A method for analyzing an inter-satellite link pointing angle

Abstract

The application provides a method for analyzing a pointing angle of an inter-satellite link, comprising: obtaining orbital elements of a satellite and orbital parameters of a target satellite matched with an SGP4 model in a J2000.0 inertial coordinate system; determining a target recursion time t; obtaining positions of the satellite and the target satellite at the time t in the J2000.0 inertial coordinate system; determining a pointing vector from the satellite to the target satellite at the time t in the J2000.0 inertial coordinate system; determining the pointing vector in a satellite orbital coordinate system; determining the pointing vector in a satellite body coordinate system; determining the pointing vector in a satellite antenna coordinate system; determining a pointing angle of the satellite antenna coordinate system at the target recursion time; and determining whether a cycle number reaches a set cycle number, if the cycle number does not reach the set cycle number, continuously obtaining the pointing angle of the satellite antenna coordinate system at a next target recursion time until the pointing angle of the satellite antenna coordinate system at the set cycle number is obtained.

Description

Technical Field

[0001] This invention belongs to the field of pointing angle analysis technology, and specifically relates to a method for analyzing the pointing angle of inter-satellite links. Background Technology

[0002] To achieve communication with the target satellite, it is necessary to predict the trajectories of both the local and target satellites and ensure that the local satellite's antenna beam is pointed towards the target satellite. Since communication satellites are typically low-Earth orbit satellites, characterized by high speeds, limited onboard resources, high communication frequencies, and narrow half-power beamwidths, the onboard communication terminal must possess the ability to calculate inter-satellite pointing angles in real time while considering the complexity of onboard processing.

[0003] Existing Ka-band inter-satellite link pointing angle analysis methods require that both the local and target satellites in the pointing algorithm be cooperative satellites, and that the six orbital root numbers of both satellites in the J2000 inertial coordinate system be obtained. The specific steps of this method are as follows: obtain the six orbital root numbers of the two satellites; calculate the position and velocity information in the J2000 system; use simplified position and velocity to recursively derive the position and velocity vector for the next moment; calculate the pointing vector in the J2000 system for the next moment; sequentially transform the pointing vector to the orbital coordinate system, the local satellite coordinate system, and the antenna coordinate system to finally complete the pointing angle calculation, and perform STK verification on the pointing results. The main drawback of this method is:

[0004] 1. This method is only applicable to cooperative satellites whose orbital root numbers under the J2000 series can be reliably obtained, and cannot be applied to satellites whose TLE ephemeris can only be obtained from NORAD;

[0005] 2. The simplified position-velocity method used in this orbit extrapolation method has poor extrapolation accuracy. Pointing accuracy can only be guaranteed by increasing the update speed of the pointing angle data, thus it is only suitable for implementation in a DSP. For some payloads, other required functions do not require a DSP module. Adding a separate DSP module for the pointing algorithm not only increases the total payload cost, system complexity, and hardware design difficulty, but also extends the debugging cycle. This makes it unsuitable for the current practical needs of short payload development cycles and limited ground development and debugging time.

[0006] Research on High-Precision Ka-Band Telemetry and Control Antenna Satellite Tracking and Forecasting Method (Zhang Junli, Journal of Instrumentation, DOI:10.19650 / j.cnki.cjsi.J1803276) This paper presents a method for orbit forecasting and tracking two-element orbital parameters (TLE) satellites using a Ka-band communication antenna. This method is mainly applicable to satellite ground stations. The specific steps are as follows: the orbit calculation software receives the latest orbital elements; according to the forecast requirements, the two-element orbital parameters (TLE) are used to calculate the satellite's position and velocity under J2000.0 inertial conditions over a certain period; the satellite coordinates are converted to the station's horizontal coordinate system; the tracking angle of the ground station for the satellite is calculated; radio wave refraction correction is performed based on meteorological information to obtain the ground station's pointing angle within the required time. The main drawback of this method is:

[0007] 1. This method is only applicable to situations where the velocity of ground stations is 0 in a geodetic fixed coordinate system, and cannot cope with situations where the onboard observation body and the target satellite move simultaneously;

[0008] 2. The radio wave refraction correction in this method is for atmospheric environments and is not applicable to on-board environments;

[0009] 3. Although the numerical integration method used in the orbit extrapolation stage has high computational accuracy, the calculation process is cumbersome and the formula is complex, making it unsuitable for satellite operating environments where computational resources are severely limited. Summary of the Invention

[0010] To overcome the shortcomings of existing technologies, the inventors have conducted intensive research and provided an analysis method for inter-satellite link pointing angles. This method introduces the SGP4 model to extrapolate the target star's orbit. A single call can calculate several sets of pointing angle data within the next 1 second at intervals of 0.05≤Δt≤0.2, e.g., 0.1s. This overcomes the shortcomings of existing technologies, such as being unsuitable for target stars whose orbital elements cannot be obtained, or the high complexity and computational time of the introduced SGP4 model, which leads to severe delays and reduced accuracy in obtaining pointing data.

[0011] The technical solution provided by this invention is as follows:

[0012] Firstly, a method for analyzing the pointing angle of inter-satellite links includes:

[0013] Obtain the six orbital roots of the local satellite in the J2000.0 inertial coordinate system;

[0014] Obtain the orbital parameters of the target star that match the SGP4 model from the two rows of TLE;

[0015] Determine the target recursion time based on the current system time, recursion time interval, and number of iterations;

[0016] Using the six roots of the local satellite's orbit, the position of the local satellite in the J2000.0 inertial coordinate system at the recursive time of the target is obtained;

[0017] Using the orbital parameters of the target star, the position of the target star in the J2000.0 inertial coordinate system at the recursive time is obtained;

[0018] Based on the positions of the local satellite and the target satellite in the J2000.0 inertial coordinate system at the target recursive time, determine the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system;

[0019] Based on the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system, determine the pointing vector in the local satellite's orbital coordinate system;

[0020] Determine the pointing vector in the local star's body coordinate system based on the pointing vector in the local star's orbital coordinate system;

[0021] Determine the pointing vector in the antenna coordinate system based on the pointing vector in the satellite's body coordinate system.

[0022] Determine the pointing angle in the local satellite antenna coordinate system at the target recursive time;

[0023] Determine if the set number of iterations has been reached. If not, continue to obtain the pointing angle in the local satellite antenna coordinate system at the next target recursion time, until the pointing angle in the local satellite antenna coordinate system is obtained at the set number of iterations.

[0024] Secondly, a link pointing angle analysis device includes:

[0025] One or more CPU or DSP processors;

[0026] Storage device for storing one or more programs.

[0027] When the one or more programs are executed by the one or more processors, the one or more processors implement the inter-satellite link pointing angle analysis method described in the first aspect.

[0028] Thirdly, a readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for analyzing the inter-satellite link pointing angle as described in the first aspect.

[0029] Fourthly, a computer program product comprising: a computer program (also referred to as code or instructions) that, when run, executes the inter-satellite link pointing angle analysis method described in the first aspect.

[0030] The method for analyzing the pointing angle of an inter-satellite link provided by the present invention has the following beneficial effects:

[0031] (1) The present invention provides an analysis method for the pointing angle of an inter-satellite link. The SGP4 model is used to extrapolate the orbit of the target star on the satellite. The SGP4 model uses TLE two-row elements as parameter input. The two-row elements are public orbital parameters, which are easy to obtain and have a certain orbital accuracy. The orbit extrapolation work is not limited to the measurement and orbit determination capability of the target star. The range of selectable targets is wider and more flexible.

[0032] (2) The present invention provides an analysis method for the pointing angle of inter-satellite links. The orbit extrapolation adopts an iterative method with a recursion time interval Δt of 0.05s≤Δt≤0.2s. A single call can calculate the pointing of several groups of antennas with an interval of Δt from the current system time. The algorithm has a low call frequency and a small burden on the on-board system, which provides feasibility for the algorithm to be implemented in the CPU. At the same time, it overcomes the problem that the extrapolation accuracy of the simplified position velocity method is poor.

[0033] (3) The present invention provides an analysis method for the pointing angle of an inter-satellite link. The time corresponding to several sets of pointing results of orbit extrapolation does not include the current time. This ensures that the pointing calculation is accurate while avoiding delay due to calculation time, thus affecting the satellite's tracking effect and tracking accuracy. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method for analyzing the pointing angle of inter-satellite links according to the present invention. Detailed Implementation

[0035] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0036] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0037] This invention provides a method for analyzing the pointing angle of inter-satellite links, such as... Figure 1 As shown, it includes the following steps:

[0038] S1, obtain the orbital six roots of the local satellite (e.g., orbital altitude 1200km) in the J2000.0 inertial coordinate system.

[0039] In this step, the six orbital parameters include the orbital semi-major axis (a), orbital eccentricity (e), orbital inclination (i), ascending node right axis (Ω), perigee distance (w), and mean perigee angle (M).

[0040] S2, obtain the orbital parameters of the target star (e.g., orbital altitude 600km) that matches the SGP4 model from the two rows of TLE.

[0041] In this step, the TLE two-line elements, also known as two-line elements orbital elements, is a standard format for describing satellite orbits developed by the North American Aerospace Defense Command (NORAD). This orbital format is available from public websites, and the orbital parameters are typically updated every 1-2 days.

[0042] The input parameters applicable to the SGP4 model include epoch time (t) TLE ), number of orbits around the Earth per day (n0), drag modulation factor (bstar), orbital inclination (i TLE ), ascending node equatorial point (Ω) TLE ), orbital eccentricity (e TLE ), angular distance from perigee (w) TLE ) and the angle of approach (M) TLE ).

[0043] The SGP4 model is a trajectory model for near-Earth targets (period < 225 min) developed by NORAD based on TLE elements. The TLE elements must be matched with this model to achieve the best prediction accuracy.

[0044] S3. Based on the current system time t0, the recursive time interval Δt, and the number of loops n, determine the next target recursive time t, t = t0 + n * Δt, where t0 is the current system time; Δt is the recursive time interval, 0.05s ≤ Δt ≤ 0.2s; and n is the number of loops, which is a positive integer (1 ≤ n ≤ 1 / Δt).

[0045] Preferably, Δt = 0.1s, and the number of cycles satisfies: 1 ≤ n ≤ 10.

[0046] S4. Substitute the six orbital roots of the local star from step S1 into the two-body model to obtain the position P of the local star in the J2000.0 inertial coordinate system at time t. Self .

[0047] S5, Substitute the target star's orbital parameters from step S2 into the SGP4 model to determine the target star's position P′ in the TEE coordinate system at time t. Target The position P of the target star in the J2000.0 inertial coordinate system is obtained through matrix (HG) transformation. Target .

[0048] In this step, P′ Target =(HG)P Target

[0049] (HG) = (EP)(ER)(NR)(PR);

[0050] Where (PR) is the precession matrix, (NR) is the nutation matrix, (ER) is the Earth's rotation matrix, and (EP) is the Earth's polar motion matrix.

[0051] S6, based on the position P of the local satellite in the J2000.0 inertial coordinate system at time t. Self and the position P of the target star Target Determine the pointing vector P from the local satellite to the target satellite in the J2000.0 inertial coordinate system. J2000 .

[0052] In this step, P J2000 =P Target -P Self .

[0053] S7, based on the pointing vector P from the local satellite to the target satellite in the J2000.0 inertial coordinate system. J2000 Determine the pointing vector P in the local orbit coordinate system. orbit .

[0054] In this step, the transformation matrix for converting the pointing vector from the J2000.0 inertial coordinate system to the local orbital coordinate system is R0. The local orbital coordinate system uses the direction of the satellite's movement as the X-axis, the right-hand side of the direction of movement as the Y-axis, and the Z-axis pointing vertically downwards. The transformation relationship is P. orbit =R0P J2000 .

[0055] S8, based on the pointing vector P in the local orbital coordinate system orbit Determine the pointing vector P in the local star's body coordinate system. Sat .

[0056] In this step, the transformation matrix for converting the pointing vector from the local orbit coordinate system to the local body coordinate system mainly considers the satellite's yaw angle α, pitch angle β, and roll angle γ, which vary depending on the rotation sequence specified on the satellite. Taking a rotation sequence of 123 as an example, the transformation formula for the pointing vector in the local body coordinate system is:

[0057]

[0058] S9, based on the pointing vector P in the local star's body coordinate system Sat Determine the pointing vector P in the local satellite antenna coordinate system. antenna .

[0059] In this step, the influence of the rotation vector R formed by the antenna's installation direction and installation error on the pointing angle is considered. The specific transformation relationship is as follows:

[0060] Where x, y, and z are the pointing vectors P in the local satellite antenna coordinate system, respectively. antenna Projected values ​​on the X, Y, and Z axes.

[0061] S10, determine the pointing angle (azimuth angle Az, off-axis angle E1) in the local satellite antenna coordinate system at time t.

[0062] In this step, the azimuth angle Off-axis angle

[0063] S11, determine if the number of iterations n is less than 1 / Δt. If n is less than 1 / Δt, the number of iterations n = n + 1, and return to step S3; otherwise, end the loop.

[0064] S12, STK simulation calculation of the off-axis angle and azimuth angle of the local star pointing to the target star.

[0065] In the STK scenario, the HPOP model is used for the local star's orbit, and the orbital epoch time and orbital six-element number are consistent with the input in step S1; the SGP4 model is established by directly reading the TLE parameters for the target star, and 10 sets of pointing angle results for the local star and the target star are calculated in the interval [t+0.1,t+1]s with an interval of 0.1s.

[0066] Comparison of S13 and STK simulation and algorithm results.

[0067] In this invention, the link pointing angle is the angle at which the local antenna beam points to the target satellite in the local antenna coordinate system, including the off-axis angle E1 and the azimuth angle A2.

[0068] The pointer angle calculation algorithm is not limited to its execution environment and can be used in both CPU and DSP.

[0069] The link pointing angle analysis method of the present invention is verified through the following examples. The link pointing angle includes, but is not limited to, the Ka-band pointing angle. This inter-satellite link pointing angle analysis method can be widely applied to link pointing angle calculation in various frequency bands. Since the Ka-band has a narrow half-power beamwidth and requires high pointing accuracy, the Ka-band is used as an example for illustration.

[0070] (1) Obtain the six orbital elements (a, e, i, Ω, w, M) of the local satellite (orbital altitude 1200km) in the J2000.0 inertial coordinate system, with the orbital epoch time being t. 本星 ;

[0071] (2) Input the orbital parameters (t) of the target star (600km) that matches the SGP4 model from the two rows of TLE. TLE n0, bstar, i TLE Ω TLE e TLE wTLE M TLE );

[0072] (3) Enter the loop, and record the number of loops as n (1≤n≤10). Calculate the time t=t0+n*0.1s for the target recursive time based on the current system time t0;

[0073] (4) Substitute the parameters from step (1) into the two-body model to calculate the position P of the local star in the J2000.0 inertial coordinate system at time t. Self ;

[0074] (5) Substitute the parameters from step (2) into the SGP4 model to calculate the target star position P′ in the TEE coordinate system at time t. Target The position P of the target star in the J2000.0 inertial coordinate system is obtained through matrix (HG) transformation. Target ,in:

[0075] P′ Target =(HG)P Target

[0076] (HG) = (EP)(ER)(NR)(PR)

[0077] Where (PR) is the precession matrix, (NR) is the nutation matrix, (ER) is the Earth's rotation matrix, and (EP) is the Earth's polar motion matrix.

[0078] (6) Based on the position P of the local satellite in the J2000.0 inertial coordinate system at time t. Self and the position P of the target star Target Determine the pointing vector P from the local satellite to the target satellite in the J2000.0 inertial coordinate system. J2000 P J2000 =P Target -P Self .

[0079] (7) According to the pointing vector P from the local satellite to the target satellite in the J2000.0 inertial coordinate system J2000 Determine the pointing vector P in the local orbit coordinate system. orbit P orbit =R0P J2000 .

[0080] (8) Based on the pointing vector P in the local orbit coordinate system orbit Determine the pointing vector P in the local star's body coordinate system. Sat Taking a satellite with yaw angle α, pitch angle β, and roll angle γ, and a rotation sequence of 123 as an example, the conversion formula for the pointing vector in the local satellite coordinate system is as follows:

[0081]

[0082] (9) Taking the installation errors of the satellite's X, Y, and Z axes as α', β', and γ', and specifying the correction sequence as 123, the pointing vector P in the local satellite antenna coordinate system antenna for:

[0083]

[0084] Where x, y, and z are the pointing vectors P in the local satellite antenna coordinate system, respectively. antenna Projected values ​​on the X, Y, and Z axes.

[0085] (10) Determine the pointing angle and azimuth angle in the local satellite antenna coordinate system. Off-axis angle

[0086] (11) Determine if the number of iterations is less than 10. If yes, the number of iterations n = n + 1, and return to step 3. Otherwise, end the loop.

[0087] (12) STK simulation calculation of the off-axis angle and azimuth angle of the local star pointing to the target star: In the STK scenario, the local star orbit is selected as the HPOP model, and the orbit epoch time and orbit six roots are consistent with the input in step 1); the target star is established by directly reading the TLE parameters to build the SGP4 model, and 10 sets of pointing angle results of the local star and the target star in the interval [t+0.1,t+1]s with an interval of 0.1s are calculated.

[0088] (13) Comparison of STK simulation and algorithm results: The combined pointing errors of the 10 pointing angles are 0.01019°, 0.01017°, 0.01016°, 0.01015°, 0.01014°, 0.01015°, 0.01015°, 0.01015°, 0.01016°, and 0.01017°, respectively. The pointing error is about 0.01°, which meets the link pointing requirements.

[0089] The present invention also provides a link pointing angle analysis device, comprising:

[0090] One or more CPU or DSP processors;

[0091] Storage device for storing one or more programs.

[0092] When the one or more programs are executed by the one or more processors, the one or more processors implement the inter-satellite link pointing angle analysis method described in the first aspect.

[0093] The present invention also provides a readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the inter-satellite link pointing angle analysis method described in the first aspect.

[0094] The readable storage media include, but are not limited to, USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0095] The present invention also provides a computer program product comprising: a computer program (also referred to as code or instructions), which, when the computer program is run, executes the inter-satellite link pointing angle analysis method described in the first aspect.

[0096] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, microwave, etc.) means.

[0097] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0098] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0099] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0100] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for analyzing the pointing angle of an inter-satellite link, characterized in that, include: Obtain the six orbital roots of the local satellite in the J2000.0 inertial coordinate system; Obtain the orbital parameters of the target star that matches the SGP4 model from the two rows of TLE, including: epoch time t. TLE Daily Earth revolutions n0, drag modulation coefficient bstar, orbital inclination i TLE Ascending node, equatorial radius Ω TLE Orbital eccentricity e TLE Angular distance from perigee w TLE and the near point angle M TLE ; Based on the current system time, the recursion time interval, and the number of iterations, the target recursion time is determined; the target recursion time is... t = t 0+ n Δ t ,in, t 0 represents the current system time; Δ t The recursive time interval is 0.05s ≤ Δ t ≤0.2s; n The loop count is 1 ≤ n ≤1 / Δ t Take a positive integer; Using the six roots of the local satellite's orbit, the position of the local satellite in the J2000.0 inertial coordinate system at the recursive time of the target is obtained; Using the orbital parameters of the target star, the position of the target star in the J2000.0 inertial coordinate system at the recursive time is obtained, including: substituting the orbital parameters of the target star into the SGP4 model to determine the position of the target star in the TEE coordinate system at the recursive time, and obtaining the position of the target star in the J2000.0 inertial coordinate system through matrix transformation; Based on the positions of the local satellite and the target satellite in the J2000.0 inertial coordinate system at the target recursive time, determine the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system; Based on the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system, determine the pointing vector in the local satellite's orbital coordinate system; Determine the pointing vector in the local star's body coordinate system based on the pointing vector in the local star's orbital coordinate system; Determine the pointing vector in the antenna coordinate system based on the pointing vector in the satellite's body coordinate system. Determine the pointing angle in the local satellite antenna coordinate system at the target recursive time; Determine if the set number of iterations has been reached. If not, continue to obtain the pointing angle in the local satellite antenna coordinate system at the next target recursion time, until the pointing angle in the local satellite antenna coordinate system is obtained at the set number of iterations.

2. The method for analyzing the pointing angle of inter-satellite links according to claim 1, characterized in that, The six elements of the orbit include: the semi-major axis a, the eccentricity e, the inclination i, the ascending node's right radius Ω, the perigee distance w, and the horizontal perigee M.

3. The method for analyzing the pointing angle of inter-satellite links according to claim 1, characterized in that, The step of obtaining the position of the local satellite in the J2000.0 inertial coordinate system at the target recursive time using the six orbital roots of the local satellite includes: substituting the six orbital roots of the local satellite into the two-body model to obtain the position of the local satellite in the J2000.0 inertial coordinate system at the target recursive time.

4. The method for analyzing the pointing angle of inter-satellite links according to claim 1, characterized in that, In the step of determining the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system based on the positions of the local satellite and the target satellite at the target recursive time, the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system is as follows: in, This is the pointing vector from the local satellite to the target satellite in the J2000.0 inertial coordinate system. This represents the position of the local satellite in the J2000.0 inertial coordinate system. This represents the position of the target star in the J2000.0 inertial coordinate system.

5. The method for analyzing the pointing angle of inter-satellite links according to claim 1, characterized in that, The pointing angle includes the azimuth angle and the off-axis angle; Azimuth Off-axis angle in, x , y , z These are the projection values ​​of the pointing vector in the local antenna coordinate system onto the X, Y, and Z axes, respectively.

6. A link pointing angle analysis device, characterized in that, include: One or more CPU or DSP processors; Storage device for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the inter-satellite link pointing angle analysis method according to any one of claims 1 to 5.

7. A computer program product, characterized in that, The computer program product includes: a computer program that, when run, executes the method for analyzing the inter-satellite link pointing angle as described in any one of claims 1 to 5.

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