Method for calculating and verifying pointing angle of inter-satellite link in Ka band

Abstract

The application provides a Ka-band inter-satellite link pointing angle calculation and verification method, comprising: calculating a pointing vector in a low-orbit satellite antenna coordinate system through conversion from a body coordinate system to an antenna coordinate system; calculating a pointing angle (off-axis angle, azimuth angle) in the low-orbit satellite antenna coordinate system; implementing the foregoing pointing angle algorithm in a DSP hardware; simultaneously, simulating and calculating the off-axis angle and the azimuth angle of a low-orbit satellite pointing a medium-orbit satellite by using STK; and finally comparing the simulation result of STK with the implementation result of the DSP hardware to draw a conclusion. The application adopts a simplified position and velocity recursive algorithm to solve the Ka-band inter-satellite link pointing angle in real time, and completes the inter-satellite link space beam pointing of a low-orbit satellite to a medium-orbit satellite. Through the DSP hardware implementation and the STK software simulation, it is verified that the Ka-band inter-satellite pointing angle algorithm has low hardware implementation complexity and small hardware resource consumption under the premise of ensuring pointing accuracy.

Description

Technical Field

[0001] This invention relates to a method for calculating and verifying pointing angles, and more particularly to a method for calculating and verifying pointing angles of Ka-band inter-satellite links. Background Technology

[0002] In recent years, as national interests have expanded globally, the need for building my country's space-based information network has become increasingly urgent. Inter-satellite links provide a guarantee for connecting satellites, realizing space-based telemetry, tracking, and command (TT&C), and enabling autonomous constellation operation, serving as a crucial foundation for constructing a space-based information network. The prerequisite for establishing each inter-satellite link is that the communicating parties successfully point at each other. Since each satellite moves in its own orbit, meaning its position changes over time, and given the limited onboard resources, high communication frequency bands, and narrow half-power beamwidth, onboard communication terminals urgently need the ability to calculate inter-satellite pointing angles in real time while accommodating the complexity of onboard processing. Summary of the Invention

[0003] To address the challenges of limited onboard hardware resources, slow computation speed, narrow half-power beamwidth of Ka-band inter-satellite antennas, and high pointing accuracy requirements, this invention provides a method for calculating and verifying the pointing angle of Ka-band inter-satellite links, while balancing antenna pointing accuracy and onboard resource utilization. This invention utilizes onboard time, satellite attitude, and GPS positioning and orbit determination information, combined with onboard ephemeris information, and employs a simplified position-velocity recursive algorithm to calculate the off-axis angle and azimuth angle of the Ka-band inter-satellite antenna in real time, thus completing the spatial beam pointing of the inter-satellite link. The hardware is implemented using a DSP. Comparison with STK software simulation results shows that after one hour of onboard recursion, the pointing angle error of the Ka-band inter-satellite antenna is within the range of 10⁻³ metric units, meeting the pointing accuracy requirements for inter-satellite link establishment.

[0004] To achieve the above-mentioned objectives, the technical solution of this invention is: a method for calculating and verifying the pointing angle of an inter-satellite link in the Ka band, comprising the following steps:

[0005] S1: Input the number of six orbital elements for low-Earth orbit satellites in the J2000.0 inertial coordinate system;

[0006] S2: Input the number of six orbital elements of the medium-orbit satellite in the J2000.0 inertial coordinate system;

[0007] S3: Calculate the position and velocity vector of the low-orbit satellite in the J2000.0 inertial coordinate system;

[0008] S4: Calculate the position and velocity vector of the medium-orbit satellite in the J2000.0 inertial coordinate system;

[0009] S5: Simplified position and velocity algorithm to recursively derive the position and velocity vector of a low-Earth orbit satellite at the next moment;

[0010] S6: Simplified position and velocity algorithm to recursively derive the position and velocity vector of a medium-Earth orbit satellite at the next moment;

[0011] S7: Pointing vector from low-Earth orbit satellite to medium-Earth orbit satellite in the J2000.0 inertial coordinate system;

[0012] S8: Calculate the pointing vector in the low-Earth orbit satellite orbital coordinate system;

[0013] S9: Calculate the pointing vector in the low-Earth orbit satellite body coordinate system;

[0014] S10: Calculate the pointing vector in the coordinate system of the low-Earth orbit satellite antenna;

[0015] S11: Calculate the pointing angle (off-axis angle, azimuth angle) of the low-orbit satellite antenna in the coordinate system;

[0016] S12: DSP hardware implementation;

[0017] S13: STK simulation calculation of the off-axis angle and azimuth angle of a low-Earth orbit satellite pointing to a medium-Earth orbit satellite;

[0018] S14: Comparison of STK emulation and DSP hardware implementation.

[0019] Furthermore, the inter-satellite link pointing angle is the angle pointing towards the medium-orbit satellite in the low-orbit satellite inter-satellite antenna coordinate system, including the off-axis angle and the azimuth angle.

[0020] Furthermore, the inter-satellite link pointing angle is a Ka-band pointing angle, which has a narrow half-power beamwidth and high pointing accuracy requirements for antennas in this band.

[0021] Furthermore, in steps S1 and S2, the six orbital elements of the low-Earth orbit and medium-Earth orbit satellites in the J2000.0 inertial frame are input, including the orbital semi-major axis (a), orbital eccentricity (e), orbital inclination (i), right ascension of the ascending node (Ω), perigee distance (ω), and mean perigee angle (M), with the data type being unsigned binary integer.

[0022] Furthermore, in steps S3 and S4, the position and velocity vectors of the low-Earth orbit and medium-Earth orbit satellites in the J2000.0 inertial coordinate system are calculated, including the position and velocity of the X, Y, and Z axes, and the data type is binary two's complement.

[0023] Furthermore, in steps S5 and S6, a simplified position-velocity algorithm is used to recursively derive the position-velocity vectors X1N.r and X2N.r of the low-Earth orbit and medium-Earth orbit satellites at the next moment. The simplified position-velocity algorithm adopts the first-order Runge-Kutta method, with a recursion interval of 10ms.

[0024] Furthermore, in step S7, the pointing vector from the low-orbit satellite to the medium-orbit satellite in the J2000.0 inertial coordinate system is X2N.r-X1N.r.

[0025] Furthermore, in step S8, the transformation matrix from the J2000.0 inertial coordinate system to the low-Earth orbit satellite orbital coordinate system is calculated using the instantaneous root of the low-Earth orbit satellite in the J2000.0 inertial coordinate system. The pointing vector in the low-Earth orbit satellite orbital coordinate system is obtained as follows

[0026]

[0027] Furthermore, in step S9, the transformation matrix from the low-Earth orbit satellite orbit coordinate system to the body coordinate system is calculated based on the platform attitude angles. The pointing vector in the low-orbit satellite body coordinate system is obtained as follows

[0028] Furthermore, in step S10, the transformation matrix from the low-Earth orbit satellite body coordinate system to the antenna coordinate system is calculated from the inter-satellite antenna coordinate system. The pointing vector in the low-orbit satellite antenna coordinate system is obtained as follows:

[0029] Furthermore, in step S11, the off-axis angle in the low-orbit satellite antenna coordinate system Azimuth ψ = atan2(y,x).

[0030] Furthermore, the pointing angle calculation method is implemented in hardware by a DSP, which fully utilizes the high-speed computing power of the DSP to complete the rapid recursion of position velocity, thereby completing continuous and accurate pointing angle calculation.

[0031] Furthermore, the pointing angle calculation method was simulated using STK software and compared with the results of the DSP hardware implementation. The error magnitudes of the off-axis angle and azimuth angle were found to be within 10. -3 The accuracy is sufficient to meet the pointing requirements for inter-satellite link establishment.

[0032] By employing the above technical solutions, this invention has the following advantages and positive effects compared with the prior art:

[0033] 1) This invention adopts a simplified position velocity recursion algorithm and implements it through DSP, which can achieve advantages such as low on-board hardware resource overhead and fast calculation speed.

[0034] 2) The inter-satellite link pointing angle calculation method provided by this invention, through comparison of DSP hardware implementation and STK software simulation, shows that the error of the hardware implementation of the Ka-band inter-satellite antenna beam pointing angle is within 10%. -3 Metric level, meeting the pointing accuracy requirements for inter-satellite link establishment. Attached Figure Description

[0035] Figure 1 This is an overall flowchart of a method for calculating and verifying the pointing angle of an inter-satellite link in the Ka band according to the present invention;

[0036] Figure 2 This is a schematic diagram of the off-axis angle and azimuth angle in the inter-satellite antenna coordinate system for calculating and verifying the pointing angle of an inter-satellite link in the Ka-band of the present invention.

[0037] Figure 3 This is a diagram illustrating the usage of DSP (SMJ320C6701GLPW14) program storage resources for a Ka-band inter-satellite link pointing angle calculation and verification method according to the present invention. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0039] Referring to the accompanying drawings of the embodiments of the present invention, the invention will be described in more detail below. However, the invention can be implemented in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, the embodiments are presented to achieve a full and complete disclosure and to enable those skilled in the art to fully understand the scope of the invention.

[0040] To address the challenges of limited onboard hardware resources, slow computation speed, narrow half-power beamwidth of Ka-band inter-satellite antennas, and high pointing accuracy requirements, this invention provides a method for calculating and verifying the pointing angle of Ka-band inter-satellite links, while balancing antenna pointing accuracy and onboard resource utilization. This invention utilizes onboard time, satellite attitude, and GPS positioning and orbit determination information, combined with onboard ephemeris information, and employs a simplified position-velocity recursive algorithm to calculate the off-axis angle and azimuth angle of the Ka-band inter-satellite antenna in real time, thus completing the spatial beam pointing of the inter-satellite link. The hardware is implemented using a DSP. Comparison with STK software simulation results shows that after one hour of onboard recursion, the pointing angle error of the Ka-band inter-satellite antenna is within the range of 10⁻³ metric units, meeting the pointing accuracy requirements for inter-satellite link establishment.

[0041] In this embodiment, as Figure 1 The diagram shows an overall flowchart of a method for calculating and verifying the pointing angle of an inter-satellite link in the Ka band, including the following steps:

[0042] S1: Input the number of six orbital elements for a low-Earth orbit satellite (orbital altitude 500km) in the J2000.0 inertial coordinate system;

[0043] S2: Input the number of six orbital elements for a medium-orbit satellite (orbital altitude 20000km) in the J2000.0 inertial coordinate system;

[0044] S3: Calculate the position (X) of the low-Earth orbit satellite in the J2000.0 inertial coordinate system. 低 Y 低 Z 低 Speed ​​(V) X低 V Y低V Z低 Vector;

[0045] S4: Calculate the position (X) of the medium-orbit satellite in the J2000.0 inertial coordinate system. 中 Y 中 Z 中 Speed ​​(V) X中 V Y中 V Z中 Vector;

[0046] S5: Simplified position and velocity algorithm to recursively derive the position and velocity vector of low-Earth orbit satellites at the next moment, with a recursion interval of 10ms;

[0047] S6: Simplified position and velocity algorithm to recursively derive the position and velocity vector of a medium-Earth orbit satellite at the next moment, with a recursion interval of 10ms;

[0048] S7: Pointing vector from low-Earth orbit satellite to medium-Earth orbit satellite in the J2000.0 inertial coordinate system;

[0049] S8: Calculate the pointing vector in the low-Earth orbit satellite orbital coordinate system;

[0050] S9: Calculate the pointing vector in the low-Earth orbit satellite body coordinate system;

[0051] S10: Calculate the pointing vector in the coordinate system of the low-Earth orbit satellite antenna;

[0052] S11: Calculate the pointing angle (off-axis angle) in the low-orbit satellite antenna coordinate system. Azimuth );

[0053] S12: DSP hardware implementation, device model SMJ320C6701GLPW14;

[0054] S13: STK simulation calculation of the off-axis angle and azimuth angle of a low-Earth orbit satellite pointing to a medium-Earth orbit satellite;

[0055] S14: Comparison of STK emulation and DSP hardware implementation.

[0056] Furthermore, the inter-satellite link pointing angle is the angle pointing towards the medium-orbit satellite in the low-orbit satellite inter-satellite antenna coordinate system, including the off-axis angle and the azimuth angle.

[0057] Furthermore, the inter-satellite link pointing angle is a Ka-band pointing angle, which has a narrow half-power beamwidth and high pointing accuracy requirements for antennas in this band.

[0058] Furthermore, in steps S1 and S2, the six orbital elements of the low-Earth orbit and medium-Earth orbit satellites in the J2000.0 inertial frame are input, including the orbital semi-major axis (a), orbital eccentricity (e), orbital inclination (i), right ascension of the ascending node (Ω), perigee distance (ω), and mean perigee angle (M), with the data type being unsigned binary integer.

[0059] Furthermore, in steps S3 and S4, the position and velocity vectors of the low-Earth orbit and medium-Earth orbit satellites in the J2000.0 inertial coordinate system are calculated, including the three-axis positions X, Y, and Z and the velocity V. X V Y V Z The data type is binary two's complement.

[0060] Furthermore, in steps S5 and S6, a simplified position-velocity algorithm is used to recursively derive the position-velocity vectors X1N.r and X2N.r of the low-Earth orbit and medium-Earth orbit satellites at the next moment. The simplified position-velocity algorithm adopts the first-order Runge-Kutta method, with a recursion interval of 10ms.

[0061] Furthermore, in step S7, the pointing vector from the low-orbit satellite to the medium-orbit satellite in the J2000.0 inertial coordinate system is X2N.r-X1N.r.

[0062] Furthermore, in step S8, the transformation matrix from the J2000.0 inertial coordinate system to the low-Earth orbit satellite orbital coordinate system is calculated using the instantaneous root of the low-Earth orbit satellite in the J2000.0 inertial coordinate system. The pointing vector in the low-Earth orbit satellite orbital coordinate system is obtained as follows

[0063]

[0064] Furthermore, in step S9, the transformation matrix from the low-Earth orbit satellite orbit coordinate system to the body coordinate system is calculated based on the platform attitude angles. The pointing vector in the low-orbit satellite body coordinate system is obtained as follows

[0065] Furthermore, in step S10, the transformation matrix from the low-Earth orbit satellite body coordinate system to the antenna coordinate system is calculated from the inter-satellite antenna coordinate system. The pointing vector in the low-orbit satellite antenna coordinate system is obtained as follows:

[0066] Furthermore, in step S11, as Figure 2 Off-axis angle in the low-orbit satellite antenna coordinate system shown Azimuth ψ = atan2(y,x).

[0067] Furthermore, the pointing angle calculation method is implemented in hardware by a DSP (SMJ320C6701GLPW14), and the program storage resource usage is as follows: Figure 3By fully utilizing the high-speed computing power of the DSP, the position velocity can be rapidly calculated, thereby enabling continuous and accurate pointing angle calculations.

[0068] Furthermore, the pointing angle calculation method employs STK software simulation. The STK simulation characteristics of the two-star link establishment are as follows: the link establishment time is 10232.928s, accounting for 11.8% of the total simulation time (24 hours); the maximum distance between the two stars is 20938km, and the minimum distance is 19597km. The off-axis angle is obtained by comparing the STK software simulation results with the DSP hardware implementation results. The azimuth (ψ) error is on the order of 10⁻³ degrees, which meets the pointing accuracy requirements for inter-satellite link establishment.

Claims

1. A method for calculating and verifying the pointing angle of a Ka-band inter-satellite link, characterized in that, include: S1: Input the number of six orbital elements for low-Earth orbit satellites in the J2000.0 inertial coordinate system; S2: Input the number of six orbital elements of the medium-orbit satellite in the J2000.0 inertial coordinate system; S3: Calculate the position and velocity vector of the low-orbit satellite in the J2000.0 inertial coordinate system; S4: Calculate the position and velocity vector of the medium-orbit satellite in the J2000.0 inertial coordinate system; S5: Simplified position and velocity algorithm to recursively derive the position and velocity vector of a low-Earth orbit satellite at the next moment; S6: Simplified position and velocity algorithm to recursively derive the position and velocity vector of a medium-Earth orbit satellite at the next moment; S7: Calculate the pointing vector from the low-Earth orbit satellite to the medium-Earth orbit satellite in the J2000.0 inertial coordinate system; S8: Calculate the pointing vector in the low-Earth orbit satellite orbital coordinate system; S9: Calculate the pointing vector in the low-Earth orbit satellite body coordinate system; S10: Calculate the pointing vector in the coordinate system of the low-Earth orbit satellite antenna; S11: Calculate the pointing angle of the Ka-band inter-satellite link in the low-Earth orbit satellite antenna coordinate system; S12: DSP hardware implementation; S13: STK simulation calculation of the off-axis angle and azimuth angle of a low-Earth orbit satellite pointing to a medium-Earth orbit satellite; S14: Compare STK emulation with DSP hardware implementation.

2. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 1, characterized in that, The Ka-band inter-satellite link pointing angle is the angle pointing towards a medium-orbit satellite in the low-orbit satellite inter-satellite antenna coordinate system, including: off-axis angle and azimuth angle.

3. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 1, characterized in that, In step S1 or S2, the orbital six elements of the J2000.0 inertial frame low-Earth orbit or medium-Earth orbit satellite include: orbital semi-major axis a, orbital eccentricity e, orbital inclination i, right ascension of ascending node Ω, perigee distance ω, and mean perigee angle M, and the data type is unsigned binary integer.

4. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 3, characterized in that, In step S3 or S4, the position and velocity vector of the low-orbit or medium-orbit satellite in the J2000.0 inertial coordinate system includes the position and velocity of the X, Y, and Z axes, respectively, and the data type is binary two's complement.

5. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 4, characterized in that, In step S5 or S6, a simplified position-velocity algorithm is used to recursively derive the position-velocity vectors of the low-Earth orbit and medium-Earth orbit satellites at the next moment. , The simplified position-velocity algorithm adopts the first-order Runge-Kutta method with a recursion interval of 10ms.

6. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 5, characterized in that, In step S7, the pointing vector from the low-Earth orbit satellite to the medium-Earth orbit satellite in the J2000.0 inertial coordinate system is: .

7. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 6, characterized in that, In step S8, the transformation matrix from the J2000.0 inertial coordinate system to the low-Earth orbit satellite orbital coordinate system is calculated using the instantaneous root of the low-Earth orbit satellite in the J2000.0 inertial coordinate system. The pointing vector in the low-Earth orbit satellite coordinate system is obtained as .

8. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 7, characterized in that, In step S9, the transformation matrix from the low-Earth orbit satellite orbital coordinate system to the body coordinate system is calculated based on the platform attitude angles. The pointing vector in the low-orbit satellite body coordinate system is obtained as follows: .

9. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 8, characterized in that, In step S10, the transformation matrix from the low-Earth orbit satellite body coordinate system to the antenna coordinate system is calculated using the inter-satellite antenna coordinate system. The pointing vector in the low-orbit satellite antenna coordinate system is obtained as follows: .

10. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 9, characterized in that, In step S11, the off-axis angle in the low-orbit satellite antenna coordinate system azimuth .

11. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 1, characterized in that, The pointing angle calculation method is implemented in hardware by a DSP, which makes full use of the high-speed computing power of the DSP to complete the rapid recursion of position and velocity, thereby completing continuous and accurate pointing angle calculation.

12. The method for calculating and verifying the pointing angle of Ka-band inter-satellite links according to claim 1, characterized in that, The pointing angle calculation method is simulated using STK software and compared with the results of the DSP hardware implementation. The error magnitude of the off-axis angle and azimuth angle is within 10-3 degrees, which meets the pointing accuracy requirements for inter-satellite link establishment.

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