Simulation construction method, system, device and medium of giant constellation

Abstract

The application relates to the field of satellite measurement and control technology, and provides a simulation construction method, system, equipment and medium of a giant constellation, the method comprises the following steps: S1: acquiring input parameters of a satellite constellation; S2: generating Kepler orbit six elements of each satellite according to the input parameters; S3: converting the Kepler orbit six elements into a TLE format; and S4: carrying out orbit extrapolation based on the TLE format. The scheme can efficiently construct a large-scale satellite constellation, realizes high-precision conversion from orbit elements to the TLE format, supports various orbit extrapolation methods, and meets the design, analysis and simulation requirements of the giant constellation.

Description

Technical Field

[0001] This invention relates to the field of satellite telemetry, tracking, and command (TT&C) technology, and in particular to a method, system, equipment, and medium for simulating the construction of a giant constellation. Background Technology

[0002] With the rapid development of global satellite communication technology, the construction and operation of mega-satellite constellations are becoming increasingly important. These constellations typically contain thousands to tens of thousands of satellites, posing new challenges to large-scale constellation construction, multi-objective orbit design optimization, high-precision orbit simulation, and efficient computing. The number of satellites in orbit globally is projected to exceed 100,000 by 2030, and commercial space companies plan to deploy tens of thousands of low-Earth orbit satellites to build globally covered communication networks. Mega-constellations have become a crucial technological path to achieving global internet coverage, low-latency communication, and IoT connectivity. However, traditional methods struggle to efficiently handle large-scale constellation construction tasks. The conversion accuracy from orbital elements to Time Limit Expiration (TLE) is insufficient, there is a lack of unified large-scale constellation simulation platforms, and computational resources are consumed in large quantities with long processing times. Therefore, there is an urgent need for an efficient, high-precision, and scalable mega-constellation construction and simulation system to support the rapid construction, accurate simulation, and efficient analysis of large-scale constellations, meeting the needs of various application scenarios such as global broadband internet services, low-latency data transmission, IoT and edge computing, emergency communication and disaster relief, military communication, and situational awareness.

[0003] The existing technology has the following problems: 1. Low constellation construction efficiency: Traditional constellation construction methods mainly use manual configuration or simple parameterization methods, which are difficult to efficiently handle large-scale constellation construction tasks, resulting in long construction times and a high risk of errors.

[0004] 2. Insufficient accuracy in the conversion of orbital elements to TLE: Existing methods often use simplified conversion algorithms when converting Kepler orbital elements to TLE format, without fully considering the effects of perturbations such as atmospheric drag and solar radiation pressure, resulting in insufficient conversion accuracy and affecting the accuracy of subsequent orbit extrapolation.

[0005] 3. Limited orbit extrapolation methods: Existing systems mainly rely on a single orbit extrapolation method, lacking comparison and optimization of multiple methods, making it difficult to meet simulation tasks with different accuracy requirements.

[0006] 4. Insufficient large-scale data processing capabilities: Existing systems struggle to efficiently handle orbit extrapolation tasks for large-scale constellations, resulting in long computation times and high resource consumption.

[0007] 5. Low level of parameterization: Existing systems lack a flexible parameterization configuration mechanism, making it difficult to support the rapid construction and simulation of different configurations (such as Walker constellations, polar constellations, etc.).

[0008] Therefore, there is a need to provide a simulation construction method, system, equipment, and medium for mega-constellations that can efficiently construct large-scale satellite constellations, achieve high-precision orbital element to TLE conversion, support multiple orbital extrapolation methods, and meet the design, analysis, and simulation requirements of mega-constellations.

[0009] The information disclosed in the background section is only intended to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0010] The main purpose of this invention is to overcome the problems of low efficiency in constellation construction, insufficient accuracy in the conversion of orbital elements to TLE, single orbit extrapolation method, insufficient large-scale data processing capability, and low parameterization in existing technologies. It provides a simulation construction method, system, equipment, and medium for mega-constellations, which can efficiently construct large-scale satellite constellations, achieve high-precision conversion of orbital elements to TLE, support multiple orbit extrapolation methods, and meet the design, analysis, and simulation needs of mega-constellations.

[0011] To achieve the above objectives, the first aspect of the present invention provides a method for simulating and constructing a giant constellation, comprising the following steps: S1: Obtain the input parameters for the satellite constellation; S2: Generate the Kepler orbit six-root number for each satellite based on the input parameters; S3: Convert to TLE format based on the six Kepler orbital roots; S4: Track extrapolation based on TLE format.

[0012] According to an exemplary embodiment of the present invention, in step S2, generating the Kepler orbit six-root number for each satellite based on the input parameters includes: S21: Calculate the track surface parameters; S22: Calculate the distribution of the mean anomaly angles of the satellites in each orbital plane; S23: Generate the Kepler orbital six-root number for each satellite.

[0013] According to an exemplary embodiment of the present invention, step S3, the conversion of the Kepler orbital six-root number to TLE format includes: S31: Convert the six roots of the Kepler orbit into position and velocity vectors; S32: Set integration conditions; S33: Perform numerical integration; S34: Parameters required for fitting the TLE format based on the results of numerical integration; S35: Generate two rows of data in TLE format based on the fitted parameters.

[0014] According to an exemplary embodiment of the present invention, step S31, converting the six Kepler orbital roots into position and velocity vectors, includes: Calculate orbital parameters; Calculate the angle of near point; Calculate the true anterior angle based on the deviated anterior angle; Calculate the position and velocity vectors in the orbital plane coordinate system based on the orbital parameters and the true anomaly angle; Transform the orbital plane coordinate system into a geocentric inertial coordinate system.

[0015] According to an exemplary embodiment of the present invention, in step S34, the parameters required for fitting the TLE format based on the result of numerical integration include: Calculate the average motion; Calculate the first derivative of the average motion; Calculate the second derivative of the average motion; Calculate the rate of change of the orbital elements.

[0016] According to an exemplary embodiment of the present invention, in step S4, the orbit extrapolation based on the TLE format includes: S41: Resolve TLE; S42: Orbit propagation based on TLE; S43: Generate sequence data according to the predetermined time step.

[0017] According to an exemplary embodiment of the present invention, in step S42, the orbit propagation based on TLE includes: Choose a propagation model; Calculate the average motion at the current time; Based on the selected propagation model and average motion, the output position vector and velocity vector are determined.

[0018] According to a second aspect of the present invention, the present invention provides a simulation construction system for a giant constellation, comprising: a data acquisition module, an orbital element generation module, a TLE data generation module, and an orbital extrapolation module; The data acquisition module is used to acquire the input parameters of the satellite constellation; The orbital element generation module is used to generate the Kepler orbit six elements for each satellite based on the input parameters; The TLE data generation module is used to convert the six Kepler orbital roots into TLE format. The orbit extrapolation module is used to perform orbit extrapolation based on the TLE format.

[0019] As a third aspect of the present invention, the present invention provides an electronic device comprising: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the simulation construction method of the mega-constellation.

[0020] As a fourth aspect of the present invention, the present invention provides a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method for simulating and constructing a giant constellation.

[0021] The advantages of this invention are: This solution can efficiently construct large-scale satellite constellations, achieve high-precision orbital element to TLE conversion, support multiple orbital extrapolation methods, and meet the design, analysis, and simulation needs of mega-constellations. Attached Figure Description

[0022] The above and other objects, features, and advantages of this application will become more apparent from the detailed description of exemplary embodiments with reference to the accompanying drawings. The drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0023] Figure 1 The diagram schematically illustrates the structure of a simulation construction system for a giant constellation.

[0024] Figure 2 The diagram illustrates the steps of a simulation method for building a giant constellation.

[0025] Figure 3 A schematic diagram of the electronic device is shown.

[0026] Figure 4 A schematic diagram of the structure of a computer medium is shown. Detailed Implementation

[0027] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, they are provided so that this application will be thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted.

[0028] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this application.

[0029] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0030] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0031] It should be understood that although the terms first, second, third, etc., may be used herein to describe various components, these components should not be limited by these terms. These terms are used to distinguish one component from another. Therefore, the first component discussed below may be referred to as the second component without departing from the teachings of this application. As used herein, the term "and / or" includes all combinations of any one and more of the associated listed items.

[0032] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of exemplary embodiments, and the modules or processes in the drawings are not necessarily essential for implementing this application, and therefore cannot be used to limit the scope of protection of this application.

[0033] According to a first specific embodiment of the present invention, the present invention provides a simulation construction system for giant constellations, such as... Figure 1 As shown, it includes: a data acquisition module, a track element generation module, a TLE data generation module, and a track extrapolation module.

[0034] The data acquisition module is used to acquire the input parameters of the satellite constellation.

[0035] The orbital element generation module is used to generate the Kepler orbit six elements for each satellite based on the input parameters.

[0036] The TLE data generation module is used to convert the Kepler orbital six-root number into TLE format.

[0037] The track extrapolation module is used for track extrapolation based on the TLE format.

[0038] According to a second embodiment of the present invention, the present invention provides a method for simulating and constructing a giant constellation, employing the giant constellation simulation and construction system of the first embodiment, such as... Figure 2 As shown, it includes the following steps: S1: Obtain the input parameters for the satellite constellation.

[0039] The input parameters for a satellite constellation include: Phase Factor: Used to control the phase difference between satellites in the same orbital plane, with a value ranging from 0 to the number of orbital planes - 1; Number of Planes: The number of orbital planes in a constellation, denoted as N_p; Number of Satellites per Plane: The number of satellites in each orbital plane, denoted as N_s; Semi-major axis: The semi-major axis of the orbit, denoted as a; Inclination: The inclination angle of the track, denoted as i, for example, i = 53°.

[0040] S2: Generate the Kepler orbit six-root number for each satellite based on the input parameters.

[0041] S21: Calculate the track surface parameters.

[0042] For the Walker constellation configuration, calculate the right ascension of the ascending nodes of each orbital plane: Difference in right ascension of ascending nodes between adjacent orbital planes: ΔΩ = 360° / N_p; Right ascension of the ascending node of the j-th orbital plane: Ω_j=Ω0+j*ΔΩ, j = 0, 1, 2, ..., N_p - 1.

[0043] The Walker constellation is a satellite constellation configuration using circular orbits with evenly distributed orbital planes. Its configuration code uses N, P, and F to represent the total number of satellites, the number of orbital planes, and the phase factor, respectively. This constellation includes five basic parameters (N, P, F, altitude, and inclination), with the right ascension of the satellite's ascending node and phase difference evenly distributed according to formulas. A typical example is the 24 / 3 / 1 configuration used by the Russian GLONASS, while GPS actually uses a customized Walker-δ configuration with 18 satellites distributed across 6 orbital planes.

[0044] The BeiDou system uses the Walker 24 / 3 / 1 constellation phase, the Galileo navigation system uses a 27 / 3 / 1 configuration, and OneWeb and some low-Earth orbit communication constellations (such as Starlink) also use this architecture. When a satellite malfunctions, energy consumption can be reduced through phase adjustment and elastic mechanical reconfiguration methods; for example, the total velocity increment is reduced by 44% in the 18 / 3 / 2 configuration reconfiguration. The Walker constellation's autonomous orbit determination technology achieves network-wide positioning through an inter-satellite ranging network, and error analysis involves the calculation of relative motion partial derivatives and constraint adjustment.

[0045] The core method for calculating the orbital plane parameters of the polar constellation configuration is the same as that for calculating the orbital plane parameters of the Walker constellation configuration.

[0046] S22: Calculate the distribution of the mean anomaly angles of satellites in each orbital plane.

[0047] Difference in mean anomaly between adjacent satellites: ΔM = 360° / N_s; The initial mean anomaly angle of the kth satellite: M_k=k*ΔM+ Phase_Factor *ΔM, k = 0, 1, 2, ..., N_s - 1.

[0048] S23: Generate the Kepler orbital six-root number for each satellite.

[0049] Satellite number: (j, k), where j is the orbital plane number and k is the satellite number within the orbital plane.

[0050] 1. Semi-major axis: a = a_input (e.g., 550km); 2. Eccentricity: e = e_input (e.g., 0.0); 3. Inclination angle: i = i_input (e.g., 53°); 4. Right ascension of the ascending node: Ω = Ω_j = Ω0 + j*(360° / N_p); 5. Perigee angle: ω = 0° (for near-circular orbits); 6. Plane anterior angle: M = M_k = k*(360° / N_s) + Phase_Factor*(360° / N_s); The total number of satellites is: N_total = N_p × N_s = 66 × 22 = 1452 satellites.

[0051] The mega-constellations described in this plan consist of at least 100 stars. There are no restrictions on the number of stars in the orbital plane or the number of planes. These are all parameters that can be entered on the page. Currently, our scenarios are mostly in the hundreds to thousands of stars.

[0052] S3: Convert to TLE format based on the six roots of the Kepler orbital.

[0053] S31: Convert the six roots of the Kepler orbit into position and velocity vectors.

[0054] S311: Calculate orbital parameters.

[0055] μ=GM = 3.986004418×10 14 m³ / s²; ; p = a*(1- e²); μ = GM, representing the Earth's gravitational constant, which indicates the strength of the Earth's gravitational pull on a satellite. It is a fundamental parameter of Kepler's Third Law and is used to calculate orbital period and average angular velocity.

[0056] This represents the average angular velocity (average motion), which is the average angular velocity of a satellite moving in its orbit, measured in radians per second (rad / s). The formula is derived from Kepler's third law and reflects the relationship between the semi-major axis of the orbit and the orbital period.

[0057] p = a*(1 - e²) represents the semi-major diameter (semi-focal sine), which is the geometric parameter of the orbit between the perigee and apogee, in meters, and is used to calculate the position of any point on the orbit. Here, a is the semi-major axis and e is the eccentricity.

[0058] S312: Calculate the near-point angle.

[0059] The Kepler equation can be solved using an iterative method: M = Ee*sin(E); Iteration formula: E_{n+1}=E_n+(M-E_n+e*sin(E_n)) / (1-e*cos(E_n)); M = Ee*sin(E) represents the Kepler equation, establishing the relationship between the mean anomaly M and the partial anomaly E. The mean anomaly M is a linear function of time t, while the partial anomaly E is an intermediate variable in calculating the true anomaly ν. ​​This equation is a transcendental equation and cannot be solved directly; an iterative method is required.

[0060] E_{n+1}=E_n+(M-E_n+e*sin(E_n)) / (1-e*cos(E_n)) represents the Newton-Raphson iterative formula used to solve Kepler's equations. This formula iteratively approximates the precise value of the anomalous angle E, with fast convergence speed; typically, 3-5 iterations are sufficient to achieve the required accuracy. The initial value can be E=M.

[0061] S313: Calculate the true anterior angle based on the deviated anterior angle.

[0062] ; Where ν represents the true anterior angle, E represents the off-anterior angle, and e represents the eccentricity.

[0063] S314: Calculate the position and velocity vectors in the orbital plane coordinate system based on the orbital parameters and the true anomaly angle.

[0064] r = p / (1+e*cos(ν)); r_orbital=[r*cos(ν), r*sin(ν), 0]ᵀ; v_orbital= *[-sin(ν), e + cos(ν), 0]ᵀ; Where r = p / (1 + e * cos(ν)) is the formula for orbital radius, and r represents the distance from the satellite to the Earth's center.

[0065] r_orbital is the representation of the position vector in the orbital plane coordinate system.

[0066] v_orbital is the representation of the velocity vector in the orbital plane coordinate system.

[0067] ν represents the true anomaly angle, p represents the semi-major diameter, μ represents the Earth's gravitational constant, and e represents the eccentricity.

[0068] S315: Transform the orbital plane coordinate system into the geocentric inertial coordinate system.

[0069] Rotation matrix: R = R_z(Ω) * R_x(i) * R_z(ω); r_ECI=R*r_orbital; v_ECI=R*v_orbital; R is the coordinate rotation matrix that transforms vectors in the orbital plane coordinate system to the geocentric inertial frame; R_z(ω) is the perigee argument ω of the rotation about the z-axis, which rotates the x-axis from the ascending node direction to the perigee direction; R_x(i) is the orbital tilt angle i around the x-axis, so that the orbital plane is tilted to the specified tilt angle; R_z(Ω) is the right ascension Ω of the ascending node rotated about the z-axis to the specified position; r_ECI is used to transform the position vector from the orbital plane coordinate system to the geocentric inertial frame, obtaining the satellite's position coordinates in the geocentric inertial frame; v_ECI is used to transform the velocity vector from the orbital plane coordinate system to the geocentric inertial frame, obtaining the velocity components of the satellite in the geocentric inertial frame.

[0070] S32: Set integration conditions.

[0071] S321: Set integrator parameters: Integrator type: RK78; RK78 is a high-order embedded numerical integration method; Integration step size: Δt = 60 seconds; Integration time range: [t0, t_end], for example [t0, t0+7 ​​days].

[0072] S322: Define the perturbation model: Total perturbation force = Earth's non-spherical gravity + atmospheric drag + solar radiation pressure + third body gravity; Earth's non-spherical gravity: using the J2-J70 spherical harmonic function model; Atmospheric drag: F_drag=-0.5*ρ*cd*sd*v_rel²*(v_rel / |v_rel|); Solar radiation pressure: F_srp=-P_sun*cr*sr*(r_sun / |r_sun|); Third-body gravity: the point mass gravity of the Sun and the Moon; Among them, the atmospheric model parameters are: cr represents the radiation pressure coefficient, for example, 1.2; cd represents the atmospheric drag coefficient, for example, 2.2; sr represents the radiation pressure area, in square meters, for example, 10 m²; sd represents the atmospheric drag area, in square meters, for example, 10 m²; ρ represents the atmospheric mass density at the satellite's location; v_rel represents the satellite's velocity vector relative to the local atmosphere; P_sun represents the equivalent radiation pressure scalar in the solar radiation pressure model; and r_sun represents the position vector from the satellite to the sun.

[0073] S33: Perform numerical integration.

[0074] Initial state: X0 = [r_ECI, v_ECI]ᵀ; For t equal to t0 to t equal to t_end, the formula X(t+Δt)=integrate(X(t), F_total, Δt) is satisfied; X0 = [r_ECI, v_ECI]ᵀ is the initial state vector, which contains the satellite's initial position vector r_ECI and initial velocity vector v_ECI.

[0075] X(t+Δt)=integrate(X(t), F_total, Δt) is a numerical integration formula, which means that the state X(t+Δt) at the next time t+Δt is calculated by integrating the state X(t) at the current time t.

[0076] X(t) represents the orbital state vector (position and velocity) at the current moment.

[0077] F_total represents the total perturbation force at the current moment, including the Earth's non-spherical gravity, atmospheric drag, solar radiation pressure, and third-body gravity. Δt represents the integration step size, which is usually 60 seconds but can be adjusted according to accuracy requirements; integrate() is a numerical integration function.

[0078] S34: Parameters required to fit the TLE format based on the results of numerical integration.

[0079] S341: Calculate the average motion.

[0080] ; n0_rev_per_day = n0*86400 / (2π); Where n0 represents the average angular velocity calculated by approximating the instantaneous semi-major axis using a two-body Keplerian circle / ellipse, also known as average motion; n0_rev_per_day represents the number of revolutions per day around the Earth, in revolutions per day; a represents the semi-major axis of the orbit; and μ represents the Earth's gravitational constant.

[0081] S342: Calculate the first derivative of the average motion.

[0082] A numerical propagator is used to propagate between time t0 and t0+Δt; Calculate the rate of change of the average motion: =(n1- n0) / Δt; in, denoted by n, n1 represents the average motion with respect to time, reflecting how quickly the orbital angular velocity changes with time; n1 represents the average motion calculated from the state obtained by numerical propagation at time (t0+Δt); n0 represents the average motion calculated from the state obtained by numerical propagation at time t0; and Δt represents the time interval between two calculations of the average motion, i.e., the time difference between t0+Δt and t0.

[0083] A numerical propagator is a computational unit that calculates the orbital state at any given time from the initial orbital state using a numerical integration method based on a selected perturbation model. It is also known as high-precision dynamic numerical integration propagation. When using a numerical propagator, the mass of the satellite, expressed in kilograms (e.g., 260 kg), needs to be considered. Satellite parameter data must be taken into account when fitting the Time-Likelihood Exceeding (TLE) to the input parameters.

[0084] S343: Calculate the second derivative of the average motion.

[0085] Using propagation data over a longer time span, i.e., obtaining orbital / average motion samples over a longer time span using numerical propagation, and then estimating based on this. The values ​​at two sufficiently distant moments are used to stably calculate the values. ; Calculate the second derivative of the average motion: =( 1- 0) / Δt; in, It represents the second derivative of the average motion with respect to time, and in physics it is often used to characterize whether the change in average motion caused by factors such as orbital decay is accelerating or decelerating; 1 represents the first derivative of the mean motion estimated at the later time (t0+Δt). 0 represents the first derivative of the average motion estimated at the previous time (t0); Δt: the time interval between the two calculations of the average motion, i.e., the time difference between t0 + Δt and t0, used to... 1 and The time interval (the difference between two moments) associated with 0 is the difference in the epochs they correspond to.

[0086] The second derivative of the mean motion represents the acceleration of the rate of change of the mean motion, measured in revolutions per day (r / d³). This parameter reflects the acceleration of orbital decay, i.e., whether the decay rate is increasing or decreasing.

[0087] in 0 and 1 represents the average first-order motion derivative at different times (referring to two (or two groups of) clearly distinguishable epochs on the same numerical propagation time axis).

[0088] This parameter (the second derivative of the mean motion) is an important field in the first row of the TLE format and is used to more accurately predict long-term orbital evolution.

[0089] S344: Calculate the rate of change of the number of orbital elements.

[0090] di / dt = (i1- i0) / Δt; dΩ / dt = (Ω1-Ω0) / Δt; di / dt = (i1-i0) / Δt represents the rate of change of the orbital inclination, which is the speed at which the orbital inclination changes with time, and is expressed in degrees / day or radians / day.

[0091] i0 represents the orbital inclination at epoch t0; i1 represents the orbital inclination at time t0+Δt, which is calculated using a numerical propagator; Due to the influence of Earth's non-spherical gravity and the gravity of a third body, the orbital inclination changes slowly. For near-Earth orbits, the inclination change is usually small, but it cannot be ignored in long-term evolution.

[0092] dΩ / dt = (Ω1-Ω0) / Δt represents the rate of change of the right ascension of the ascending node, which is the speed at which the right ascension of the ascending node changes with time, and is expressed in degrees / day or radians / day.

[0093] Ω0 represents the right ascension of the ascending node at epoch t0; Ω1 represents the right ascension of the ascending node at time t0+Δt, which is calculated using a numerical propagator; Physical significance: The change in right ascension of the ascending node is mainly caused by the Earth's non-spherical gravitational pull. This rate of change is a key parameter in the long-term evolution of the orbit.

[0094] S35: Generate two rows of data in TLE format based on the fitted parameters.

[0095] Based on the fitted parameters, generate two rows of data in standard TLE format: TLE example: 1 12345U 24001A 24001.00000000 .00001234 00000-0 12345-4 0 9999 1 is the line number.

[0096] 12345U: Satellite International Designer (NORAD Catalog Number), which includes the last two digits (24) of the launch year and a letter (U) to identify the satellite.

[0097] 12345 is the satellite's serial number.

[0098] U is a type identifier; for example, U represents Unclassified.

[0099] 24001A - The launch number of this satellite, usually consisting of the launch year (24), launch serial number (001), and a letter (A), indicating a specific satellite in the launch mission.

[0100] 24001.00000000 represents the metadata time (Epoch), expressed in years and decimals within the year, indicating the specific time of the orbital parameters. Here, 24001.00000000 represents the first day of the year 2400 (i.e., January 1, 2400).

[0101] .00001234 represents the average rate of change of the satellite's orbit over the past (first derivative), in radians per day, indicating minute changes in the satellite's orbit.

[0102] 00000-0 represents the second derivative, indicating the change in orbital acceleration. It is usually a number less than 1 and expressed in scientific notation.

[0103] 12345-4 represents the orbital disturbance number (B*), which is also a decimal number, representing the non-gravitational disturbances affecting the satellite.

[0104] 0 indicates the orbit specification (the number of complete orbital revolutions), which is usually 0.

[0105] 9999 is a check bit, which is usually used to verify the integrity of TLE. 2 12345 53.0000 0.0000 0001234 0.0000 8.1818 15.12345678901234 2 represents the row number (the sequence number of the row), which is usually "2".

[0107] 12345 represents the satellite's international designator (NORAD Catalog Number), which is the same as the first line, indicating the satellite's serial number.

[0108] 53.0000 represents the orbital inclination, in degrees, which is the angle between the satellite's orbital plane and the equatorial plane.

[0109] 0.0000 represents the Right Ascension of Ascending Node (RAAN) longitude of the satellite, in degrees, indicating the location of the satellite's orbital intersection point on the equator.

[0110] 0001234 represents the orbital eccentricity, which indicates the degree of orbital eccentricity. The number is represented by removing the leading "0."

[0111] 0.0000 represents the Argument of Perigee, in degrees, which is the angle at the point in the satellite's orbit closest to Earth.

[0112] 8.1818 represents mean motion, measured in revolutions per day, indicating the number of times a satellite orbits the Earth each day.

[0113] 15.12345678901234 represents the revolution period, measured in minutes, which is the time required for a satellite to complete one orbit. It is usually rounded to 14 decimal places.

[0114] S4: Track extrapolation based on TLE format.

[0115] S41: Resolution of TLE.

[0116] Parse TLE format data and extract orbital parameters: Parsing the first line of TLE: Satellite ID: NORAD_ID=12345; Epoch time: t_epoch=2024-01-01 00:00:00 UTC; The second derivative of the mean motion: n̈ = 0.12345 × 10 -4 Turns / day³; B* parameter: B_star = 0.12345 × 10 -4 ; Parsing the second line of TLE: Right ascension of the ascending node: Ω = 0.0000°; Eccentricity: e = 0.0001234; Argument of perigee: ω = 0.0000°; The angle of approach to the point of view: M = 8.1818°; Average motion: n = 15.12345678901234 revolutions / day.

[0117] S42: Orbit propagation based on TLE.

[0118] S421: Selection propagation model.

[0119] Orbital period: T = 86400 / n (seconds).

[0120] If T < 225 minutes, use the SGP4 model (low Earth orbit); if T ≥ 225 minutes, use the SDP4 model (deep space orbit).

[0121] S422: Calculate the average motion at the current time.

[0122] Time difference: Δt_epoch = t - t_epoch; Corrected mean motion: n(t) = n0 + *Δt_epoch+0.5* *Δt_epoch²; Where Δt_epoch represents the time difference in days, t represents the target time (i.e., the time at which orbit propagation, state calculation, or average motion correction is performed), t_epoch represents the epoch, n(t) represents the average motion used at the target time t, reflecting the evolution of the average motion from the epoch to t, and n0 represents the average motion corresponding to the epoch t_epoch. dn / dt represents the first derivative of the average motion with respect to time, and the coefficients used around the epoch; The second derivative of the average motion with respect to time, d 2 n / dt 2 Used to depict the changes in ṅ.

[0123] The correction is to reflect the evolution of n over time; the formula is based on using n0 at the epoch. , Achieving a second-order local approximation of n(t) is a classic approach with low computational cost.

[0124] S423: Output position and velocity vectors based on the selected propagation model and average motion.

[0125] If using the SGP4 model for propagation: Input: TLE parameters, target time t; Output: Position vector r_ECI, velocity vector v_ECI; If using the SDP4 model for propagation: Input: TLE parameters, target time t (same as SGP4, using the TLE orbital parameters obtained from step S41). In the case of deep space orbits with orbital periods of T≥225 minutes, the SDP4 transducer is used for extrapolation based on TLE. Based on the effects of Earth's central gravity and non-spherical gravity, SDP4 introduces perturbations from third bodies such as the Sun and Moon, as well as long-term and periodic terms applicable to deep space / high-eccentricity orbits, to compensate for error sources that SGP4 is not applicable under the near-Earth assumption. In the case of deep space orbits with orbital periods of T≥225 minutes, the SDP4 transducer is used for extrapolation based on TLE. Based on the effects of Earth's central gravity and non-spherical gravity, SDP4 introduces perturbations from third bodies such as the Sun and Moon, as well as long-term and periodic terms applicable to deep space or large eccentricity orbits, to compensate for error sources that SGP4 is not applicable under the near-Earth assumption. Output: Position vector r_ECI, velocity vector v_ECI.

[0126] S43: Generate sequence data according to the predetermined time step.

[0127] When constructing a constellation, extrapolation is performed on each satellite after the Time Limit Exceeded (TLE) of the first satellite.

[0128] Generate time series data according to the set time step: Input parameters: Start time: t_start = 2024-01-01 00:00:00 UTC; End time: t_end = 2024-01-02 00:00:00 UTC; Time step: Δt = 60 seconds; Output: Orbit extrapolation data, output content for example: [ { "epoch": "2025-12-02T11:56:00.000", "lon": 137.3263312524001, "lat": -48.83602203382523, "alt": 652233.6630136387 }, { "epoch": "2025-12-02T11:56:10.000", "lon": 137.37432381802526, "lat": -49.44740182865722, "alt": 652386.1027287045 }, { "epoch": "2025-12-02T11:56:20.000", "lon": 137.42457361664336, "lat": -50.05863597665385, "alt": 652537.2203180948 }, { "epoch": "2025-12-02T11:56:30.000", "lon": 137.4771883610124, "lat": -50.669721513449765, "alt": 652686.9322901644 }, { "epoch": "2025-12-02T11:56:40.000", "lon": 137.53228243669724, "lat": -51.28065529981017, "alt": 652835.1555982515 }, { "epoch": "2025-12-02T11:56:50.000", "lon": 137.58997743218006, "lat": -51.89143400463173, "alt": 652981.8076800893 },].

[0129] In summary, this scheme can efficiently construct large-scale satellite constellations and achieve high-precision conversion of orbital elements to TLE (this scheme uses a numerical propagator when extrapolating based on input parameters, and then performs TLE fitting, and fully considers the conversion between flat roots and instantaneous roots during fitting, that is, when converting from Kepler six-roots to TLE, the Kepler six-roots extrapolate to obtain the instantaneous orbit state; it is then fitted to flat roots and encoded as TLE; when used, it extrapolates from the TLE flat roots and then back-calculates to instantaneous roots to calculate the instantaneous orbit), supports multiple orbit extrapolation methods (supports extrapolation using TLE and six-roots methods, but extrapolation of six-roots to multiple satellites will be slower), and meets the design, analysis, and simulation needs of mega-constellations.

[0130] According to a third specific embodiment of the present invention, the present invention provides an electronic device, such as... Figure 3 As shown, Figure 3 This is a block diagram illustrating an electronic device according to an exemplary embodiment.

[0131] The following reference Figure 3 To describe an electronic device 300 according to this embodiment of the present application. Figure 3 The electronic device 300 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0132] like Figure 3 As shown, the electronic device 300 is presented in the form of a general-purpose computing device. The components of the electronic device 300 may include, but are not limited to: at least one processing unit 310, at least one storage unit 320, a bus 330 connecting different system components (including storage unit 320 and processing unit 310), a display unit 340, etc.

[0133] The storage unit stores program code that can be executed by the processing unit 310, causing the processing unit 310 to perform the steps described in this specification according to various exemplary embodiments of this application. For example, the processing unit 310 can perform the steps shown in the second specific embodiment.

[0134] The storage unit 320 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 3201 and / or a cache storage unit 3202, and may further include a read-only memory unit (ROM) 3203.

[0135] The storage unit 320 may also include a program / utility 3204 having a set (at least one) program module 3205, such program module 3205 including but not limited to: an operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0136] Bus 330 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0137] Electronic device 300 can also communicate with one or more external devices 300' (e.g., keyboard, pointing device, Bluetooth device, etc.), enabling users to communicate with devices that interact with electronic device 300, and / or any device (e.g., router, modem, etc.) that allows electronic device 300 to communicate with one or more other computing devices. This communication can be performed via input / output (I / O) interface 350. Furthermore, electronic device 300 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 360. Network adapter 360 can communicate with other modules of electronic device 300 via bus 330. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 300, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0138] Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware.

[0139] Therefore, according to a fourth specific embodiment of the present invention, the present invention provides a computer-readable medium. For example... Figure 4 As shown, the technical solution according to the embodiments of the present invention can be embodied in the form of a software product. The software product can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, mobile hard drive, etc.) or on a network, and includes several instructions to cause a computing device (such as a personal computer, server, or network device, etc.) to execute the above-described method according to the embodiments of the present invention.

[0140] The software product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0141] The computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0142] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0143] The aforementioned computer-readable medium carries one or more programs, which, when executed by a device, cause the computer-readable medium to perform the functions of the second specific embodiment.

[0144] Those skilled in the art will understand that the above modules can be distributed in the device as described in the embodiments, or they can be modified to be uniquely different from one or more devices in this embodiment. The modules in the above embodiments can be combined into one module, or they can be further divided into multiple sub-modules.

[0145] Through the description of the above embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions of the embodiments of the present invention can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, portable hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of the present invention.

[0146] Exemplary embodiments of the present invention have been specifically shown and described above. It should be understood that the present invention is not limited to the detailed structures, arrangements, or implementations described herein; rather, the present invention is intended to cover various modifications and equivalent arrangements contained within the spirit and scope of the appended claims.

Claims

1. A method for simulating and constructing a giant constellation, characterized in that, Includes the following steps: S1: Obtain the input parameters for the satellite constellation; S2: Generate the Kepler orbit six-root number for each satellite based on the input parameters; S3: Convert to TLE format based on the six Kepler orbital roots; S4: Track extrapolation based on TLE format.

2. The method for simulating and constructing giant constellations according to claim 1, characterized in that, In step S2, generating the Kepler orbit six-root numbers for each satellite based on the input parameters includes: S21: Calculate the track surface parameters; S22: Calculate the distribution of the mean anomaly angles of the satellites in each orbital plane; S23: Generate the Kepler orbital six-root number for each satellite.

3. The method for simulating and constructing giant constellations according to claim 1, characterized in that, In step S3, the conversion from the six Kepler orbital roots to TLE format includes: S31: Convert the six roots of the Kepler orbit into position and velocity vectors; S32: Set integration conditions; S33: Perform numerical integration; S34: Parameters required for fitting the TLE format based on the results of numerical integration; S35: Generate two rows of data in TLE format based on the fitted parameters.

4. The method for simulating and constructing giant constellations according to claim 3, characterized in that, In step S31, converting the six roots of the Kepler orbit into position and velocity vectors includes: Calculate orbital parameters; Calculate the angle of near point; Calculate the true anterior angle based on the deviated anterior angle; Calculate the position and velocity vectors in the orbital plane coordinate system based on the orbital parameters and the true anomaly angle; Transform the orbital plane coordinate system into a geocentric inertial coordinate system.

5. The method for simulating and constructing a giant constellation according to claim 3, characterized in that, In step S34, the parameters required for fitting the TLE format based on the numerical integration result include: Calculate the average motion; Calculate the first derivative of the average motion; Calculate the second derivative of the average motion; Calculate the rate of change of the orbital elements.

6. The method for simulating and constructing a giant constellation according to claim 1, characterized in that, In step S4, the orbit extrapolation based on the TLE format includes: S41: Resolve TLE; S42: Orbit propagation based on TLE; S43: Generate time series data according to the predetermined time step.

7. The method for simulating and constructing giant constellations according to claim 6, characterized in that, In step S42, the orbit propagation based on TLE includes: Choose a propagation model; Calculate the average motion at the current time; Based on the selected propagation model and average motion, the output position vector and velocity vector are determined.

8. A simulation construction system for giant constellations, characterized in that, include: Data acquisition module, track element generation module, TLE data generation module, and track extrapolation module; The data acquisition module is used to acquire the input parameters of the satellite constellation; The orbital element generation module is used to generate the Kepler orbit six elements for each satellite based on the input parameters; The TLE data generation module is used to convert the six Kepler orbital roots into TLE format. The orbit extrapolation module is used to perform orbit extrapolation based on the TLE format.

9. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the simulation construction method of the mega-constellation as described in any one of claims 1-7.

10. A computer-readable medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the simulation construction method for giant constellations as described in any one of claims 1-7.

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