixel resolution

[0073]

[0074] c. Calculation method of the number of visible stars

[0075] like Figure 2 The model of satellite visibility analysis is shown in Figure 1. The angle between the observation vector between the ground observation station and the satellite and the horizontal plane formed by the east axis and the north axis in the station center coordinate system is called the satellite altitude angle. The positioning performance of the satellite navigation system is affected by many indicators, among which satellite visibility is one of the core indicators. Its determination depends on the comparison between the satellite altitude angle and the preset cutoff altitude angle. Specifically, when the satellite's altitude angle reaches or exceeds this preset cutoff value, the satellite is considered visible.

[0076] The analysis process is as follows:

[0077] First, take the geocentric rectangular coordinate system as the reference system and assume that the coordinates of the ground observation station O are (x o ,y o ,z o ), let the coordinates of the satellite be (x i ,y i ,z i ). Through the coordinates of these two points, the observation vector (Δx, Δy, Δz) from the ground observation station O to the satellite can be calculated. The calculation method is shown in formula (6).

[0078]

[0079] After that, assume that the current latitude and longitude of the ground observation station O is (α, β). The geocentric earth-fixed coordinate system, i.e., the geocentric rectangular coordinate system, is first rotated around the Z axis (90°+α) and then around the X axis (90°-β), and the geocentric earth-fixed coordinate system is converted to the station-centered coordinate system. Assume that the observation vector in the station-centered coordinate system is [Δe Δn Δu] T According to the matrix rotation formula, the coordinate rotation matrix T can be obtained as shown in formula (7):

[0080]

[0081] According to the matrix transformation principle, the observation vector in the station center coordinate system is obtained as shown in formula (8):

[0082]

[0083] It is known that the satellite is visible to the ground observation station only when the preset altitude cutoff angle is less than the satellite altitude angle. Therefore, the satellite altitude angle ξ at the current moment needs to be calculated. The calculation formula is shown in formula (9).

[0084]

[0085] The average number of visible stars is obtained by calculating the sum of the number of visible stars at all feature points in the target area at each moment and dividing it by the total simulation time.

[0086] d. Geometric Dilution of Precision

[0087] like Figure 3 The diagram shows the distribution of satellites involved in the positioning solution when calculating GDOP. The meaning of GDOP is explained from a geometric perspective, which means that the volume of the geometric body formed by the unit vectors pointing from the user to the four satellites in space is inversely proportional to the GDOP value. Therefore, if the volume of the geometric body formed by the satellites and users participating in the positioning solution is larger, it means that the distribution area of ​​these satellites is wider and more uniform, the GDOP value is smaller, and the positioning accuracy is higher. On the contrary, it means that the angles from the user to each satellite are very close, the GDOP value will become larger, and the navigation positioning accuracy will also deteriorate.

[0088] The calculation method is as follows:

[0089] The coefficient matrix H of the observation equation can be obtained using the satellite elevation angle ξ and the satellite azimuth angle α, as shown in equation (10).

[0090]

[0091] Where n represents the total number of satellites involved in the positioning solution, and the subscripts 1, 2, ..., n represent the satellite numbers corresponding to the parameters.

[0092] so,

[0093]

[0094] Where D 11 , D 22 , D 33 , D 44 Respectively represent the three-dimensional position (x, y, z) and clock deviation of the feature point in the observation area The mean square error of .

[0095] The value of GDOP can be expressed as formula (12):

[0096]

[0097] 2. Optimization process description

[0098] The large language model used in the present invention is ChatGPT-3.5-turbo. This method can generate various large models that adapt to different task requirements and application scenarios. The optimization method using a large language model as an optimizer refers to using the large model as a black box to optimize the constellation configuration. Its main advantage is that natural language can be used to describe task requirements, and the readability and versatility of the code are better than traditional algorithms.

[0099] An overview of the large language model optimization algorithm is shown below: Figure 4 As shown, the specific steps are as follows:

[0100] (1) Initially, LLM randomly generates n solutions based on the task description, where the solutions include different values ​​for the designs of different satellites in the constellation. In each subsequent iteration, LLM randomly generates m solutions based on the task description and historical solutions.

[0101] (2) Pass the newly generated solution to the evaluation function for performance evaluation and obtain the corresponding evaluation score;

[0102] (3) Compare the scores of the new solutions with the original n solutions, retain the n best solutions and write them into the solution library;

[0103] (4) Combine the solution library and task requirements to generate a new meta-prompt;

[0104] (5) LLM then generates m new and better solutions based on the task description and historical solutions, and repeats step (1);

[0105] (6) Until the number of optimization steps reaches the maximum, the optimal solution is output, and the satellites under the constellation are configured through the optimal solution to achieve the above-mentioned multi-objective optimization design.

[0106] like Figure 5 As shown, the specific implementation steps of the present invention are as follows:

[0107] (1) Determine the fixed parameters of the Walker-δ constellation configuration, including the total number of satellites T, the number of orbital planes P, and the phase parameter F, as well as the longitude and latitude range of the area to be observed; take the orbital inclination i and orbital altitude h as design variables, and determine the value range of each design variable [i min ,i max ],[h min ,h max ]; on this basis, the coverage percentage of earth observation is C r, Payload ground pixel resolution R P , the average number of visible satellites N and the geometric precision factor GDOP are used as performance indicators, and the mathematical model of the multi-objective optimization design problem of the satellite constellation is established as shown in formula (13):

[0108] find x=[h,i]

[0109]

[0110] st i min ≤i≤i max ,h min ≤h≤h max ,C r =100

[0111] (2) According to the above-mentioned method, the Gaussian constellation orbit dynamics equation, satellite constellation ground coverage analysis model, satellite constellation ground observation resolution model, visibility analysis model and precision factor model are established respectively, and then the simulation platform built by STK is used to calculate the four performance indicators;

[0112] (3) Using a large language model as an optimization method to generate new constellation configuration schemes;

[0113] (4) The evaluation function takes the maximum coverage percentage and the average number of visible stars, and the minimum ground pixel resolution and GDOP as the optimization objectives. A single-objective optimization function, namely the evaluation function F(x), is constructed by a weighted method, as shown in formula (14), which converts the multi-objective problem into a single-objective optimization problem. The new solution is passed to the evaluation function to obtain the corresponding score.

[0114] find x=[h,i]

[0115]

[0116] st i min ≤i≤i max ,h min ≤h≤h max , C r =100

[0117] Among them, w1, w2, w3, and w4 are the weights of the corresponding targets respectively.

[0118] (5) Retain n optimal solutions based on the scores of the new solution and the original solution, and generate a meta-prompt together with the task description and pass it to the LLM. The task description mainly includes some constraints and requirements for the output of the large model. The specific constraints include the range of orbital altitude and inclination. The output requirement is the number of better solutions generated according to the above objectives and the specific format of LLM output.

[0119] (6) Determine whether the number of analysis model calls has reached the maximum value. If not, return to step 3 to continue the optimization process. Otherwise, the optimization process terminates and outputs a set of satellite constellation design solutions with the optimal target value. A high coverage percentage of the constellation to the target observation area and a smaller pixel resolution of the payload are achieved, thereby reducing the calculation cost and design cost of the satellite constellation.

[0120] In order to better demonstrate the effectiveness and engineering practicability of the present invention, the present invention is further explained below by taking a specific multi-functional satellite constellation optimization design problem as an example.

[0121] In this case, a low-orbit Walker constellation is established, with a total of 18 satellites, 3 orbital planes, 6 satellites in each orbital plane, and a phase factor of 1; each satellite carries a sensor, the sensor's half-angle is set to 5°, the earth observation payload pixel size d = 10μm, and the focal length f = 500mm; the longitude and latitude range of the observed target area is 73°E~135°E, 3°N~53°N. Then, the TLE ephemeris data of the BeiDou-3 satellite is imported into the current STK scene to analyze the navigation enhancement effect of the Walker constellation on the BDS-3 constellation. During the simulation process, the orbital height h and orbital inclination i are used as optimization variables, and the value ranges are orbital height h∈[500km, 2000km] and orbital inclination i∈[30°, 60°]. During the optimization process, the large model generates 10 solutions according to the task requirements in the first round, and then the number of new solutions generated in each optimization is 4, the maximum number of model calls is 20, and the designed evaluation function is The optimization results of the multi-functional satellite constellation configuration design are as follows: Figure 6 At the same time, the present invention also uses the improved genetic algorithm as a control group to conduct experiments, and the optimization results obtained are as follows Figure 7 The comparison results of the large language model optimization method and the improved genetic algorithm optimization results are shown in Table 1.

[0122] Table 1

[0123]

[0124] from Figure 6-7 It can be seen that the optimization method of the large language model has obtained better results than the improved genetic algorithm, has greater advantages in dealing with complex optimization problems, improves the disadvantage of the traditional algorithm that is prone to fall into the local optimum, and has better adaptability and flexibility than the traditional method. In addition, the advantages in the generalization ability of the code are more obvious. Finally, the solution obtained by the large model optimization algorithm was selected as the final design solution.

[0125] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A multifunctional satellite constellation configuration design optimization method based on a large language model, characterized in that: include: Setting design variables and fixed variables, wherein the design variables include orbital inclinations and orbital altitudes of satellites in the satellite constellation; An evaluation function is constructed based on coverage percentage, ground pixel resolution, average number of visible stars and geometric precision factor; Based on the design variables and fixed variables, solutions are iteratively generated through a large language model, and the solutions are evaluated through an evaluation function. Based on the evaluation results, the optimal satellite constellation configuration design solution is obtained.

2. The method according to claim 1, characterized in that The objective optimization function is find x = [h, i] s.t i min ≤i≤i max ,h min ≤h≤,C r =100 Among them, w1, w2, w3, and w4 are the weights of the corresponding targets, F(x) is the evaluation function, and C r is the coverage percentage, is the dimensionless ground pixel resolution after normalization, N is the average number of visible stars, GDOP is the geometric dilution of precision, x is the design variable, h is the orbit altitude, i is the orbit inclination, and the subscripts min and max represent the corresponding minimum and maximum values.

3. The method according to claim 1, characterized in that The process of obtaining the coverage percentage includes: The coverage angle, the center angle and the coverage bandwidth are calculated according to the orbital height of a single satellite and the corresponding sub-satellite point; the longitude and latitude of the ground target and the longitude and latitude of the sub-satellite point of the satellite are obtained according to the coverage angle, the center angle and the coverage bandwidth; the geocentric angle is calculated according to the longitude and latitude of the ground target and the longitude and latitude of the sub-satellite point of the satellite, and the geocentric angle and the coverage angle are judged. If the geocentric angle is less than or equal to the coverage angle, the ground target is included in the coverage range of the current satellite; Make a grid map of the observation area, use the grid points as feature points, and use the feature points as ground targets to determine whether the ground targets are included in the coverage of the current satellite. Obtain the total time that all feature points in the observation area are covered by one or more satellites, and divide the total time by the total simulation time to get the coverage percentage.

4. The method according to claim 1, characterized in that The process of obtaining ground pixel resolution includes: The ground pixel resolution of the payload is calculated according to the orbital altitude, the pixel size of the satellite payload and the focal length of the satellite's optical system, and the ground pixel resolution of the payload is normalized to obtain a normalized dimensionless ground pixel resolution.

5. The method according to claim 1, characterized in that: The process of obtaining the average number of visible stars includes: Taking the geocentric space rectangular coordinate system as the reference system, the coordinates of the ground observation station and the satellite are obtained. According to the coordinates of the ground observation station and the satellite, the observation vector from the ground observation station to the satellite is obtained. The observation vector is converted from the geocentric space rectangular coordinate system to the station-centered coordinate system based on the ground observation station. According to the converted observation vector, calculation is performed to obtain the satellite altitude angle. When the preset altitude cutoff angle is less than the satellite altitude angle, the satellite is visible to the ground observation station. Make a grid map of the observation area, use the grid points as feature points, and use the feature points as ground observation stations to determine whether the satellite is visible to the ground observation station. Get the sum of the number of visible stars at all feature points at each moment, and divide the sum of the number of visible stars by the total simulation time to get the average number of visible stars.

6. The method according to claim 5, characterized in that The process of obtaining the geometric precision factor includes: According to the satellite elevation angle and satellite azimuth angle, a coefficient matrix is ​​obtained. According to the coefficient matrix, the mean square error of the three-dimensional position and clock deviation is obtained. According to the mean square error of the three-dimensional position and clock deviation, the geometric precision factor is calculated.

7. The method according to claim 1, characterized in that Fixed parameters include the total number of satellites, number of orbital planes, phase parameters and the longitude and latitude range of the observation area.

8. The method according to claim 1, characterized in that The process of obtaining the optimal satellite constellation configuration design solution includes: Initializing design variables, optimizing the design variables by using a large language model as an optimizer, and obtaining a solution, wherein the solution is a new constellation configuration scheme; Evaluate the solution through the evaluation function to obtain the evaluation score; According to the evaluation scores, the solutions are screened to obtain the better solutions. Meta-prompts are generated based on the better solutions and task descriptions. The meta-prompts are predicted and optimized through the large language model to generate new solutions. Repeat the solution generation, evaluation and screening steps until the maximum number of iterations is reached, and then obtain the solution with the best evaluation score as the optimal satellite constellation configuration design solution.

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