Azimuth angle calculation method for ground measurement and control antenna pointing satellite

文档序号：1336782 发布日期：2020-07-17 浏览：17次中文

阅读说明：本技术 地面测控天线指向卫星的方位角计算方法 (Azimuth angle calculation method for ground measurement and control antenna pointing satellite ) 是由俞航易灵郑渊刘登岭辛阁霖宋效正吕旺边志强于 2020-03-19 设计创作，主要内容包括：本发明公开了一种地面测控天线指向卫星的方位角计算方法,包括：利用以星历时刻t0、t0时刻的轨道平根数[a0,e0,i0,Ω0,ω0,M0]和地面测站天线的地理位置信息,经过卫星轨道的相关计算以及多个相关坐标系的转换计算,最终转换为t1时刻在站心系下的天线指向方位角度：高低角<Image he="56" wi="67" file="DDA0002418106560000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>水平角ψ,以完成地面测站天线对卫星指向方位的预报过程。本发明不依赖于仿真软件或过多假设内容,考虑卫星实际运行情况计算地面测站天线对卫星的指向,并且在计算中考虑地球引力场摄动中的J2至J4项摄动,适合长时间、高精度的卫星位置预测,可以适用于卫星在轨的多种任务需求,有效解决了地面站接收天线对卫星的指向控制问题,而且达到了比较高的指向精度。(The invention discloses a method for calculating an azimuth angle of a ground measurement and control antenna pointing to a satellite, which comprises the following steps: using ephemeris time t 0 、t 0 Number of orbital flat at time [ a ] 0 ,e 0 ,i 0 ,Ω 0 ,ω 0 ,M 0 ]And the geographic position information of the ground survey station antenna is finally converted into t through the correlation calculation of the satellite orbit and the conversion calculation of a plurality of correlation coordinate systems 1 Pointing azimuth angle of antenna under standing center system at time: high and low angle And the horizontal angle psi is used for completing the prediction process of the satellite pointing direction by the ground station antenna. The method does not depend on simulation software or excessive assumed contents, considers the actual running condition of the satellite to calculate the direction of the ground survey station antenna to the satellite, considers the perturbation of J2-J4 in the earth gravitational field shooting in the calculation, is suitable for long-time and high-precision satellite position prediction, and can be suitable for various in-orbit satellite positionsThe task requirement effectively solves the problem of pointing control of the receiving antenna of the ground station to the satellite, and achieves higher pointing accuracy.)

1. A method for calculating an azimuth angle of a ground measurement and control antenna pointing to a satellite is characterized by comprising the following steps:

2. The method for calculating the azimuth angle of the ground measurement and control antenna pointing to the satellite according to claim 1, comprising the following steps:

the input parameter non-singular processing steps:

when the track eccentricity is small, i.e. near circular track, e ≈ 0, to avoid the occurrence of singularities in the calculation, we turn to 3 singularity-free variables, i.e.:

ξ₀＝e₀cos(ω₀)

η₀＝-e₀sin(ω₀)

λ₀＝ω₀+M_0。

3. the method of claim 2, further comprising:

input parameter normalization processing:

normalization processing is performed for the recursion time dt:

dt＝t₁-t₀

wherein the content of the first and second substances,

t₀recursion of the starting moment for the track；

t₁Representing the track recursion end time;

dt_nthe result of normalization processing of the recursion time is shown, and the subscript n shows normalization;

for semi-major axis a₀And (3) carrying out normalization treatment:

the normalized unit of the time is

Wherein the content of the first and second substances,

ge is a gravitational constant;

re represents the earth equatorial radius.

4. The method of claim 3, further comprising:

perturbation item calculation step:

considering the perturbations of items J2 to J4 in the earth gravity field, including the calculation of first-order long-term, first-order short-term and second-order long-term terms, the expressions for the individual perturbation terms are as follows:

first order long term calculation:

wherein the content of the first and second substances,

Ω₁indicating satellite orbital riseThe first-order long period variation of the crossing right ascension;

ω₁representing the first-order long period variation of the argument of the satellite orbit in the near place;

λ₁represents the first-order long-period variation of the singularity-free variable λ introduced by the calculations herein;

p is a radius, and the expression is p ═ a × (1-e)₀ ²) Mean angular velocity of trackJ₂＝1.624×10^-3；

First order short period term calculation:

wherein the content of the first and second substances,

representing the first-order short period variable quantity of the semi-major axis of the satellite orbit;

representing the first-order short-period variation of the satellite orbit inclination angle;

the first-order short-period variation of the right ascension of the satellite orbit intersection point is represented;

respectively representing the first order short period variations of the three singularity-free variables ξ, η, λ introduced by the calculations herein;

the u is calculated by a first-order long-term, and the calculation process is as follows:

ξ_z1＝ξ₀cos(ω₁dt_n)+η₀sin(ω₁dt_n)

η_z1＝η₀cos(ω₁dt_n)-ξ₀sin(ω₁dt_n)

λ_z1＝λ₀+(n+λ₁)dt_n

ω_z1＝arc cos(ξ_z1/e_z1)

M_z1＝mod(λ_z1-ω_z1，2π)

u＝f_z1+ω_z1

wherein the content of the first and second substances,

ξ_z1、η_z1、λ_z1respectively, the results of integration according to first-order long-term variation of the three singularity-free variables ξ, η, λ introduced by the calculations herein;

e_z1an integral result which represents the eccentricity of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

ω_z1an integral result which represents the argument of the satellite orbit near place and takes the first-order long period variable quantity as integral quantity;

M_z1an integration result which represents the mean-near point angle of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

f_z1an integral result which represents the true near point angle of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

second-order long-term calculation:

wherein the content of the first and second substances,

Ω₂representing the second-order long-period variation of the right ascension of the satellite orbit;

ξ₂、λ₂second-order long-period variations representing singularity-free variables ξ, λ introduced by the calculations herein, respectively;

J₃＝2.5356×10^-6,J₄＝7.1022×10^-6。

5. the method of claim 4, further comprising:

and (3) calculating a recursion main formula:

for introduced singularity-free variables, an analytic solution structure is carried out by combining a long-term item perturbation item and a short-period item perturbation item, the long-period item perturbation is ignored, and a track recursion main formula is as follows:

wherein the content of the first and second substances,

α_trepresents t₁At the moment, the normalization result of the satellite orbit semi-major axis;

i_srepresents t₁At that time, the satellite orbit inclination;

Ω_srepresents t₁At the moment, the rising point of the satellite orbit is right ascension;

ξ_s、η_s、λ_srespectively represent t₁At time, the values of the three singularity-free variables ξ, η, λ introduced are calculated.

6. The method of claim 5, further comprising:

a singular point-free variable reduction step:

after the calculation is finished, 3 singularity-free variables are restored

ω_s＝arccos(ξ_s/e_s)

M_s＝mod(λ_s-ω_s,2π) 。

7. The method of claim 6, further comprising:

and (3) normalization variable reduction step:

will be the long axis a of the satellite orbit_tReduction to conventional units:

a_s＝a_t×Re

a is described_sUnit: and m is selected.

8. The method of claim 7, further comprising:

calculating the position of the inertial system satellite:

input t₁Instantaneous number of satellite orbits [ a ] of time_s,e_s,i_s,Ω_s,ω_s,M_s]Outputting the component R of the position vector of the satellite in the J2000.0 coordinate system_wECIThe calculation method comprises the following steps:

R_wECI＝Q*r_p

wherein the rotation matrix Q is described in a 3-1-3 rotation order:

vector r_p：

Wherein M is₁True proximal angle:

9. the method of claim 8, further comprising:

and a step of calculating the position of the earth-fixed satellite:

inputting a target time t₁And said calculated position R of the satellite in the inertial system_wECIOutput t₁Position R of time satellite under earth's fixation_wECFThe specific method comprises the following steps:

according to a given target time t₁Calculating a second counting value t from epoch J2000.0 (1/12/2000) to a predetermined target time_cInputting t₁Year, month, day, hour, minute, second of the moment, calculate julian day JD:

wherein, floor () is a round-down operation;

calculating a second count value t from epoch J2000.0 to a given target time based on the julian day JD_c：

t_c＝(JD-2455197.5)×86400+315547200

According to the calculated epoch J2000.0 to the second counting value t of the given target time_cCalculating a rotation matrix ER, a nutation matrix NR and a precision matrix PR of the earth, and calculating a conversion matrix M from an inertia system to a ground-fixed system_ECI2ECF：

M_ECI2ECF＝ER*NR*PR

And according to t obtained by the calculation₁Position R of time satellite under inertial system_wECICalculating t₁Position R of time satellite under earth's fixation_wECF：

R_wECF＝M_ECI2ECF*R_wECI。

10. The method of claim 9, further comprising:

and the antenna position calculation step of the earth-fixed system survey station:

according to the longitude, latitude and elevation of the given ground measurement station antenna, the position R of the ground measurement station antenna under the ground fixation system is calculated_tECFThe specific method comprises the following steps:

inputting longitude lon, latitude lat and elevation h of an antenna of the ground station;

computing coordinate components G1, G2:

wherein f is the geometric oblateness of the earth ellipsoid, and f is 1/298.257;

calculating the position R of the ground survey station antenna under the ground fixing system_tECF：

11. The method of claim 10, further comprising:

and a step of calculating the position of the satellite in the station center system:

inputting calculated t₁Position R of time satellite under earth's fixation_wECFAnd said calculated position R of the ground station antenna under the ground anchor system_tECFOutputting the position R of the satellite under the station center system_wCTThe specific method comprises the following steps:

under the system of the station center, a conversion matrix M from the earth fixation system to the system of the station center is calculated_ECF2CTDescribed as one rotation about the Z-axis of the earth fixation system and one rotation about the X-axis of the earth fixation system:

M_ECF2CT＝R_x(90°-lat)R_z(90°+lon)

wherein lon is the geographic longitude of the antenna of the ground survey station; lat is the geographical latitude of the antenna of the ground station;

and according to said t₁Position R of time satellite under earth's fixation_wECFPosition R of the ground station antenna under the ground anchor_tECFTranslating the origin of coordinates from the geocentric to the antenna of the ground survey station, and calculating t₁Position R of time satellite under the system of the center of the station_wCT：

R_wCT＝M_ECF2CT*(R_wECF-R_tECF) 。

12. The method of claim 11, further comprising:

the method comprises the following steps of:

inputting the position of the satellite under the station center system and outputting t₁The antenna pointing azimuth angle of the ground survey station at any moment: high and low angleThe horizontal angle psi is specifically as follows:

the high and low angles and the horizontal angle are defined under the station center system O_CTX_CTY_CTZ_CTIn, O_CTRepresenting the origin of the coordinate system, X_CTX-axis, Y, representing a coordinate system_CTY-axis, O, representing a coordinate system_CTX_CTY_CTThe plane, elevation angle, of X-axis and Y-axis of the coordinate systemIs a directorQuantity R_wCTAnd O_CTX_CTY_CTAngle of plane, define R_wCTVector sum of O_CTZ_CTThe included angle is less than 90 degrees and is positive; the horizontal angle psi being the director vector R_wCTAt O_CTX_CTY_CTProjection of plane and O_CTX_CTAngle of axis, defined around O_CTZ_CTShaft driven O_CTX_CTShaft clockwise steering pointing vector R_wCTAt O_CTX_CTY_CTThe projection of the surface is positive, and the antenna pointing azimuth angle is found according to the definition. Assuming that the position of the ground survey station is located at the origin of the station center system, the projection of the antenna pointing vector of the survey station under the station center system is R_wCTRecord R_wCTComprises the following steps:

wherein the content of the first and second substances,

x_CT、y_CT、z_CTrespectively representing the pointing vectors R of antennas of the stations_wCTAt the station center is O_CTX_CTY_CTZ_CTCoordinate components of corresponding X-axis, Y-axis and Z-axis;

calculation of elevation angle of antenna pointing azimuthThe horizontal angle ψ is:

and according to x_CT、y_CT、z_CTPositive and negative of (2), angle of elevationThe horizontal angle psi being divided into corresponding anglesAnd in the range of degrees, completing the process of forecasting the antenna pointing direction:

if z is_CTMore than or equal to 0, the height and angle will be changedDivision into ranges

If x_CT≥0,y_CTThe horizontal angle psi is divided into ranges

If x_CT＜0,y_CTThe horizontal angle psi is divided into ranges

If x_CT＜0,y_CTIf < 0, the horizontal angle psi is divided into ranges

If x_CT≥0,y_CTIf < 0, the horizontal angle psi is divided into ranges

Technical Field

The invention relates to the field of satellite orbit calculation in orbit dynamics, in particular to a method for calculating an azimuth angle of a ground measurement and control antenna pointing to a satellite.

Background

The radar plays a very important role in the scientific and technological construction of China, and along with the requirements of detecting and controlling an outer space target, the practical radar is rapidly developed and is applied to a plurality of important fields such as guidance, beyond-the-horizon detection and the like at present. With the development of the space detection technology, higher and higher requirements are put forward on the tracking and searching capabilities of a radar antenna, because a satellite signal is weak and has strong directivity, in order to capture a communication signal on a moving satellite, the deviation between the attitude of the antenna and the position of the satellite must be adjusted in real time to meet the communication requirement, because the signal-to-noise ratio of link transmission information is reduced due to the satellite-to-ground directional deviation, and if the signal-to-noise ratio exceeds the maximum station tolerance, the signal loss phenomenon can even occur. This requires that the radar antenna must adjust the pointing direction according to the command to track the moving target in real time. Therefore, the dynamic precision of the radar antenna pointing process becomes one of the important indexes of the antenna system function, and the design of the pointing calculation method with high pointing precision has general practical significance.

The method for forecasting the pointing direction of the satellite by the ground survey station antenna mainly comprises the steps of calculating an antenna pointing azimuth angle at a target moment according to orbit information and time information of the satellite and position information of the ground survey station antenna, and realizing accurate pointing of the satellite at the target moment through antenna pointing control. The prediction of the position of a satellite at a given moment has become an increasingly important issue in recent years. 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.

The existing satellite-ground pointing algorithm research in China mostly focuses on the optimization design of the pointing of a satellite to a ground survey station under the condition that the position of the ground survey station is fixed, and the research on the pointing of a ground survey station antenna to the satellite is less. Under the condition that the ground survey station is movable, under the condition that the geographical longitude, latitude and elevation of the ground survey station are known and the track information of the on-orbit aircraft is tracked, the pointing control of the aircraft is automatically completed, and the pointing azimuth angle of the antenna is calculated in real time. 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 computer comprises a high-precision integral algorithm and a high-precision dynamic model. Aiming at the actual situation, the invention provides a ground measurement station real-time positioning method with higher precision for a ground measurement station antenna, and the method can realize the prediction of the autonomous pointing direction of the satellite by the ground measurement station antenna.

The patent "design method of deep space probe antenna pointing" (patent number: CN104369877A) describes a method of pointing a deep space probe antenna to the ground center, which is used to realize the deep space probe antenna to the ground center orientation. The patent is directed to the orientation of the antenna to the geocenter and not to the given position of the earth surface, and the pointing vector of the detector antenna to the geocenter is directly given, and no algorithm for calculating the satellite position through the orbit parameters exists. The method is different from the method in that a method for calculating the satellite pointing direction of the ground station aiming at the given position of the earth surface is designed, the positioning calculation of the ground station is completed, and a calculation process for calculating the ground station-satellite pointing vector through the satellite orbit parameters at the given moment is designed.

The patent "simulation analysis method of pointing angle of data transmission antenna" (patent number: CN105184002A) introduces a method for calculating pointing direction of satellite-borne data transmission antenna to ground station, which uses existing satellite orbit simulation software STK to perform simulation solution on actual position of satellite and calculates two-dimensional pointing angle of data transmission antenna. The disadvantage of the patent is that the satellite position calculation depends on the satellite orbit simulation software STK, no specific calculation process is needed, the description of the coordinate system conversion is simple, and no algorithm of a conversion matrix is given. The invention has the advantages of providing a method for calculating the actual position of the satellite according to the orbit parameters of the satellite at the appointed time without depending on STK software and designing a set of detailed calculation flow of a related coordinate system conversion matrix.

The patent "a method for controlling the pointing direction of a dual-axis antenna to the ground around a moon satellite" (patent number: CN101204994A) describes a method for calculating the pointing direction of a satellite to the earth center around a moon satellite, which estimates the position of the satellite according to ephemeris data on the ground, calculates the visible area of the satellite to the earth, and calculates the pointing angle of the dual-axis antenna. The patent is directed to the geocenter, does not orient the surface location, and is mainly calculated in combination with a moon-related coordinate system. The invention is different from the method in that the calculation is mainly combined with the earth and the earth surface position related coordinate system to complete the position calculation of the ground survey station antenna and the directional calculation of the ground survey station antenna to the satellite, and the definition and the calculation method of the antenna directional angle are different.

Ledan et al propose a method 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 differentiation 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 a circular orbit satellite' (patent number: CN103995800A), a method for orbit recursion suitable for the circular orbit satellite is introduced. But this method only takes perturbation into account.

Based on the above consideration, the azimuth angle calculation method for the ground measurement and control antenna pointing satellite disclosed by the invention has the advantages of high precision and suitability for long-term prediction.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to provide a method for calculating the azimuth angle of a ground measurement and control antenna pointing to a satellite.

The method for calculating the azimuth angle of the ground measurement and control antenna pointing to the satellite comprises the following steps:

using ephemeris time t₀、t₀Number of orbital flat at time [ a ]₀,e₀,i₀,Ω₀,ω₀,M₀]And the geographic position information of the ground survey station antenna is finally converted into t through the correlation calculation of the satellite orbit and the conversion calculation of a plurality of correlation coordinate systems₁Pointing azimuth angle of antenna under standing center system at time: high and low angleAnd the horizontal angle psi is used for completing the prediction process of the satellite pointing direction by the ground station antenna. Further, ephemeris time t₀、t₀Number of orbital flat at time [ a ]₀,e₀,i₀,Ω₀,ω₀,M₀]And the geographic position information of the ground station antenna are known quantities and are directly obtained by inquiring the ephemeris of the satellite.

Preferably, the method comprises the following steps:

the input parameter non-singular processing steps:

when the track eccentricity is small, i.e. near circular track, e ≈ 0, to avoid the occurrence of singularities in the calculation, we turn to 3 singularity-free variables, i.e.:

ξ₀＝e₀cos(ω₀)

η₀＝-e₀sin(ω₀)

λ₀＝ω₀+M₀

preferably, the method further comprises the following steps:

input parameter normalization processing:

normalization processing is performed for the recursion time dt:

dt＝t₁-t₀

wherein the content of the first and second substances,

t₀recursion of the starting moment for the track;

t₁representing the track recursion end time;

dt_nthe result of normalization processing of the recursion time is shown, and the subscript n shows normalization;

for semi-major axis a₀And (3) carrying out normalization treatment:

the normalized unit of the time is

Wherein the content of the first and second substances,

ge is a gravitational constant;

re represents the earth equatorial radius.

Preferably, the method further comprises the following steps:

perturbation item calculation step:

first order long term calculation:

wherein the content of the first and second substances,

Ω₁representing the first-order long period variable quantity of the right ascension of the satellite orbit intersection point;

ω₁representing the first-order long period variation of the argument of the satellite orbit in the near place;

λ₁represents the first-order long-period variation of the singularity-free variable λ introduced by the calculations herein;

p is a radius, and the expression is p ═ a × (1-e)₀ ²) Mean angular velocity of trackJ₂＝1.624×10^-3；

First order short period term calculation:

wherein the content of the first and second substances,

representing the first-order short period variable quantity of the semi-major axis of the satellite orbit;

representing the first-order short-period variation of the satellite orbit inclination angle;

the first-order short-period variation of the right ascension of the satellite orbit intersection point is represented;

respectively representing the first order short period variations of the three singularity-free variables ξ, η, λ introduced by the calculations herein;

the u is calculated by a first-order long-term, and the calculation process is as follows:

ξ_z1＝ξ₀cos(ω₁dt_n)+η₀sin(ω₁dt_n)

η_z1＝η₀cos(ω₁dt_n)-ξ₀sin(ω₁dt_n)

λ_z1＝λ₀+(n+λ₁)dt_n

ω_z1＝arc cos(ξ_z1/e_z1)

M_z1＝mod(λ_z1-ω_z1，2π)

u＝f_z1+ω_z1

wherein the content of the first and second substances,

ξ_z1、η_z1、λ_z1respectively, the results of integration according to first-order long-term variation of the three singularity-free variables ξ, η, λ introduced by the calculations herein;

e_z1an integral result which represents the eccentricity of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

ω_z1an integral result which represents the argument of the satellite orbit near place and takes the first-order long period variable quantity as integral quantity;

M_z1an integration result which represents the mean-near point angle of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

f_z1an integral result which represents the true near point angle of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

second-order long-term calculation:

wherein the content of the first and second substances,

Ω₂representing the second-order long-period variation of the right ascension of the satellite orbit;

ξ₂、λ₂second-order long-period variations representing singularity-free variables ξ, λ introduced by the calculations herein, respectively;

J₃＝2.5356×10^-6,J₄＝7.1022×10^-6。

preferably, the method further comprises the following steps:

and (3) calculating a recursion main formula:

wherein the content of the first and second substances,

α_trepresents t₁At the moment, the normalization result of the satellite orbit semi-major axis;

i_srepresents t₁At that time, the satellite orbit inclination;

Ω_srepresents t₁At the moment, the rising point of the satellite orbit is right ascension;

ξ_s、η_s、λ_srespectively represent t₁At time, the values of the three singularity-free variables ξ, η, λ introduced are calculated.

Preferably, the method further comprises the following steps:

a singular point-free variable reduction step:

after the calculation is finished, 3 singularity-free variables are restored

ω_s＝arc cos(ξ_s/e_s)

M_s＝mod(λ_s-ω_s,2π)

Preferably, the method further comprises the following steps:

and (3) normalization variable reduction step:

will be the long axis a of the satellite orbit_tReduction to conventional units:

a_s＝a_t×Re

a is described_sUnit: and m is selected.

Preferably, the method further comprises the following steps:

calculating the position of the inertial system satellite:

R_wECI＝Q*r_p

wherein the rotation matrix Q is described in a 3-1-3 rotation order:

vector r_p：

Wherein M is₁True proximal angle:

preferably, the method further comprises the following steps:

and a step of calculating the position of the earth-fixed satellite:

wherein, floor () is a round-down operation;

calculating a second count value t from epoch J2000.0 to a given target time based on the julian day JD_c：

t_c＝(JD-2455197.5)×86400+315547200

M_ECI2ECF＝ER*NR*PR

And according to t obtained by the calculation₁Position R of time satellite under inertial system_wECICalculating t₁Position R of time satellite under earth's fixation_wECF：

R_wECF＝M_ECI2ECF*R_wECI

Preferably, the method further comprises the following steps:

and the antenna position calculation step of the earth-fixed system survey station:

inputting longitude lon, latitude lat and elevation h of an antenna of the ground station;

computing coordinate components G1, G2:

wherein f is the geometric oblateness of the earth ellipsoid, and f is 1/298.257;

calculating the position R of the ground survey station antenna under the ground fixing system_tECF：

Preferably, the method further comprises the following steps:

and a step of calculating the position of the satellite in the station center system:

M_ECF2CT＝R_x(90°-lat)R_z(90°+lon)

wherein lon is the geographic longitude of the antenna of the ground survey station; lat is the geographical latitude of the antenna of the ground station;

R_wCT＝M_ECF2CT*(R_wECF-R_tECF)

Preferably, the method further comprises the following steps:

the method comprises the following steps of:

inputting the position of the satellite under the station center system, and outputting the pointing azimuth angle of the ground station antenna at the time t 1: height ofLow angleThe horizontal angle psi is specifically as follows:

the high and low angles and the horizontal angle are defined under the station center system O_CTX_CTY_CTZ_CTIn, O_CTRepresenting the origin of the coordinate system, X_CTX-axis, Y, representing a coordinate system_CTY-axis, O, representing a coordinate system_CTX_CTY_CTZ_CTThe plane, elevation angle, of X-axis and Y-axis of the coordinate systemTo point to a vector R_wCTAnd O_CTX_CTY_CTAngle of plane, define R_wCTVector sum of O_CTZ_CTThe included angle is less than 90 degrees and is positive; the horizontal angle psi being the director vector R_wCTAt O_CTX_CTY_CTProjection of plane and O_CTX_CTAngle of axis, defined around O_CTZ_CTShaft driven O_CTX_CTShaft clockwise steering pointing vector R_wCTAt O_CTX_CTY_CTThe projection of the surface is positive, and the antenna pointing azimuth angle is found according to the definition. Assuming that the position of the ground survey station is located at the origin of the station center system, the projection of the antenna pointing vector of the survey station under the station center system is R_wCTRecord R_wCTComprises the following steps:

wherein the content of the first and second substances,

calculation of elevation angle of antenna pointing azimuthThe horizontal angle ψ is:

and according to x_CT、y_CT、z_CTPositive and negative of (2), angle of elevationDividing the horizontal angle psi into corresponding angle ranges to finish the process of forecasting the antenna pointing direction:

if z is_CTMore than or equal to 0, the height and angle will be changedDivision into ranges

If x_CT≥0,y_CTThe horizontal angle psi is divided into ranges

If x_CT＜0,y_CTThe horizontal angle psi is divided into ranges

If x_CT＜0,y_CTIf < 0, the horizontal angle psi is divided into ranges

If x_CT≥0,y_CTIf < 0, the horizontal angle psi is divided into ranges

Compared with the prior art, the invention has the following beneficial effects:

the method does not depend on simulation software or excessive assumed contents, calculates the direction of the ground station antenna to the satellite by considering the actual running condition of the satellite, considers the perturbation of J2-J4 in the earth gravitational field shooting in the calculation, is suitable for long-time and high-precision satellite position prediction, can be suitable for various task requirements of the satellite in orbit, effectively solves the problem of controlling the direction of the ground station receiving antenna to the satellite, and achieves higher direction precision.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

fig. 1 is a schematic flow chart of a method for calculating an azimuth angle of a ground measurement and control antenna pointing to a satellite.

Fig. 2 is a schematic diagram of autonomous prediction of the satellite orbit position.

FIG. 3 is a schematic diagram of the pointing direction of the ground station antenna to the satellite.

FIG. 4 shows a standing system O_CTX_CTY_CTZ_CTSchematic representation.

FIG. 5 shows the elevation angle of the standing heart systemAnd horizontal angle psi.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.

The method for calculating the azimuth angle of the ground measurement and control antenna pointing to the satellite comprises the following steps:

using duration of starsMoment t₀、t₀Number of orbital flat at time [ a ]₀,e₀,i₀,Ω₀,ω₀,M₀]And the geographic position information of the ground survey station antenna is finally converted into t through the correlation calculation of the satellite orbit and the conversion calculation of a plurality of correlation coordinate systems₁Pointing azimuth angle of antenna under standing center system at time: high and low angleAnd the horizontal angle psi is used for completing the prediction process of the satellite pointing direction by the ground station antenna. Further, ephemeris time t₀、t₀Number of orbital flat at time [ a ]₀,e₀,i₀,Ω₀,ω₀,M₀]And the geographic position information of the ground station antenna are known quantities and are directly obtained by inquiring the ephemeris of the satellite.

Specifically, the method comprises the following steps:

the input parameter non-singular processing steps:

when the track eccentricity is small, i.e. near circular track, e ≈ 0, to avoid the occurrence of singularities in the calculation, we turn to 3 singularity-free variables, i.e.:

ξ₀＝e₀cos(ω₀)

η₀＝-e₀sin(ω₀)

λ₀＝ω₀+M₀

specifically, the method further comprises the following steps:

input parameter normalization processing:

normalization processing is performed for the recursion time dt:

dt＝t₁-t₀

wherein the content of the first and second substances,

t₀recursion of the starting moment for the track;

t₁representing the track recursion end time;

dt_nthe result of normalization processing of the recursion time is shown, and the subscript n shows normalization;

for semi-major axis a₀And (3) carrying out normalization treatment:

the normalized unit of the time is

Wherein the content of the first and second substances,

ge is a gravitational constant;

re represents the earth equatorial radius.

Specifically, the method further comprises the following steps:

perturbation item calculation step:

first order long term calculation:

wherein the content of the first and second substances,

Ω₁representing the first-order long period variable quantity of the right ascension of the satellite orbit intersection point;

ω₁representing the first-order long period variation of the argument of the satellite orbit in the near place;

λ₁first order length representing the singularity-free variable λ introduced by the calculations hereinA period variation;

p is a radius, and the expression is p ═ a × (1-e)₀ ²) Mean angular velocity of trackJ₂＝1.624×10^-3；

First order short period term calculation:

wherein the content of the first and second substances,

representing the first-order short period variable quantity of the semi-major axis of the satellite orbit;

representing the first-order short-period variation of the satellite orbit inclination angle;

the first-order short-period variation of the right ascension of the satellite orbit intersection point is represented;

respectively representing the first order short period variations of the three singularity-free variables ξ, η, λ introduced by the calculations herein;

the u is calculated by a first-order long-term, and the calculation process is as follows:

ξ_z1＝ξ₀cos(ω₁dt_n)+η₀sin(ω₁dt_n)

η_z1＝η₀cos(ω₁dt_n)-ξ₀sin(ω₁dt_n)

λ_z1＝λ₀+(n+λ₁)dt_n

ω_z1＝arc cos(ξ_z1/e_z1)

M_z1＝mod(λ_z1-ω_z1，2π)

u＝f_z1+ω_z1

wherein the content of the first and second substances,

ξ_z1、η_z1、λ_z1respectively, the results of integration according to first-order long-term variation of the three singularity-free variables ξ, η, λ introduced by the calculations herein;

e_z1an integral result which represents the eccentricity of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

ω_z1an integral result which represents the argument of the satellite orbit near place and takes the first-order long period variable quantity as integral quantity;

M_z1representing the variation of the mean and the anomaly of the satellite orbit in a first-order long periodThe quantity is the integration result of the integration quantity;

f_z1an integral result which represents the true near point angle of the satellite orbit and takes the first-order long period variable quantity as an integral quantity;

second-order long-term calculation:

wherein the content of the first and second substances,

Ω₂representing the second-order long-period variation of the right ascension of the satellite orbit;

ξ₂、λ₂second-order long-period variations representing singularity-free variables ξ, λ introduced by the calculations herein, respectively;

J₃＝2.5356×10^-6,J₄＝7.1022×10^-6。

specifically, the method further comprises the following steps:

and (3) calculating a recursion main formula:

wherein the content of the first and second substances,

α_trepresents t₁At the moment, the normalization result of the satellite orbit semi-major axis;

i_srepresents t₁At that time, the satellite orbit inclination;

Ω_srepresents t₁At the moment, the rising point of the satellite orbit is right ascension;

ξ_s、η_s、λ_srespectively represent t₁At time, the values of the three singularity-free variables ξ, η, λ introduced are calculated.

Specifically, the method further comprises the following steps:

a singular point-free variable reduction step:

after the calculation is finished, 3 singularity-free variables are restored

ω_s＝arc cos(ξ_s/e_s)

M_s＝mod(λ_s-ω_s,2π)

Specifically, the method further comprises the following steps:

and (3) normalization variable reduction step:

will be the long axis a of the satellite orbit_tReduction to conventional units:

a_s＝a_t×Re

a is described_sUnit: and m is selected.

Specifically, the method further comprises the following steps:

calculating the position of the inertial system satellite:

R_wECI＝Q*r_p

wherein the rotation matrix Q is described in a 3-1-3 rotation order:

vector r_p：

Wherein M is₁True proximal angle:

specifically, the method further comprises the following steps:

and a step of calculating the position of the earth-fixed satellite:

wherein, floor () is a round-down operation;

calculating a second count value t from epoch J2000.0 to a given target time based on the julian day JD_c：

t_c＝(JD-2455197.5)×86400+315547200

M_ECI2ECF＝ER*NR*PR

And according to t obtained by the calculation₁Position R of time satellite under inertial system_wECICalculating t₁Position R of time satellite under earth's fixation_wECF：

R_wECF＝M_ECI2ECF*R_wECI

Specifically, the method further comprises the following steps:

and the antenna position calculation step of the earth-fixed system survey station:

inputting longitude lon, latitude lat and elevation h of an antenna of the ground station;

computing coordinate components G1, G2:

wherein f is the geometric oblateness of the earth ellipsoid, and f is 1/298.257;

calculating the position R of the ground survey station antenna under the ground fixing system_tECF：

Specifically, the method further comprises the following steps:

and a step of calculating the position of the satellite in the station center system:

M_ECF2CT＝R_x(90°-lat)R_z(90°+lon)

wherein lon is the geographic longitude of the antenna of the ground survey station; lat is the geographical latitude of the antenna of the ground station;

R_wCT＝M_ECF2CT*(R_wECF-R_tECF)

Specifically, the method further comprises the following steps:

the method comprises the following steps of:

The high and low angles and the horizontal angle are defined under the station center system O_CTX_CTY_CTZ_CTIn, O_CTRepresenting the origin of the coordinate system, X_CTX-axis, Y, representing a coordinate system_CTY-axis, O, representing a coordinate system_CTX_CTY_CTThe plane, elevation angle, of X-axis and Y-axis of the coordinate systemTo point to a vector R_wCTAnd O_CTX_CTY_CTAngle of plane, define R_wCTVector sum of O_CTZ_CTThe included angle is less than 90 degrees and is positive; the horizontal angle psi being the director vector R_wCTAt O_CTX_CTY_CTProjection of plane and O_CTX_CTAngle of axis, defined around O_CTZ_CTShaft driven O_CTX_CTShaft clockwise steering pointing vector R_wCTAt O_CTX_CTY_CTThe projection of the surface is positive, and the antenna pointing azimuth angle is found according to the definition. Assuming that the position of the ground survey station is located at the origin of the station center system, the projection of the antenna pointing vector of the survey station under the station center system is R_wCTRecord R_wCTComprises the following steps:

wherein the content of the first and second substances,

calculation of elevation angle of antenna pointing azimuthThe horizontal angle ψ is:

if z is_CTMore than or equal to 0, the height and angle will be changedDivision into ranges

If x_CT≥0,y_CTThe horizontal angle psi is divided into ranges

If x_CT＜0,y_CTThe horizontal angle psi is divided into ranges

If x_CT＜0,y_CTIf < 0, the horizontal angle psi is divided into ranges

If x_CT≥0,y_CTIf < 0, the horizontal angle psi is divided into ranges

The present invention will be described more specifically below with reference to preferred examples.

Preferred example 1:

the technical problem to be solved by the invention is as follows: the method comprises the steps of performing satellite orbit correlation calculation and conversion calculation of a plurality of correlation coordinate systems by satellite ephemeris data and geographical position information of a ground measurement station antenna at a given target moment, and finally converting the satellite ephemeris data and the geographical position information into an antenna pointing azimuth angle under a station center system to finish the prediction process of the ground measurement station antenna on the satellite azimuth.

The invention combines a practical engineering situation: under the condition that the ground survey station is movable, under the condition that the geographical latitude, longitude and altitude of the ground survey station are known and the track information of the on-orbit aircraft is tracked, the pointing tracking of the aircraft is automatically completed, and the pointing azimuth angle of the antenna is calculated in real time. The ground measurement station real-time positioning method is used for the ground measurement station antenna with high precision, and the autonomous pointing direction of the satellite can be forecasted by the ground measurement station antenna.

The method for calculating the azimuth angle of the ground measurement and control antenna pointing to the satellite calculates the position of the satellite in real time through satellite ephemeris information, considers influence factors of a coordinate system conversion relation comprehensively, has high calculation precision, provides the pointing azimuth angle definition suitable for the ground measurement station antenna, and effectively meets the prediction requirement of the ground measurement station antenna on the satellite pointing azimuth in real time.

In order to realize the method, the following technical scheme is adopted:

a method for calculating the azimuth angle of a ground measurement and control antenna pointing to a satellite comprises the following steps:

1. input parameter non-singular processing module

When the track eccentricity is very small (near-circular track, e ≈ 0), in order to avoid the occurrence of singular points in the calculation, the method is converted into 3 singular point-free variables, namely

ξ₀＝e₀cos(ω₀)

η₀＝-e₀sin(ω₀)

λ₀＝ω₀+M₀

2. Input parameter normalization processing module

The normalization process is performed with respect to the recursion time dt,

dt＝t₁-t₀

for semi-major axis a₀The normalization treatment is carried out, and the normalization treatment is carried out,

the normalized unit of the time is that,

wherein Ge is a gravitational constant;

the normalized unit of the length is Re-6378140 m

3. Perturbation item calculation module

Considering the perturbations of items J2 to J4 in the earth gravity field, including computing first order long term, first order short term, and second order long term terms, the expressions for the respective perturbation terms:

first order long term calculation:

p is a radius, and the expression is p ═ a × (1-e)₀ ²) Mean angular velocity of trackJ₂＝1.624×10^-3。

First order short period term calculation:

and u is calculated by a first-order long-term.

ξ_z1＝ξ₀cos(ω_c1dt_n)+η₀sin(ω_c1dt_n)

η_z1＝η₀cos(ω_c1dt_n)-ξ₀sin(ω_c1dt_n)

λ_z1＝λ₀+(n+λ_c1)dt_n

ω_z1＝arc cos(ξ_z1/e_z1)

M_z1＝mod(λ_z1-ω_z1,2π)

u＝f_z1+ω_z1

Second-order long-term calculation:

said, J₃＝2.5356×10^-6,J₄＝7.1022×10^-6。

4. Recursion main formula calculation module

And for the introduced singularity-free variable, analyzing solution construction is carried out by combining a long-term item perturbation item and a short-period item perturbation item, and the long-period item perturbation is ignored. The track recursion main formula is as follows:

5. variable recovery module without singularity

After the calculation is finished, 3 singularity-free variables are restored

ω_s＝arc cos(ξ_s/e_s)

M_s＝mod(λ_s-ω_s,2π)

6. Normalized variable reduction module

Will be the long axis a of the satellite orbit_tReduction to conventional units:

a_s＝a_t×Re

a is described_sUnit: and m is selected.

7. Inertial system satellite position module

Passing through t₁Instantaneous number of satellite orbits [ a ] of time_s,e_s,i_s,Ω_s,ω_s,M_s]Calculating the component R of the position vector of the satellite in the J2000.0 coordinate system_wECIThe calculation method comprises the following steps:

R_wECI＝Q*r_p

wherein the rotation matrix Q is described in a 3-1-3 rotation order:

vector r_p：

Wherein M is₁True proximal angle:

8. earth fixed satellite position module

According to a given target time t₁And the position R of the satellite calculated in the step (7) in the inertial system_wECICalculating t₁Position R of time satellite under earth's fixation_wECFThe method comprises the following steps:

according to a given target time t₁Calculating a second counting value t from epoch J2000.0 (1/12/2000) to a predetermined target time_cInputting t₁Year (year), month (month), day (day), hour (hour), minute (min), and second (sec) of time (UTC time), julian day JD is calculated:

wherein floor () is a round-down operation.

Calculating a second counting value t from epoch J2000.0 (1 month, 1 day, 12 hours in 2000) to a given target time according to the julian day JD_c：

t_c＝(JD-2455197.5)×86400+315547200

A second counting value t from the epoch J2000.0 (1 month, 1 day, 12 hours in 2000) to a given target time_cAnd calculating a terrestrial rotation matrix ER, a nutation matrix NR and a time offset matrix PR, wherein the term is not considered in the invention because polar shift has little influence on the calculation of the conversion matrix. Calculating a transformation matrix M from an inertial system to a ground-based system_ECI2ECF：

M_ECI2ECF＝ER*NR*PR

And calculating t according to the step (7)₁Position R of time satellite under inertial system_wECICalculating t₁Position R of time satellite under earth's fixation_wECF：

R_wECF＝M_ECI2ECF*R_wECI

9. Antenna position module of ground fixing system measuring station

The method is characterized in that the position R of the antenna of the ground measuring station under the ground fixation system is calculated according to the longitude, latitude and elevation of the given antenna of the ground measuring station_tECFThe method comprises the following steps:

and inputting longitude lon, latitude lat and elevation h of the antenna of the ground station.

Computing coordinate components G1, G2:

wherein f is the geometric oblateness of the earth ellipsoid, and f is 1/298.257.

Calculating the position R of the ground survey station antenna under the ground fixing system_tECF：

10. Satellite position module for station center system

T calculated according to the step (8)₁Position R of time satellite under earth's fixation_wECFAnd the position R of the ground survey station antenna calculated in the step (9) under the ground system_tECFCalculating t₁Position R of time satellite under the system of the center of the station_wCTThe method comprises the following steps:

M_ECF2CT＝R_x(90°-lat)R_z(90°+lon)

wherein lon is the geographic longitude of the antenna of the ground survey station; lat is the geographic latitude of the ground station antenna.

And according to t calculated in the step (8)₁Position R of time satellite under earth's fixation_wECFThe position R of the ground survey station antenna under the ground fixation system calculated in the step (9)_tECFTranslating the origin of coordinates from the geocentric to the antenna of the ground survey station, and calculating t₁Position R of time satellite under the system of the center of the station_wCT：

R_wCT＝M_ECF2CT*(R_wECF-R_tECF)

11. Direction-finding module for antenna of survey station

Calculating t from the position of the satellite under the satellite constellation calculated in the step (10)₁The antenna pointing azimuth angle of the ground survey station at any moment: high and low angleThe method of the horizontal angle ψ is as follows:

high and low angles, horizontal angle. The high and low angles and the horizontal angle are defined under the station center systemTo point to a vector R_wCTAnd O_CTX_CTY_CTAngle of plane, define R_wCTVector sum of O_CTZ_CTThe included angle is less than 90 degrees and is positive; the horizontal angle psi being the director vector R_wCTAt O_CTX_CTY_CTProjection of plane and O_CTX_CTAngle of axis, defined around O_CTZ_CTShaft driven O_CTX_CTShaft clockwise steering pointing vector R_wCTAt O_CTX_CTY_CTThe projection of the surface is positive, as shown in fig. 5, and the antenna pointing azimuth is found according to this definition. Assuming that the position of the ground survey station is located at the origin of the station center system, the projection of the antenna pointing vector of the survey station under the station center system is R_wCTRecord R_wCTComprises the following steps:

calculation of elevation angle of antenna pointing azimuthThe horizontal angle ψ is:

and according to x_CT、y_CT、z_CTPositive and negative of (2), angle of elevationDividing the horizontal angle psi into corresponding angle ranges to finish the forecasting process of the antenna pointing direction:

preferred example 2:

the coordinate system required by the invention is as follows: the inertial system is a J2000.0 inertial coordinate system, and the earth fixation system is a WGS-84 coordinate system. The definition of the station center system is given below.

Standing heart system O_CTX_CTY_CTZ_CT

The center of the station is defined as the origin O_CTIs the ground antenna origin, the basic plane O_CTX_CTY_CTThe surface is a local horizontal surface, O_CTX_CTPointing to true north, O, along the meridian of the local area_CTZ_CTVertical base plane pointing to zenith, O_CTY_CTDetermined by the right hand rule, as shown in fig. 4.

The calculation process of the present invention is detailed below:

the algorithm was simulated with MAT L AB [ a ]₀,e₀,i₀,Ω₀,ω₀,M₀]Verification, the earth-related parameters and the station center are set as described above, and the ephemeris data of a certain type of satellite at the time 1, month 1, day 5 and day 4 of the UTC time 2019 are as follows:

six orbits of the satellite at 2019, 1, 6, 4 are recurred from 2019, 1, 5, 4, and the azimuth angle (elevation angle, horizontal angle) of the antenna pointing at 2019, 1, 6, 4 is calculated.

1. Input parameter non-singular processing module

ξ₀＝e₀cos(ω₀)

η₀＝-e₀sin(ω₀)

λ₀＝ω₀+M₀

2. Input parameter normalization processing module

The normalization process is performed with respect to the recursion time dt,

dt＝t₁-t₀

for semi-major axis a₀The normalization treatment is carried out, and the normalization treatment is carried out,

the normalized unit of the time is that,

wherein Ge is a gravitational constant;

the normalized unit of the length is Re-6378140 m

3. Perturbation item calculation module

first order long term calculation:

p is a radius, and the expression is p ═ a × (1-e)₀ ²) Mean angular velocity of trackJ₂＝1.624×10^-3。

First order short period term calculation:

and u is calculated by a first-order long-term.

ξ_z1＝ξ₀cos(ω_c1dt_n)+η₀sin(ω_c1dt_n)

η_z1＝η₀cos(ω_c1dt_n)-ξ₀sin(ω_c1dt_n)

λ_z1＝λ₀+(n+λ_c1)dt_n

ω_z1＝arc cos(ξ_z1/e_z1)

M_z1＝mod(λ_z1-ω_z1,2π)

u＝f_z1+ω_z1

Second-order long-term calculation:

said, J₃＝2.5356×10^-6,J₄＝7.1022×10^-6。

4. Recursion main formula calculation module

5. variable recovery module without singularity

After the calculation is finished, 3 singularity-free variables are restored

ω_s＝arc cos(ξ_s/e_s)

M_s＝mod(λ_s-ω_s,2π)

6. Normalized variable reduction module

Will be the long axis a of the satellite orbit_tReduction to conventional units:

a_s＝a_t×Re

a is described_sUnit: and m is selected.

The result obtained by the calculation in the steps is as follows:

7. inertial system satellite position module

R_wECI＝Q*r_p

wherein the rotation matrix Q is described in a 3-1-3 rotation order:

vector r_p：

Wherein M is₁True proximal angle:

the calculation result is as follows:

8. earth fixed satellite position module

wherein floor () is a round-down operation.

Calculating a second counting value t from epoch J2000.0 (1 month, 1 day, 12 hours in 2000) to a given target time according to the julian day JD_c：

t_c＝(JD-2455197.5)×86400+315547200

M_ECI2ECF＝ER*NR*PR

And calculating t according to the step (7)₁Position R of time satellite under inertial system_wECICalculating t₁Position R of time satellite under earth's fixation_wECF：

R_wECF＝M_ECI2ECF*R_wECI

The calculation result is as follows:

9. antenna position module of ground fixing system measuring station

and inputting longitude lon, latitude lat and elevation h of the antenna of the ground station.

Computing coordinate components G1, G2:

wherein f is the geometric oblateness of the earth ellipsoid, and f is 1/298.257.

Calculating the position R of the ground survey station antenna under the ground fixing system_tECF：

The calculation result is as follows:

10. satellite position module for station center system

T calculated according to the step (8)₁Position R of time satellite under earth's fixation_wECFAnd the position R of the ground survey station antenna calculated in the step (9) under the ground system_tECFCalculating t₁Position of time satellite under the center of the stationR_wCTThe method comprises the following steps:

M_ECF2CT＝R_x(90°-lat)R_z(90°+lon)

wherein lon is the geographic longitude of the antenna of the ground survey station; lat is the geographic latitude of the ground station antenna.

R_wCT＝M_ECF2CT*(R_wECF-R_tECF)

The calculation result is as follows:

11. direction-finding module for antenna of survey station

calculation of elevation angle of antenna pointing azimuthThe horizontal angle ψ is:

the calculation result is as follows:

in the description of the present application, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience in describing the present application and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present application.

Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

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Azimuth angle calculation method for ground measurement and control antenna pointing satellite

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