Automatic division method and system for satellite constellation orbital plane

Abstract

The invention discloses an automatic division method and system for a satellite constellation orbital plane, and relates to the technical field of spaceflight measurement and control. The method comprises the following steps: firstly, calculating an orbital plane unit normal vector based on a satellite orbit inclination angle and an ascending node right ascension, and performing first-level spatial pointing clustering by adopting a density clustering algorithm to form an orbital plane group; secondly, in the same orbital plane group, by taking a semi-major axis and an eccentricity rate as characteristics, automatically determining an optimal shell layer number by utilizing a Gaussian mixture model and a Bayesian information criterion, and realizing second-stage orbital energy shell layer division; and finally, in the same shell layer, sorting and interval statistical analysis are performed on the right ascension of the ascending node, recursive subdivision is performed through dynamic threshold segmentation in combination with a range-based dual-condition verification mechanism, and fine division of a third-level orbital plane is completed. The method realizes full-process automation from orbit data to division results, has the advantages of high division precision, strong adaptability, good engineering practicability and the like, and is suitable for operation and maintenance management of large-scale heterogeneous satellite constellations.

Description

Technical Field

[0001] This invention relates to the field of aerospace telemetry and control technology, and in particular to an automatic method and system for dividing the orbital plane of a satellite constellation. Background Technology

[0002] With the rapid development of large-scale low-Earth orbit satellite constellations for communication, remote sensing, and other applications, the number of satellites in a constellation can reach tens of thousands. These satellites are typically deployed in multiple orbital planes with specific inclinations, altitudes, and right ascension of the ascending node to achieve global coverage. Accurately and efficiently assigning satellites within a constellation to their respective orbital planes is fundamental for subsequent operation and maintenance management tasks such as constellation status monitoring, collision avoidance, and performance analysis.

[0003] Currently, the division of satellite constellation orbital planes mainly relies on manual experience or simple rules, and these methods have significant drawbacks: 1. Limited clustering strategy: Simple algorithms such as the K-Mean step S require a preset number of clusters and cannot adapt to changes in constellation configuration. For shells with different inclination angles and altitudes, the optimal number of orbital planes should be dynamically determined.

[0004] 2. Inaccurate partitioning logic: During RAAN clustering, due to the Walker distribution characteristics of constellations, multiple orbital planes with similar aspects are easily merged incorrectly, requiring subsequent complex criteria for manual intervention and separation.

[0005] Traditional orbital plane delineation methods often rely on manually preset orbital plane parameters, lacking flexibility and unable to adapt to large-scale, multi-layered constellation structures. This is especially problematic when multiple dimensions such as orbital inclination, altitude, and argument of perigee (RAAN) are coupled, leading to inaccurate delineation and overlapping clusters. Therefore, there is an urgent need in this field for an automatic, accurate, and physically meaningful orbital plane delineation method to address these issues. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing technologies and provide an automatic orbital plane partitioning method for satellite constellations based on orbital normal vectors and hierarchical clustering. This method achieves fully automated, high-precision, and highly adaptable orbital plane partitioning through a three-level progressive data processing and iterative judgment process: orbital normal vector spatial clustering, shell partitioning based on orbital energy and shape, and RAAN fine clustering.

[0007] To achieve the above objectives, this application proposes an automatic method for dividing the orbital plane of a satellite constellation, comprising the following steps: Step S1: Obtain the orbital parameters of all satellites in the constellation, including at least the orbital inclination, right ascension of the ascending node, semi-major axis, and eccentricity; Step S2: Calculate the unit normal vector of the orbital plane based on the orbital inclination and right ascension of the ascending node, and perform first-level clustering on the normal vectors of all satellites to divide at least one group of space orbital planes with different spatial orientations. Step S3: For each of the space orbital plane groups, a second-level clustering is performed using the semi-major axis and eccentricity of the satellites within the group as joint features to divide at least one orbital shell with different orbital energies. Step S4: For each orbital shell, perform third-level clustering based on the right ascension of the ascending node of the satellites within the shell, and recursively subdivide the data in conjunction with the orbital plane consistency verification conditions to finally divide at least one orbital plane.

[0008] As a further solution, the formula for calculating the unit normal vector of the orbital plane in step S2 is: Where i is the orbital inclination and Ω is the right ascension of the ascending node.

[0009] As a further solution, step S2 uses the DBSCAN algorithm to perform the first-level clustering of the normal vectors, and the distance metric uses the spherical distance formula: in, Let each represent the dot product of the unit normal vectors of the two orbital planes; (*) indicates the inverse cosine function, which returns a value in radians; This represents the angle between the unit normal vectors of the two orbital planes.

[0010] As a further solution, in step S3, a Gaussian mixture model is used to perform a second-level clustering of the semi-major axis and eccentricity, and the optimal number of clusters is automatically determined by the Bayesian information criterion.

[0011] As a further solution, the parameters of the Gaussian mixture model are iteratively optimized using the expectation-maximization algorithm until the change in the log-likelihood function is less than a preset threshold or the maximum number of iterations is reached.

[0012] As a further solution, step S4 performs third-level clustering and recursive subdivision through the following sub-steps: Step S41: Normalize and sort the right ascension of the ascending nodes of all satellites within the shell, and calculate the interval between adjacent values; Step S42: Calculate the dynamic segmentation threshold based on the median, upper quartile, and preset minimum threshold of the interval; Step S43: Perform initial segmentation of the ascending node right ascension sequence according to the dynamic segmentation threshold to obtain several initial orbital plane clusters; Step S44: Perform consistency verification on each initial orbital plane cluster. If the verification fails, proceed to K-Mean step S for further subdivision and recursive verification.

[0013] As a further solution, the conditions for the consistency verification are: and in, Let the right ascension range of the ascending node within the k-th cluster be denoted as . This is the absolute tolerance threshold. This is the relative tolerance coefficient. It represents the minimum interval between adjacent cluster centers.

[0014] As a further solution, the formula for calculating the dynamic segmentation threshold is: in, The median of the interval. The upper quartile is the interval. and For preset coefficients, This is the minimum segmentation threshold.

[0015] As a further solution, when subdividing the initial orbital plane clusters that do not meet the consistency verification conditions, the number of subdivided clusters is determined according to the following formula: in, The adjustment factor is (0.8–1.2), and "round" means rounding to the nearest integer. It is the minimum interval between adjacent cluster centers, and satisfy , This represents the number of satellites within the initial orbital plane cluster.

[0016] On the other hand, the present invention also provides an automatic partitioning system for satellite constellation orbital planes, characterized in that it is used to execute an automatic partitioning method for satellite constellation orbital planes as described in any of the preceding claims, comprising: Data parsing module: Obtains the orbital parameters of all satellites in the constellation, including at least the orbital inclination, right ascension of the ascending node, semi-major axis, and eccentricity; Normal vector clustering module: Calculates the unit normal vector of the orbital plane based on the orbital inclination and right ascension of the ascending node, and performs first-level clustering on the normal vectors of all satellites to divide at least one group of space orbital planes with different spatial orientations; Shell partitioning module: For each of the space orbital plane groups, a second-level clustering is performed using the semi-major axis and eccentricity of the satellites within the group as joint features to partition at least one orbital shell with different orbital energies. Orbital plane segmentation module: For each orbital shell, a third-level clustering is performed based on the right ascension of the ascending node of the satellites within the shell, and recursively subdivided in combination with the orbital plane consistency verification conditions, so as to finally segment at least one orbital plane. The output module is used to output the orbital plane division results.

[0017] Compared with related technologies, the automatic division method and system for satellite constellation orbital planes provided by this invention has the following advantages: 1. This invention starts with the parsing of raw TLE data and automatically completes orbital plane identification, shell division, and fine verification through a three-level progressive clustering algorithm until the final division result is output. The entire process does not require manual pre-setting of prior parameters such as the number of orbital planes, inclination angle, or RAAN interval, completely changing the traditional method's reliance on manual rules and repeated debugging. It is suitable for rapid, batch-processing orbital plane division of large-scale constellations with tens of thousands of satellites, resulting in an order-of-magnitude improvement in processing efficiency.

[0018] 2. This invention pioneers a three-level hierarchical clustering framework: "orbital normal vector (spatial orientation) → orbital energy and shape (semi-major axis, eccentricity) → right ascension of the ascending node (phase)". Each level corresponds to a clear physical meaning of orbital dynamics: the first level locks the spatial orientation of the orbital plane, the second level distinguishes energy shells at different altitudes, and the third level precisely separates orbital planes with different phases within the shells. This progressive division from macroscopic to microscopic, from spatial to phase, is logically rigorous, and the results are more consistent with the principles of celestial mechanics, with a division accuracy far exceeding that of traditional single-dimensional clustering methods.

[0019] 3. The core algorithm of this invention possesses strong adaptability: ① In the orbital normal vector clustering stage, the DBSCAN isodense clustering algorithm is used, which can automatically discover and form spatial orbital surface groups of arbitrary shapes and numbers without pre-setting the number of clusters. ② In the orbital shell partitioning stage, the Gaussian mixture model combined with the Bayesian information criterion is used to automatically determine the optimal number of shells based on data characteristics, adapting to changes in altitude layers within the constellation. ③ In the RAAN fine partitioning stage, through dynamic calculation of the segmentation threshold and a recursive verification mechanism, it can automatically identify and split orbital surfaces with closely adjacent phases caused by Walker constellation characteristics or orbital perturbations, effectively overcoming the "phase confusion" problem in traditional RAAN clustering.

[0020] 4. This invention effectively improves the robustness of the method through a multi-level processing and verification mechanism: ① Orbital normal vector clustering can identify abnormal orbital satellites that deviate significantly from the mainstream direction as "noise," facilitating subsequent investigation. ② The dual verification conditions of "absolute tolerance and relative tolerance" in the RAAN partitioning stage, as well as the K-Mean step S recursive subdivision mechanism when the conditions are not met, constitute a closed-loop self-verification and optimization process. This process can automatically correct errors caused by data noise or unreasonable initial partitioning, ensuring the consistency within each orbital plane. The output results are direct and reliable, providing high-quality input for subsequent engineering applications such as constellation collision warning and resource scheduling.

[0021] 5. The method of this invention does not rely on the configuration design of any specific constellation (such as Walker, Rose, etc.). Its core is to mine and cluster the geometric and physical characteristics implied by the orbital elements. Therefore, this method can be universally applied to satellite constellations of various inclinations, different altitudes, single or multiple layers, and regular or non-uniform distributions, providing a universal intelligent orbital plane analysis tool for the increasingly complex and diverse constellation systems of the future. Attached Figure Description

[0022] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0023] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram illustrating the steps of an automatic division method for the orbital plane of a satellite constellation provided by the present invention. Figure 2 A schematic diagram of an automatic partitioning system for satellite constellation orbital planes provided by the present invention; Figure 3 This invention provides a satellite distribution map of a constellation at an inclination of 43 degrees on orbital plane 1. Figure 4 This invention provides a satellite distribution map of a constellation with an inclination of 43 degrees on orbital plane 2. Figure 5 This invention provides a satellite distribution map of a constellation with a 43-degree inclination orbital plane. The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0026] Example 1 Please see Figure 1 This embodiment provides an automatic method for dividing the orbital plane of a satellite constellation, including the following steps: Step S1: Obtain the orbital parameters of all satellites in the constellation, including at least the orbital inclination, right ascension of the ascending node, semi-major axis, and eccentricity; Step S2: Calculate the unit normal vector of the orbital plane based on the orbital inclination and right ascension of the ascending node, and perform first-level clustering on the normal vectors of all satellites to divide at least one group of space orbital planes with different spatial orientations. Step S3: For each of the space orbital plane groups, a second-level clustering is performed using the semi-major axis and eccentricity of the satellites within the group as joint features to divide at least one orbital shell with different orbital energies. Step S4: For each orbital shell, perform third-level clustering based on the right ascension of the ascending node of the satellites within the shell, and recursively subdivide the data in conjunction with the orbital plane consistency verification conditions to finally divide at least one orbital plane.

[0027] It should be noted that this embodiment automates the entire process from TLE data input to orbital plane partitioning output, greatly reducing manual intervention and improving efficiency. Through a three-level hierarchical clustering strategy of "orbital normal vector-altitude-RAAN," and by introducing orbital plane condition judgment and iterative subdivision mechanisms, it can accurately distinguish compactly adjacent orbital planes, effectively overcoming interference from orbital perturbations and parameter dispersion, resulting in partitioning results that better conform to orbital dynamics principles. Automatic identification of space orbital plane groups through orbital normal vector clustering requires no prior knowledge, enabling this method to adaptively handle satellite constellations of different sizes and configurations, demonstrating strong versatility. The partitioning results can be directly used in constellation simulation, collision risk assessment, on-orbit management, and other engineering practices, providing key technical support for the efficient and safe operation and maintenance of large-scale constellations.

[0028] In one possible implementation, step S2 includes: calculating the unit normal vector of the orbital plane. The process involves assembling the orbital normal vectors of all satellites into a dataset, determining the distance metric, the neighborhood radius ε, the minimum number of samples MinPt step S, performing DBSCAN clustering, and then processing, analyzing, and outputting the results.

[0029] The orbital plane normal vector is a unit vector perpendicular to the orbital plane, and its direction follows the right-hand rule (viewed along the satellite's motion, the orbit rotates counterclockwise). Its expression in the geocentric inertial coordinate system (ECI) is: In one possible implementation, step S2 uses the DBSCAN algorithm to cluster the normal vectors, identifying satellite clusters with consistent spatial orientation. The normal vector directions are normalized to ensure that all normal vectors point to the hemisphere of the unit sphere. The orbital normal vectors of all satellites are then combined into a dataset. The satellite's orbital normal vector The mathematical formula for the ε-neighborhood (Ep step Silon-Neighborhood) is as follows: This represents the orbital normal vector of any satellite in the dataset. Representative dataset The orbital normal vectors of other satellites in the array. A distance metric function representing two vectors (spherical distance is used for orbital normal vectors). The neighborhood radius parameter (typically 0.035-0.087 radians, corresponding to 2°-5° in orbit clustering) is used in orbit normal vector clustering. Indicates connection with satellite The angle between the orbital normal vectors does not exceed The set of all other satellites in radians.

[0030] Distance measurement uses spherical distance calculation, mathematical formula: This represents the dot product of two unit normal vectors. Represents the inverse cosine function and returns the value in radians. The result represents the angle between the two orbital normal vectors.

[0031] ε is a parameter in the DBSCAN algorithm that represents the neighborhood radius. In the clustering of orbital normal vectors, ε represents the maximum angle (in radians) between two normal vectors that are considered to be in the same neighborhood. Typically, ε can be chosen based on prior knowledge or experimentation, for example, between 2° and 5° (approximately 0.035 to 0.087 radians). It can also be determined based on the distribution of spherical distances between all normal vectors in the dataset, such as choosing a quantile of the distance distribution.

[0032] The MinPt step S is the minimum number of samples required to form a dense region. In satellite orbital plane clustering, the MinPt step S can be set as the minimum expected number of satellites in an orbital plane. For example, it can be set according to the minimum number of satellites in the orbital plane designed for the constellation, or according to a proportion of the total number of satellites in the dataset (e.g., 1%-5%), but at least 2.

[0033] The DBSCAN clustering execution phase steps are as follows: 1) Initialization. Initialize a tag for each satellite to indicate its status (unvisited, noisy, or assigned to a cluster). Initialize the cluster number (clu) to 0 in the Ster_id step.

[0034] 2) Traverse the satellites. For each satellite p, mark it as visited if it has not yet been visited. Query the ε-neighborhood of satellite p, that is, find all satellites whose distance (i.e., the angle) from p does not exceed ε, and denote them as the neighborhood. .

[0035] 3) Core point determination. If the neighborhood... If the number of satellites in the cluster (including p itself) is greater than or equal to the number of satellites in step S (MinPt), then satellite p is marked as a core point, a new cluster is created (Ster_id is incremented by 1 in step clu), and p is assigned to that cluster. If the neighborhood... If the number of satellites in the sequence is less than the number in step S of MinPt, then p is temporarily marked as noise (it may be reclassified later).

[0036] 4) Cluster Expansion. For a core point p, add all satellites in its ε-neighborhood to a seed set. For each satellite q in the seed set, if q has not been visited, mark it as visited and query its ε-neighborhood. .if If the number of satellites is greater than or equal to MinPt step S, then... Satellites that have not yet been added to the seed set are added to the seed set. If q has not been assigned to any cluster, then q is assigned to the current cluster. This process is repeated until the seed set is empty.

[0037] 5) Continue traversing. Repeat steps 1) through 4) until all satellites have been visited.

[0038] In the results processing, analysis, and output phase, the number of satellites in each cluster is counted. For each cluster, its average orbital normal vector (the mean of all normal vectors within the cluster) is calculated, normalized, and the average orbital inclination and right ascension of the ascending node are calculated. Satellites marked as noise are examined, their orbital characteristics are analyzed, and it is determined whether they are anomalous or special orbits. It is verified whether satellites within the same cluster have similar orbital inclinations and right ascensions of the ascending node. It is checked whether there is significant separation between different clusters (i.e., the interval between orbital planes). Finally, a list of satellites and orbital parameter statistics (average inclination, average RAAN, number of satellites, etc.) for each cluster are output. A list of noisy satellites is output. Satellites with the same cluster label are grouped into the same orbital plane cluster. We can group satellites with the same orbital plane pointing together, thereby identifying different orbital planes in the constellation. The spatial orbital plane groups and noise points are output; a scatter plot of orbital normal vectors is drawn in 3D space, and different clusters are marked with different colors.

[0039] In one possible implementation, step S3 includes: for N satellites within the same space orbital plane group, extracting their orbital semi-major axis a and eccentricity e to form a two-dimensional joint feature vector, and standardizing the features to obtain a standardized feature matrix. Based on the standardized feature matrix, setting the number of candidate shells K, constructing a Gaussian mixture model (GMM) containing K mixture components, and optimizing the model parameters using the expectation-maximization algorithm. Based on the Bayesian information criterion (BIC), automatically determining the optimal number of orbital shells from multiple candidate cluster numbers; according to the Gaussian mixture model corresponding to the optimal number of shells, dividing the satellites into each orbital shell, and outputting the physical property statistics of each shell.

[0040] When the features are standardized, for N satellites within the same space orbital plane group, the orbital parameters of each satellite i are: semi-major axis a i (Unit: km), Eccentricity e i Standardized formulas for calculating semi-major axis and eccentricity: in, For the standardized semi-major axis, The standardized eccentricity The sample mean of the semi-major axis. , The eccentricity sample mean. , The sample standard deviation is the semi-major axis. , The standard deviation of the eccentricity is the sample standard deviation. .

[0041] Construct the feature matrix: ,in .

[0042] Assuming the satellite's feature data is generated by mixing K Gaussian distributions, with each Gaussian distribution corresponding to an orbital shell, the Gaussian mixture model formula is: For all parameters of the model, The number of mixed components, i.e., the number of orbital shell layers to be identified. Let be the mixing coefficient of the k-th component, satisfying and . Let be the mean vector of the k-th component. . Let be the covariance matrix of the k-th component. . It follows a multivariate Gaussian distribution. The formula for the Gaussian distribution is as follows: in, For feature dimension, Let be the determinant of the covariance matrix. The inverse of the covariance matrix, It is a natural exponential function.

[0043] The model parameters are estimated using the expectation-maximization algorithm, which includes the following two iterative steps: E-step (expected step) calculation formula: This represents the posterior probability (responsibility value) that sample i belongs to the k-th shell.

[0044] M-step (maximum step) update formula: in, The number of valid samples in the k-th shell. Updated mixing coefficients, The updated mean vector, The updated covariance matrix.

[0045] Iteratively execute the E-step and M-step until the change in the log-likelihood function is less than a preset threshold, such as... Or it may reach the maximum number of iterations.

[0046] For each candidate shell number Calculate the corresponding Bayesian information criterion value: This represents the maximum likelihood value of the model. For the maximum likelihood estimation of model parameters, The number of free parameters in the model. This represents the total number of samples. The calculation of the number of model parameters is as follows: when hour: The range of candidate K values ​​is determined: This indicates that all satellites are distributed in one shell, and each shell generally contains at least 5 satellites to ensure that the number of each candidate shell has sufficient physical meaning and statistical reliability.

[0047] Choose K that minimizes the BIC value as the optimal number of shell layers: For each satellite i, assign it to the shell with the highest posterior probability: Calculate the actual physical parameter statistics for each shell layer, including the semi-major axis statistics: Eccentricity statistics: Let be the average semi-major axis of the k-th shell. Let be the standard deviation of the semi-major axis of the k-th shell. Let be the average eccentricity of the k-th shell layer. Let be the standard deviation of the eccentricity of the k-th shell. These are the two components of the mean vector of the k-th component. is the diagonal element of the covariance matrix of the k-th component.

[0048] Based on the above calculations, the final output includes a list of satellites in each shell layer and statistical data on their physical parameters. .

[0049] In one possible implementation, step S4 is based on a satellite orbital plane fine division method that uses ascending node right ascension value sorting, interval statistical analysis, dynamic threshold segmentation, and recursive verification to achieve fully automatic, high-precision, and highly adaptive orbital plane division.

[0050] 1) Ascending node right ascension data preprocessing and sorting. Obtain the ascending node right ascension values ​​Ω1, Ω2, …, Ω for all satellites within the same altitude shell. n Normalize each Ω value to the interval [0°, 360°) using the following formula: Sort the normalized values ​​in ascending order to obtain an ordered sequence: And establish a mapping relationship between the sorting index and the satellite identifier.

[0051] 2) Calculation of adjacent intervals and extraction of statistical features. The intervals between the right ascension values ​​of adjacent ascending nodes are calculated, including n-1 regular intervals and 1 first-to-last cyclic interval: Calculate the interval statistic: median Upper quartile Standard deviation .

[0052] 3) Determination of dynamic segmentation threshold and initial orbital plane segmentation. The dynamic segmentation threshold is calculated based on interval statistics: This is the median coefficient, with a value ranging from 1.5 to 2.5. The upper quartile coefficients range from 1.0 to 1.5. The minimum segmentation threshold is set based on the accuracy of the track design, with a value ranging from 3° to 8°. Traverse the ordered sequence. ,like Then, segmentation is performed at that position to obtain M initial orbital plane clusters. .

[0053] 4) Orbital plane consistency verification. For each initial cluster Calculate the range of right ascension of the ascending nodes within a cluster: Calculate the interval between all adjacent cluster centers and take the minimum value: like If both of the following conditions are met, then Mark as "Qualified" or otherwise mark as "Requires further subdivision".

[0054] in The absolute tolerance threshold is (3°–8°). The relative tolerance coefficient is (0.2–0.4).

[0055] 5) K-Mean step S-subdivision for clusters that do not meet the conditions. For clusters marked as "need subdivision". Determine the number of sub-clusters: in, The adjustment factor is (0.8–1.2), and `round` rounds to the nearest integer. satisfy .

[0056] Using the right ascension of the ascending nodes of satellites within a cluster as a feature, perform K-Mean step S-clustering to obtain individual clusters. Sub-clusters. Recursively perform the consistency verification in step 4) on each sub-cluster.

[0057] 6) Recursive verification and iterative optimization. For the subclusters generated by the subdivision, repeat steps 4) and 5) until any of the following termination conditions are met: All clusters passed consistency verification; The number of satellites in the cluster is less than the minimum threshold (usually 2–3). Reach the preset maximum recursion depth (usually 3–5 levels).

[0058] 7) Final orbital plane determination and output. Integrate all qualified clusters (including the initial qualified clusters and qualified subclusters after subdivision) to form the final orbital plane set; calculate the statistical characteristics of each orbital plane: mean right ascension of the ascending node, number of satellites, and standard deviation of right ascension of the ascending node; output the orbital plane subdivision result table.

[0059] Example 2 Please see Figure 2 This embodiment provides an automatic partitioning system for satellite constellation orbital planes, used to execute an automatic partitioning method for satellite constellation orbital planes as described in any of the preceding embodiments, including: Data parsing module: Obtains the orbital parameters of all satellites in the constellation, including at least the orbital inclination, right ascension of the ascending node, semi-major axis, and eccentricity; Normal vector clustering module: Calculates the unit normal vector of the orbital plane based on the orbital inclination and right ascension of the ascending node, and performs first-level clustering on the normal vectors of all satellites to divide at least one group of space orbital planes with different spatial orientations; Shell partitioning module: For each of the space orbital plane groups, a second-level clustering is performed using the semi-major axis and eccentricity of the satellites within the group as joint features to partition at least one orbital shell with different orbital energies. Orbital plane segmentation module: For each orbital shell, a third-level clustering is performed based on the right ascension of the ascending node of the satellites within the shell, and recursively subdivided in combination with the orbital plane consistency verification conditions, so as to finally segment at least one orbital plane. The output module is used to output the orbital plane division results.

[0060] I. Constellation Simulation Data Constellation size: 24 satellites, comprising two different orbital plane groups (with different inclinations), each orbital plane group containing a different altitude shell. The constellation simulation data is shown in Table 1.

[0061] Table 1. Constellation Simulation Data Table In terms of constellation design, orbital plane group A has an inclination of 55° and contains two altitude shells (6778km and 6878km); orbital plane group B has an inclination of 97.6° (polar orbit) and one altitude shell (6978km); each orbital plane has 4 satellites, and each shell contains 2 orbital planes with right ascension intervals of 30° or 180°.

[0062] II. Detailed Calculation Steps Step S1: Data preprocessing. The orbital parameters of all 24 satellites are parsed from the TLE (Time Limit Examined) and standardized to an equatorial time reference.

[0063] Step S2: Orbit Normal Vector Clustering (DBSCAN) 1. Calculate the unit normal vector of the orbital plane. Example calculation (Satellite 1: i=55°, Ω=0°): Check normalization: The normalization is correct.

[0064] 2. DBSCAN parameter settings. The distance metric uses spherical distance, with a neighborhood radius ε = 0.087 rad (≈5°), and a minimum sample size MinPts = 2 (minimum number of satellites per orbital plane). 3. DBSCAN clustering execution.

[0065] For example, calculate the normal vector, dot product of the normal vectors, and the included angle between satellites 1 and 5: The angle between satellites 1 and 5 indicates they are not in the same neighborhood. For example, calculating the angle between the normal vectors of satellites 1 and 2 shows that their Ω values ​​are the same, their normal vectors are the same, and the angle = 0° < ε, therefore satellites 1 and 2 are in the same neighborhood.

[0066] 4. Calculate the DBSCAN clustering results. After algorithm iteration, the following results are obtained: Cluster 1: Satellites 1-16 (normal vector at an inclination of 55°) Cluster 2: Satellites 17-24 (normal vector at an inclination of 97.6°) No noise point Cluster statistics calculation (taking cluster 1 as an example): Average normal vector: Calculate the average of the 16 normal vectors and then normalize them. Inverse calculation of average dip angle: Inverse calculation of mean right ascension: Step S3: Orbital shell partitioning (Gaussian mixture model). Taking cluster 1 (satellites 1-16) as an example: 1. Data extraction and standardization 1) Extract the semi-major axis a and eccentricity e. For satellites 1-8: a = 6778.0 km, e = 0.0010; for satellites 9-16: a = 6878.0 km, e = 0.0012.

[0067] 2) Calculate the statistic 3) Standardization (Satellite 1) 2. Construct the feature matrix 3. Gaussian mixture model fitting 1) Candidate K value: , .

[0068] 2) Fitting the GMM with K=2: Initializing parameters Random initialization , The EM iterations converged.

[0069] 3) BIC calculation. Assuming K=2, the model parameters are: Mixing coefficient: 1 free parameter (because) ) Mean vector: Parameters Covariance matrix: Each 2×2 symmetric matrix has 3 independent parameters, totaling... Total parameters: Using the BIC formula The calculation yields: Therefore, the optimal K is... 4. Shell division results: Shell 1 contains satellites 1-8 ( , Shell 2 contains satellites 9-16. , ) Step S4: RAAN fine-grained partitioning (taking shell 1 satellites 1-8 as an example) 1. RAAN data preprocessing. Ω value: [0, 0, 0, 0, 30, 30, 30, 30] (°); normalized sort: [0, 0, 0, 0, 30, 30, 30, 30].

[0070] 2. Calculation of adjacent intervals. Regular interval: ΔΩ1=0, ΔΩ2=0, ΔΩ3=0, ΔΩ4=30, ΔΩ5=0, ΔΩ6=0, ΔΩ7=0; Cyclic interval: ΔΩ8= (0+360) - 30 = 330°; Interval set: [0, 0, 0, 30, 0, 0, 0, 330].

[0071] 3. Statistical characteristics. Median Upper quartile Standard deviation 4. Determination of dynamic threshold Parameters: α=2.0, β=1.2, 5. Initial segmentation. Traverse the ordered sequence and segment at ΔΩ4=30>9 to obtain cluster C1: satellites 1-4 (Ω=0°) and cluster C2: satellites 5-8 (Ω=30°).

[0072] 6. Track plane conformity verification. Absolute tolerance threshold. Relative tolerance coefficient For cluster C1: Range Cluster center Interval between adjacent cluster centers Verification condition 1: Satisfies condition 2: The condition is met. Cluster C2 is similarly verified.

[0073] 7. Output the final orbital plane partitioning result for cluster 1.

[0074] Orbital plane 1: Satellites 1-4 (Ω=0°, i=55°, a=6778.0km) Orbital plane 2: Satellite 5-8 (Ω=30°, i=55°, a=6778.0km) 8. Other shell treatments for cluster 1. Shell 2 (satellites 9-16) is also divided into two orbital planes: orbital plane 3 contains satellites 9-12 (Ω=0°), and orbital plane 4 contains satellites 13-16 (Ω=30°).

[0075] III. Summary and Output of Final Division Results: The final division results of the orbital plane are shown in Table 2.

[0076] Table 2 Final Track Surface Division Results Figure 3 , Figure 4 , Figure 5 This paper demonstrates the visualization effect in STK software after dividing the orbital plane of a constellation at a 43° inclination using the method of this invention. The illustration clearly presents the satellite distribution and orbital plane division results, intuitively verifying the technical advantages of this invention in terms of high-precision division, strong adaptability, and good engineering applicability.

[0077] The above are only some embodiments of this application and do not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. An automatic division method for satellite constellation orbital planes, characterized in that, Includes the following steps: Step S1: Obtain the orbital parameters of all satellites in the constellation, including at least the orbital inclination, right ascension of the ascending node, semi-major axis, and eccentricity; Step S2: Calculate the unit normal vector of the orbital plane based on the orbital inclination and right ascension of the ascending node, and perform first-level clustering on the normal vectors of all satellites to divide at least one group of space orbital planes with different spatial orientations. Step S3: For each of the space orbital plane groups, a second-level clustering is performed using the semi-major axis and eccentricity of the satellites within the group as joint features to divide at least one orbital shell with different orbital energies. Step S4: For each orbital shell, perform third-level clustering based on the right ascension of the ascending node of the satellites within the shell, and recursively subdivide the data in conjunction with the orbital plane consistency verification conditions to finally divide at least one orbital plane.

2. The method according to claim 1, characterized in that, The formula for calculating the unit normal vector of the orbital plane in step S2 is: Where i is the orbital inclination and Ω is the right ascension of the ascending node.

3. The method according to claim 1, wherein, In step S2, the DBSCAN algorithm is used to perform the first-level clustering of the normal vectors, and the spherical distance formula is used as the distance metric. wherein denotes the dot product of two orbital plane unit normal vectors; (*) denotes the inverse cosine function, returning the radian value; denotes the angle between two orbital plane unit normal vectors.

4. The automatic division method for satellite constellation orbital planes according to claim 1, characterized in that, In step S3, a Gaussian mixture model is used to perform second-level clustering of the semi-major axis and eccentricity, and the optimal number of clusters is automatically determined by the Bayesian information criterion.

5. The automatic division method for satellite constellation orbital planes according to claim 4, characterized in that, The parameters of the Gaussian mixture model are iteratively optimized using the expectation-maximization algorithm until the change in the log-likelihood function is less than a preset threshold or the maximum number of iterations is reached.

6. The automatic division method for satellite constellation orbital planes according to claim 1, characterized in that, Step S4 performs third-level clustering and recursive subdivision through the following sub-steps: Step S41: Normalize and sort the right ascension of the ascending nodes of all satellites within the shell, and calculate the interval between adjacent values; Step S42: Calculate the dynamic segmentation threshold based on the median, upper quartile, and preset minimum threshold of the interval; Step S43: Perform initial segmentation of the ascending node right ascension sequence according to the dynamic segmentation threshold to obtain several initial orbital plane clusters; Step S44: Perform consistency verification on each initial orbital plane cluster. If the verification fails, proceed to K-Mean step S for further subdivision and recursive verification.

7. The automatic division method for satellite constellation orbital planes according to claim 6, characterized in that, The conditions for the consistency verification are as follows: and in, Let the right ascension range of the ascending node within the k-th cluster be denoted as . This is the absolute tolerance threshold. This is the relative tolerance coefficient. It represents the minimum interval between adjacent cluster centers.

8. The automatic division method for satellite constellation orbital planes according to claim 6, characterized in that, The formula for calculating the dynamic segmentation threshold is: in, The median of the interval. The upper quartile is the interval. and For preset coefficients, This is the minimum segmentation threshold.

9. The automatic division method for satellite constellation orbital planes according to claim 6, characterized in that, When subdividing an initial orbital plane cluster that does not meet the consistency verification conditions, the number of subdivided clusters is determined according to the following formula: in, To adjust the coefficients, round is used for rounding to the nearest integer. It is the minimum interval between adjacent cluster centers, and satisfy , This represents the number of satellites within the initial orbital plane cluster.

10. An automatic division system for satellite constellation orbital planes, characterized in that, A method for automatically dividing the orbital plane of a satellite constellation as described in any one of claims 1 to 9, comprising: Data parsing module: Obtains the orbital parameters of all satellites in the constellation, including at least the orbital inclination, right ascension of the ascending node, semi-major axis, and eccentricity; Normal vector clustering module: Calculates the unit normal vector of the orbital plane based on the orbital inclination and right ascension of the ascending node, and performs first-level clustering on the normal vectors of all satellites to divide at least one group of space orbital planes with different spatial orientations; Shell partitioning module: For each of the space orbital plane groups, a second-level clustering is performed using the semi-major axis and eccentricity of the satellites within the group as joint features to partition at least one orbital shell with different orbital energies. Orbital plane segmentation module: For each orbital shell, a third-level clustering is performed based on the right ascension of the ascending node of the satellites within the shell, and recursively subdivided in combination with the orbital plane consistency verification conditions, so as to finally segment at least one orbital plane. The output module is used to output the orbital plane division results.

Images