Low-orbit satellite ephemeris analysis method based on satellite orbit plane coordinate system

Abstract

The invention relates to the field of satellite orbit calculation, in particular to a low-orbit satellite ephemeris analysis method based on a satellite orbit plane coordinate system, which comprises the following steps: acquiring TLE two-line orbit data of a target satellite, geodetic coordinates of a terminal, UTC time and earth rotation average angular velocity; calculating the state of the satellite in the orbital plane; calculating a transformation matrix from a geocentric inertial coordinate system ECI to a satellite orbit plane coordinate system; the LBH coordinates of the terminal are converted into ECEF rectangular coordinates; a rotation matrix from the ECEF to the ECI is constructed, and the ECI system speed of the terminal is calculated; according to the transformation matrix, transforming the ECI coordinate of the terminal into a final satellite orbit plane coordinate system; performing simplified calculation based on a unified calculation framework of a satellite orbit plane coordinate system; and outputting the distance, the relative speed, the Doppler frequency offset and the propagation time delay result which are calculated under the satellite orbit plane coordinate system. And the calculation complexity and the realization difficulty of high-precision orbit forecasting are obviously reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite orbit calculation, in particular to a low-orbit satellite ephemeris analysis method based on a satellite orbit plane coordinate system. BACKGROUND

[0002] In the ephemeris analysis and link calculation of low-orbit satellite communication, all calculations ultimately rely on a unified coordinate system. The known technical solution usually selects the Earth-Centered Earth-Fixed coordinate system (ECEF) or the Earth-Centered Inertial coordinate system (ECI) as the reference frame for calculation.

[0003] The ECEF coordinate system (such as WGS-84): This coordinate system is fixed to the Earth and rotates with the Earth. The position of the terminal is usually directly given in this coordinate system (longitude, latitude, altitude), which is very intuitive. However, the disadvantage is that the motion trajectory of the satellite in this coordinate system is very complex, which is the superposition of the Earth's rotation and the satellite's orbital motion, and it is relatively cumbersome to calculate the relative velocity vector (used for Doppler calculation).

[0004] The ECI coordinate system (such as J2000): This coordinate system does not rotate with the Earth and is an ideal framework for describing the orbital motion of the satellite. Satellite ephemeris data is usually provided directly in this coordinate system. However, the disadvantage is that the position of the terminal must be converted to the ECI system through the Earth's rotation parameters (such as GAST), and the final result needs to be converted back to the ECEF or local coordinate system to be used by the communication system.

[0005] The most similar prior art to the present application is a scheme that performs all calculations in the ECEF coordinate system. However, the traditional scheme of performing calculations in the ECEF common coordinate system described above, although the concept is clear, has inherent calculation complexity and precision problems: 1. Complex calculation with redundant conversion: This scheme must convert all entities (satellites and terminals) to a third coordinate system (ECEF) to perform calculations. In particular, the velocity vector of the satellite needs to go through complex rotation calculations (including the derivative term of coordinate rotation) to convert from the ECI system to the ECEF system, which is computationally intensive and prone to errors. 2. Physical meaning is not intuitive, and the calculation formula is complex: In the ECEF system, the motion of the satellite is the combination of two kinds of motion, which leads to a complex expression of the satellite's relative velocity vector with respect to the terminal. When calculating the radial velocity, the dot product of two three-dimensional vectors needs to be calculated, and its geometric meaning is not intuitive in the ECEF system, which is not conducive to subsequent error analysis and optimization. 3. Unable to fully utilize the characteristics of orbital motion: The core motion law of the satellite is determined by its orbital plane, and its motion in the orbital plane is a regular two-body problem. The representation in the ECEF or ECI coordinate system obscures this inherent simplicity and does not take advantage of the characteristics of orbital mechanics itself to simplify the calculation. SUMMARY

[0006] The present application aims to provide a low-orbit satellite ephemeris analysis method based on a satellite orbit plane coordinate system. In the research on how to optimize the on-board computing resources or terminal computing efficiency, it is found that the defects of the prior art are caused by the non-optimality of the coordinate system selection. That is, the conventional method introduces unnecessary calculation and complexity in order to seek a "common" reference without selecting a coordinate system that best reflects the physical nature of the problem.

[0007] However, through in-depth research on orbital mechanics and coordinate transformation theory, it is found that the satellite orbit plane coordinate system is a neglected key. The geometric relationship of the satellite relative to any terminal on the earth is complex in initial conditions, but all motion states (position, velocity) of the satellite itself have the simplest and most certain expression in its orbit plane. If the position of the terminal is also mapped into this plane, all subsequent calculations (such as distance, relative velocity) will be completed in this two-dimensional plane, and the problem will be greatly simplified. This idea completely breaks out of the traditional framework of solving in the ECI or ECEF three-dimensional space, which is the technical difficulty and breakthrough point of the present application.

[0008] In order to solve the above technical problems, the present application provides the following technical solutions:

[0009] A low-orbit satellite ephemeris analysis method based on a satellite orbit plane coordinate system, the method comprising:

[0010] S100, acquiring TLE two-line orbit data of a target satellite, geodetic coordinates of a terminal, UTC time and average angular velocity of the earth rotation, respectively;

[0011] S200, calculating the state of the satellite in the orbit plane according to the acquired data, obtaining the position and velocity of the satellite in the plane coordinate system;

[0012] S300, calculating the transformation matrix from the Earth-Centered Inertial coordinate system (ECI) to the satellite orbit plane coordinate system;

[0013] S400, converting the terminal LBH coordinates into ECEF rectangular coordinates; and constructing a rotation matrix from ECEF to ECI using the Greenwich Sidereal Time angle to calculate the terminal ECI system velocity; then transforming the ECI coordinates of the terminal to the final satellite orbit plane coordinate system according to the transformation matrix;

[0014] S500, performing simplified calculation based on the unified calculation framework of the satellite orbit plane coordinate system;

[0015] S600, outputting the distance, relative velocity, Doppler frequency offset and propagation delay results calculated in the satellite orbit plane coordinate system.

[0016] Preferably, S100 comprises:

[0017] S101, obtaining and analyzing TLE data of the target satellite to obtain orbital elements ;

[0018] S102, obtaining geodetic coordinates of the terminal: longitude , latitude , and height ;

[0019] S103, obtaining UTC time and converting it into mechanical time required for calculation: ;

[0020] S104, obtaining the average angular velocity of the earth rotation .

[0021] Preferably, S200 includes:

[0022] S201, calculating the average motion angular velocity according to the orbital elements : ;

[0023] wherein, denotes the period, denotes the earth's gravitational constant;

[0024] S202, calculating the mean anomaly according to time : ;

[0025] wherein, denotes the starting time;

[0026] By iteratively solving the Kepler equation, the eccentric anomaly is obtained: ;

[0027] and the satellite's radial distance is calculated according to the eccentric anomaly and the parameters in the orbital elements : ;

[0028] S203, directly calculating the position and velocity of the satellite in the satellite orbital plane coordinate system;

[0029] wherein, ;

[0030] ,

[0031] ;

[0032] wherein, denotes the earth's gravitational constant.​

[0033] Preferably, S300 comprises:

[0034] calculating a transformation matrix from the ECI coordinate system to the satellite orbital plane coordinate system :

[0035] ;

[0036] The transformation matrix is determined by three Euler rotation angles, wherein, represents the Euler rotation angle around the Z axis, represents the Euler rotation angle around the X axis, represents the Euler rotation angle around the Y axis, and this matrix only needs to be calculated once.

[0037] Preferably, S400 comprises:

[0038] S401, converting the terminal LBH coordinates into ECEF rectangular coordinates: :

[0039] ;

[0040] S402, using the calculated Greenwich Mean Sidereal Time value GAST to construct a rotation matrix from ECEF to ECI : ;

[0041] and convert the terminal coordinates to the ECI system: ;

[0042] According to the average angular velocity of the earth rotation calculate the terminal ECI system speed:

[0043] ;

[0044] S403, obtain the transformation matrix , transform the ECI coordinates of the terminal to the final satellite orbital plane coordinate system: , ;

[0045] At this time, the coordinates of the terminal in the satellite orbital plane coordinate system are obtained as: , .

[0046] Preferably, S500 comprises:

[0047] S501, based on the coordinates in the satellite orbital plane coordinate system, obtain the satellite position and the terminal position: ;

[0048] S502, calculate distance vector: , geometric position ;

[0049] S503, calculate relative velocity vector: satellite velocity , relative velocity vector: ;

[0050] S504, calculate Doppler frequency offset and time delay, the formula compared with the traditional method, the previous calculation process has been greatly simplified:

[0051] ;

[0052] ;

[0053] Wherein, is the speed of light, is the carrier frequency, is the Doppler shift, is the time delay.

[0054] A computer readable storage medium, having stored thereon a computer program, which, when executed by a processor, implements the steps of a low earth orbit satellite ephemeris analysis method based on a satellite orbital plane coordinate system as described above.

[0055] A computer device comprising a memory, a processor and a computer program stored on the memory and running on the processor, the processor implementing the steps of a low earth orbit satellite ephemeris analysis method based on a satellite orbital plane coordinate system as described above when executing the program.

[0056] Compared with the prior art, the beneficial effects achieved by the present application are:

[0057] ① The orbital plane coordinate system calculation method described in the present application, because it is directly coupled with the orbital elements describing the nature of satellite motion, provides a more concise and more direct mathematical framework for introducing high-order perturbation models, significantly reducing the computational complexity and implementation difficulty of high-precision orbit prediction.

[0058] ② The method decouples the mixed error in the traditional three-dimensional coordinate system into independent components along the track direction, radial direction and normal direction, greatly improving the intuitiveness and interpretability of error analysis, and providing a clear guide for system performance evaluation and subsequent optimization.

[0059] ③ The present application provides a highly unified and parallel processing framework for multi-satellite link calculation in constellation systems. Although the orbits of each satellite are different, the coordinate transformation and calculation process have high consistency, and are particularly suitable for simultaneously processing the link budget of a large number of satellites through parallel computing architecture, significantly improving the overall computing efficiency under the constellation system.

[0060] IV. The result obtained in the orbital plane coordinate system has stronger regularity and fitting property, so that it is possible to efficiently compress Doppler, time delay and other prediction data by using a small amount of parameters (such as polynomial coefficients), thereby achieving the effect of compressing data amount and reducing signaling overhead, and effectively reducing the transmission pressure of the star-ground or ground-air downlink channel. BRIEF DESCRIPTION OF DRAWINGS

[0061] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, illustrate the present application and explain the technical solutions of the present application, and do not constitute a limitation on the present application. In the drawings:

[0062] Figure 1 is a flowchart of a low-orbit satellite ephemeris analysis method based on a satellite orbital plane coordinate system. DETAILED DESCRIPTION

[0063] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0064] Please refer to Figure 1 , the present application provides technical solutions:

[0065] Embodiment 1: A low-orbit satellite ephemeris analysis method based on a satellite orbital plane coordinate system, comprising:

[0066] S100, respectively acquiring TLE two-line orbital data of a target satellite, geodetic coordinates of a terminal, UTC time and average angular velocity of the earth rotation;

[0067] Preferably, S100 comprises:

[0068] S101, acquiring and analyzing TLE data of the target satellite to obtain orbital six elements ;

[0069] S102, acquiring geodetic coordinates of the terminal: longitude , latitude , height ;

[0070] S103, acquiring UTC time , and converting it into a required mechanical time for calculation: ;

[0071] S104, acquiring average angular velocity of the earth rotation .

[0072] Selection and definition of coordinate system: the idea of using satellite orbit plane coordinate system as the core calculation framework is proposed. The definition of this coordinate system: the origin is the center of the earth, and the XY plane is the instantaneous orbit plane of the satellite (the X axis can point to the ascending node or the perigee).

[0073] S200, calculate the state of the satellite in the orbit plane according to the obtained data, and obtain the position and velocity of the satellite in the plane coordinate system;

[0074] Preferably, S200 includes:

[0075] S201, calculate the average motion angular velocity according to the six orbital elements : ;

[0076] Wherein, represents the period, represents the gravitational constant of the earth;

[0077] S202, calculate the mean anomaly according to the time : ; ;

[0078] Wherein, represents the initial time;

[0079] By iteratively solving the Kepler equation, the eccentric anomaly : ;

[0080] And according to the eccentric anomaly and the parameters in the six orbital elements, the radial direction of the satellite : ;

[0081] S203, directly calculate the position and velocity of the satellite in the satellite orbit plane coordinate system;

[0082] Wherein, ;

[0083] ,

[0084] ;

[0085] Wherein, represents the gravitational constant of the earth.

[0086] S300, calculate the transformation matrix from the earth-centered inertial coordinate system ECI to the satellite orbit plane coordinate system;

[0087] Preferably, S300 includes:

[0088] calculating a transformation matrix from the ECI coordinate system to the satellite orbit plane coordinate system :

[0089] ;

[0090] The transformation matrix is determined by three Euler rotation angles, wherein, denotes the Euler rotation angle around the Z axis, denotes the Euler rotation angle around the X axis, denotes the Euler rotation angle around the Y axis, and the matrix only needs to be calculated once.

[0091] S400, convert the terminal LBH coordinates into ECEF rectangular coordinates; and construct a rotation matrix from ECEF to ECI using the Greenwich mean sidereal time angle to calculate the terminal ECI system speed; then transform the terminal ECI coordinates to the final satellite orbit plane coordinate system according to the transformation matrix;

[0092] Preferably, S400 comprises:

[0093] S401, convert the terminal LBH coordinates into ECEF rectangular coordinates: :

[0094] ;

[0095] S402, construct a rotation matrix from ECEF to ECI using the calculated Greenwich mean sidereal time value GAST : ;

[0096] and convert the terminal coordinates to the ECI system: ;

[0097] According to the average angular velocity of the earth rotation calculate the terminal ECI system speed:

[0098] ;

[0099] S403, obtain the transformation matrix , transform the terminal ECI coordinates to the final satellite orbit plane coordinate system: , ;

[0100] At this time, the coordinates of the terminal in the satellite orbit plane coordinate system are obtained as: , .

[0101] Mapping transformation of terminal coordinates: the specific mathematical transformation method and steps of protecting the terminal from the geodetic coordinate system (LBH) via ECEF, ECI, and finally transforming to the satellite orbit plane coordinate system.

[0102] S500, simplified calculation based on the unified calculation framework of the satellite orbit plane coordinate system;

[0103] Preferably, S500 includes:

[0104] S501, based on the coordinates in the satellite orbit plane coordinate system, obtaining the satellite position and the terminal position: ;

[0105] S502, calculating the distance vector: , geometric position ;

[0106] S503, calculating the relative velocity vector: satellite velocity , relative velocity vector: ;

[0107] S504, calculating the Doppler frequency offset and time delay, the formula is greatly simplified compared with the traditional method:

[0108] ;

[0109] ;

[0110] where, is the speed of light, is the carrier frequency, is the Doppler shift, is the time delay.

[0111] Simplified calculation in the plane: in this two-dimensional plane coordinate system, geometric calculations of distance, relative velocity, Doppler frequency offset, and other communication key parameters are performed.

[0112] S600, output the distance, relative velocity, Doppler frequency offset, and propagation time delay results calculated in the satellite orbit plane coordinate system.

[0113] Intrinsic expression of satellite coordinates: the position and velocity of the satellite in this coordinate system can be directly calculated from the orbital elements (such as the true anomaly), without complex rotation calculations.

[0114] Embodiment 2: A computer readable storage medium of the present embodiment, which stores a computer program, the program being executed by a processor to realize the steps of a low-orbit satellite ephemeris analysis method based on a satellite orbit plane coordinate system in embodiment 1.

[0115] The computer readable storage medium of the embodiment can be an internal storage unit of the terminal, for example, a hard disk or a memory of the terminal; the computer readable storage medium of the embodiment can also be an external storage device of the terminal, for example, a plug-in hard disk, a smart memory card, a secure digital card, a flash memory card and the like equipped on the terminal; further, the computer readable storage medium can include both the internal storage unit and the external storage device of the terminal.

[0116] The computer readable storage medium of the embodiment is used to store a computer program and other programs and data required by the terminal, and can also be used to temporarily store data that has been output or will be output.

[0117] Embodiment 3: The computer device of the embodiment comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the steps in the low-orbit satellite ephemeris analysis method based on a satellite orbit plane coordinate system of embodiment 1 when executing the program.

[0118] In the embodiment, the processor can be a central processing unit, and can also be other general-purpose processors, digital signal processors, application-specific integrated circuits, ready programmable gate arrays or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components and the like, the general-purpose processor can be a microprocessor or the processor can also be any conventional processor and the like; the memory can comprise read-only memories and random access memories, and provide instructions and data for the processor, and a part of the memory can also comprise non-volatile random access memories, for example, the memory can also store device type information.

[0119] Those skilled in the art should understand that the embodiments disclosed herein can be provided as a method, a system or a computer program product. Therefore, the embodiments can be in the form of hardware embodiments, software embodiments or embodiments combining software and hardware aspects. Moreover, the embodiments can be in the form of a computer program product implemented on one or more computer usable storage media (including but not limited to magnetic disks and optical storage media and the like) containing computer usable program code.

[0120] The embodiments are described with reference to flowcharts and / or block diagrams of the method and the computer program product according to the embodiments, and it should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be realized by computer program instructions; these computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing devices to produce a machine, so that the instructions executed by the computer or other programmable data processing devices produce a machine for realizing the functions described in the flowcharts and / or block diagrams. Figure 1one or more processes and / or schematic diagrams Figure 1 an apparatus that performs functions specified in one or more blocks or a block.

[0121] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions apparatus implementing the flow Figure 1 one or more processes and / or schematic diagrams Figure 1 an apparatus that performs functions specified in one or more blocks or a block.

[0122] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process so that the instructions that are executed on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 one or more processes and / or schematic diagrams Figure 1 an apparatus that performs functions specified in one or more blocks or a block.

[0123] Those of ordinary skill in the art can understand that all or part of the flow of the above-mentioned embodiment method can be completed by a computer program instructing relevant hardware, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the flow of the above-mentioned embodiment method. The storage medium can be a magnetic disc, an optical disc, a read-only memory (ROM) or a random access memory (RAM), etc.

[0124] Finally, it should be noted that: the above only describes the preferred embodiments of the present application and is not used to limit the present application, although the above-mentioned embodiments of the present application are described in detail, those skilled in the art can still modify the technical solutions recorded in the above-mentioned embodiments, or make equivalent replacement for part of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for analyzing the ephemeris of low-Earth orbit satellites based on a satellite orbital plane coordinate system, characterized in that: The method includes: S100: Acquire the TLE two-line orbital data of the target satellite, the terminal's geodetic coordinates, UTC time, and the average angular velocity of the Earth's rotation; S200. Calculate the satellite's state in the orbital plane based on the acquired data, and obtain the satellite's position and velocity in the plane coordinate system; S300, Calculate the transformation matrix from the geocentric inertial coordinate system (ECI) to the satellite orbital plane coordinate system; S400. Convert the terminal LBH coordinates to ECEF rectangular coordinates; and construct the rotation matrix from ECEF to ECI using the Greenwich Mean Time (GMT) sidereal hour angle, calculate the terminal ECI system velocity; then transform the terminal's ECI coordinates to the final satellite orbital plane coordinate system according to the transformation matrix. S500 simplifies calculations using a unified calculation framework based on the satellite orbital plane coordinate system; S600 outputs the distance, relative velocity, Doppler frequency offset, and propagation delay results calculated in the satellite orbital plane coordinate system.

2. The method for analyzing the ephemeris of low-Earth orbit satellites based on a satellite orbital plane coordinate system as described in claim 1, characterized in that, The S100 includes: S101. Acquire and analyze the TLE data of the target satellite to obtain the orbital root numbers. ; S102. Obtain the terminal's geodetic coordinates: longitude ,latitude ,high ; S103, Obtain UTC Time And convert it into the mechanics required for the calculation: ; S104. Obtain the average angular velocity of Earth's rotation. .

3. The method for analyzing the ephemeris of low-Earth orbit satellites based on a satellite orbital plane coordinate system as described in claim 1, characterized in that, The S200 includes: S201. Calculate the average angular velocity based on the six track elements. : ; in, Indicates period, Represents the gravitational constant; S202, According to time Calculate the angle of approach. : ; in, Indicates the start time; The aperitone angle is obtained by iteratively solving the Kepler equation. : ; And based on the near point angle Calculate the satellite radial distance using parameters from the six orbital root numbers. : ; S203. Calculate the satellite's position directly in the satellite orbital plane coordinate system. and speed ; in, ; ， ； in, This represents the Earth's gravitational constant.

4. The method for analyzing the ephemeris of low-Earth orbit satellites based on a satellite orbital plane coordinate system as described in claim 1, characterized in that, The S300 includes: Calculate the transformation matrix from the ECI coordinate system to the satellite orbital plane coordinate system. : ； The transformation matrix is ​​determined by three Euler rotation angles, where, This represents the Euler rotation angle about the Z-axis. This represents the Euler rotation angle about the X-axis. This represents the Euler rotation angle about the Y-axis; this matrix only needs to be calculated once.

5. The method for analyzing the ephemeris of low-Earth orbit satellites based on a satellite orbital plane coordinate system as described in claim 1, characterized in that, The S400 includes: S401, Set the terminal LBH coordinates Convert to ECEF rectangular coordinates: : ； S402. Using the calculated Greenwich true sidereal time (GAST), construct the rotation matrix from ECEF to ECI. : ; And transform the terminal coordinates to the ECI system: ; Based on the average angular velocity of Earth's rotation Calculate the speed of the terminal ECI system: ； S403. Obtain the transformation matrix Transform the terminal's ECI coordinates to the final satellite orbital plane coordinate system: , ; At this point, the coordinates of the terminal in the satellite orbital plane coordinate system are: , .

6. The method for analyzing the ephemeris of low-Earth orbit satellites based on a satellite orbital plane coordinate system as described in claim 1, characterized in that, The S500 includes: S501. Obtain the satellite position based on the coordinates in the satellite orbital plane coordinate system. Terminal location: ; S502, Calculate the distance vector: Geometric position ; S503. Calculate the relative velocity vector: satellite velocity Relative velocity vector: ; S504. Calculate Doppler frequency offset and time delay: ； ； in, At the speed of light, For carrier frequency, For Doppler frequency shift, For time delay.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the steps in the low-orbit satellite ephemeris analysis method based on the satellite orbital plane coordinate system as described in any one of claims 1-6.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the program, it implements the steps in the low-orbit satellite ephemeris analysis method based on the satellite orbital plane coordinate system as described in any one of claims 1-6.

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