Method for correcting keplerian orbital elements of igso satellite based on perigee angular distance correction

Abstract

The application provides an IGSO satellite Kepler orbit root number correction method based on perigee angular distance correction and belongs to the satellite navigation system constellation simulation field.The application takes the six-root satellite ephemeris of the Kepler orbit of the satellite as the simulation parameter, calculates the angle difference between the initial ascending node right ascension and the fixed value according to the fixed value of the fixed point longitude when the IGSO satellite passes the upper space of the equator, obtains the time difference information by combining the earth rotation angular velocity, corrects the perigee angular distance of the ephemeris parameter, simulates the IGSO trajectory information, and the subsatellite point trajectory is consistent with the theoretical orbit, and can be used in the satellite navigation system constellation simulation field.

Description

Technical Field

[0001] This invention relates to a method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction, belonging to the field of satellite navigation system constellation simulation. Background Technology

[0002] As a key national information infrastructure, satellite navigation systems have brought immense convenience to human society's production and daily life. Therefore, major countries worldwide have strengthened their research and development of satellite navigation systems and their augmentation systems. Current navigation system constellations are evolving from single MEO constellations to hybrid constellations incorporating GSO, IGSO, and MEO. The nadir trajectory (projection of the satellite's orbit onto the ground) of IGSO satellites in hybrid constellations exhibits a repeating figure-eight pattern, and the geostationary characteristics of GEO satellites enhance positioning and navigation performance within key service areas, thereby improving overall system performance.

[0003] Meanwhile, because the IGSO's nadir trajectory is figure-eight shaped, its constellation can only serve a portion of the Earth's surface. Therefore, the system performance simulation of hybrid constellations places higher demands on the simulation of IGSO satellite trajectories. Satellites are celestial bodies that do not move with the Earth, making a celestial coordinate system, i.e., an inertial coordinate system, suitable. The Keplerian orbital elements of a satellite constellation include: orbital radius, eccentricity, orbital inclination, right ascension of the ascending node, perigee distance, and mean anomaly. The reference coordinate system for the satellite operation model is the geocentric inertial coordinate system (ECI), whose orbit is insensitive to the Earth's rotation. Since the right ascension of the ascending node and the argument of latitude (including the perigee distance and mean anomaly) in the Keplerian orbital elements are reference values ​​of the satellite relative to the Earth's center and equatorial plane at a certain orbital epoch, they change over time; that is, the right ascension of the ascending node and the argument of latitude are time-sensitive parameters. Therefore, when performing constellation simulations for IGSO, it is necessary to consider eliminating the time correlation of Kepler orbital elements to ensure the accuracy of satellite trajectories relative to Earth and improve the accuracy of constellation service performance system simulations.

[0004] To eliminate the time-dependent influence of the right ascension of the ascending node and the argument of latitude on IGSO satellite Kepler orbit elements, adjustments need to be made based on the longitude of the intersection point. Because the nadir trajectory of an IGSO satellite exhibits an "8" shape, its longitude is always the intersection longitude whenever the satellite crosses the equator. Simultaneously, the satellite rotates through a certain arc within its inertial plane, and the fixed relationship between the initial right ascension of the ascending node, the longitude of the intersection point, and the argument of latitude facilitates the elimination of the time-dependent influence of Kepler orbit element parameters. Therefore, this invention can eliminate the time sensitivity of the IGSO ascending node's right ascension and argument of latitude. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of time correlation between the right ascension of the ascending node and the latitude argument of the Kepler orbit elements of IGSO satellites. It proposes a method for correcting the Kepler orbit elements of IGSO satellites based on perigee distance correction. This method can correct the perigee distance of the ephemeris parameters, and the simulated IGSO trajectory information shows that the nadir point trajectory is consistent with the theoretical orbit. It can be used in the field of satellite navigation system constellation simulation.

[0006] This invention is achieved through the following technical solution:

[0007] A method for correcting the Kepler orbit elements of IGSO satellites based on perigee offset correction specifically includes the following steps:

[0008] Step 1: Calculate the angle through which the Earth rotates based on the right ascension of the initial ascending node of the reference ephemeris and the longitude of the intersection point of the IGSO satellite;

[0009] Step 2: Calculate the Earth's rotational angular velocity based on the Earth's rotation period, and calculate the Earth's rotation time difference information by combining the angles through which the Earth has rotated; at the same time, calculate the satellite's orbital period based on the orbital radius of the Kepler orbital elements ephemeris, and obtain the average angular velocity of the satellite's orbit; obtain the initial latitude argument of the satellite's orbit by summing the perigee distance and true perigee angle based on the Kepler orbital elements.

[0010] Step 3: Based on the principle that the sum of the initial latitude argument and the angle of rotation when the IGSO satellite passes over the equator is an integer multiple of the circular period, the satellite orbital latitude argument increment is calculated using the Earth's rotation time difference information, the average angular velocity of the satellite, and the initial latitude argument of the satellite orbit.

[0011] Step 4: Correct the perigee angle using the satellite orbital latitude argument increment, and calculate the corrected perigee angular distance.

[0012] Furthermore, the specific process of step 1 is as follows:

[0013] The longitude of the intersection point of the IGSO satellites in the constellation design is used as the starting angle Ω of the IGSO satellites. start The termination angle Ω of the IGSO satellite is determined by the right ascension of the initial ascending node of the Keplerian orbital element reference ephemeris. end The angle ΔΩ through which the Earth rotates is calculated:

[0014] ΔΩ=Ω end -Ω start .

[0015] Furthermore, the calculation in step 3 is as follows:

[0016] Δu=2π-n*ΔT-u s

[0017] In the formula, Δu is the satellite orbital latitude argument increment, ΔT is the Earth's rotation time difference information, n is the average angular velocity of the satellite, and u s This is the initial latitude argument of the satellite's orbit.

[0018] Furthermore, the calculation in step 4 is as follows:

[0019] ω=ω0+Δu

[0020] In the formula, ω is the corrected perigee angular distance, Δu is the satellite orbital latitude argument increment, and ω0 is the perigee angular distance.

[0021] The advantages of this invention compared to the prior art are:

[0022] This invention uses the Kepler orbit ephemeris of a satellite as a simulation parameter. Based on the fixed longitude of the IGSO satellite when it flies over the equator, the angular difference between the right ascension of the starting ascending node and this fixed value is calculated. Combined with the time difference information obtained by the Earth's rotation angular velocity, the perigee angular distance of the ephemeris parameters is corrected. The simulated IGSO trajectory information shows that the nadir trajectory is consistent with the theoretical orbit. Attached Figure Description

[0023] Figure 1 The flowchart of the method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction is presented in this invention.

[0024] Figure 2 The nadir trajectory of the second Beidou IGSO satellite before correction.

[0025] Figure 3 The present invention corrects the nadir trajectory of the second Beidou IGSO satellite. Detailed Implementation

[0026] To better illustrate the objectives and advantages of this invention, the technical solution of this invention will be further described below with reference to the accompanying drawings and implementation examples. In specific implementations, the parameters submitted at the ITU 609 meeting are used as examples for description.

[0027] Table 1. Reference ephemeris for the six elements of BeiDou IGSO Kepler orbit submitted at ITU Meeting 609

[0028]

[0029] Using the Keplerian orbit six-ephemeris number of satellite 2 as the reference ephemeris, the nadir trajectory of the second satellite was plotted, and the result is as follows. Figure 2 As shown, the trajectory is not over China, so the Kepler orbit six-root number needs to be corrected so that the longitude of the satellite's intersection point is 118°E.

[0030] like Figure 1As shown, this invention discloses a method for correcting the Keplerian orbit elements of an IGSO satellite based on perigee distance correction. Using the satellite's Keplerian orbit ephemeris as simulation parameters, and taking the fixed longitude of the IGSO satellite as its point of origin when it crosses the equator as a fixed value, the angular difference between the right ascension of the initial ascending node and this fixed value is calculated. Combined with the Earth's rotational angular velocity to obtain time difference information, the perigee distance of the ephemeris parameters is corrected. The simulated IGSO trajectory information shows that the nadir trajectory is consistent with the theoretical orbit. Specifically, the method includes the following steps:

[0031] Step 1: Use the longitude of the intersection point of the IGSO satellites in the constellation design as the starting angle Ω of the IGSO satellites. start =118, with the initial ascending node right ascension of the Keplerian orbital element reference ephemeris as the termination angle Ω of the IGSO satellite. end =120, the difference between the two is the angle ΔΩ through which the Earth rotates:

[0032] ΔΩ=Ω end -Ω start =2.

[0033] Step 2, based on the Earth's rotation period T e =86164.0989s Calculate the Earth's rotational angular velocity Ω e And combined with the angle ΔΩ obtained in step 1, calculate the Earth's rotation time difference information ΔT:

[0034]

[0035] ΔT=ΔΩ / Ω e ≈478.6894s.

[0036] Meanwhile, the satellite's orbital period T is calculated based on the orbital radius a = 42364.137 km from the Kepler orbital element ephemeris. s And calculate the average angular velocity n of the satellite's orbit:

[0037] μ = GM = 3.986005 × 10 5 km 3 / s 2

[0038] T s =2π(a 3 / μ) 1 / 2 =86163.98s

[0039] n = 2π / T s =7.29212485×10 -5 m / s

[0040] In the formula, μ is the gravitational constant of the Earth, G is the gravitational constant, and M is the mass of the Earth;

[0041] Simultaneously, by summing the input Keplerian orbital elements perigee distance ω0=0 and true anomaly angle 67.6, the initial latitude argument u of the satellite orbital operation is calculated. s

[0042] u s =u0+ω0=67.6.

[0043] Step 3: Based on the principle that the sum of the initial latitude argument and the angle through which the IGSO satellite passes over the equator is an integer multiple of the circular period, calculate the satellite orbital latitude argument increment Δu using the Earth's rotation time difference information, the satellite's average angular velocity, and the initial latitude argument of the satellite's orbit:

[0044] Δu=2π-n*ΔT-u s =290.4002

[0045] Step 4: Use the latitude argument increment Δu obtained in Step 3 to correct the perigee angular distance ω0 = 0, and calculate the corrected perigee angular distance ω:

[0046] ω=ω0+Δu=290.4002

[0047] This concludes the method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction.

[0048] The corrected ephemeris is shown in the table below.

[0049] Table 2 Ephemeris parameters after IGSO correction

[0050]

[0051] Substituting the original ephemeris parameters and the corrected parameters into the Kepler orbit model of the celestial body, the simulation lasted 24 hours. The longitude of the intersection point of the nadir trajectory of the corrected BeiDou IGSO satellite is as follows: Figure 3 As shown, the longitude of the intersection point is located at 118 degrees east longitude in the design.

Claims

1. A method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction, characterized in that, Specifically, the steps include the following: Step 1: Calculate the angle through which the Earth rotates based on the right ascension of the initial ascending node of the reference ephemeris and the longitude of the intersection point of the IGSO satellite; Step 2: Calculate the Earth's rotational angular velocity based on the Earth's rotation period, and calculate the Earth's rotation time difference information by combining the angles through which the Earth rotates; calculate the satellite's orbital period based on the orbital radius of the Kepler orbital elements ephemeris, and obtain the average angular velocity of the satellite's orbit; obtain the initial latitude argument of the satellite's orbit by summing the perigee distance and true perigee angle based on the Kepler orbital elements. Among them, Earth's rotation time difference information for: ； In the formula, This is the Earth's rotational angular velocity. This is the Earth's rotation period. This represents the angle through which the Earth rotates. Step 3: Based on the principle that the sum of the initial latitude argument and the angle through which the Earth rotates when the IGSO satellite passes over the equator is an integer multiple of the circumference, calculate the satellite orbital latitude argument increment using the Earth's rotation time difference information, the average angular velocity of the satellite, and the initial latitude argument of the satellite orbit. Step 4: Correct the perigee angular distance using the satellite orbital latitude amplitude increment, and calculate the corrected perigee angular distance.

2. The method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction according to claim 1, characterized in that, Step 1 is as follows: The longitude of the intersection point of IGSO satellites in the constellation design is used as the starting angle for IGSO satellites. The termination angle of the IGSO satellite is determined by the right ascension of the initial ascending node of the Keplerian orbital element reference ephemeris. Calculate the angle through which the Earth rotates. : 。 3. The method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction according to claim 1, characterized in that, The calculation in step 3 is as follows: ； In the formula, This represents the increment of the satellite's orbital latitude angle. Information on Earth's rotation time difference. The average angular velocity of the satellite's orbit. This is the initial latitude argument of the satellite's orbit.

4. The method for correcting the Kepler orbit elements of IGSO satellites based on perigee angular distance correction according to claim 1, characterized in that, The calculation in step 4 is as follows: ； In the formula, This is the corrected perigee angular distance. This represents the increment of the satellite's orbital latitude angle. This is the angular distance from the perigee.

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