CN114002710A - On-satellite orbit position autonomous prediction method for small-eccentricity low-orbit satellite - Google Patents

On-satellite orbit position autonomous prediction method for small-eccentricity low-orbit satellite Download PDF

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CN114002710A
CN114002710A CN202111220941.2A CN202111220941A CN114002710A CN 114002710 A CN114002710 A CN 114002710A CN 202111220941 A CN202111220941 A CN 202111220941A CN 114002710 A CN114002710 A CN 114002710A
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orbit
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刘伟亮
吕旺
俞航
宋玉亭
王豪
钱元元
余润清
肖灿明
顾军
张健军
沈松涛
辛阁霖
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Shanghai Aerospace Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position

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Abstract

The invention relates to an on-satellite orbit position autonomous forecasting method of a small-eccentricity low-orbit satellite, which is implemented by using an initial ephemeris time t0Normalized satellite singular point-free orbital element [ a, i ]0,Ω0,ξ0,η0,λ0]As input, consider J in Earth's gravity field shot2To J4Item perturbation, and target time t is obtained through track recursion1Number of orbital elements of satellite without singular point [ a ]s,is,Ωs,ξs,ηs,λs]Thereby obtaining a target time t1The position of the satellite in the J2000.0 coordinate system. The invention can predict the position of the satellite at the appointed time through orbit recursion and consider J in the earth gravitational field shooting in the calculation2To J4The method is suitable for long-time and high-precision satellite position prediction, and can be suitable for various in-orbit task requirements of satellites.

Description

On-satellite orbit position autonomous prediction method for small-eccentricity low-orbit satellite
Technical Field
The invention relates to the field of satellite orbit calculation in satellite orbit dynamics, in particular to an on-satellite orbit position autonomous forecasting method for a small-eccentricity low-orbit satellite.
Background
In recent years, the prediction of the position of an artificial satellite at a given time has become an increasingly important issue. The high-precision orbit prediction is an important technology in the aerospace technology, plays an important role in satellite orbit design and orbit optimization, and can provide reliable orbit information reference for satellite in-orbit tasks such as antenna pointing, tracking and positioning and the like.
At present, a satellite orbit recursion method and a high-precision orbit determination algorithm applied to a ground station are generally realized by a high-performance computer, wherein the high-precision orbit determination algorithm and the high-precision orbit determination algorithm comprise a high-precision integral algorithm and a high-precision dynamic model, and the demand on computing resources is high. A common approach for satellite tracking when the satellite is in orbit is to receive its orbit data by a GNSS receiver, which has the following disadvantages: the GNSS real-time orbit determination has errors, and the visible number of navigation satellites is less than 4 easily caused by the conditions of satellite pointing, electronic interference or environmental shielding, and the like, so that the continuity and the accuracy of satellite orbit data are influenced. Another approach is to extrapolate from the number of tracks injected above ground, which has the following disadvantages: the extrapolation model applied at present is generally too simple, so that the accuracy of orbit data is poor, and the extrapolation model is generally not suitable for long-term prediction.
In the Chinese invention patent "a satellite position acquisition method and system" (publication number: CN104459732A), a GLONASS satellite position calculation method is introduced. This method can obtain the position and velocity of the satellites at the time of observation, but employs a numerical integration method and relies on the GLONASS receiver.
In the Chinese invention patent of 'an orbit data interpolation method based on Lagrange interpolation and Kalman filtering' (publication number: CN103268407A), an orbit data interpolation method based on Lagrange interpolation and Kalman filtering is introduced. The algorithm can realize high-precision real-time simulation of the satellite position, but occupies larger computing resources, and can increase the burden of a satellite computer.
In the Chinese invention patent "short arc orbit determination instantaneous radical accuracy assessment method for low orbit spacecraft" (publication number: CN111060934A), a forecast comparison method in an external coincidence accuracy assessment method is adopted, parameters of a rear-stage measurement time are forecasted according to an orbit determination result of front-stage measurement data, and orbit determination accuracy is judged according to the external coincidence degree of the forecast parameters and the rear-stage measurement data. The method needs to take the atmospheric damping coefficient in the orbit determination input menu as the quantity to be estimated, and does not consider J in the earth gravitational field shooting2To J4An item. Obviously, for the small eccentricity orbit prediction, the atmospheric damping coefficient is far less effective than J2To J4The term is obvious, even additional errors are brought, and the track prediction precision is influenced.
Ledan et al propose an algorithm for predicting satellite orbits by using elliptic curves in a 'low orbit satellite orbit prediction algorithm based on orbital elements' (see optical precision engineering, 2016, 10 th), but the partial differential of coefficients needs to be calculated in the process of solving.
In the Chinese invention patent 'an on-satellite autonomous orbit extrapolation method suitable for circular orbit satellite' (publication number: CN103995800A), an orbit recursion suitable for circular orbit satellite is introducedThe method of (1). But the method only considers J2Item perturbation, not considering J4Item perturbation is not suitable for small eccentricity orbit satellites.
Disclosure of Invention
The invention aims to provide an on-satellite orbit position autonomous prediction method of a small-eccentricity low-orbit satellite, which recurs the position of the satellite at a specified moment based on the orbital flat root, and takes the J in the earth gravitational field shooting into consideration in the recursion process2To J4Item perturbation improves forecast precision.
In order to achieve the above purpose, the present invention provides an autonomous prediction method for the on-satellite orbit position of a low-eccentricity low-orbit satellite, which uses an initial ephemeris time t0Normalized satellite singular point-free orbital element [ a, i ]0,Ω0,ξ0,η0,λ0]As input, consider J in Earth's gravity field shot2To J4Item perturbation, and target time t is obtained through track recursion1Number of orbital elements of satellite without singular point [ a ]s,is,Ωs,ξs,ηs,λs]Thereby obtaining a target time t1The position of the satellite in the J2000.0 coordinate system; wherein a is normalized t0Time of day satellite orbit long semi-axis, i0Is t0Time of day satellite orbit inclination angle, omega0Is t0Time rising point declination, xi0、η0And λ0Are all t0No singular value exists at any moment; a issIs t1Time of day satellite orbit long semi-axis, isIs t1Time of day satellite orbit inclination angle, omegasIs t1Time rising point declination, xis、ηsAnd λsAre all t1And no singular quantity exists at the moment.
The on-satellite orbit position autonomous forecasting method of the small eccentricity and low orbit satellite comprises the following steps: perturbation term calculation and track recursion main formula calculation.
The method for autonomously forecasting the on-satellite orbit position of the small-eccentricity low-orbit satellite comprises a perturbation term, a perturbation term and a perturbation term, wherein the perturbation term comprises a first-order long period term, a first-order short period term and a second-order long period term.
The on-satellite orbit position autonomous forecasting method of the small eccentricity and low orbit satellite comprises the following main orbit recursion formula:
Figure BDA0003312586290000031
Figure BDA0003312586290000032
Figure BDA0003312586290000033
Figure BDA0003312586290000034
Figure BDA0003312586290000035
Figure BDA0003312586290000036
wherein, the first-order long-period term lower elevation crossing right ascension omega1Argument of near place omega1No singular variable lambda1(ii) a Satellite orbit semi-major axis under first-order short period term
Figure BDA0003312586290000037
Inclination angle of satellite orbit
Figure BDA0003312586290000038
Ascending crossing point of the right ascension
Figure BDA0003312586290000039
No singular variables
Figure BDA00033125862900000310
No singular variables
Figure BDA00033125862900000311
No singular variables
Figure BDA00033125862900000312
Second order long period term lower elevation crossing right ascension omega2No singular variable xi2No singular variable lambda2；dtmIs the normalized recurrence time; n is the average angular velocity of the track; a istIs normalized t1The time satellite orbit major semiaxis.
The on-satellite orbit position autonomous forecasting method of the small eccentricity and low orbit satellite is characterized in that,
(1) first order long period term
Figure BDA0003312586290000041
Figure BDA0003312586290000042
Figure BDA0003312586290000043
Wherein the semi-diameter is p ═ a × (1-e)0 2) Mean angular velocity of track
Figure BDA0003312586290000044
J2＝1.624×10-3；
(2) First order short period term
Figure BDA0003312586290000045
Figure BDA0003312586290000046
Figure BDA0003312586290000047
Figure BDA0003312586290000048
Figure BDA0003312586290000049
Figure BDA00033125862900000410
Wherein u is calculated from a first-order long period term:
Figure BDA00033125862900000411
Figure BDA00033125862900000412
ξz1＝ξ0 cos(ωc1dtm)+η0 sin(ωc1dtm)
ηz1＝η0 cos(ωc1dtm)-ξ0 sin(ωc1dtm)
λz1＝λ0+(n+λc1)dtm
Figure BDA00033125862900000413
ωz1＝arc cos(ξz1/ez1)
Mz1＝mod(λz1-ωz1,2π)
Figure BDA0003312586290000051
u＝fz1+ωz1
(3) second order long period term
Figure BDA0003312586290000052
Figure BDA0003312586290000053
Figure BDA0003312586290000054
Wherein, J3＝2.5356×10-6,J4＝7.1022×10-6。
The on-satellite orbit position autonomous forecasting method of the small eccentricity and low orbit satellite further comprises the step of passing t1Instantaneous root calculation t of satellite orbit at moment1Component R of position vector of time satellite in J2000.0 coordinate systemwECIThe calculation method comprises the following steps:
Figure BDA0003312586290000055
Figure BDA0003312586290000056
Figure BDA0003312586290000057
Qpx＝(RZ(Ωs))T(RX(is))T(RZ(ws))T
RwECI＝Qpx·rp
wherein f issIs a true proximal angle, h1Is an intermediate quantity, mu is the gravitational constant, RX(is) Indicating a rotation about the X axis isCoordinate transformation matrix of angle, RZ(Ωs) Indicating a rotation omega about the Z axissCoordinate transformation matrix of angle, RZ(ωs) Representing rotation omega about the Z-axissA coordinate transformation matrix of the angle; e.g. of the typesIs t1Moment satellite orbital eccentricity, omegasIs t1Amplitude and angle of time and place, MsIs t1The time is close to the point angle.
Compared with the prior art, the invention has the beneficial technical effects that:
the invention discloses an on-satellite orbit position autonomous prediction method of a small-eccentricity low-orbit satellite, which is characterized in that satellite orbit information is recurred according to the average number of current orbits, the position of the satellite at a specified moment is predicted, and J in the earth gravitational field shooting is considered in the calculation2To J4The method has the advantages of high precision, suitability for long-term recursion, capability of meeting precision requirements of various on-orbit tasks and no occupation of too much resource of on-board computers.
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The autonomous prediction method for the satellite orbit position of the small eccentricity low orbit satellite is provided by the following embodiments and accompanying drawings.
Fig. 1 is a flowchart of the autonomous prediction method of the satellite orbit position of the small eccentricity low orbit satellite of the present invention.
Fig. 2 is a schematic diagram of the autonomous prediction method of the satellite orbit position of the small eccentricity low orbit satellite of the present invention.
Detailed Description
The autonomous prediction method of the satellite orbit position of the low-eccentricity low-orbit satellite of the present invention will be described in further detail with reference to fig. 1 to 2.
FIG. 1 is a flow chart of the method for autonomous prediction of the orbit position on the satellite for a low eccentricity and low orbit satellite according to the present invention; fig. 2 is a schematic diagram of the autonomous prediction method of the satellite orbit position of the small eccentricity low orbit satellite of the present invention.
The invention relates to an on-satellite orbit position autonomous forecasting method of a small-eccentricity low-orbit satellite, which is implemented by using an initial ephemeris time t0、t0Time-normalized satellite non-singular point orbital element [ a, i ]0,Ω0,ξ0,η0,λ0]And a target time t1As input, consider J in Earth's gravity field shot2To J4Item perturbation, input parameters are recurred by a satellite computer.
Normalized satellite non-singular point orbital element [ a, i ]0,Ω0,ξ0,η0,λ0]Number of parallel to satellite orbit [ a ]0,e0,i0,Ω0,ω0,M0]The relationship of (1) is:
ξ0＝e0 cos(ω0)
η0＝-e0 sin(ω0)
λ0＝ω0+M0
Figure BDA0003312586290000071
wherein, a0Is t0Time of day satellite orbit major semi-axis, e0Is t0Moment satellite orbital eccentricity, i0Is t0Time of day satellite orbit inclination angle, omega0Is t0Time-rising intersection declination, ω0Is t0Amplitude and angle of time and place, M0Is t0The time is equal to the approximate point angle; re is length normalized unit, Re is 6378140 m;
referring to fig. 1 and 2, the method for autonomously forecasting the orbit position on the satellite of the small eccentricity low orbit satellite of the present invention comprises:
1) perturbation item calculation in earth gravitational field shooting
The invention considers perturbation of earth gravitational field in the process of orbit recursionJ in (1)2To J4Item perturbation (i.e. consider J)2、J3And J4Terms) including a first order long period term, a first order short period term, and a second order long period term, expressions of the respective perturbation terms:
(1) first order long period term
Figure BDA0003312586290000072
Figure BDA0003312586290000073
Figure BDA0003312586290000074
Wherein, the first-order long-period term lower elevation crossing right ascension omega1Argument of near place omega1No singular variable lambda1The semi-diameter is p ═ a × (1-e)0 2) Mean angular velocity of track
Figure BDA0003312586290000075
J2＝1.624×10-3；
(2) First order short period term
Figure BDA0003312586290000081
Figure BDA0003312586290000082
Figure BDA00033125862900000816
Figure BDA0003312586290000083
Figure BDA0003312586290000084
Figure BDA0003312586290000085
Wherein, the satellite orbit semi-major axis under the first order short period term
Figure BDA0003312586290000086
Inclination angle of satellite orbit
Figure BDA0003312586290000087
Ascending crossing point of the right ascension
Figure BDA0003312586290000088
No singular variables
Figure BDA0003312586290000089
No singular variables
Figure BDA00033125862900000810
No singular variables
Figure BDA00033125862900000811
u is calculated from the first order long period term:
Figure BDA00033125862900000812
Figure BDA00033125862900000813
ξz1＝ξ0 cos(ωc1dtm)+η0 sin(ωc1dtm)
ηz1＝η0 cos(ωc1dtm)-ξ0 sin(ωc1dtm)
λz1＝λ0+(n+λc1)dtm
Figure BDA00033125862900000814
ωz1＝arc cos(ξz1/ez1)
Mz1＝mod(λz1-ωz1,2π)
Figure BDA00033125862900000815
u＝fz1+ωz1
(3) second order long period term
Figure BDA0003312586290000091
Figure BDA0003312586290000092
Figure BDA0003312586290000093
Wherein, the second-order long period term of the right ascension cross point under the second-order long period term has no singular variable xi2No singular variable lambda2，J3＝2.5356×10-6,J4＝7.1022×10-6；
2) Recursive main formula calculation
For the introduced non-singular point variables, the long period term and the short period term perturbation term can be combined to carry out analytic solution construction; in the track recursion process, ignoring the long period item perturbation, the track recursion main formula is as follows:
Figure BDA0003312586290000094
Figure BDA0003312586290000095
Figure BDA0003312586290000096
Figure BDA0003312586290000097
Figure BDA0003312586290000098
Figure BDA0003312586290000099
to this end, t is obtained by a track recursion method1Number of non-singular point orbits [ a ] of time satellites,is,Ωs,ξs,ηs,λs]；
From t1Number of non-singular point orbits [ a ] of time satellites,is,Ωs,ξs,ηs,λs]Can obtain t1Instantaneous number of satellite orbits [ a ] of times,es,is,Ωs,ωs,Ms]：
Figure BDA00033125862900000910
ωs＝arc cos(ξs/es)
Ms＝mod(λs-ωs,2π)
as＝at×Re，asUnit:m；
asis t1Time of day satellite orbit major semi-axis, esIs t1Moment satellite orbital eccentricity, isIs t1Time of day satellite orbit inclination angle, omegasIs t1Time-rising intersection declination, ωsIs t1Amplitude and angle of time and place, MsIs t1The time is equal to the approximate point angle; xis、ηsAnd λsAre all t1No singular variable exists at any moment;
3) satellite position calculation
Passing through t1The instantaneous number of the satellite orbit at the moment can be calculated1Component R of position vector of time satellite in J2000.0 coordinate systemwECIThe calculation method comprises the following steps:
Figure BDA0003312586290000101
Figure BDA0003312586290000102
Figure BDA0003312586290000103
Qpx＝(RZ(Ωs))T(RX(is))T(RZ(ωs))T
RwECI＝Qpx·rp
wherein f issIs a true proximal angle, h1Is an intermediate quantity, mu is the gravitational constant, RX(is) Indicating a rotation about the X axis isCoordinate transformation matrix of angle, RZ(Ωs) Indicating a rotation omega about the Z axissCoordinate transformation matrix of angle, RZ(ωs) Representing rotation omega about the Z-axissCoordinate transformation matrix of the angle.
The method for autonomously forecasting the orbit position on the satellite of the small eccentricity low orbit satellite of the invention is described in detail by specific embodiments.
The position forecast of the satellite can provide reliable orbit information reference for the on-orbit task of the satellite, and the position of the satellite can be expressed by the number of orbits and also can be expressed by coordinates. The invention is characterized in that the method is based on the given initial ephemeris time t0And t0Time-normalized satellite non-singular point orbital element [ a, i ]0,Ω0,ξ0,η0,λ0]At a given target time t1In the case of (1), the recursion of the satellite at t is obtained by mathematical calculation1Number of satellites at time of day without singular points [ a ]s,is,Ωs,ξs,ηs,λs]. The input 6 track numbers are shown in the following table:
a i0 Ω0 ξ0 η0 λ0
1.1291104273 98.6150792000 305.7682620000 -0.0001233451 -0.0011622901 2.9002237584
in the embodiment, the simulation analysis is carried out by taking the in-orbit running actual measurement data of the FY-3D star in the J2000.0 coordinate system as reference. The measured data of the on-orbit operation are as follows:
actual measurement orbit data of FY-3D satellite in Beijing at 2019, 1 month, 4 days, 00 minutes and 00 seconds at 16 days
Figure BDA0003312586290000111
Actual measurement orbit data of FY-3D satellite in Beijing at 2019, 1 month, 5 days, 16 hours, 00 minutes and 00 seconds
Figure BDA0003312586290000112
In the track recursion process, a first-order long period term, a first-order short period term and a second-order long period term need to be calculated, and the perturbation terms are calculated as follows:
(1) first order long period term
Figure BDA0003312586290000113
Figure BDA0003312586290000114
Figure BDA0003312586290000115
(2) First order short period term
Figure BDA0003312586290000121
Figure BDA0003312586290000122
Figure BDA0003312586290000123
Figure BDA0003312586290000124
Figure BDA0003312586290000125
Figure BDA0003312586290000126
Wherein u is calculated from a first-order long period term:
Figure BDA0003312586290000127
Figure BDA0003312586290000128
ξz1＝ξ0 cos(ωc1dtm)+η0 sin(ωc1dtm)
ηz1＝η0 cos(ωc1dtm)-ξ0 sin(ωc1dtm)
λz1＝λ0+(n+λc1)dtm
Figure BDA0003312586290000129
ωz1＝arc cos(ξz1/ez1)
Mz1＝mod(λz1-ωz1,2π)
Figure BDA00033125862900001210
u＝fz1+ωz1＝4.0898522230
(3) second order long period term
Figure BDA0003312586290000131
Figure BDA0003312586290000132
Figure BDA0003312586290000133
Substituting the perturbation term into the track recursion main formula for calculation, wherein the result is as follows:
Figure BDA0003312586290000134
Figure BDA0003312586290000135
Figure BDA0003312586290000136
Figure BDA0003312586290000137
Figure BDA0003312586290000138
Figure BDA0003312586290000139
thus, the satellite at t is obtained1Number of satellites at time of day without singular points [ a ]t,is,Ωs,ξs,ηs,λs]。
In order to verify recursion precision, 3 singular point-free variables are restored
Figure BDA00033125862900001310
ωs＝arc cos(ξs/es)＝1.1565124686
Ms＝mod(λs-ωs,2π)＝2.9330038039
Will be the semi-major axis a of the satellite orbittReduction to conventional units: a iss＝at×Re＝7.1987513438×106m, converting radian system parameters into angle system to obtain t1Instantaneous number of satellite orbits [ a ] of times,es,is,Ωs,ωs,Ms]. The 24-hour recursion error of the transient root of the orbit is shown in the following table
Figure BDA00033125862900001311
Figure BDA0003312586290000141
The component R of the position vector of the satellite in the J2000.0 coordinate system can be calculated through the orbit transient numberwECIThe calculation method comprises the following steps:
Figure BDA0003312586290000142
Figure BDA0003312586290000143
Figure BDA0003312586290000144
Qpx＝(RZ(Ωs))T(RX(is))T(RZ(ws))T
RwECI＝Qpx·rp
24-hour recursion error of coordinate component of satellite position in J2000.0 coordinate system
Figure BDA0003312586290000145
The basic function, the forecasting precision and the main advantages of the method are proved through the mathematical simulation result, and the method has practical engineering application value. The foregoing is only a preferred embodiment of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.

Claims (6)

1. The method for autonomously forecasting the on-satellite orbit position of the low-eccentricity and low-orbit satellite is characterized in that the initial ephemeris time t is used0Normalized satellite singular point-free orbital element [ a, i ]0,Ω0,ξ0,η0,λ0]As input, consider J in Earth's gravity field shot2To J4Item perturbation, and target time t is obtained through track recursion1Number of orbital elements of satellite without singular point [ a ]s,is,Ωs,ξs,ηs,λs]Thereby obtaining a target time t1The position of the satellite in the J2000.0 coordinate system; wherein a is normalized t0Time of day satellite orbit long semi-axis, i0Is t0Time of day satellite orbit inclination angle, omega0Is t0Time of dayDeclination, xi of ascending cross point0、η0And λ0Are all t0No singular value exists at any moment; a issIs t1Time of day satellite orbit long semi-axis, isIs t1Time of day satellite orbit inclination angle, omegasIs t1Time rising point declination, xis、ηsAnd λsAre all t1And no singular quantity exists at the moment.
2. The autonomous on-satellite orbit position prediction method of a small eccentricity low orbit satellite according to claim 1, wherein the autonomous on-satellite orbit position prediction method of a small eccentricity low orbit satellite comprises: perturbation term calculation and track recursion main formula calculation.
3. The autonomous method of orbit position on-satellite for small-eccentricity low-orbit satellites according to claim 2, wherein the perturbation terms include a first-order long-period term, a first-order short-period term and a second-order long-period term.
4. The method as claimed in claim 3, wherein the orbit recursion principal formula is as follows:
Figure FDA0003312586280000011
Figure FDA0003312586280000012
Figure FDA0003312586280000013
Figure FDA0003312586280000014
Figure FDA0003312586280000015
Figure FDA0003312586280000016
wherein, the first-order long-period term lower elevation crossing right ascension omega1Argument of near place omega1No singular variable lambda1(ii) a Satellite orbit semi-major axis under first-order short period term
Figure FDA0003312586280000017
Inclination angle of satellite orbit
Figure FDA0003312586280000018
Ascending crossing point of the right ascension
Figure FDA0003312586280000019
No singular variables
Figure FDA00033125862800000110
No singular variables
Figure FDA00033125862800000111
No singular variables
Figure FDA00033125862800000112
Second order long period term lower elevation crossing right ascension omega2No singular variable xi2No singular variable lambda2；dtmIs the normalized recurrence time; n is the average angular velocity of the track; a istIs normalized t1The time satellite orbit major semiaxis.
5. The method as claimed in claim 3, wherein the term of the first-order long period term is (1)
Figure FDA0003312586280000021
Figure FDA0003312586280000022
Figure FDA0003312586280000023
Wherein the semi-diameter is p ═ a × (1-e)0 2) Mean angular velocity of track
Figure FDA0003312586280000024
J2＝1.624×10-3；
(2) First order short period term
Figure FDA0003312586280000025
Figure FDA0003312586280000026
Figure FDA0003312586280000027
Figure FDA0003312586280000028
Figure FDA0003312586280000029
Figure FDA00033125862800000210
Wherein u is calculated from a first-order long period term:
Figure FDA00033125862800000211
Figure FDA00033125862800000212
ξz1＝ξ0cos(ωc1dtm)+η0sin(ωc1dtm)
ηz1＝η0cos(ωc1dtm)-ξ0sin(ωc1dtm)
λz1＝λ0+(n+λc1)dtm
Figure FDA0003312586280000031
ωz1＝arc cos(ξz1/ez1)
Mz1＝mod(λz1-ωz1,2π)
Figure FDA0003312586280000032
u＝fz1+ωz1
(3) second order long period term
Figure FDA0003312586280000033
Figure FDA0003312586280000034
Figure FDA0003312586280000035
Wherein, J3＝2.5356×10-6,J4＝7.1022×10-6。
6. The method of claim 1, wherein the method further comprises passing t1Instantaneous root calculation t of satellite orbit at moment1Component R of position vector of time satellite in J2000.0 coordinate systemwECIThe calculation method comprises the following steps:
Figure FDA0003312586280000036
Figure FDA0003312586280000037
Figure FDA0003312586280000038
Qpx＝(RZ(Ωs))T(RX(is))T(RZ(ws))T
RwECI＝Qpx·rp
wherein f issIs a true proximal angle, h1Is an intermediate quantity, mu is the gravitational constant, RX(is) Indicating a rotation about the X axis isCoordinate transformation matrix of angle, RZ(Ωs) Indicating a rotation omega about the Z axissCoordinate transformation matrix of angle，RZ(ωs) Representing rotation omega about the Z-axissA coordinate transformation matrix of the angle; e.g. of the typesIs t1Moment satellite orbital eccentricity, omegasIs t1Amplitude and angle of time and place, MsIs t1The time is close to the point angle.
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