An analytical evaluation method for average access delay of large-scale satellite constellation

Abstract

The application discloses an analytical evaluation method for average access delay of a large-scale satellite constellation, and aims at solving the technical problem that traditional dynamic simulation is difficult to be used for iterative optimization due to large calculation amount. The steps of the application comprise the following steps: a probability density function of satellite latitude distribution is established to describe non-uniform characteristics; a non-uniform satellite distribution in the world is discretized into K latitude partitions; the satellite distribution is approximated as a homogeneous Poisson point process in the partition, and the density thereof is calculated; then, geometric boundary parameters are derived analytically; finally, the integral solving method based on a cavity probability theory is used to obtain the delay of each partition, and the global delay is obtained by weighted average, so that the fast analytical evaluation of the average access delay of the large-scale satellite constellation is realized.

Description

Technical Field

[0001] This invention belongs to the field of satellite network technology, specifically relating to a performance evaluation technology for large-scale satellite constellations, and in particular a method for quickly and analytically calculating the average access latency of a constellation. Background Technology

[0002] In recent years, large-scale Low Earth Orbit (LEO) satellite internet constellations, represented by Starlink, GuoWang, and OneWeb, have been rapidly deployed globally. These constellations consist of thousands or even tens of thousands of satellites and aim to provide high-speed, low-latency internet access services worldwide. A core challenge in the design and optimization of these large-scale satellite constellations is how to quickly and accurately evaluate different constellation design options (e.g., different total numbers of satellites). Track height Track inclination The performance of a network is measured by its average access latency, which is the signal propagation time from a ground user to the nearest visible satellite. This is a key indicator for measuring network service quality (QoS) and user experience.

[0003] Traditional performance evaluation methods heavily rely on full-cycle dynamic simulations based on orbital mechanics. However, when constellations reach thousands or more satellites, the computational complexity of these simulations becomes extremely high, and evaluating a complete constellation design can take hours or even days. This inefficiency prevents the method from being used in modern optimization algorithms requiring massive iterations (such as genetic algorithms), severely limiting the constellation design and optimization capabilities for large-scale satellite internet. Therefore, there is an urgent need in this field for a computationally efficient and accurate analytical evaluation model to replace time-consuming dynamic simulations and enable rapid design and iterative optimization of large-scale satellite constellations. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing dynamic simulation methods in terms of low computational efficiency, and to provide an evaluation method based on stochastic geometry that can quickly and analytically calculate the average access delay of large-scale satellite constellations.

[0005] The technical solution of this invention is: an analytical evaluation method for the average access delay of a large-scale satellite constellation, implemented through the following steps:

[0006] S1. Parameter Definition and Probabilistic Modeling: Obtain the core parameters of the constellation to be evaluated, including the total number of satellites. Track height Track inclination and the cutoff altitude angle for ground users Based on orbital inclination Establish satellite nadir latitude probability density function This function forms the theoretical basis for subsequent calculations of non-uniform density, and its expression is:

[0007] ,

[0008] S2. Spatial Discretization and Density Calculation: Establish a stochastic geometric model based on latitudinal partitioning to discretize the non-uniform global satellite distribution into K latitudinal partitions. The k-th partition corresponds to the latitude interval Through the Perform numerical integration over the aforementioned interval to calculate the probability that a satellite will fall into that region. :

[0009] ,

[0010] Subsequently, within each partition, the satellite distribution is approximated as a homogeneous Poisson point process (HPPP), and its spatial density is calculated. :

[0011] ,

[0012] in , For the Earth's radius, The radius of the orbital spherical shell;

[0013] S3. Geometric Boundary Parameter Calculation: Based on Earth geometry and user elevation angle constraints, the key boundary conditions required for evaluating latency are analytically derived, including the farthest distance at which the user can access the network. and the area function of the search region on the orbital spherical shell. :

[0014] ,

[0015] Where d is the straight-line distance between the ground user and the satellite;

[0016] S4. Calculation of Average Delay by Partition: Using the hole probability theory of HPPP, a system is established regarding the access distance. The integral of this integral, the solution of which is the average access distance for each partition. Therefore, based on the speed of light Calculate the average access latency:

[0017] ,

[0018] S5, Global Performance Weighted Aggregation: Finally, calculate the surface area of ​​each partition. :

[0019] ,

[0020] Based on the Earth's surface area of ​​each region As a weight, the latency of all partitions A weighted average is then performed to obtain the final global average access latency. :

[0021] .

[0022] In a preferred embodiment of the present invention, in S3, the farthest distance that the user can access is... The following formula is used to calculate the maximum geocentric angle. :

[0023] ,

[0024] Subsequently, the maximum access distance was calculated using the law of cosines. :

[0025] .

[0026] In another preferred embodiment of the present invention, in S4, the average access distance of each partition is... The analytical calculation formula is based on the random variable Expectations The derivation shows that, Represents the nearest neighbor access distance; By its survival function exist By integrating, we can obtain the integral by splitting it into... , and Three segments, utilizing the hole probability characteristics of HPPP. The final analytical form of the integral is derived as follows:

[0027] ,

[0028] This integral can be solved quickly using numerical integration.

[0029] The beneficial effects of this invention are as follows:

[0030] 1. Computational Efficiency: This invention transforms the time-domain dynamic simulation problem into a static numerical integration problem. The computational speed is tens of thousands of times faster than traditional simulations, enabling evaluation to be completed in an extremely short time.

[0031] 2. Feasibility of optimization: The high efficiency of this invention allows it to be directly embedded into iterative optimization frameworks such as genetic algorithms and particle swarm optimization as a fitness function, solving the major problem of automatic optimization in large-scale satellite constellation design due to simulation performance bottlenecks.

[0032] 3. Theoretical Insight: This invention provides a clear analytical model that can explicitly reveal the core parameters of constellations. Access latency The inherent mathematical relationship between them provides theoretical guidance for constellation design. Attached Figure Description

[0033] Figure 1 This is a flowchart of the evaluation method of the present invention. Detailed Implementation

[0034] The following is in conjunction with the appendix Figure 1 The invention is further illustrated by specific embodiments. Embodiment: Evaluation of a large-scale satellite constellation consisting of 1000 satellites at its orbital altitude... track inclination Cut-off altitude angle for ground users .

[0035] (1) Parameter definition and probabilistic modeling: Obtaining input parameters: , , , Set physical constants: , , Calculate the latitude of the satellite's nadir point. probability density function :

[0036] .

[0037] (2) Spatial discretization and density calculation: The latitude range, with Divide the space into 10 partitions, spaced out. For each partition... The probability of a satellite falling into this zone is calculated using numerical integration. :

[0038] ;

[0039] Because the Northern and Southern Hemispheres are symmetrical, only the results for the Southern Hemisphere are listed:

[0040] .

[0041] Then calculate its spatial density. :

[0042] .

[0043] The corresponding results are:

[0044] .

[0045] (3) Calculation of geometric boundary parameters: Calculate the maximum geocentric angle based on the parameters determined in (1). :

[0046] ;

[0047] The result is: Subsequently, the maximum access distance was calculated using the law of cosines. :

[0048] ;

[0049] The result is: km. Simultaneously, the area function of the search region on the orbital spherical shell is obtained. :

[0050] .

[0051] (4) Calculation of average latency per partition: For each partition The average access distance for each partition is calculated through numerical integration. :

[0052] ;

[0053] The corresponding results are:

[0054] .

[0055] Calculated Then, the average delay can be calculated. :

[0056] .

[0057] The corresponding results are:

[0058] .

[0059] (5) Global performance weighted aggregation: After obtaining 10 partitions Then, calculate the surface area corresponding to each zone. :

[0060] ;

[0061] The corresponding results are:

[0062] .

[0063] Finally, the global average access latency of this constellation was obtained through weighted averaging. :

[0064] .

[0065] The result is: Global average access latency This embodiment verifies the effectiveness of the method proposed in this invention. Compared to traditional simulations that take hours or even longer, this method can calculate the average user access latency for large-scale satellite constellations in seconds using programming scripts. This improvement in computational efficiency can accelerate the design and optimization process of large-scale satellite constellations.

Claims

1. An analytical evaluation method for average access latency in large-scale satellite internet, characterized in that, Includes the following steps: S1. Parameter Definition and Probabilistic Modeling: Obtain the core parameters of the constellation to be evaluated, including the total number of satellites. Track height Track inclination and the cutoff altitude angle for ground users Based on orbital inclination Establish satellite nadir latitude probability density function Its expression is: ， S2. Spatial Discretization and Density Calculation: Establish a stochastic geometric model based on latitudinal partitioning to discretize the non-uniform global satellite distribution into K latitudinal partitions. The k-th partition corresponds to the latitude interval By analyzing the latitude of the satellite's nadir point probability density function Perform numerical integration over the aforementioned interval to calculate the probability that a satellite will fall into that region. : ， Subsequently, within each partition, the satellite distribution is approximated as a homogeneous Poisson point process HPPP, and its spatial density is calculated. : ， in , For the Earth's radius, The radius of the orbital spherical shell; S3. Geometric Boundary Parameter Calculation: Based on Earth geometry and user elevation angle constraints, the key boundary conditions required for evaluating latency are analytically derived, including the farthest distance at which the user can access the network. and the area function of the search region on the orbital spherical shell. : ， Where d is the straight-line distance between the ground user and the satellite; S4. Calculation of Average Delay by Partition: Using the hole probability theory of HPPP, a system is established regarding the access distance. The integral of this integral, the solution of which is the average access distance for each partition. Therefore, based on the speed of light Calculate the average access latency : ， S5, Global Performance Weighted Aggregation: Finally, calculate the surface area of ​​each partition. : ， Based on the Earth's surface area of ​​each region As a weight, the average access latency of all partitions A weighted average is then performed to obtain the final global average access latency. : 。 2. The method according to claim 1, characterized in that, The furthest distance that the user can access, as described in step S3. The calculation method is as follows: First, calculate the maximum geocentric angle. : ， Subsequently, the maximum access distance was calculated using the law of cosines. : 。 3. The method according to claim 1, characterized in that, Step S4 describes the average access distance for each partition. The analytical calculation formula is based on the random variable Expectations The derivation shows that, Represents the nearest neighbor access distance; By its survival function exist By integrating, we can obtain the integral by splitting it into... , and Three segments, utilizing the hole probability characteristics of HPPP. The final analytical form of the integral is derived as follows: ， This integral can be solved quickly using numerical integration.

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