A fast computation method for non-geostationary orbit internet constellation compatibility analysis

Abstract

This invention relates to the field of constellation interference analysis technology, specifically to a rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations. The method includes establishing a computational loop, performing a three-dimensional coordinate transformation in the Earth-fixed coordinate system, and calculating a third parameter; and obtaining the first and second parameters corresponding to the current incident angles of the interfered and interfering satellites through a lookup table, and adding the constant, the first parameter, the second parameter, and the third parameter to obtain the gain value. This invention replaces the gain calculation with a lookup table method, significantly reducing the computational density and time consumption within the loop. Furthermore, the lookup table method, formula decomposition, rapid coordinate transformation, and parallel acceleration work synergistically, simplifying the originally complex interference-to-noise ratio formula to a few additions, multiplications, and lookup table operations. This allows the overall solution to achieve a leapfrog speedup from tens of minutes to tens of seconds while maintaining interference analysis errors far below engineering requirements.

Description

Technical Field

[0001] This invention relates to the field of constellation interference analysis technology, and more specifically, to a rapid calculation method for compatibility analysis of non-stationary orbit Internet constellations. Background Technology

[0002] In recent years, with the rise of satellite internet, non-geostationary orbit (NGSO) satellite constellations have become a key development focus in order to meet the demands for global 24 / 7 coverage and high-speed broadband applications. Currently, according to data submitted by various countries to the International Telecommunication Union (ITU), at least 100 countries or organizations worldwide intend to build NGSO constellations.

[0003] The NGSO constellation is now in a rapid deployment phase. With a large number of satellites entering orbit, the interference problem between NGSO satellites is becoming increasingly prominent, and extensive compatibility analysis is required before satellite launch.

[0004] However, due to the large scale and complex scenarios of constellations, the use of mainstream software such as STK and Visualyse for step-by-step deduction involves a large amount of computation and is time-consuming in terms of constellation orbit simulation and radio wave propagation model, which cannot meet the timeliness requirements of analysis. Therefore, a fast and effective analysis method is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to provide a rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations, comprising the following steps:

[0006] Calculate the fixed parameters to obtain the constant. ;

[0007] Based on the incident angles of the disturbed satellite and the interfering satellite relative to the ground station antenna, a reference table corresponding to the first and second parameters from 0 to 180° is constructed in advance.

[0008] A computational loop is established, which performs a three-dimensional coordinate transformation in the Earth-fixed coordinate system and calculates the third parameter; and, by referring to a table, obtains the first and second parameters corresponding to the current incident angles of the disturbed satellite and the interfering satellite, and sets constants... The gain value is obtained by adding the first, second, and third parameters.

[0009] Furthermore, the constant The calculation formula is as follows:

[0010] ;

[0011] In the formula, To interfere with the satellite's transmission power; This is the bandwidth adjustment factor for the link; The wavelength corresponding to the carrier frequency of the interfering link; Boltzmann's constant; The downlink bandwidth of the disrupted system; This is the equivalent noise temperature of the ground station antenna.

[0012] Furthermore, the first parameter is the gain of the disturbed satellite on the ground station antenna.

[0013] Furthermore, the second parameter is the gain of the interfering satellite on the ground station antenna.

[0014] Furthermore, the third parameter is ,in To interfere with the distance between the satellite and the ground station.

[0015] Furthermore, the three-dimensional coordinates of the Earth-fixed coordinate system are converted to:

[0016] The positions of the disturbed and interfering satellites are converted from three-dimensional coordinates in the inertial coordinate system to three-dimensional coordinates in the Earth-fixed coordinate system.

[0017] The three-dimensional coordinate transformation formula for the Earth-fixed coordinate system is as follows:

[0018] ;

[0019] In the formula, These are the three-dimensional coordinates in the Earth-fixed coordinate system. The coordinates are in the three-dimensional coordinates of the inertial coordinate system; It is a 3x3 matrix, with the following elements:

[0020]

[0021] in:

[0022] ;

[0023] ;

[0024] ;

[0025] ; The number of days counted from 00:00:00 UTC on January 1, 2000.

[0026] Transforming the positions of both the affected and interfering satellites from three-dimensional coordinates in the inertial coordinate system to three-dimensional coordinates in the ground-fixed coordinate system is a crucial step for achieving rapid calculations in compatibility analysis. If satellite orbits are calculated in the inertial coordinate system, while ground station and antenna angles and distances must be calculated in the ground-fixed coordinate system, direct calculation between the two is impossible. Therefore, coordinate transformation is the only way to achieve spatiotemporal unification. This invention simplifies the complex transformations that traditionally rely on astronomical libraries, multi-step trigonometric functions, and polynomials into lightweight matrix multiplications, while meeting the accuracy requirements of constellation interference analysis, thereby fundamentally reducing the computational load of single-step loops.

[0027] Furthermore, the current incident angles of the disturbed satellite and the interfering satellite are:

[0028] At the current moment, the incident angles of the disturbed satellite and the interfering satellite relative to the ground station antenna. and .

[0029] Preferably, the step size of the angle in the lookup table is set to 0.01° or 1'.

[0030] Preferably, the computation loop is accelerated using OpenMP or CUDA.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] This invention replaces gain calculation with a lookup table method, moving the gain calculation from inside the high-frequency loop to the offline preprocessing stage. By pre-establishing an angle-gain lookup table, the complex real-time calculation within the loop is transformed into extremely simple lookup table and interpolation operations, significantly reducing the computational density and time consumption within the loop.

[0033] The lookup table method, formula decomposition, rapid coordinate transformation, and parallel acceleration work together to achieve synergistic effects. Formula decomposition fixes constant terms, the lookup table method simplifies gain terms, and rapid coordinate transformation provides real-time position. Together, these three methods simplify the originally complex interference-to-noise ratio formula into a small number of addition, multiplication, and lookup table operations, significantly reducing the workload of calculation. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the calculation process for compatibility analysis based on the downlink interference-to-noise ratio between NGSO constellations according to the present invention;

[0035] Figure 2 This is a schematic diagram of the rapid calculation method for compatibility analysis of the present invention;

[0036] Figure 3 This is a schematic diagram of the method steps for calculating the loop body of the present invention;

[0037] Figure 4This is a schematic diagram illustrating the compatibility analysis results of the present invention. Detailed Implementation

[0038] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0039] The first embodiment discloses a fast calculation method for compatibility analysis of non-geostationary orbit Internet constellations. Taking the downlink interference-to-noise ratio (I / N) analysis between NGSO constellations, an important scenario in compatibility analysis, as an example, the gain calculation is changed to a lookup table method, and a fast satellite orbit algorithm is used, which significantly reduces the workload of calculation.

[0040] The interference-to-noise ratio (I / N) is an important indicator of communication system performance. In the scenario described above, it can be described as a ground station of an interfering constellation being interfered with by one or more interfering satellites while tracking a single interfering satellite in real time. The maximum value of the following formula is calculated:

[0041] Formula 1;

[0042] In Equation 1, To interfere with the satellite's transmission power; The gain of the ground station antenna to the disturbed satellite; To interfere with the satellite's gain on the ground station's antenna; This is the bandwidth adjustment factor for the link; The wavelength corresponding to the carrier frequency of the interfering link; To interfere with the distance between the satellite and the ground station; Boltzmann's constant; The downlink bandwidth of the disrupted system; This is the equivalent noise temperature of the ground station antenna.

[0043] Figure 1 The calculation process for compatibility analysis based on the downlink interference-to-noise ratio (I / N) between NGSO constellations is shown. Figure 2 The steps of a fast calculation method for compatibility analysis are shown, including:

[0044] Step S100: Pre-calculation of fixed parameter values.

[0045] Calculate the constants in advance :

[0046] Formula 2;

[0047] According to the principle of logarithms, equation 1 is equivalent to:

[0048] Formula 3.

[0049] Step S200: Generate an antenna angle-gain lookup table.

[0050] After the antenna type is determined and The value is only related to the incident angle of the disturbed satellite and the interfering satellite relative to the ground station antenna at the current moment. and Related. Therefore, the 0-180° correspondence can be generated in advance. and Comparison table and Then store it, and set the step size of the angle in the lookup table to 0.01° or 1'.

[0051] Step S300: Calculate the initial position of each satellite in the constellation and the normal coordinates of the ground station.

[0052] To ensure global coverage, a reasonable constellation configuration needs to be selected in the constellation design. For example, the Walker configuration consists of multiple satellites with the same orbital semi-major axis and orbital inclination, divided into several orbital planes. The number of satellites in each orbital plane is the same, and the relative phase between satellites in different orbital planes maintains a specific relationship.

[0053] Based on the specific parameters of the constellation configuration, the initial positions of each satellite in the constellation are calculated. Simultaneously, in order to subsequently use the cosine theorem to calculate the antenna pointing angle, it is necessary to calculate the ground station's normal coordinates, i.e., its position in the Earth-fixed coordinate system 500km directly above the ground station.

[0054] Step S400: Calculate the loop body.

[0055] Compatibility analysis of internet constellations typically involves performing calculations over a specified timeframe (e.g., 30-100 days) at fixed intervals (e.g., 5-10 seconds). A computational loop is established based on the specific analysis requirements. Furthermore, depending on the relevant hardware and software environment, parallel frameworks such as OpenMP / CUDA can be used within the loop for acceleration.

[0056] Figure 3 The method steps for calculating the loop body are shown, including:

[0057] Step S410: Rapid calculation of the coordinate transformation matrix.

[0058] Because satellite position calculations use an inertial coordinate system (a reference frame stationary or in uniform motion in inertial space, with its origin at the Earth's center of mass, the z-axis parallel to the Earth's mean rotation axis and pointing towards the common North Pole, the x-axis pointing towards the vernal equinox, and the z-axis lying in the equatorial plane and perpendicular to the x and z axes, forming a right-handed coordinate system, with all three axes fixed in inertial space), while ground stations use a geostationary coordinate system (with its origin at the Earth's center of mass, fixed to the Earth and rotating with it, the x-axis pointing towards the intersection of the equator and the prime meridian, the z-axis pointing towards the Earth's mean rotation axis, and the y-axis perpendicular to the x and z axes and satisfying the right-hand rule), it is necessary to transform the three-dimensional coordinates of the inertial coordinate system to the three-dimensional coordinates of the geostationary coordinate system when calculating the satellite's position and antenna angle. The overall transformation formula is:

[0059] Equation 4;

[0060] In Equation 4, For the three-dimensional coordinates in the Earth-fixed coordinate system, , and They are respectively The Earth's polar motion, nutation, and precession matrices at any given time. Let be the sidereal time matrix rotated about the z-axis. These are the three-dimensional coordinates of the inertial coordinate system.

[0061] The common practice is to perform calculations using software such as STK or relevant astronomical computing libraries, but in addition to... Apart from that, all other terms require dozens of polynomial or trigonometric function calculations, which is too time-consuming.

[0062] This invention implements a rapid calculation method based on the actual needs of compatibility analysis:

[0063] Formula 5;

[0064] In Equation 5, It is a 3x3 matrix, with the following elements:

[0065]

[0066] in:

[0067] ;

[0068] ;

[0069] ;

[0070]

[0071] The number of days counted from 00:00:00 UTC on January 1, 2000.

[0072] The principle of this rapid calculation method is that, under the condition that the maximum permissible error is within 2", the original formula... Ignore The result can be simplified to (X and Y have the same meaning as above):

[0073]

[0074] and Represented as (ERA has the same meaning as above):

[0075]

[0076] Based on the matrix multiplication principle, the final fast formula is obtained. The error of 2” is accurate enough for constellation compatibility analysis, which greatly reduces the amount of calculation.

[0077] Step S420: Calculate the real-time position of the satellite.

[0078] Based on the actual needs of compatibility analysis, the real-time three-dimensional position of each satellite in the inertial coordinate system can be calculated using an ideal circular orbit, a two-body model, or a J2 perturbation model. All these models utilize mature algorithms and will not be elaborated upon here. After performing the multiplication operation, the real-time position of each satellite in the Earth-fixed coordinate system is obtained.

[0079] Step S430: Angle and gain calculation.

[0080] Using the law of cosines, based on the ground station and ground station normal coordinates in the Earth-fixed coordinate system, and the real-time Earth-fixed coordinate system positions of each satellite in the disturbed and interfering constellations, the corresponding... , and .calculate Then, by using the antenna angle-gain lookup table in step S200, and in conjunction with linear interpolation, the corresponding antenna angle-gain can be obtained. and The three items are the same as the pre-calculated fixed values. The summation yields the gain value, and the maximum value is then determined according to the requirements.

[0081] This invention only needs to target A single logarithmic operation is performed, while other time-consuming gain calculation steps in traditional methods are simplified to quick table lookups and addition / multiplication operations, greatly improving efficiency. With the angle step size in the lookup table set to 0.01° or 1', the error in the gain value calculated by this invention is considered negligible compared to the generally required 0.5dB error in engineering requirements.

[0082] The second embodiment, taking a disrupted constellation of 5000 satellites (100 orbital planes, 50 satellites per orbital plane, orbital altitude 1000km, eccentricity 0, orbital inclination 45°) and an interfering constellation of 3000 satellites (100 orbital planes, 30 satellites per orbital plane, orbital altitude 1200km, eccentricity 0, orbital inclination 80°), a minimum antenna elevation angle of 15 degrees, a shortest distance following strategy, a ground station longitude of 116°E, latitude of 40°N, an antenna model of ITU-R S.1528 Ln=-15, a frequency of 20GHz, and a receiving system noise temperature of 300K as an example, with an analysis duration of 100 days and a step size of 10 seconds, uses the fast calculation method for non-geostationary orbit Internet constellation compatibility analysis disclosed in the first embodiment, combined with CUDA parallel acceleration, to achieve a computation time of only 31 seconds.

[0083] The calculation using traditional Visualyse software takes 38.6 minutes.

[0084] See Table 1:

[0085]

[0086] Table 1

[0087] Table 1 shows that, compared with the calculation results of Visualyse software, the errors at each checkpoint are far less than the engineering requirement of 0.5dB. Here, CCDF (Complementary Cumulative Distribution Function) is a concept in statistics and communications, used to calculate the probability of a value greater than a specified value. Figure 4 The compatibility analysis results are shown, displaying only the first few lines of the results file, i.e., the gain values ​​corresponding to CCDF starting from 100%. Figure 2 In the diagram, the first column represents the gain value, and the second column represents the CCDF.

[0088] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent scope of this application.

Claims

1. A fast calculation method for compatibility analysis of non-geostationary orbit Internet constellations, characterized in that, Includes the following steps: Calculate the fixed parameters to obtain the constant. ; Based on the incident angles of the disturbed satellite and the interfering satellite relative to the ground station antenna, a reference table corresponding to the first and second parameters from 0 to 180° is constructed in advance. A computational loop is established, which performs a three-dimensional coordinate transformation in the Earth-fixed coordinate system and calculates the third parameter; and, by referring to a table, obtains the first and second parameters corresponding to the current incident angles of the disturbed satellite and the interfering satellite, and sets constants... The gain value is obtained by adding the first, second, and third parameters.

2. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The constant The calculation formula is as follows: ； In the formula, To interfere with the satellite's transmission power; This is the bandwidth adjustment factor for the link; The wavelength corresponding to the carrier frequency of the interfering link; Boltzmann's constant; The downlink bandwidth of the disrupted system; This is the equivalent noise temperature of the ground station antenna.

3. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The first parameter is the gain of the disturbed satellite to the ground station antenna.

4. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The second parameter is the gain of the interfering satellite on the ground station antenna.

5. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The third parameter is ,in To interfere with the distance between the satellite and the ground station.

6. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The three-dimensional coordinates of the Earth-fixed coordinate system are converted to: The positions of the disturbed and interfering satellites are converted from three-dimensional coordinates in the inertial coordinate system to three-dimensional coordinates in the Earth-fixed coordinate system.

7. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The current incident angles of the disturbed satellite and the interfering satellite are: At the current moment, the incident angles of the disturbed satellite and the interfering satellite relative to the ground station antenna. and .

8. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The step size of the angle in the reference table is set to 0.01° or 1'.

9. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 1, characterized in that, The computation loop is accelerated using OpenMP or CUDA.

10. The rapid calculation method for compatibility analysis of non-geostationary orbit Internet constellations according to claim 6, characterized in that, The three-dimensional coordinate transformation formula for the Earth-fixed coordinate system is as follows: ； In the formula, These are the three-dimensional coordinates in the Earth-fixed coordinate system. The coordinates are in the three-dimensional coordinates of the inertial coordinate system; It is a 3x3 matrix, with the following elements: in: ； ； ； ; The number of days counted from 00:00:00 UTC on January 1, 2000.

Images