A method for calculating the topological stability of low-orbit satellite networks based on constellation configuration parameters

Abstract

This paper discloses a method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters. This method obtains basic constellation configuration parameters from a terrestrial user requesting the low-orbit satellite network. The method then calculates and evaluates the topological stability of the low-orbit satellite network based on three aspects: over-the-top time, remaining over-the-top time, and session stability time. Based on the calculation of cumulative distribution functions, probability density functions, and mathematical expectations, this method accurately characterizes the stability of the low-orbit satellite network topology and is more efficient than traditional statistical methods based on satellite trajectory simulation.

Description

Technical Field

[0001] The present invention relates to topological stability calculation and evaluation of a low-orbit satellite network, and belongs to the technical field of network communications. Background Art

[0002] Low-orbit satellites are located between 500 and 2,000 kilometers above the Earth. In recent years, low-orbit satellite networks have rapidly developed, with the emergence of constellations such as Starlink, OneWeb, Kuiper, and Iridium. While low-orbit altitudes and short orbital periods are advantageous, low-orbit satellites provide shorter coverage periods for specific terrestrial nodes, making these networks highly dynamic.

[0003] In the multi-layered, heterogeneous satellite internet, time-varying network topology, dynamic link quality, unstable satellite nodes, and massive amounts of high-dimensional data pose significant challenges to network operation and management. Artificial intelligence (AI) is considered an effective solution to these challenges, as it can learn from massive amounts of historical data and interactive feedback from the dynamic environment.

[0004] The satellite internet operation and management system collects various data from sensors, satellite tracking and control stations, operation and maintenance system logs, and business traffic data monitoring systems to perform applications such as resource management, business traffic management, and network status management. Its overall architecture refers to the "Intelligent Satellite Internet Operation and Management: Current Situation and Opportunities" published in "Integrated Space and Earth Information Network", Volume 2, Issue 2, December 2021. Figure 1 Content, author Tang Siqi et al.

[0005] As a satellite communication resource management and control system, the satellite network management system controls the satellite beams, channel resources, satellite power resources, earth station configuration resources, user frequency band resources, etc. of the entire network.

[0006] Satellite Internet needs to provide fair and stable services for user businesses, so the operation and maintenance and management systems need to manage business traffic, including predicting traffic trends and, based on congestion control protocols, intelligently sensing and preventing network congestion through traffic prediction and optimized scheduling.

[0007] At the same time, as a system operation status management system, satellite network management needs to ensure stable network operation, detect network attacks and network failures in a timely manner, evaluate network operation status, and optimize networking.

[0008] In recent years, numerous studies have used large-scale trajectory simulations to assess the topological stability of low-orbit satellite networks. However, trajectory simulations are not only computationally complex and time-consuming, but also difficult to extract analytical models and understand the underlying patterns. Therefore, this paper discloses a method for calculating the topological stability of low-orbit satellite networks. This method utilizes a small number of basic configuration parameters obtained from the low-orbit satellite network to calculate the statistical patterns of the over-the-top time, remaining over-the-top time, and session stability time. Summary of the Invention

[0009] The technical problem solved by the present invention is: how to efficiently calculate the topological stability of a low-orbit satellite network.

[0010] The purpose of the present invention is to provide a simple and efficient method for calculating the topological stability of a low-orbit satellite network; and to calculate the statistical laws of the over-the-top time, the remaining over-the-top time, and the session stability time, namely the cumulative distribution function, the probability density function, and the mathematical expectation, by obtaining the constellation configuration parameters from the low-orbit satellite network.

[0011] The present invention provides a method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters, characterized in that a low-orbit satellite network topological structure stability assessment module is provided between a state monitoring module and a measurement and control subsystem;

[0012] The topology stability assessment module first receives satellite information output by a satellite tracking and control station, wherein the satellite information includes orbit height, antenna pitch angle, number of orbits, and number of satellites on a single track;

[0013] The topology stability assessment module secondly receives the number of users in the session output by the service flow monitoring data module;

[0014] The topology stability assessment module thirdly outputs the satellite network topology stability performance parameters to the measurement and control subsystem;

[0015] The low-orbit satellite network topology structure stability assessment module includes a statistical law module for assessing over-the-top time, a statistical law module for assessing remaining over-the-top time, and a statistical law module for assessing session stability time;

[0016] The statistical law module for evaluating the time to top is used to calculate the cumulative distribution function of the time to top , the probability density function of the time to the top and expectations of overhead time ;

[0017] The statistical law module for evaluating the remaining time to pass the top is used to calculate the cumulative distribution function of the remaining time to pass the top , the probability density function of the remaining time to pass and expectations of remaining overhead time ;

[0018] The statistical law module for evaluating session stability time is used to calculate session stability time. Cumulative distribution function of , Session stability time Expectations .

[0019] The technical effects achieved by the technical solution of the present invention are:

[0020] ① The method for calculating the topological stability of a low-orbit satellite network of the present invention only uses the constellation configuration parameters of the low-orbit satellite network to calculate the statistical laws of the over-the-top time, the remaining over-the-top time, and the session stability time.

[0021] ② The method for calculating the topological stability of the low-orbit satellite network of the present invention does not require trajectory simulation like traditional methods, and can obtain the cumulative distribution function, probability density function, and mathematical expectation related to the topological stability, with good analytical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a diagram of the low-orbit satellite network architecture.

[0023] Figure 2 It is a structural block diagram of the low-orbit satellite network topology stability assessment of the present invention.

[0024] Figure 3 It is a flow chart of the method for calculating the topological stability of a low-orbit satellite network of the present invention.

[0025] Figure 4 This is a schematic diagram of the low-orbit satellite network topology during the example simulation.

[0026] Figure 5 This is the result of calculating the statistical laws of the Starlink constellation's transit time using MATLAB.

[0027] Figure 6 This is the result of calculating the statistical laws of the remaining overheight time of the Starlink constellation using MATLAB.

[0028] Figure 7 This is the calculation result of the statistical law of the stable time of Starlink constellation sessions performed by MATLAB. DETAILED DESCRIPTION

[0029] The present invention will be further described in detail below with reference to the accompanying drawings. The parameters listed are merely exemplary embodiments of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

[0030] See also Figure 2 As shown, the low-orbit satellite network topology structure stability assessment module designed by the present invention is set Figure 1 The topology stability assessment module, shown between the status monitoring module and the measurement and control subsystem, first receives satellite information output by the satellite measurement and control station, including orbital altitude, antenna pitch angle, number of orbits, and number of satellites on a single track. Secondly, it receives the number of users in a session output by the traffic monitoring data module. Thirdly, it outputs satellite network topology stability performance parameters to the measurement and control subsystem.

[0031] The low-orbit satellite network topology structure stability assessment module includes a statistical law module for assessing over-the-top time, a statistical law module for assessing remaining over-the-top time, and a statistical law module for assessing session stability time.

[0032] In the low-orbit satellite network topology, to represent the low-orbit satellite network; Indicates the orbital altitude of the low-orbit satellite network, in meters; Indicates the antenna elevation angle of the low-orbit satellite network, unit: radian. represents the number of terrestrial users who established sessions via the LEO satellite network; and Represents any land user.

[0033] In the statistical law module for evaluating the time of passing the top of the present invention, Represents a low-orbit satellite network A single satellite in the The time it takes to pass the top is in seconds. The cumulative distribution function of the time to the top is expressed as The probability density function of the time to the top is expressed as Indicates the expectation of overhead time.

[0034] In the statistical law module for evaluating the remaining overhead time of the present invention, Represents a low-orbit satellite network A single satellite targets any land user The remaining time of passing the top is in seconds. The cumulative distribution function of the remaining time to the top is expressed as The probability density function of the remaining over-the-top time is expressed as Indicates the expectation of remaining overhead time.

[0035] In the statistical law module for evaluating the session stability time of the present invention, Indicates land users When switching the satellite-to-ground link, the number of low-orbit satellites to be queried is in units of . express The stabilization time of a session established by a land user. Indicates session stability time The cumulative distribution function of Indicates the expected session stabilization time.

[0036] See also Figure 1 、 Figure 2 、 Figure 3 As shown, a method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters of the present invention includes the following steps:

[0037] Step 1: The user obtains the low-orbit satellite network parameters;

[0038] Step 101: The user accesses the low-orbit satellite network;

[0039] Land users Access to low-orbit satellite networks via satellite-to-ground links .

[0040] For the sake of convenience, Figure 4 Low-orbit satellite network structure as an example . The network is formed by the edges between satellite nodes.

[0041] Step 102: The user requests to obtain configuration parameters of the low-orbit satellite network;

[0042] Land users Request access to low-orbit satellite network constellation configuration parameters.

[0043] In the present invention, the constellation configuration parameters include the altitude of the orbit , satellite-to-ground link antenna elevation angle .

[0044] Step 2: Calculate auxiliary parameters;

[0045] Land users Using the obtained constellation configuration parameters, calculate the following auxiliary parameters.

[0046] Step 201, calculating the orbital period;

[0047] Land users Calculate the orbital period according to formula (1) (Unit: seconds).

[0048]

[0049] represents the orbital period.

[0050] is the radius of the Earth.

[0051] Indicates the orbital altitude of the low-orbit satellite network.

[0052] is the gravitational constant.

[0053] is the mass of the Earth.

[0054] In the present invention, Figure 4 In the network topology shown in is pi, is the radius of the Earth (in meters), is the gravitational constant (unit: ), is the mass of the Earth in kilograms.

[0055] Step 202, calculating the central angle;

[0056] Land users Calculate the central angle according to formula (2) (Unit: radians),

[0057]

[0058] Indicates the central angle.

[0059] Indicates the antenna elevation angle of the low-orbit satellite network.

[0060] In the present invention, is the radius of the Earth (unit: meter). According to formula (2), the central angle The value range is ,in .

[0061] Step 3: Calculate the statistical law of overhead time;

[0062] Land users Leveraging the acquired low-orbit satellite network Constellation configuration parameters and calculated auxiliary parameters are used to further calculate the low-orbit satellite network The statistical law of the overhead time.

[0063] Step 301, calculating the cumulative distribution function of the time to top;

[0064] Land users The cumulative distribution function of the time to pass through the top is calculated according to formula (3):

[0065]

[0066] Represents the cumulative distribution function of the time to the top.

[0067] use Represents a low-orbit satellite network A single satellite in the The time it takes to pass the top of the object, in seconds.

[0068] Indicates the maximum potential time of passing the top. Calculated, where is the orbital period calculated in step 2, is the central angle calculated in step 2.

[0069] Step 302, calculating the probability density function of the overhead time;

[0070] Land users The probability density function of the time to pass through the top is calculated according to formula (4):

[0071]

[0072] The probability density function of the time to the top.

[0073] use Represents a low-orbit satellite network A single satellite in the The time it takes to pass the top of the object, in seconds.

[0074] Step 303, calculating the expected time over the top;

[0075] Land users The expected time of passing the top is calculated according to formula (5):

[0076]

[0077] Indicates the expectation of overhead time.

[0078] use Represents a low-orbit satellite network A single satellite in the The time it takes to pass the top of the object, in seconds.

[0079] represents the orbital period.

[0080] Indicates the central angle.

[0081] Step 4: Calculate the statistical law of the remaining overhead time;

[0082] Land users Leveraging the acquired low-orbit satellite network Constellation configuration parameters and calculated auxiliary parameters, calculate low-orbit satellite network The statistical law of the remaining overhead time.

[0083] Step 401, calculating the cumulative distribution function of the remaining overhead time;

[0084] Land users The cumulative distribution function of the remaining over-the-top time is calculated according to formula (6):

[0085]

[0086] Represents the cumulative distribution function of the remaining time to the top.

[0087] use Represents a low-orbit satellite network A single satellite targets any land user The remaining time to fly over the top is in seconds.

[0088] Indicates the maximum potential overhead time.

[0089] Step 402, calculating the probability density function of the remaining overhead time;

[0090] Land users The probability density function of the remaining over-the-top time is calculated according to formula (7):

[0091]

[0092] The probability density function of the remaining time to the top

[0093] use Represents a low-orbit satellite network A single satellite targets any land user The remaining time to fly over the top is in seconds.

[0094] Step 403, calculating the expected remaining overhead time;

[0095] Land users The expected remaining overhead time is calculated according to formula (5):

[0096]

[0097] Indicates the expectation of remaining overhead time.

[0098] use Represents a low-orbit satellite network A single satellite targets any land user The remaining time to fly over the top is in seconds.

[0099] represents the orbital period.

[0100] Indicates the central angle.

[0101] Step 5: Calculate the statistical regularity of session stability time;

[0102] Land users Leveraging the acquired low-orbit satellite network Constellation configuration parameters and calculated auxiliary parameters are calculated in the low-orbit satellite network middle, The statistical regularity of session stability time of sessions established by each user.

[0103] Step 501, satellite-to-ground link switching strategy;

[0104] Here Among users, when any user When the satellite-to-ground link is disconnected due to orbital motion, the user will be in the low-orbit satellite network. Random query It then establishes a new satellite-to-ground link with a low-orbit satellite that can cover the user, and establishes a new satellite-to-ground link with the low-orbit satellite with the longest remaining overhead time, thereby completing the satellite-to-ground link switching.

[0105] Satellite-to-ground link switching will break this The stability of the session established by the land users is calculated below. The statistical regularity of the session stability time of sessions established by land users.

[0106] Step 502, calculating the cumulative distribution function of the session stability time;

[0107] Land users Calculate the session stability time according to formula (9) Cumulative distribution function of :

[0108]

[0109] Indicates session stability time The cumulative distribution function of .

[0110] Indicates the session stabilization time.

[0111] Indicates the number of terrestrial users establishing sessions via the LEO satellite network.

[0112] Indicates land users When switching the satellite-to-ground link, the number of low-orbit satellites that need to be queried, unit: pieces.

[0113] represents the cumulative distribution function of the remaining overhead time under the satellite-to-ground link switching strategy. The specific form is given in formula (6).

[0114] Step 503: Calculate the expected session stability time;

[0115] Land users Calculate the session stability time according to formula (10) Expectations:

[0116]

[0117] Indicates the expected session stabilization time.

[0118] yes about The derivative of .

[0119] represents the orbital period.

[0120] Indicates the central angle.

[0121] Indicates the coefficient. Given in Table 1:

[0122] Table 1

[0123]

[0124] Example 1

[0125] The performance of the evaluation method of the present invention is simulated using MATLAB simulation software, and the constellation used in the simulation experiment is the Starlink constellation. The network topology is as follows: Figure 4 shown.

[0126] Figure 5 The cumulative distribution function of the Starlink low-orbit satellite network's over-the-top time is presented, including results from traditional trajectory simulation methods and the method of the present invention. Comparison shows that the statistical regularity calculation method for the low-orbit satellite network's over-the-top time, disclosed in the present invention, matches the traditional trajectory simulation results. Furthermore, the method disclosed in the present invention requires only simple calculations based on formula (3) and does not require large-scale trajectory simulation. Therefore, the method disclosed in the present invention is both accurate and efficient.

[0127] Figure 6 The cumulative distribution function of the remaining time over the top of the Starlink low-orbit satellite network is presented, including the results of traditional trajectory simulation methods and the results of the method of the present invention. By comparison, it can be found that the statistical regularity calculation method of the remaining time over the top of the low-orbit satellite network disclosed in the present invention matches the traditional trajectory simulation results. Moreover, the method disclosed in the present invention only requires a simple calculation according to formula (6) and does not require large-scale trajectory simulation. Therefore, the method disclosed in the present invention is accurate and efficient.

[0128] Figure 7 The cumulative distribution function of the session stability time of the Starlink low-orbit satellite network is presented, including the results of a traditional trajectory simulation method and the results of the method of the present invention. A comparison shows that the statistical regularity calculation method for the session stability time of the low-orbit satellite network disclosed in the present invention matches the traditional trajectory simulation results. Furthermore, the method disclosed in the present invention only requires a simple calculation according to formula (9) and does not require large-scale trajectory simulation. Therefore, the method disclosed in the present invention is accurate and efficient.

Claims

1. A method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters, characterized by: A low-orbit satellite network topology stability assessment module is set between the status monitoring module and the measurement and control subsystem; the topology stability assessment module first receives satellite information output by the satellite measurement and control station, and the satellite information includes orbital altitude, antenna pitch angle, number of orbits, and number of single-orbit satellites; the topology stability assessment module secondly receives the number of users in the session output by the service traffic monitoring data module; the topology stability assessment module thirdly outputs satellite network topology stability performance parameters to the measurement and control subsystem; the low-orbit satellite network topology stability assessment module includes a statistical law module for evaluating over-the-top time, a statistical law module for evaluating remaining over-the-top time, and a statistical law module for evaluating session stability time; the statistical law module for evaluating over-the-top time is used to calculate the cumulative distribution function of the over-the-top time , the probability density function of the time to pass and expectations of overhead time ;use Represents a low-orbit satellite network A single satellite in the The time of passing the top is The cumulative distribution function of the time to the top is expressed as The probability density function of the time to the top is expressed as Indicates the expectation of the time of passing the top, Indicates the maximum potential time to pass the top, is the orbital period, is the central angle; the statistical law module for evaluating the remaining time to pass is used to calculate the cumulative distribution function of the remaining time to pass , the probability density function of the remaining time to pass and expectations of remaining overhead time ;use Represents a low-orbit satellite network A single satellite targets any land user The remaining time to pass the top is The cumulative distribution function of the remaining time to the top is expressed as The probability density function of the remaining over-the-top time is expressed as Indicates the expectation of the remaining overhead time; the statistical law module for evaluating the session stability time is used to calculate the session stability time Cumulative distribution function of , Session stability time Expectations ;use express The stabilization time of a session established by a land user, The number of terrestrial users who establish sessions through the low-orbit satellite network is represented by Indicates land users When switching the satellite-to-ground link, the number of low-orbit satellites needs to be queried. Indicates session stability time The cumulative distribution function of represents the expected session stability time, yes about The derivative of Represents the coefficient.

2. A method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters, characterized in that The process includes the following steps: Step 1: The user obtains the low-orbit satellite network parameters; Step 101: The user accesses the low-orbit satellite network; The terrestrial user Access to low-orbit satellite networks via satellite-to-ground links ; Step 102, the user requests to obtain the configuration parameters of the low-orbit satellite network; terrestrial user Request access to low-orbit satellite network constellation configuration parameters; Step 2: Calculate auxiliary parameters; Land users Using the acquired constellation configuration parameters, calculate the following auxiliary parameters; Step 201, calculate the orbital period; land user Calculate the orbital period according to formula (1) , unit: second; represents the orbital period; is the radius of the Earth; represents the orbital altitude of the low-orbit satellite network; is the gravitational constant; is the mass of the Earth; Step 202, calculate the central angle; Land users Calculate the central angle according to formula (2) , unit: radian, represents the central angle; Indicates the antenna elevation angle of the low-orbit satellite network; Step 3: Calculate the statistical law of the overhead time; Land users Leveraging the acquired low-orbit satellite network Constellation configuration parameters and calculated auxiliary parameters are used to further calculate the low-orbit satellite network Statistical law of the time of passing the top; Step 301, calculate the cumulative distribution function of the time of passing the top; Land users The cumulative distribution function of the time to pass through the top is calculated according to formula (3): represents the cumulative distribution function of the time to the top; Represents a low-orbit satellite network A single satellite in the The time it takes to pass the top, in seconds; represents the maximum potential time over the top; Calculation is obtained; Step 302, calculate the probability density function of the overhead time; Land users The probability density function of the time to pass through the top is calculated according to formula (4): represents the probability density function of the time of passing the top; Represents a low-orbit satellite network A single satellite in the The passing time of the image is in seconds; Step 302, calculating the expected passing time; Land users The expected time of passing the top is calculated according to formula (5): Express the expectation of the time of passing the top; Represents a low-orbit satellite network A single satellite in the The time it takes to pass the top, in seconds; represents the orbital period; Indicates the central angle; Step 4: Calculate the statistical law of the remaining overhead time; Land users Leveraging the acquired low-orbit satellite network Constellation configuration parameters and calculated auxiliary parameters, calculate low-orbit satellite network Statistical law of the remaining overhead time; Step 401, calculate the cumulative distribution function of the remaining overhead time; Land users The cumulative distribution function of the remaining over-the-top time is calculated according to formula (6): The cumulative distribution function of the remaining time to the top is expressed as Represents a low-orbit satellite network A single satellite targets any land user The remaining time of passing the top, unit: seconds; Indicates the maximum potential over-the-top time; Step 402, calculate the probability density function of the remaining over-the-top time; Land users The probability density function of the remaining over-the-top time is calculated according to formula (7): The probability density function of the remaining time to pass the top is expressed as Represents a low-orbit satellite network A single satellite targets any land user The remaining time of passing the top, unit: seconds; Step 402, calculate the expected remaining overhead time; land users The expected remaining overhead time is calculated according to formula (5): Indicates the expected remaining overhead time; Represents a low-orbit satellite network A single satellite targets any land user The remaining time of passing the top, unit: seconds; represents the orbital period; Represents the central angle; Step 5: Calculate the statistical law of session stability time; Land users Leveraging the acquired low-orbit satellite network Constellation configuration parameters and calculated auxiliary parameters are calculated in the low-orbit satellite network middle, Statistical law of session stability time of sessions established by users; Step 501, satellite-to-ground link switching strategy; Step 502, calculate the cumulative distribution function of session stability time; terrestrial users Calculate the session stability time according to formula (9) Cumulative distribution function of : Indicates session stability time The cumulative distribution function of Indicates the session stability time; represents the number of terrestrial users establishing sessions via the LEO satellite network; Indicates land users When switching the satellite-to-ground link, the number of low-orbit satellites that need to be queried, unit: pieces; represents the cumulative distribution function of the remaining overhead time under the satellite-to-ground link switching strategy; where the function The specific form is given in formula (6); Step 503, calculate the expected session stability time; land user Calculate the session stability time according to formula (10) Expectations: Indicates the expectation of session stability time; yes about The derivative of represents the orbital period; represents the central angle; Represents the coefficient.

3. The method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters according to claim 2, wherein: Configuration parameters include the altitude of the track , satellite-to-ground link antenna elevation angle .

4. The method for calculating the topological stability of a low-orbit satellite network based on constellation configuration parameters according to claim 1 or 2, characterized in that: coefficient Obtained by looking up the table.

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