A method and system for analyzing the coverage characteristics of visible low-orbit satellites considering spherical distribution characteristics

Abstract

The present invention discloses a method and system for analyzing the coverage characteristics of visible low-orbit satellites taking into account the spherical distribution characteristics. The method comprises: establishing a first probability distribution model of the visible satellite orbital surface based on the spherical distribution characteristics of the visible low-orbit satellites; establishing a second probability distribution model of the geocentric angle corresponding to the sub-satellite point of the low-orbit satellite based on the first probability distribution model; obtaining the probability distribution function of the geocentric angle random variable based on the second probability distribution model; calculating the average coverage time of the satellites in the low-orbit constellation to the ground terminal based on the probability distribution function; calculating the visible satellite change frequency based on the average coverage time; the visible satellite change frequency is used to analyze the coverage characteristics of the visible low-orbit satellites. The present invention fully considers the spherical distribution characteristics of the low-orbit satellite constellation, and effectively reduces the computational complexity compared to the traditional orbit simulation method.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite coverage analysis, and in particular relates to a visible low-orbit satellite coverage characteristic analysis method and a system thereof taking into account spherical distribution characteristics. Background Art

[0002] In recent years, many companies and institutions such as SpaceX and Eutelsat have begun to plan and build low-orbit constellations. The number of low-orbit satellites has increased dramatically, and there are currently more than 5,000 low-orbit satellites in orbit. Compared with medium- and high-orbit satellites, low-orbit satellites have the characteristics of short orbital period, fast operation speed, small coverage of a single satellite, and high satellite density in the constellation. Relative to ground observers, these characteristics lead to frequent changes in the number of visible satellites and rapid evolution of the geometric structure of the low-orbit constellation, which is closely related to the positioning performance of low-orbit satellites.

[0003] However, traditional satellite constellation coverage analysis usually assumes that satellites are distributed in many different circular orbits, and complex system-level simulations are required to evaluate coverage performance and satellite visibility. In addition, with the construction of giant constellations, the satellite de-orbit rate has soared. Taking Starlink as an example, the de-orbit rate of the Starlink Phase I constellation in 2022 was as high as about 9%. The high de-orbit rate will cause the constellation configuration to gradually deviate from the designed walker configuration, showing a certain degree of randomness. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a visible low-orbit satellite coverage characteristics analysis method and system taking into account the spherical distribution characteristics, so as to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above object, the present invention provides a method for analyzing the coverage characteristics of visible low-orbit satellites taking into account the spherical distribution characteristics, comprising:

[0006] Based on the spherical distribution characteristics of visible low-orbit satellites, a first probability distribution model of the visible satellite orbit surface is established; based on the first probability distribution model, a second probability distribution model of the geocentric angle corresponding to the sub-satellite point of the low-orbit satellite is established;

[0007] Based on the second probability distribution model, a probability distribution function of the geocentric angle random variable is obtained;

[0008] Based on the probability distribution function, the average coverage time of the satellites in the low-orbit constellation to the ground terminal is calculated;

[0009] Based on the average coverage duration, a visible satellite change frequency is calculated; the visible satellite change frequency is used to analyze the coverage characteristics of visible low-orbit satellites.

[0010] Preferably, the spherical distribution characteristic is that the positions of visible low-orbit satellites on the orbital ellipsoid surface meet the requirements of periodicity, infinity and equal probability, wherein the visible low-orbit satellites are evenly distributed on the orbital ellipsoid surface with the center of the earth as the center.

[0011] Preferably, the probability distribution function is:

[0012]

[0013] Among them, γ(t 0 ) is the geocentric angle corresponding to surface A, i.e., the geocentric angle random variable, t 0 is the moment when the satellite has the maximum elevation angle relative to the ground station during its motion, γ max is the geocentric angle corresponding to surface B.

[0014] Preferably, the process of calculating the average coverage time of the satellites in the low-orbit constellation to the ground terminal includes:

[0015] Based on the geometric parameters of the target walker constellation, calculate the maximum geocentric angle from the ground terminal to the sub-satellite point;

[0016] Based on the satellite angular velocity and the earth angular velocity in the ECI coordinate system, the satellite angular velocity in the ECEF coordinate system is calculated;

[0017] The maximum geocentric angle and the satellite angular velocity are substituted into a calculation formula for the average coverage time of the satellite to the ground terminal to calculate the average coverage time of the satellite to the ground terminal.

[0018] Preferably, the formula for calculating the maximum geocentric angle from the ground terminal to the sub-satellite point is:

[0019]

[0020] Where h is the orbital height, θ min is the minimum elevation angle under which the satellite can be observed, R e is the earth radius parameter.

[0021] Preferably, the formula for calculating the satellite angular velocity in the ECEF coordinate system is:

[0022] ω=ω s -ω e cosi o

[0023] Among them, ω s ,ω e are the angular velocities of the satellite and the earth in the ECI coordinate system, i o is the orbital inclination, and ω is the satellite angular velocity in the ECEF coordinate system.

[0024] Preferably, the derivation process of the calculation formula of the average coverage time of the satellite to the ground terminal includes:

[0025] Covering time t c The distribution function of is:

[0026]

[0027] The probability density function of the coverage time is obtained by derivation:

[0028]

[0029] The expected coverage time probability density function is obtained to obtain the average coverage time of the satellite to the ground terminal.

[0030]

[0031] Among them, R is the ground terminal, γ(t 0 ) 0 is the moment when the satellite has the maximum elevation angle relative to the ground station during its motion, γ max is the maximum geocentric angle from the ground terminal to the sub-satellite point, t c is the coverage time, and ω is the satellite angular velocity in the ECEF coordinate system.

[0032] Preferably, the formula for calculating the visible satellite change frequency is:

[0033]

[0034] Where m is the average number of visible satellites, E(t c ) is the average coverage time of visible satellites, and k is determined according to the actual situation.

[0035] In order to achieve the above technical objectives, the present invention also provides a visible low-orbit satellite coverage characteristics analysis system considering spherical distribution characteristics, which is used to implement the visible low-orbit satellite coverage characteristics analysis method considering spherical distribution characteristics, and the system includes:

[0036] A model building module is used to establish a first probability distribution model of the visible satellite orbit surface based on the spherical distribution characteristics of the visible low-orbit satellites; based on the first probability distribution model, establish a second probability distribution model of the geocentric angle corresponding to the sub-satellite point of the low-orbit satellite;

[0037] A function determination module, used for obtaining a probability distribution function of a geocentric angle random variable based on the second probability distribution model;

[0038] A first calculation module is used to calculate the average coverage time of the satellites in the low-orbit constellation to the ground terminal based on the probability distribution function;

[0039] The second calculation module is used to calculate the visible satellite change frequency based on the average coverage duration; the visible satellite change frequency is used to analyze the coverage characteristics of visible low-orbit satellites.

[0040] In addition, the present invention also provides a computer storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method for analyzing the coverage characteristics of visible low-orbit satellites taking into account spherical distribution characteristics is implemented.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] The present invention provides a method for analyzing the coverage characteristics of visible low-orbit satellites taking into account spherical distribution characteristics, comprising: establishing a first probability distribution model of the visible satellite orbital surface based on the spherical distribution characteristics of the visible low-orbit satellites; establishing a second probability distribution model of the geocentric angle corresponding to the sub-satellite point of the low-orbit satellite based on the first probability distribution model; obtaining a probability distribution function of a geocentric angle random variable based on the second probability distribution model; calculating the average coverage time of satellites in a low-orbit constellation to a ground terminal based on the probability distribution function; calculating the visible satellite change frequency based on the average coverage time; the visible satellite change frequency is used to analyze the coverage characteristics of the visible low-orbit satellites.

[0043] Based on the satellite coverage characteristics modeling method using stochastic geometry (SG), the present invention fully considers the spherical distribution characteristics of the low-orbit satellite constellation, uses the probability distribution model to derive the probability distribution function of the satellite corresponding to the geocentric angle, and obtains the analytical expression for calculating the average coverage time of the satellite and the estimation model for the change frequency of visible satellites. Compared with the traditional orbit simulation method, the computational complexity is effectively reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0045] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0046] Figure 2 A geometric relationship diagram between a ground station and a low-orbit satellite according to an embodiment of the present invention;

[0047] Figure 3 This is a geometric relationship diagram of the walker constellation coverage of an embodiment of the present invention;

[0048] Figure 4The Walker 600 / 60 / 10 constellation diagram of the embodiment of the present invention;

[0049] Figure 5 This is a constellation diagram of Walker 300 / 60 / 5 according to an embodiment of the present invention;

[0050] Figure 6 This is a schematic diagram of a LEO constellation coverage characteristic simulation experiment 1 according to an embodiment of the present invention;

[0051] Figure 7 Schematic diagram of LEO constellation coverage characteristic simulation experiment 2 according to an embodiment of the present invention;

[0052] Figure 8 It is a schematic diagram of a simulation experiment 3 of LEO constellation coverage characteristics according to an embodiment of the present invention;

[0053] Fig. 9 A schematic diagram of a LEO constellation coverage characteristic simulation experiment 4 according to an embodiment of the present invention;

[0054] Fig.10 is a simulation result of the frequency of change of the number of visible satellites according to an embodiment of the present invention;

[0055] Fig.11 This is the calculation result of the visible satellite number change frequency model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0057] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0058] Embodiment 1

[0059] like Figure 1 As shown, this embodiment provides a method for analyzing the coverage characteristics of visible low-orbit satellites taking into account the spherical distribution characteristics, including:

[0060] S1. Based on the spherical distribution characteristics of visible low-orbit satellites, a first probability distribution model of the visible satellite orbit surface is established; based on the first probability distribution model, a second probability distribution model of the geocentric angle corresponding to the sub-satellite point of the low-orbit satellite is established;

[0061] Specifically, this step can obtain the following formula based on the triangle OPS and the spherical right triangle PMN:

[0062] cosγ(t)=cosψ(t)cosγ(t 0 ) (1)

[0063]

[0064] Considering that the satellite orbit is relative to t 0 The symmetry of time can be used to obtain the coverage time t of a single satellite to the ground terminal. c .

[0065]

[0066] Figure 2 is a geometrical diagram of the present invention, wherein R is the ground terminal, O is the center of the earth; γ(t 0 ) 0 The maximum elevation angle is the moment when the satellite reaches the maximum elevation angle relative to the ground station during its motion. The maximum elevation angle is θ max ;t 0 The satellite position and sub-satellite point at time t are S and M respectively; the satellite position and sub-satellite point at time t are S′ and N. γ(t) is the corresponding geocentric angle between points P and N; γ(t 0 ) is the geocentric angle between P and M; ψ(t) is the geocentric angle corresponding to the sub-satellite point trajectory MN. e and h are the radius of the earth and the altitude of the satellite orbit respectively; θ(t) is the elevation angle of the satellite relative to the ground terminal at time t. In addition, θ min is the minimum elevation angle under which the satellite can be observed, which corresponds to the maximum geocentric angle γ from the ground terminal to the sub-satellite point max ;ω=ω s -ω e cos i o ,ω s ,ω e are the angular velocities of the satellite and the earth in the ECI coordinate system, i o is the orbital inclination, ω is the satellite angular velocity in the ECEF coordinate system. When t c With maximum value T max .

[0067] T max =max(t c )=2γ max / ω (4)

[0068] Assuming that the positions of satellites on the orbital plane satisfy infinity and equal probability, the constraints of the spherical distribution characteristics of low-orbit satellites are added, and a probability distribution model is used to describe the corresponding geocentric angle γ(t 0 )’s probability distribution.

[0069] S2. Based on the second probability distribution model, obtain a probability distribution function of the geocentric angle random variable;

[0070] Specifically, the orbital surface of the constellation is approximately considered to be a sphere with a radius of R e +h,R e is the radius of the Earth and h is the orbital altitude. Figure 2 This is a geometric diagram of this scene. Surface A and surface B are two spherical caps on the orbital sphere. The geocentric angle corresponding to surface B is γ max , the geocentric angle corresponding to the surface A is the geocentric angle random variable γ(t 0 ). The surface areas of A and B are

[0071]

[0072] According to the second probability distribution model, the geocentric angle random variable γ(t 0 ) is calculated by the probability distribution function

[0073]

[0074] S3. Based on the probability distribution function, calculate the average coverage time of the satellites in the low-orbit constellation to the ground terminal;

[0075] Specifically, the walker constellation covers a geometric relationship diagram, such as Figure 3 As shown, according to the geocentric angle random variable γ(t 0 ) probability distribution function; the maximum satellite transit time T max The calculation formula of single satellite coverage time t for ground terminals c The calculation formula of . The coverage time t can be obtained c The distribution function of

[0076]

[0077] The probability density function of the coverage time is obtained by derivation:

[0078]

[0079] By finding the expectation of the coverage time probability density function, the calculation formula for the average coverage time of the satellite to the ground terminal can be obtained as follows:

[0080]

[0081] As a more preferred implementation, this step specifically includes:

[0082] Step 3.1: Get the orbital height h of the target walker constellation and the minimum elevation angle θ when the satellite can be observedmin , and the Earth radius parameter R e According to the formula

[0083]

[0084] Calculate the maximum geocentric angle γ from the ground terminal to the sub-satellite point max .

[0085] Step 3.2: The formula for calculating the satellite angular velocity ω in the ECEF coordinate system is:

[0086] ω=ω s -ω e cosi o (12)

[0087] Among them, ω s ,ω e are the angular velocities of the satellite and the earth in the ECI coordinate system, respectively. Substituting the two calculation formulas (12) and (11) into formula (10), the average coverage time can be obtained.

[0088] S4. Based on the average coverage duration, a visible satellite change frequency is calculated; the visible satellite change frequency is used to analyze the coverage characteristics of visible low-orbit satellites.

[0089] Specifically, according to the visible satellite orbit surface probability distribution model, the visible satellite change frequency can be estimated by the following formula.

[0090]

[0091] Where m is the average number of visible satellites, E(t c ) is the average coverage time of visible satellites, and k is determined according to the actual situation. Generally, the lower the output frequency of observations and the more visible satellites there are, the smaller the k value is and it is between 1 and 2.

[0092] The experimental scenario is built using the satellite communication toolbox (SCT). SCT is a MATLAB toolbox that provides a series of standardized tools that can be used to simulate and visualize satellite orbits and perform link analysis and access calculations.

[0093] Figure 4 and Figure 5 These are two typical application scenarios of the present invention. Further, for Figure 1 The satellite average coverage duration model and the experimental scenario are shown in Table 1.

[0094] Table 1

[0095]

[0096] Figure 6-9 It is the result of the satellite average coverage time model verification experiment. Their horizontal coordinates are the minimum observation elevation angle, constellation orbit inclination, orbit height, and number of constellation satellites, and the vertical coordinate is the satellite average coverage time. It can be seen from the experimental results that the average coverage time calculation formula of the present invention has a higher degree of fit than the calculation formula derived by treating the geocentric angle random variable as a uniform distribution. The average error of the comparison model calculation result is 22.03%; the average error of the calculation result of the present invention is 5.23%, and the error is reduced by 76.27%.

[0097] in addition, Figure 1 The verification experiment scenario of the visible satellite number change characteristic model is shown in Table 2

[0098] Table 2

[0099]

[0100] Fig.10 and Fig.11 They are respectively the simulation experiment results of the frequency of changes in the number of visible satellites and the calculation results of the model of the frequency of changes in the number of visible satellites. The frequency of changes in the number of visible satellites is highest in the latitude range of [30°, 40°] and [-30°, -40°]. When the sampling interval is 1s, the proportion of moments with changes in the number of satellites is distributed between 10% and 60%, that is, within 10s, there will be 1 to 6 seconds in which the number of visible satellites has changed compared to the previous moment. And in the latitude band where the number of visible satellites is clearly stratified, the frequency of changes in the number of visible satellites will increase. Figure 8 In the calculation of the visible satellite change frequency of the present invention, because multiple satellites may be added or subtracted within a second, in order to make the calculation result closer to the true value, the value of the correction factor K needs to be more biased towards 1. When the K value is 1.32 in the calculation, the average error of the calculation result is 0.077.

[0101] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for analyzing the coverage characteristics of visible low-orbit satellites considering spherical distribution characteristics, characterized in that: The following steps are involved: Based on the spherical distribution characteristics of visible low-orbit satellites, a first probability distribution model of the visible satellite orbit surface is established; based on the first probability distribution model, a second probability distribution model of the geocentric angle corresponding to the sub-satellite point of the low-orbit satellite is established; Based on the second probability distribution model, a probability distribution function of the geocentric angle random variable is obtained; Based on the probability distribution function, the average coverage time of the satellites in the low-orbit constellation to the ground terminal is calculated; Based on the average coverage duration, a visible satellite change frequency is calculated; the visible satellite change frequency is used to analyze the coverage characteristics of visible low-orbit satellites; The spherical distribution characteristic is that the positions of visible low-orbit satellites on the orbital ellipsoid surface meet the requirements of periodicity, infinity and equal probability, wherein the visible low-orbit satellites are evenly distributed on the orbital ellipsoid surface with the center of the earth as the circle center; The probability distribution function is: Among them, γ(t0) is the geocentric angle corresponding to the A surface, that is, the geocentric angle random variable, t0 is the moment when the satellite has the maximum elevation angle relative to the ground station during its motion, and γ max is the geocentric angle corresponding to surface B; The process of calculating the average coverage time of satellites in the low-orbit constellation to ground terminals includes: Based on the geometric parameters of the target walker constellation, calculate the maximum geocentric angle from the ground terminal to the sub-satellite point; Based on the satellite angular velocity and the earth angular velocity in the ECI coordinate system, the satellite angular velocity in the ECEF coordinate system is calculated; The maximum geocentric angle and the satellite angular velocity are substituted into a calculation formula for the average coverage time of the satellite to the ground terminal to calculate the average coverage time of the satellite to the ground terminal.

2. The method for analyzing the coverage characteristics of visible low-orbit satellites considering spherical distribution characteristics according to claim 1, characterized in that: The formula for calculating the maximum geocentric angle from the ground terminal to the sub-satellite point is: Where h is the orbital height, θ min is the minimum elevation angle under which the satellite can be observed, R e is the earth radius parameter.

3. The method for analyzing the coverage characteristics of visible low-orbit satellites considering spherical distribution characteristics according to claim 1, characterized in that: The formula for calculating the satellite angular velocity in the ECEF coordinate system is: oh = oh s -oh e cos i o Among them, ω s ,ω e are the angular velocities of the satellite and the earth in the ECI coordinate system, i o is the orbital inclination, and ω is the satellite angular velocity in the ECEF coordinate system.

4. The method for analyzing the coverage characteristics of visible low-orbit satellites considering spherical distribution characteristics according to claim 1, characterized in that: The derivation process of the calculation formula of the average coverage time of the satellite to the ground terminal includes: Covering time t c The distribution function of is: The probability density function of the coverage time is obtained by derivation: The expected coverage time probability density function is obtained to obtain the average coverage time of the satellite to the ground terminal. Where R is the ground terminal, t0 in γ(t0) is the moment when the satellite has the maximum elevation angle relative to the ground station during its motion, and γ max is the maximum geocentric angle from the ground terminal to the sub-satellite point, t c is the coverage time, and ω is the satellite angular velocity in the ECEF coordinate system.

5. The method for analyzing the coverage characteristics of visible low-orbit satellites considering spherical distribution characteristics according to claim 1, characterized in that: The formula for calculating the frequency of visible satellite changes is: Where m is the average number of visible satellites, E(t c ) is the average coverage time of visible satellites, and k is determined according to the actual situation.

6. A visible low-orbit satellite coverage characteristic analysis system considering spherical distribution characteristics, characterized in that: A method for analyzing the coverage characteristics of visible low-orbit satellites taking into account spherical distribution characteristics according to any one of claims 1 to 5, the system comprising: A model building module is used to establish a first probability distribution model of the visible satellite orbital surface based on the spherical distribution characteristics of the visible low-orbit satellites; based on the first probability distribution model, a second probability distribution model of the low-orbit satellite sub-satellite point corresponding to the geocentric angle is established; the spherical distribution characteristics are that the positions of the visible low-orbit satellites on the orbital ellipsoid surface meet the requirements of periodicity, infinity and equal probability, wherein the visible low-orbit satellites are evenly distributed on the orbital ellipsoid surface with the center of the earth as the circle center; A function determination module, used for obtaining a probability distribution function of a geocentric angle random variable based on the second probability distribution model; The probability distribution function is: Among them, γ(t0) is the geocentric angle corresponding to the A surface, that is, the geocentric angle random variable, t0 is the moment when the satellite has the maximum elevation angle relative to the ground station during its motion, and γ max is the geocentric angle corresponding to surface B; A first calculation module is used to calculate the average coverage time of the satellites in the low-orbit constellation to the ground terminal based on the probability distribution function; The first calculation module specifically includes: Based on the geometric parameters of the target walker constellation, calculate the maximum geocentric angle from the ground terminal to the sub-satellite point; Based on the satellite angular velocity and the earth angular velocity in the ECI coordinate system, the satellite angular velocity in the ECEF coordinate system is calculated; Substituting the maximum geocentric angle and the satellite angular velocity into a calculation formula for the average coverage time of the satellite to the ground terminal, the average coverage time of the satellite to the ground terminal is calculated; The second calculation module is used to calculate the visible satellite change frequency based on the average coverage duration; the visible satellite change frequency is used to analyze the coverage characteristics of visible low-orbit satellites.

7. A computer storage medium, characterized in that: The computer storage medium stores computer program instructions, which, when executed by a processor, implement the method for analyzing the coverage characteristics of visible low-orbit satellites taking into account spherical distribution characteristics as described in any one of claims 1 to 5.

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