A collision risk satellite combination processing sequencing optimization method

Abstract

The application provides a collision risk satellite combination processing sequencing optimization method, steps are as follows: according to TLE orbit root number data, orbit pre-division is carried out, satellites located on the same orbit plane are divided together; a perigee-apogee pre-screening method is used to carry out pre-screening of satellite collision combination, and satellite and debris combinations generating collision risks are obtained; TLE orbit root number data is combined with an orbit prediction model and a fast screening trajectory space intersection algorithm to determine the position of trajectory intersection and overlap in space; high collision risk satellite combinations and high collision risk regions are determined; a collision combination priority processing sequencing model is constructed in combination with satellite states and satellite characteristics; and a gradient descent method is used to optimize parameters of the multi-factor collision combination priority processing sequencing model. The application improves the screening speed of high collision risk combinations and improves the overall safety of a satellite constellation by using the geometric screening method of the intersection angle between two orbits and the gradient descent method to optimize multi-factor parameters.

Description

Technical Field

[0001] This invention relates to the technical field of satellite communication reliability, and in particular to a collision risk satellite combination processing ranking optimization method. Based on satellites in an integrated space-ground network, when it is necessary to predict the probability of collision risk of on-orbit satellites, the method uses satellite orbital parameters to determine high-risk space regions and satellite combinations, and uses gradient descent to perform multi-factor, self-feedback, and self-adjusting ranking of high collision risk satellite combinations to achieve long-term optimal results and lay a good foundation for satellite collision avoidance. Background Technology

[0002] With the rapid development of space programs worldwide, the number of spacecraft launches globally has been increasing year by year. More than 30 countries and regions have carried out launch missions, sending over 10,000 spacecraft into space. Entering the 21st century, driven by national security strategic needs, the task of deploying a comprehensive strategic layout for outer space has become increasingly urgent for countries worldwide, leading to a further increase in launches. The increasing amount of near-Earth space debris and the deteriorating operating environment for near-Earth satellites pose a growing threat to their successful launches and safe, stable operation.

[0003] With the rapid development of low-Earth orbit (LEO) satellite manufacturing and launch technologies, the launch cost of LEO satellites has been decreasing, and they also have advantages such as low orbital altitude, short transmission latency, and low path loss. Therefore, mega-constellations of LEO satellites are in a phase of rapid development. International companies such as SpaceX, Boeing, OneWeb, Kepler Communications, Samsung, and Amazon have all proposed LEO constellation plans, with Starlink, Telesat, and OneWeb being the most representative. Domestically, China's satellite internet plan has been included in the "New Infrastructure" initiative, signifying that the project has risen to the level of a national strategic project.

[0004] Space debris poses a significant threat to the safe operation of satellites. In low Earth orbit, there are approximately 750,000 pieces of debris between 1 and 10 centimeters in size, about 30,000 pieces larger than 10 centimeters, and over 100 million pieces smaller than 1 centimeter. Furthermore, this debris lacks maneuverability and cannot autonomously avoid collisions.

[0005] To ensure the safe and normal operation of the satellite, the following issues still need to be addressed:

[0006] (1) During the operation of a satellite in orbit, it is necessary to quickly, efficiently and accurately locate and screen high-collision-risk areas in the satellite's orbit to reduce the spatial range of predicted collisions.

[0007] (2) For high-collision-risk combinations of satellites located in high-risk space regions of satellite orbits, sort them in order of calculation to minimize the overall risk of collision.

[0008] In summary, in order to ensure the safe and stable operation of large constellations of low-Earth orbit satellites, improve the collision calculation speed of multiple satellites, and allow sufficient collision avoidance time for satellites that generate collision warnings, it is necessary to provide a method that can optimize the processing and sequencing of high-collision-risk satellite combinations. Summary of the Invention

[0009] To address the technical problems of slow screening of high-collision-risk combinations in giant low-Earth orbit constellations, insufficient consideration of factors in the sorting process, and inability to meet practical needs, this invention proposes an optimization method for sorting and processing high-risk satellite combinations. It employs a high-risk region calculation algorithm based on orbital parameters to determine the location of high-risk regions, and uses gradient descent to select the optimal sorting strategy under multiple factors. Finally, it selects the sorting scheme with the lowest overall collision risk, reducing computational load and improving the speed of constellation collision risk assessment.

[0010] To achieve the above objectives, the technical solution of the present invention is as follows: a collision risk satellite combination processing and sorting optimization method, the steps of which are as follows:

[0011] Step 1: Perform orbit pre-division based on TLE orbital element data, grouping satellites located in the same orbital plane together;

[0012] Step 2: Based on the satellite orbital plane data, a perigee-apogee pre-screening method is used to pre-screen satellite collision combinations to obtain combinations of satellites and debris that may pose a collision risk;

[0013] Step 3: Based on the obtained satellite and debris combination, use TLE orbital element data combined with orbital prediction model and fast trajectory spatial intersection point screening algorithm to determine the position of trajectory intersection and overlap in space; calculate the spatial distance between multiple satellites in the same orbit, and when the spatial distance is less than the safe distance, mark the satellite and debris as a high collision risk satellite combination, and the spatial area corresponding to the debris coordinates is the high collision risk area.

[0014] Step 4: Based on the high-collision-risk areas and high-collision-risk satellite combinations generated in Step 3, and combining the satellite status and satellite characteristics, construct a priority processing ranking model for collision combinations.

[0015] Step 5: Use the gradient descent method to optimize the parameters of the multi-factor collision combination priority processing ranking model, and obtain the optimization results with the longest total satellite collision avoidance time, priority processing of high-level satellites, and the highest overall security of the satellite constellation.

[0016] Preferably, each TLE orbital element data consists of three lines of data, including the six orbital parameters of Kepler's laws: orbital inclination i, orbital semi-major axis a, orbital eccentricity e, right ascension of the ascending node Ω, perihelion depression angle α, and level anterior angle β;

[0017] The method for pre-dividing orbits based on the orbital parameters contained in the TLE orbital elements data is as follows: An array is created based on the orbital inclination i, right ascension Ω of the ascending node, orbital eccentricity e, and the number of orbits around the Earth per day for each satellite or debris. Following the order in which the array is read, satellites with orbital inclination differences less than 0.1, ascending node right ascension differences less than 0.1, and equal orbital eccentricities with period differences less than 0.0001 are classified into the same orbital plane.

[0018] Preferably, the perigee-apogee pre-screening method involves comparing data from the satellite orbital plane pairwise, and identifying satellites and debris whose perigee and apogee conditions are met. At that time, collisions may occur between the corresponding satellite orbital planes. These collisions are stored to prepare data for the next step of fine screening. The perigee of the satellite orbit is Perigee1 and the apogee is Apogee1. The perigee of the debris orbit is Perigee2 and the apogee is Apogee2.

[0019] Preferably, the orbit prediction model is the SGP4 space orbit prediction model. The TLE orbital elements data are substituted into the SGP4 space orbit prediction model. The polar coordinates at a specified time are obtained according to physical principles, and then converted to the geocentric coordinate system. Finally, the position vector and velocity vector of the satellite at the specified time can be obtained.

[0020] The implementation method of the fast trajectory spatial intersection point screening algorithm is as follows: Using TLE orbital element data, the right ascension Ω of the ascending node and the orbital inclination i of each of the two satellite orbital planes are obtained. Two important angles are calculated through the spatial geometric relationship of the orbital planes, and these two important angles are used for high collision risk discrimination and screening. The two important angles are the angles formed by the line connecting the intersection point and the geocenter, and the line connecting the intersection point's perpendicular projection onto the equatorial plane and the geocenter. The degree measure is used to filter possible intersection points on the satellite orbit; the degree measure of the angle ω formed by the line connecting the vertical projection point of the intersection point on the equatorial plane and the Earth's center with the x-axis of the J2000 geocentric coordinate system is used to determine the "true intersection point".

[0021] Preferably, the method for determining the positions where the trajectories intersect and overlap in space in step two is as follows:

[0022] Substitute the TLE orbital element data into the SGP4 space orbit prediction model, set the time period to one cycle, set the time interval to 1 minute, and output the list of satellite position coordinates for the next cycle in the J2000 coordinate system.

[0023] Quadrant determination: Determine the quadrant of the spatial intersection point based on the included angle ω: If 0° < ω < 90°, the spatial intersection point is located in the first or fifth quadrant, 0 < x and 0 < y; if 90° < ω < 180°, the spatial intersection point is located in the second or sixth quadrant, 0 > x and 0 < y; if 180° < ω < 270°, the spatial intersection point is located in the third or seventh quadrant, 0 > x and 0 > y; if 270° < ω < 360°, the spatial intersection point is located in the fourth or eighth quadrant, 0 < x and 0 > y.

[0024] When the x and y coordinates of the corresponding quadrant are satisfied, the included angle The values ​​are compared, the time interval is adjusted to 1 second, and a search is performed to find those that meet the criteria. The established coordinate values ​​represent the corresponding positions of the spatial intersection points on the satellite trajectory; where x1, y1, and z1 are the satellite's position coordinates in the J2000 coordinate system.

[0025] Find Formula The position of the established coordinate values ​​is the corresponding position of the spatial intersection point on the debris trajectory; where x2, y2, and z2 are the position coordinate values ​​of the debris in the J2000 coordinate system.

[0026] Preferably, the time and position of the SGP4 space orbit prediction model are in one-to-one correspondence, and the motion of both the satellite and the debris is periodic. The time to reach the intersection point plus the time of one period can be used to obtain the time to pass through this intersection point again.

[0027] Based on the time when each debris reaches the intersection of its trajectory, the spatial distance between multiple satellites in the same orbit is calculated periodically:

[0028]

[0029] Where, x sat y sat z sat Here are the coordinates of the satellite in the J2000 coordinate system, x deb y deb z deb d represents the coordinates of the debris in the J2000 coordinate system, where d is the distance between the satellite and the debris.

[0030] When the spatial distance between a satellite and debris is less than a safe distance, the satellite and debris are marked as a high-collision-risk combination. The spatial region corresponding to the debris's coordinates is then designated as a high-collision-risk region, and time t is marked as the time t when the satellite and debris are closest. c The spatial distance d is the closest distance between the satellite and the debris. c .

[0031] Preferably, the calculation method for the two important angles is as follows: when the right ascensions Ω of the ascending nodes of the two orbital planes differ by 180° and the orbital inclinations i are complementary, without considering the direction of the satellite's trajectory, and only considering the spatial position of the satellite's trajectory, it is simplified to the same case, that is, when Ω > 180°, Ω′ = Ω - 180°, i′ = 180° - i; where Ω is the right ascension of the ascending node before simplification, Ω′ is the right ascension of the ascending node after simplification; i is the orbital inclination before simplification, and i′ is the orbital inclination after simplification.

[0032] Let Ω1 be the ascending node with the smaller right ascension value in the satellite and debris trajectories, and i1 be its corresponding orbital inclination value. Let Ω2 be the ascending node with the larger right ascension value, and i2 be its corresponding orbital inclination value. We get Ω1 < Ω2 < 180°. Considering the range of orbital inclination values ​​i1 and i2, we can simplify the 16 relative position cases into 4:

[0033]

[0034] Where i1 and i2 are the orbital inclinations of the satellite and debris, respectively;

[0035] When i2 < 90° or i1 < 90° and i2 > 90°, the included angle ω and the included angle can be obtained by solving the triangle according to geometric relationships. They are respectively:

[0036]

[0037]

[0038] When i1 > 90° and i2 > 90°, the included angle ω and the included angle can be obtained by solving the triangle according to geometric relationships. They are respectively:

[0039]

[0040]

[0041] Preferably, the method for constructing the collision combination priority processing sorting model is as follows:

[0042] The satellite and debris information corresponding to the high-collision-risk combinations obtained in step three are stored to form a proximity event dataset. Each tuple in the proximity event dataset contains the following attributes: satellite name n s Debris name nd, satellite and debris closest time t c The closest distance d between the satellite and the debris c The position of the satellite in the J2000 coordinate system at the closest moment (x sat y sat , z sat The velocity of the satellite projected onto the coordinate axes at the closest moment The position of the fragment in the J2000 coordinate system at the closest moment (x deb y deb , z deb Fragment velocity at the closest moment

[0043] Taking into account the processing order of satellite collision combinations under multiple factors, the priority value P of the multi-factor collision combination sorting model is given priority, and then sorted according to the value.

[0044] The priority value P = α1B + α2L + α3M + α4(t - t) c )+α5G+α6N+α7H+α8d c ;

[0045] Where α1-α8 are parameters; B represents the satellite service load, with a value range of [0, 1], where the density of the densest area is 1, and the rest are values ​​based on the proportion of the density of the densest area; L represents the satellite lifetime; M represents the maneuverability of the space objects included in the combination, where both are 1 for satellites and 0 for debris; t represents the current time. c Indicates the time of approach; G represents the satellite class, with a value ranging from [0, 1]; N represents the number of satellites in the same orbit, with a value of 1 if the number of satellites in the same orbit is greater than 10, and 0 if the number of satellites in the same orbit is less than 10; H represents the satellite's orbital altitude; d c This indicates the closest distance between the satellite and the debris.

[0046] Preferably, the initial values ​​of parameters α1-α8 are all defined as follows: The gradient descent method continuously optimizes and adjusts parameters α1-α8 in a cyclical operation, calculates the gradient matrix of the multivariate function, and modifies new variables in the gradient direction to maximize the safety of the satellite constellation while maintaining performance. The indicators of satellite constellation safety are the collision combinations with the longest total collision avoidance time, the longest total remaining satellite lifetime, and the highest satellite service density, thereby changing the priority value P of the collision combination and changing the processing order of the satellite collision combination.

[0047] Preferably, the satellite constellation is secure.

[0048] Where t represents the current time, t c L represents the estimated closest time for the i-th satellite combination. i Let B be the remaining lifetime of the satellites in the i-th satellite combination. If the collision combination consists entirely of satellites, take the maximum value between the two. i The percentage of the service population density of the i-th satellite combination relative to the maximum service population density.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] 1. This invention addresses the challenges of large constellations with numerous satellites by establishing a rapid screening algorithm for high-collision-risk areas in the orbits of satellites in orbit. It combines satellite ephemeris data with orbital prediction models to screen and analyze key spatial areas of all satellites in the protected constellation. Instead of real-time comparison of satellite positions, it finds orbital intersection points and calculates the orbital intersection points of a single satellite and debris in a given orbit. This significantly reduces the computational load of real-time comparison of satellite spatial positions, thereby improving the speed of constellation collision risk assessment.

[0051] 2. This invention considers multiple factors, including the satellite's own characteristics and the individual states of the two satellites at the moment of approach. This provides a more comprehensive and reasonable analysis for the ranking of high-collision-risk satellite combinations. By optimizing multi-factor parameters through geometric screening based on the angular geometric relationship between the two intersecting orbits and gradient descent, the screening speed for high-collision-risk combinations is improved, and the factors determining the ranking of high-collision-risk combinations are considered more comprehensively, thereby enhancing the overall safety of the satellite constellation.

[0052] 3. This invention uses the gradient descent method to optimize the parameter proportions of the multi-factor collision combination priority processing sorting model, and continuously adjusts it through self-feedback. If the constellation safety is improved, it continues to be adjusted along the gradient direction; if the constellation safety is reduced, it is adjusted in the opposite direction. This improves the applicability and sorting effect of this invention, provides sufficient time for subsequent collision avoidance processing, and improves the overall reliability of the constellation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a schematic diagram of the process of the present invention.

[0055] Figure 2 This is a schematic diagram of the main geometric screening process in this invention.

[0056] Figure 3 This is a schematic diagram of important angles for the first orbital scenario in this invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] like Figure 1 As shown, a collision risk satellite combination processing and ranking optimization method consists of two stages: The first stage involves geometric calculations using orbital parameters obtained from TLE orbital element data, deriving the characteristics of orbital intersection points through mathematical formulas, and calculating the distances between satellites and debris. The second stage involves constructing a multi-factor collision risk combination priority processing ranking model and optimizing the parameters corresponding to each factor using gradient descent, ultimately achieving the goal of rapid collision risk event calculation and improved constellation safety. The steps of this invention are as follows:

[0059] Step 1: Perform orbit pre-division based on TLE orbital element data, grouping satellites located in the same orbital plane together.

[0060] The Celestrak website regularly updates TLE (Two Line Elements) orbital element data. The TLE orbital element data downloaded from this website is relatively messy, so orbital pre-division is necessary before screening for collision combinations. Orbital pre-division based on the two lines of TLE orbital elements groups satellites in the same orbit together, reducing the complexity of later calculations. Once a satellite, spacecraft, or flying object enters space, it is listed in the NORAD (North American Aerospace Defense Command) satellite ephemeris catalog and will be tracked for its entire lifespan. Each TLE orbital element data set consists of three lines of data, including the six orbital parameters according to Kepler's laws: orbital inclination i, semi-major axis a, orbital eccentricity e, right ascension of the ascending node Ω, perihelion depression α, and mean anomaly β. Satellite ephemeris uses the mathematical relationships between the six orbital parameters of Kepler's laws to determine the time, coordinates, azimuth, velocity, and other parameters of the flying object with extremely high accuracy. Satellite ephemeris can accurately calculate, predict, depict, and track the operational status of satellites and flying objects, including time, position, and velocity; it can express the precise parameters of celestial bodies, satellites, spacecraft, missiles, space debris, and other flying objects.

[0061] Orbital division is achieved based on the orbital parameters contained in the TLE orbital elements data. An array is created for each satellite or debris segment based on its orbital inclination *i*, right ascension of the ascending node *Ω*, orbital eccentricity *e*, and number of orbits around the Earth per day. These parameters can be directly obtained from the TLE orbital elements data. Following the order of array input, satellites with orbital inclination differences less than 0.1, ascending node right ascension differences less than 0.1, and equal orbital eccentricities with period differences less than 0.0001 are grouped into the same orbital plane. In subsequent steps, high-risk collision areas are filtered by orbital plane rather than by individual satellites; multiple satellites in the same orbital plane only require a single calculation. Analysis of currently deployed LEO mega-constellations shows that LEO satellites do not occupy a single orbital plane, but rather multiple satellites share a single orbital plane. Calculating trajectory intersections by orbital plane reduces computational complexity and improves efficiency.

[0062] Step 2: Based on the satellite orbital plane data, a perigee-apogee pre-screening method is used to pre-screen satellite collision combinations to obtain combinations of satellites and debris that may pose a collision risk.

[0063] After orbital delineation based on TLE data, a perigee-apogee pre-screening method is used to pre-screen satellite collision combinations before fine-tuning, identifying combinations of satellites and debris that may pose a collision risk. If the altitude difference between the satellite and debris orbits is too large, and there are no human-induced orbital maneuvers, a collision is unlikely. The perigee and apogee of the satellite and debris must meet one of the following conditions:

[0064]

[0065] The perigee of the satellite orbit is Perigee1 and the apogee is Apogee1, while the perigee of the debris orbit is Perigee2 and the apogee is Apogee2.

[0066] By comparing satellite orbital data pairwise, collisions may occur between corresponding satellite orbital planes when the above conditions are met. These collisions are stored to prepare data for the next step of fine-tuning. Two sets of satellite orbital data that do not meet the above conditions are located in different orbital layers in space and have no possibility of orbital intersection, so they do not need to be stored or processed further.

[0067] Step 3: Based on the obtained satellite and debris combination, use TLE orbital element data combined with orbital prediction model and fast trajectory spatial intersection filtering algorithm to determine the position of trajectory intersection and overlap in space; calculate the spatial distance between multiple satellites in the same orbit, and when the spatial distance is less than the safe distance, mark the satellite and debris as a high collision risk satellite combination, and the spatial region corresponding to the debris coordinates is the high collision risk region.

[0068] This step mainly involves more refined screening. Using TLE orbital element data, the right ascension Ω of the ascending node and the orbital inclination i of each of the two satellite orbital planes are obtained. Combined with the orbital prediction model and a fast trajectory spatial intersection screening algorithm, the locations where the trajectories intersect and overlap in space are determined, i.e., areas with frequent collision risk warnings.

[0069] The orbit prediction model and the fast trajectory spatial intersection screening algorithm are combined to form a high-risk area calculation algorithm. The high-risk area calculation algorithm first determines the situation by the orbital parameters of two intersecting satellite orbits in space, based on the right ascension of the ascending node and the orbital inclination, and then uses different formulas for derivation. Second, the intersection position is calculated based on the specific values. Finally, the calculation results are used to screen the area. If two satellites appear near the orbital intersection point at the same time and the distance is less than the safe distance, it is marked as a high-risk area.

[0070] The orbit prediction model used is the SGP4 (Simplified General Perturbations 4) model. This model considers the long-term and periodic perturbations of Earth's non-spherical gravity, the gravitational forces of the Sun and Moon, as well as gravitational resonance and orbital decay caused by atmospheric drag. It is currently a widely used satellite orbit calculation model and can calculate the satellite's position and velocity at a specified time. The SGP4 model has the advantage of open-source code. By substituting TLE orbital element data into the SGP4 orbit prediction model, the polar coordinates at the specified time are first obtained according to physical principles, then converted to the geocentric coordinate system, and finally the satellite's position and velocity vectors at the specified time can be obtained.

[0071] The fast trajectory spatial intersection filtering algorithm can calculate the intersection point for any two spacecraft in space, but the following explanation focuses on the case of a satellite and a piece of debris. Two space objects with different orbital parameters must have a spatial intersection angle γ. Even if two trajectories do not intersect, an intersection point may exist after their altitude is changed by translation; this angle will not change due to translation, and is called the spatial intersection angle γ. The fast trajectory spatial intersection filtering algorithm calculates two important angles based on the spatial geometric relationship between the orbits, and then uses these two important angles to filter for high collision risk. For example... Figure 3 As shown, the two important angles are the angles formed by the line connecting the intersection point and the Earth's center, and the line connecting the intersection point's perpendicular projection onto the equatorial plane and the Earth's center. The degree value is used to filter possible intersection points on the satellite orbit; the degree value of the angle ω formed by the line connecting the vertical projection point of the intersection point on the equatorial plane and the Earth's center with the x-axis of the J2000 geocentric coordinate system is used to determine the "true intersection point".

[0072] Using the right ascension Ω of the ascending node and the orbital inclination i of the satellite and debris orbits, where the right ascension Ω may be greater than or less than 180° and the orbital inclination i may be greater than or less than 90°, these four angles can be divided into two ranges. Therefore, there are 16 possible relative positions of the two orbital planes in space. When the right ascension Ω of the ascending nodes of the two orbital planes differs by 180° and the orbital inclinations i are complementary, and the direction of the satellite's trajectory is not considered, only the spatial position of the satellite's trajectory is considered, which simplifies to the same case:

[0073] Ω′=Ω-180° (2)

[0074] Where Ω is the right ascension of the ascending node before simplification, and Ω′ is the right ascension of the ascending node after simplification. To reduce the types of subsequent analysis cases, when Ω > 180°, the calculation of equation (2) is required. After performing the calculation of equation (2), in order to ensure that the relative relationship between the satellite trajectory and the space orbit remains unchanged, the calculation of equation (3) is required.

[0075] i′=180°-i (3) where i is the track inclination angle before simplification and i′ is the track inclination angle after simplification.

[0076] Let Ω1 be the ascending node with the smaller right ascension value in the satellite and debris orbits, and i1 be its corresponding orbital inclination value. Let Ω2 be the ascending node with the larger right ascension value, and i2 be its corresponding orbital inclination value. It is easy to see that Ω1 < Ω2 < 180°. Therefore, we only need to consider the range of orbital inclinations i1 and i2, thus simplifying the 16 relative position cases into 4:

[0077]

[0078] Where i1 and i2 are the orbital inclinations of the satellite and debris, respectively.

[0079] When i2 < 90° or i1 < 90° and i2 > 90°, given i1, i2, Ω1, and Ω2, the included angle ω and the included angle can be obtained by solving the triangle according to geometric relationships. They are respectively:

[0080]

[0081]

[0082] Where ω is the angle formed by the line connecting the perpendicular projection of the intersection point onto the equatorial plane and the geocenter, and the x-axis of the J2000 geocentric coordinate system; Ω1 is the right ascension of the ascending node with the smaller value; i1 is its corresponding orbital inclination; Ω2 is the right ascension of the ascending node with the larger value; and i2 is its corresponding orbital inclination. The angle is formed by the line connecting the intersection point and the Earth's center, and the line connecting the intersection point's perpendicular projection onto the equatorial plane and the Earth's center.

[0083] When i1 > 90° and i2 > 90°, given i1, i2, Ω1, and Ω2, the included angle ω can be obtained by solving the triangle using geometric relationships. Since the equation for solving the included angle ω is the same as that in equation (5), it will not be repeated here.

[0084]

[0085] Where ω is the angle formed by the line connecting the perpendicular projection of the intersection point onto the equatorial plane and the geocenter, and the x-axis of the J2000 geocentric coordinate system; Ω1 is the right ascension of the ascending intersection point with the smaller value; and i1 is its corresponding orbital inclination. The angle is formed by the line connecting the intersection point and the Earth's center, and the line connecting the intersection point's perpendicular projection onto the equatorial plane and the Earth's center.

[0086] After calculating the two important screening angles, a refined screening of high-risk areas in space is performed. To improve algorithm efficiency and further enhance the speed and accuracy of collision pair finding, a combination of coarse and fine-grained temporal methods is used to find collision pairs, based on the SGP4 space orbit prediction model.

[0087] First, substitute the TLE orbital element data into the SGP4 space orbit prediction model, set the time period to one cycle, and set the time interval to 1 minute. This will output a list of satellite position coordinates for the next cycle in the J2000 coordinate system.

[0088] Next, determine the quadrant. The quadrant of the spatial intersection can be determined based on the included angle ω: if 0° < ω < 90°, the spatial intersection is located in the first or fifth quadrant, 0 < x and 0 < y; if 90° < ω < 180°, the spatial intersection is located in the second or sixth quadrant, 0 > x and 0 < y; if 180° < ω < 270°, the spatial intersection is located in the third or seventh quadrant, 0 > x and 0 > y; if 270° < ω < 360°, the spatial intersection is located in the fourth or eighth quadrant, 0 < x and 0 > y.

[0089] Secondly, when the x and y coordinates corresponding to the quadrant are satisfied, the included angle... The values ​​are compared. The time interval is then adjusted to 1 second for a more precise position comparison.

[0090]

[0091] Where x1, y1, and z1 are the satellite's position coordinates in the J2000 coordinate system. The angle between the line connecting the intersection point and the Earth's center, and the line connecting the point of intersection's perpendicular projection onto the equatorial plane and the Earth's center. As calculated above, the location of the coordinate value for which equation (8) holds is the corresponding position of the spatial intersection point on the satellite trajectory.

[0092]

[0093] Where x2, y2, and z2 are the position coordinates of the fragment in the J2000 coordinate system. The angle between the line connecting the intersection point and the Earth's center, and the line connecting the point of intersection's perpendicular projection onto the equatorial plane and the Earth's center. As calculated above, the location of the coordinate value for which equation (9) holds true is the corresponding position of the spatial intersection point on the debris trajectory. Under the SGP4 space orbit prediction model, time and position are in one-to-one correspondence, and the motion of both the satellite and the debris is periodic. The time to reach the intersection point plus the time of one period can be used to obtain the time to pass through this intersection point again.

[0094] In current domestic and international low-Earth orbit constellation launch plans, the same orbit typically contains dozens or even hundreds of satellites. Based on current space observation data, debris usually occupies a single orbital plane. Therefore, the spatial distance between multiple satellites in the same orbit is periodically calculated, using the time when each debris reaches the intersection of its trajectory. When the spatial distance between them is less than the safe distance (generally 10km), the satellite and debris are marked as a high-collision-risk combination. The spatial region corresponding to the debris's coordinates is then designated as the high-collision-risk region, and time t is marked as the closest time t between the satellite and debris. c The closest distance between satellite d and debris d c The formula for calculating spatial distance is:

[0095]

[0096] Where, x sat y sat z sat Here are the coordinates of the satellite in the J2000 coordinate system, x deb y deb z deb d represents the coordinates of the debris in the J2000 coordinate system, and d is the distance between the satellite and the debris.

[0097] Step 4: Based on the high-collision-risk areas and high-collision-risk satellite combinations generated in Step 3, and combining the satellite status and satellite characteristics, construct a priority processing ranking model for collision combinations.

[0098] The satellite and debris information corresponding to the high-collision-risk combinations obtained in step three is stored, including the characteristics of the satellites and debris themselves and the time attribute of the approach time, forming a proximity event dataset. Each tuple in the proximity event dataset contains the following attributes: satellite name ns Fragment name n d The closest time t between the satellite and the debris c The closest distance d between the satellite and the debris c The position of the satellite in the J2000 coordinate system at the closest moment (x sat y sat , z sat The velocity of the satellite projected onto the coordinate axes at the closest moment. The position of the fragment in the J2000 coordinate system at the closest moment (x deb y deb , z deb The velocity of the fragment at the closest moment. Satellite Name n s The fragment name nd can be obtained from the 0th row of the corresponding TLE orbital element data, and the remaining parameters can be obtained from the calculation in step three.

[0099] Construct a multi-factor collision combination priority processing ranking model: comprehensively consider the processing order of satellite collision combinations under multiple factors, give a priority value P, and then sort according to the value.

[0100] P=α1B+α2L+α3M+α4(tt c )+α5G+α6N+α7H+α8d c (7)

[0101] Where α1-α8 are parameters, and their initial values ​​are set to... Then, adjustments are made based on the gradient optimization results. Adjusting the parameter values ​​means adjusting the proportion of each factor's influence at a certain level; B represents the satellite's service load, determined by the population density of the area served by the satellite, with a value range of [0, 1], where the density of the most densely populated area is 1, and the rest are values ​​based on the proportion of the density of the most densely populated area; L represents the satellite's lifetime, determined by the satellite's remaining lifetime, in years; M represents the maneuverability of the space objects included in the combination, with both being 1 for satellites and 0 for debris; t represents the current time, t c The approximation time is calculated in step three; G represents the satellite class, determined by various factors, with a value range of [0, 1]; N represents the number of satellites in the same orbit, with a value of 1 for a number greater than 10 and 0 for a number less than 10; H represents the satellite's orbital altitude, which can be directly read from the TLE orbital element data as the number of cycles the satellite completes each day. Dividing the length of a day by the number of cycles gives the time it takes for the satellite to complete one cycle, which, when substituted into Kepler's third law, yields the satellite's orbital altitude; d c This indicates the closest distance between the satellite and the debris.

[0102] Satellite workload (B) directly reflects a satellite's importance. A satellite with a high workload (including transmission and computation) is likely a critical satellite located at a central routing node, and its collision would cause significant damage to the satellite communication network. Satellites with high workloads have higher priority. Satellite lifetime is the satellite's designed lifespan minus its current service time. Satellites with longer lifetimes have higher priority. Due to limitations in battery capacity and functionality, satellites do not always possess the maneuverability to adjust their orbit or attitude to avoid collisions. Satellites with good maneuverability (M) have higher priority. Subtracting the closest approach time between the satellite and debris (calculated using the SGP4 model in step three) from the current moment yields the countdown for satellite collision calculation tasks. The smaller the value, the higher the urgency of the satellite collision warning and pre-processing. Satellite class (G) is determined by factors such as satellite purpose, cost, and country of origin. Military satellites are prioritized over civilian or commercial satellites, high-cost satellites over low-cost satellites, and Chinese satellites are prioritized over satellites from friendly countries, which are in turn prioritized over satellites from non-friendly countries. The impact of a collision is considered more comprehensively in terms of physical factors. For example, if a satellite is operating in a densely populated area, the impact on other satellites after a collision could be excessive. The more satellites (N) in the same orbit, the higher the priority. Within the safe distance of the satellite's orbital altitude (H), the more satellites, the higher the priority. The smaller the closest approach distance, the higher the priority. Real-time services take precedence over data packet transmission services, and online services take precedence over offline services.

[0103] Step 5: Use the gradient descent method to optimize the parameters of the multi-factor collision combination priority processing ranking model, and obtain the optimization results with the longest total satellite collision avoidance time, priority processing of high-level satellites, and the highest overall security of the satellite constellation.

[0104] Initially, the initial values ​​of parameters α1-α8 are all defined as follows: However, it's clear that the impact of each factor on the overall safety of different constellations is not entirely the same, and not all of these factor values ​​are available for all satellites. Therefore, gradient descent is needed to optimize parameters α1-α8 to achieve the highest overall constellation safety while maintaining performance. The indicators of satellite constellation safety are the collision combinations with the longest total collision avoidance time, the longest total remaining satellite lifetime, and the highest satellite service density. This involves continuously optimizing and adjusting the parameters α1-α8, thereby changing the processing priority value P of the collision combinations, and further altering the processing order of satellite collision combinations. The processing order will affect the overall safety of the satellite constellation.

[0105]

[0106] Where S represents the overall security of the satellite constellation, t represents the current time, and t c L represents the estimated closest time for the i-th satellite combination.i Let B be the remaining lifetime of the satellites in the i-th satellite combination. If the collision combination consists entirely of satellites, take the maximum value between the two. i The percentage of the service population density of the i-th satellite combination relative to the maximum service population density.

[0107] Gradient descent, also known as the steepest descent method, is based on the concept of the gradient. The relationship between the gradient and the directional derivative is as follows: the direction of the gradient is the same as the direction in which the directional derivative is maximized, and the magnitude of the gradient is the maximum value of the directional derivative of the function at that point. First, initialize α1-α8... Subsequently, a loop is performed to calculate the gradient matrix of the multivariate function and modify the new variables in the direction of the gradient. The loop then checks if termination has been reached: if the absolute value of the difference between two consecutive function values ​​is less than a threshold, the loop exits; otherwise, it continues. The loop checks if the constellation with the highest safety is achieved according to the new order. If it achieves both the highest safety and best overall performance, the loop ends. A multi-factor optimization method is used to achieve the highest constellation safety, replacing the traditional first-come, first-served approach, balancing efficiency and effectiveness. The parameter proportions in the final output correspond to different constellations, and the results are not entirely the same. Gradient descent is used to optimize the parameter proportions based on the characteristics of different constellations. In most cases, the parameter proportions can be evenly distributed.

[0108] Through the processing operations in steps one through five, we can quickly locate high-collision-risk areas in space and achieve the best results in terms of total satellite collision avoidance time, priority processing of high-level satellites, and overall safety of the satellite constellation. Ultimately, this ensures the stable operation of the constellation.

[0109] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A collision risk satellite constellation processing ordering optimization method, characterized by, The steps are as follows: Step 1: Perform orbit pre-division based on TLE orbital element data, grouping satellites located in the same orbital plane together; Step 2: Based on the satellite orbital plane data, a perigee-apogee pre-screening method is used to pre-screen satellite collision combinations to obtain combinations of satellites and debris that may pose a collision risk; Step 3: Based on the obtained satellite and debris combination, use TLE orbital elements data combined with orbital prediction models and a fast trajectory spatial intersection point screening algorithm to determine the locations where the trajectories intersect and overlap in space; Calculate the spatial distance between multiple satellites in the same orbit. When the spatial distance is less than the safe distance, mark the satellite and debris as a high-collision-risk satellite combination. At this time, the spatial region corresponding to the debris coordinates is the high-collision-risk region. The implementation method of the fast screening track space intersection algorithm is: using TLE track root number data to obtain the ascending node right ascension of each satellite orbit plane and the orbit inclination , calculating two important angles through the spatial geometric relationship of the orbit plane, and using the two important angles to discriminate and screen high collision risk; the two important angles are the degree of the angle between the connecting line between the intersection point and the center of the earth and the vertical projection point of the intersection point on the equatorial plane , which is used to screen the possible intersection point on the satellite orbit. The angle between the line connecting the vertical projection point of the intersection on the equatorial plane and the center of the earth and the x axis of the J2000 center of the earth coordinate system The degree of the angle is used to determine the "true intersection". The method for determining the location of the intersection and overlap of trajectories in space in step three is as follows: Substitute the TLE orbital element data into the SGP4 space orbit prediction model, set the time period to one cycle, set the time interval to 1 minute, and output the list of satellite position coordinates for the next cycle in the J2000 coordinate system. Quadrant determination: based on the included angle Determine the quadrant in which the spatial intersection point lies: If If the spatial intersection point is located in the first or fifth quadrant, and ;like If the spatial intersection point is located in the second or sixth quadrant, and ;like If the spatial intersection point is located in the third or seventh quadrant, and ;like If the spatial intersection point is located in the fourth or eighth quadrant, and ; When the corresponding quadrant is satisfied When considering the coordinate range, the included angle The values ​​are compared, the time interval is adjusted to 1 second, and a search is performed to find those that meet the criteria. = The established coordinate values ​​represent the corresponding positions of the spatial intersection points on the satellite trajectory; where, , , These are the satellite's position coordinates in the J2000 coordinate system. Find Formula = The location of the established coordinate values ​​is the corresponding position of the spatial intersection point on the debris trajectory; where, , , These are the position coordinates of the fragment in the J2000 coordinate system. Step 4: Based on the high-collision-risk areas and high-collision-risk satellite combinations generated in Step 3, and combining the satellite status and satellite characteristics, construct a priority processing ranking model for collision combinations. Step 5: Use the gradient descent method to optimize the parameters of the multi-factor collision combination priority processing ranking model, and obtain the optimization results with the longest total satellite collision avoidance time, priority processing of high-level satellites, and the highest overall security of the satellite constellation.

2. The collision risk satellite combination processing and sorting optimization method according to claim 1, characterized in that, Each TLE orbital element data point consists of three lines of data, including the six orbital parameters from Kepler's laws: orbital inclination. , semi-major axis of orbit a, eccentricity of orbit e, right ascension of ascending node Perihelion depression angle , and the near point angle ; The method for pre-dividing orbits based on the orbital parameters contained in the TLE orbital elements data is as follows: based on the orbital inclination of each satellite or debris... Right ascension of ascending node An array is created containing the orbital eccentricity e and the number of orbits around the Earth per day. Based on the order of reading into the array, satellites with orbital inclination differences less than 0.1, ascending node right ascension differences less than 0.1, and equal orbital eccentricities with period differences less than 0.0001 are selected and classified into the same orbital plane.

3. The collision risk satellite combination processing and sorting optimization method according to claim 2, characterized in that, The perigee-apogee pre-screening method is as follows: Data from the satellite orbital plane are compared pairwise; when the perigee and apogee of the satellite and debris meet the conditions... At this time, collisions may occur between the corresponding satellite orbital planes; these collisions are stored to prepare data for the next step of fine screening; the perigee of the satellite orbit is... apogee is The perigee of the debris orbit is The apogee is Apogee2.

4. The collision risk satellite combination processing and sorting optimization method according to claim 2 or 3, characterized in that, The orbit prediction model is the SGP4 space orbit prediction model. By substituting the TLE orbital element data into the SGP4 space orbit prediction model, the polar coordinates at a specified time are obtained according to physical principles, and then converted to the geocentric coordinate system. Finally, the position vector and velocity vector of the satellite at the specified time can be obtained.

5. The collision risk satellite combination processing and sorting optimization method according to claim 4, characterized in that, The time and position of the SGP4 space orbit prediction model are in one-to-one correspondence, and the motion of both the satellite and the debris is periodic. The time to reach the intersection point plus the time of one period can be used to obtain the time to pass through the intersection point again. Based on the time when each debris reaches the intersection of its trajectory, the spatial distance between multiple satellites in the same orbit is calculated periodically: ； in, , , These are the coordinate values ​​of the satellite in the J2000 coordinate system. , , These are the coordinates of the fragment in the J2000 coordinate system. The distance between the satellite and the debris; When the spatial distance between a satellite and debris is less than a safe distance, the satellite and debris are marked as a high-collision-risk combination. The spatial region corresponding to the debris's coordinates is then designated as a high-collision-risk region, and time t is marked as the closest point between the satellite and debris. The spatial distance d is the closest distance between the satellite and the debris. .

6. The collision risk satellite combination processing and sorting optimization method according to claim 5, characterized in that, The two important angles are calculated as follows: the right ascension of the ascending nodes of the two orbital planes. When the orbital inclinations differ by 180° and are complementary, and the direction of the satellite's trajectory is not considered, only its spatial location is considered. This simplifies to the same case, i.e., when... hour, , ;in, It is the simplified right ascension of the anterior ascending node. It is the simplified right ascension of the ascending node; It simplifies the front track inclination angle. It is the simplified orbital inclination angle; The right ascension of the ascending node with the smaller right ascension value among the satellite and debris trajectories is... The corresponding orbital inclination angle is marked as The point with the larger right ascension value of the ascending node is marked as The corresponding orbital inclination angle is marked as ,have to Considering the track inclination angle , Within the given range, the 16 relative positional scenarios are simplified to 4: ； in, , It refers to the orbital inclination of satellites and debris; when or When solving a triangle using geometric relationships, the included angle can be obtained. They are respectively: ； ； when When solving a triangle using geometric relationships, the included angle can be obtained. They are respectively: ； 。 7. The collision risk satellite combination processing and sorting optimization method according to claim 6, characterized in that, The method for constructing a collision combination priority processing sorting model is as follows: The satellite and debris information corresponding to the high-collision-risk combinations obtained in step three are stored to form a proximity event dataset. Each tuple in the proximity event dataset contains the following attributes: satellite name. Fragment Name The closest time between the satellite and the debris The closest distance between the satellite and the debris The position of the satellite in the J2000 coordinate system at the closest moment ( The velocity of the satellite projected onto the coordinate axes at the closest moment ( The position of the fragment in the J2000 coordinate system at the closest moment ), the fragment velocity at the closest moment ( ; Taking into account the processing order of satellite collision combinations under multiple factors, the priority value of the multi-factor collision combination priority processing ranking model is determined. Then sort them according to the size of the values; The priority value ; in, - For parameters; This represents the satellite service load, with a value range of [value range missing]. The density of the densest area is set to 1, and the rest are assigned values ​​according to their proportion of the density of the densest area. Indicates satellite lifespan; This indicates the maneuverability of the space objects included in the combination; both satellites are assigned a value of 1, and debris is assigned a value of 0. Indicates the current moment. Indicates the time approaching the time of occurrence; Indicates satellite class, with a range of values. ; This indicates the number of satellites in the same orbit as the satellite. A value of 1 is used if the number of satellites in the same orbit is greater than 10, and a value of 0 is used if the number of satellites in the same orbit is less than 10. Indicates the satellite's orbital altitude; This indicates the closest distance between the satellite and the debris.

8. The collision risk satellite combination processing and sorting optimization method according to claim 7, characterized in that, parameter - The initial values ​​are all defined as follows: The gradient descent method continuously optimizes and adjusts the parameters. - The process involves looping to calculate the gradient matrix of the multivariate function and modifying the new variables in the direction of the gradient, thereby maximizing the security of the satellite constellation while also ensuring performance. The safety metrics for a satellite constellation are the collision combinations with the longest total collision avoidance time, the longest total remaining satellite lifetime, and the highest satellite service density, thereby changing the priority value of the collision combinations. This changes the processing order of satellite collision combinations.

9. The collision risk satellite combination processing and sorting optimization method according to claim 7, characterized in that, The security of the satellite constellation ; in, Representing the current moment, Representing the The estimated closest time for each satellite combination For the first The remaining lifetime of satellites in a collision combination is determined by the maximum of the two values, if all satellites in the combination are involved. For the first The percentage of the population density served by a satellite constellation relative to the maximum population density served.

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