CN107515410B - A kind of spacecraft Shuo Chuan antenna tracking earth station test verifying system and method - Google Patents

A kind of spacecraft Shuo Chuan antenna tracking earth station test verifying system and method Download PDF

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Publication number
CN107515410B
CN107515410B CN201710607688.3A CN201710607688A CN107515410B CN 107515410 B CN107515410 B CN 107515410B CN 201710607688 A CN201710607688 A CN 201710607688A CN 107515410 B CN107515410 B CN 107515410B
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earth station
antenna
satellite
information
earth
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CN107515410A (en
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孙小松
黎康
彭洲
史晓霞
陶景桥
王浩
石郑伟
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Beijing Institute of Control Engineering
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/23Testing, monitoring, correcting or calibrating of receiver elements
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00Testing or monitoring of control systems or parts thereof
    • G05B23/02Electric testing or monitoring

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Automation & Control Theory (AREA)
  • Computer Networks & Wireless Communication (AREA)
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Abstract

A kind of spacecraft of the present invention tests verifying system and method with Shuo Chuan antenna tracking earth station, according to the orbital position for the satellite that the dynamics software received calculates, the attitude angle and attitude angular velocity of satellite, the number that software calculates on star passes the direction angle of antenna, it has invented a kind of several biography antenna traceback earth station's algorithms and has calculated number at this time and passed earth station pointed by antennas, and the longitude and latitude of earth station is shown in the enterprising Mobile state of monitoring software in real time, then the earth station's longitude and latitude data bound in software on star the result of calculating and in advance are compared, can real-time continuous dynamic authentication number pass the correctness of antenna traceback earth station.

Description

A kind of spacecraft Shuo Chuan antenna tracking earth station test verifying system and method
Technical field
Antenna is passed with number the present invention relates to a kind of spacecraft and accurately tracks earth station's test verification method, is suitable for spacecraft Logarithm passes the test verifying that antenna accurately tracks earth station in control system ground test, belongs to spacecraft control test skill Art field.
Background technique
It is one of the important component in large-scale remote sensing satellite load system that number, which passes antenna, and major function is realization figure As data high-speed under reach earth station.Wave beam for the high rate data transmission that data are effectively ensured, antenna is relatively narrow, outside wave beam Energy attenuation is very fast, and antenna is needed accurately to be directed toward earth station.Especially satellite in-orbit service operation when need frequently it is quickly small Angle is motor-driven, the motor-driven angle of the attitude of satellite, orbital position, attitude control error and its stability characteristic etc. all to antenna accurately with Track earth station brings biggish challenge.Subsystem is controlled according to the track of satellite, the attitude of satellite and earth station's information, is counted in real time It counts and passes antenna pointing angle, and be sent to number and pass antenna, number passes antenna according to calculated direction angle, and driving number passes antenna and refers to Ground station.It is not a research institute since number passes antenna and control subsystem, controls subsystem to antenna directional angle Calculate whether correct, number and pass the pointing accuracies of antennas and how to verify, especially in each stage test process of the whole star of satellite its Real-time continuous verifying under various operating conditions is problem in the urgent need to address.
In previous control system test, there is not the verification method of the Shuo Chuan antenna tracking earth station published, It is also only to carry out simple verifying, and have the disadvantage that 1) Shuo Chuan antenna tracking earth station is only in actual test macro Be only the simple computation of single point in time, cannot implement the continuous verifying of real-time dynamic in entire test process, calculating process compared with It is cumbersome;2) can not accomplish to merge posture information, orbit information, the motor-driven information of satellite obtained in satellite dynamics emulation, And calculating process is cumbersome, efficiency is lower;3) factors such as consideration earth ellipsoid that can not be accurate influence, the ground of calculated direction Precision of standing is not high, can not accomplish effectively to verify.
Summary of the invention
Present invention solves the technical problem that: the deficiencies in the prior art are overcome, a kind of spacecraft number biography antenna essence is provided True tracking earth station tests verification method, can pass antenna direction ground by real-time, Dynamically Announce number in the overall process of satellite test The error at face station.
Technical solution of the present invention: a kind of spacecraft passes antenna with number and accurately tracks earth station's test verifying system, including Remote control system, control subsystem, number pass antenna control module, satellite dynamics module and data processing module;Remote control system hair Send satellite motor-driven control instruction, after control subsystem receives maneuver autopilot instruction, control satellite platform carries out corresponding posture It is motor-driven, and executing agency's information is sent to dynamics module;Simultaneously control subsystem according to the track of satellite, the attitude of satellite and Earth station's information calculates number in real time and passes antenna pointing angle, and is sent to number and passes antenna control module;Number passes antenna control module According to antenna pointing angle information, driving number passes antenna and is directed toward earth station;Satellite dynamics module receives the executing agency on star Information emulates satellite dynamics, exports the true attitude of satellite, orbit information, and is sent to number with passing antenna tracking Face station computing module;Data processing module handles received data, judge number pass antenna be directed toward whether can accurately with Track earth station.
The data processing module includes Shuo Chuan antenna tracking earth station's computing module and data comparing module;Number passes antenna Posture of earth station's computing module according to satellite, orbit information are tracked, number is calculated and passes direction of the antenna in inertial space, then The earth's core to earth station vector is calculated in inertia according to the orbital position of satellite, earth ellipsoid information and earth station's elevation information Finally earth station is calculated according to earth rotation information, earth ellipsoid information, the precession of the equinoxes and nutating matrix in direction in space Latitude and longitude information is simultaneously sent to data comparing module;The ground that data comparing module binds earth station's latitude and longitude information and theory Information of standing is compared, and the tracking error of Shuo Chuan antenna tracking earth station is calculated, if the tracking error is less than setting Threshold value, then it is assumed that number passes antenna and is directed to accurately track earth station;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track ground It stands.
A kind of spacecraft passes antenna with number and accurately tracks earth station's test verification method, comprises the following steps that
(1) remote control system to send the motor-driven control instruction of satellite;
(2) control subsystem calculates number in real time and passes antenna direction according to the track of satellite, the attitude of satellite and earth station's information Angle, and be sent to number and pass antenna control module, number passes antenna control module according to calculated antenna directional angle, and driving number passes Antenna is directed toward earth station;
(3) satellite dynamics module receives executing agency's information on star, emulates to satellite dynamics, and exports true The attitude of satellite of reality, orbit information, and it is sent to Shuo Chuan antenna tracking earth station computing module;
(4) latitude and longitude information of earth station is calculated and is sent to data comparing module;
(5) earth station's latitude and longitude information is compared data comparing module with earth station's information of theory bookbinding, calculates The tracking error of Shuo Chuan antenna tracking earth station is obtained, if the error is less than specified threshold value, then it is assumed that number passes antenna and is directed toward Earth station can accurately be tracked;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track earth station.
The step (4) the specific implementation process is as follows:
(2a) related data updates;
(2b) number passes antenna pointing vector and calculates;
(2c) iterates to calculate the latitude and longitude information that number passes the earth station that antenna is directed toward.
What related data updated in the step (2a) is implemented as follows:
The time and orbit information of (2a1) according to satellite calculate the Greenwich sidereal time for obtaining sub-satellite point position Angle LamdaG0;
(2a2) updates antenna pointing angle azimuth angle alpha and pitch angle β.
Step (2b) number passes the detailed process that antenna pointing vector calculates are as follows:
(2b1) is calculated according to the time of satellite, posture information, orbit information and is obtained satellite health coordinate system relative to used The transition matrix C of property systemibAnd position vector of the satellite in inertial system
(2b2) installs Matrix C according to updated antenna pointing angle α, β, antennaab, antenna installation deviation Matrix CarbWith Transition matrix Cib, calculate the antenna for obtaining and indicating in inertial system and be directed toward
Iterative calculation number passes the specific implementation of the latitude and longitude information for the earth station that antenna is directed toward such as in the step (2c) Under:
(2c1) is directed toward according to antennaWith position vector of the satellite in inertial systemIt calculates and obtains antenna vector and star Angle between ground vector:
(2c2) calculates the angle theta for obtaining earth station's vector and satellite to earth station's vectorsERelevant formula are as follows:
SsE=sin (θsE)=rs sin(θsa)/rE0
WhereinE is eccentricity of the earth, REFor earth radius, For the latitude of earth station, initial value 0,
As the S of calculatingsEThere are when following situations, it may occur in which a variety of situations:
When | SsE| when >=1, illustrates that antenna is directed toward at this time and the earth is without intersection point, set longitude, the latitude E of earth stationλ It is 0, and stops the calculating of this period, and jumps back to the calculating that step (2a) carries out next period;
When | SsE| when < 1, illustrate that antenna direction has earth station at this time, with calculating earth station's vector at this time and star between vector Angle thetarErsAre as follows:
θrErssEsa
θsE=sin-1(SsE);
(2c3) is according to θsE、θrErsWith position r of the satellite in inertial systems, calculate the arrow for obtaining earth station to satellite Amount
(2c4) is according to satellite vectorWithIt calculates and obtains earth station's vectorAre as follows:
(2c5) according to the Greenwich sidereal time angle LamdaG0 of sub-satellite point position, by earth station's vector median filters to ground Ball is connected in coordinate system;
(2c6) calculates earth station's longitude and latitude E according to earth station's vector in terrestrial coordinate systemλAnd to earth station Longitude and latitude carries out the precession of the equinoxes and the compensation of nutating item;
(2c7) willIt brings into step (2c2), computes repeatedly to step (2c6), until calculatedWith last time It calculatesDifference is less than the threshold value of setting, then Eλ(n)、As earth station's final longitude and latitude value.
The step (5) the specific implementation process is as follows:
Earth station's latitude and longitude information is compared data comparing module with earth station's information of theory bookbinding, is calculated The tracking error of Shuo Chuan antenna tracking earth station, if the error is less than specified threshold value, then it is assumed that number passes antenna and is directed to Accurate tracking earth station;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track earth station.
The invention has the following advantages over the prior art:
(1) present invention devises a kind of several algorithms for passing antenna real-time continuous tracking earth station, and the algorithm is embedded into In test macro, the continuous verifying of real-time dynamic in the entire test process of satellite is realized, applicability and versatility greatly enhance, It improves work efficiency.
(2) present invention merged satellite dynamics emulation, attitude maneuver and pose stabilization control posture information obtained, Antenna pointing control information, satellite-orbit information improve number and pass the flexibility that antenna accurately tracks earth station's verifying, and efficiency is big It is big to improve.
(3) present invention accurately considers the influence of earth ellipsoid factor while merging various postures and orbit information, and The precision that Shuo Chuan antenna tracking earth station is effectively improved using iterative algorithm improves Shuo Chuan antenna tracking earth station authentication The accuracy of method.
Detailed description of the invention
Fig. 1 is method flow schematic diagram of the invention.
Specific embodiment
Remote control system sends the motor-driven control instruction of satellite;After control subsystem receives maneuver autopilot instruction, satellite is controlled Platform carries out corresponding attitude maneuver, and executing agency's information is sent to dynamics module.Subsystem is controlled simultaneously according to defending Track, the attitude of satellite and the earth station's information of star calculate number in real time and pass antenna pointing angle, and is sent to number and passes day line traffic control mould Block.Number passes antenna control module according to antenna pointing angle information, and driving number passes antenna and is directed toward earth station;Satellite dynamics module Executing agency's information on star is received, satellite dynamics is emulated, exports the true attitude of satellite, orbit information, concurrently Give Shuo Chuan antenna tracking earth station computing module;Posture of the Shuo Chuan antenna tracking earth station's computing module according to satellite, track Information calculates number and passes direction of the antenna in inertial space, then according to the orbital position of satellite, earth ellipsoid information and ground Direction of the earth's core to the earth station vector in inertial space is calculated in elevation information of standing, finally according to earth rotation information, Ball ellipsoid information, the precession of the equinoxes and nutating matrix are calculated the latitude and longitude information of earth station and are sent to data comparing module;Data Earth station's latitude and longitude information is compared comparison module with earth station's information of theory bookbinding, and number is calculated and passes antenna tracking The tracking error of earth station, if the error is less than specified threshold value, then it is assumed that number passes antenna and is directed to accurately track ground It stands;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track earth station.
The present invention is described in detail with reference to the accompanying drawing.
It is comprised the following steps that as shown in Figure 1, a kind of spacecraft accurately tracks earth station's test verification method with number biography antenna
(1) remote control system sends the motor-driven control instruction of satellite;
(2) control subsystem calculates number in real time and passes antenna direction according to the track of satellite, the attitude of satellite and earth station's information Angle, and be sent to number and pass antenna control module, number passes antenna control module according to calculated antenna directional angle, and driving number passes Antenna is directed toward earth station;
(3) satellite dynamics module receives executing agency's information on star, emulates to satellite dynamics, and exports true The attitude of satellite of reality, orbit information, and it is sent to Shuo Chuan antenna tracking earth station computing module;
(4) when receive satellite posture and orbit information, antenna pointing angle information after, Shuo Chuan antenna tracking earth station Posture of the computing module according to satellite, orbit information calculate number and pass direction of the antenna in inertial space, then according to satellite Finger of the earth's core to the earth station vector in inertial space is calculated in orbital position, earth ellipsoid information and earth station's elevation information To the latitude and longitude information of earth station is finally calculated according to earth rotation information, earth ellipsoid information, the precession of the equinoxes and nutating matrix And it is sent to data comparing module;
(5) earth station's latitude and longitude information is compared data comparing module with earth station's information of theory bookbinding, calculates The tracking error of Shuo Chuan antenna tracking earth station is obtained, if the error is less than specified threshold value, given threshold is 0.2 here Degree, then it is assumed that number passes antenna and is directed to accurately track earth station;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track ground It stands.
Antenna tracking earth station algorithm is implemented as follows in the step (4):
The time and orbit information of (2a) according to satellite calculate the Greenwich sidereal time angle for obtaining sub-satellite point position LamdaG0;
(2b) updates antenna pointing angle azimuth angle alpha and pitch angle β;
(2c) is calculated according to the time of satellite, posture information, orbit information and is obtained satellite health coordinate system relative to inertia The transition matrix C of systemibAnd position vector of the satellite in inertial system
(2d) installs Matrix C according to updated antenna pointing angle α, β, antennaab, antenna installation deviation Matrix CarbWith Transition matrix Cib, calculate the antenna for obtaining and indicating in inertial system and be directed toward
(2e) is directed toward according to antennaWith position vector of the satellite in inertial systemIt calculates with obtaining antenna vector and star Angle between vector:
(2f) calculates the angle theta for obtaining earth station's vector and satellite to earth station's vectorsERelevant formula are as follows:
SsE=sin (θsE)=rs sin(θsa)/rE0
WhereinE is eccentricity of the earth, REFor earth radius, For the latitude of earth station, initial value 0,
As the S of calculatingsEThere are when following situations, it may occur in which a variety of situations:
When | SsE| when >=1, illustrates that antenna is directed toward at this time and the earth is without intersection point, set longitude, the latitude E of earth stationλ It is 0, and stops the calculating of this period, and jumps back to the calculating that (2a) carries out next period;
When | SsE| when < 1, illustrate that antenna direction has earth station at this time, with calculating earth station's vector at this time and star between vector Angle thetarErsAre as follows:
θrErssEsa
θsE=sin-1(SsE)
Continue following calculating
(2g) is according to θsE、θrErsWith position r of the satellite in inertial systems, the vector of calculating earth station to satellite
(2h) is according to satellite vectorWithCalculably face station vectorAre as follows:
(2i) will be arrived earth station's vector median filters at this time according to the Greenwich sidereal time angle LamdaG0 of sub-satellite point position The earth is connected in coordinate system;
(2j) calculates earth station longitude and latitude E at this time according to earth station's vector in terrestrial coordinate systemλAnd to year Difference and nutating item compensate;
(2k) willIt brings into (3f), computes repeatedly to (3j), until calculatedWith last computationDifference is less than the threshold value of setting, and given threshold is 0.1 degree here, then Eλ(n)、As earth station is final Longitude and latitude value;
In actual test process, test result is following, and (longitude of theoretical earth station is 116.86 degree, and latitude is 40.45 degree):
When satellite is when pitch axis and the axis of rolling carry out motor-driven, the tracking error of Shuo Chuan antenna tracking earth station is less than 0.2 Degree, demonstrates the correctness of this method.
During the test, on the one hand there are different control models in satellite, the gesture stability of satellite under different control models There are difference for precision;On the other hand under same control model, number pass antennas motor-driven angles also change in real time, these because Element all influences the precision of Shuo Chuan antenna tracking earth station.Number biography antenna accurately tracks earth station's test verification method and can defend Star tests in overall process real-time, the dynamic authentication for carrying out antenna direction;The present invention combine satellite gravity anomaly, attitude maneuver, Track operation, antenna be directed toward, data transmission, calculated result in real time and the technologies such as Dynamically Announce, are taken into account on relevant ground and star Function, flexibility and ease for use, and the degree of automation with higher.
The present invention has been applied in corresponding model, and achieves good effect.
Non-elaborated part of the present invention belongs to techniques well known.

Claims (6)

1. a kind of spacecraft with number pass antenna accurately track earth station test verifying system, it is characterised in that: including remote control system, Control subsystem, number passes antenna control module, satellite dynamics module and data processing module;It is motor-driven that remote control system sends satellite Control instruction, after control subsystem receives maneuver autopilot instruction, control satellite platform carries out corresponding attitude maneuver, and will hold Row organization information is sent to dynamics module;Subsystem is controlled simultaneously according to the track of satellite, the attitude of satellite and earth station's information, Number is calculated in real time and passes antenna pointing angle, and is sent to number and is passed antenna control module;Number passes antenna control module and is referred to according to antenna To angle information, driving number passes antenna and is directed toward earth station;Satellite dynamics module receives executing agency's information on star, to satellite Dynamics is emulated, and exports the true attitude of satellite, orbit information, and be sent to data processing module;Data processing module Received data are handled, judge that number passes whether antenna direction can accurately track earth station;
The data processing module includes Shuo Chuan antenna tracking earth station's computing module and data comparing module;Number passes antenna tracking Posture of earth station's computing module according to satellite, orbit information calculate number and pass direction of the antenna in inertial space, then basis The earth's core to earth station vector is calculated in inertial space in orbital position, earth ellipsoid information and the earth station's elevation information of satellite In direction, the longitude and latitude of earth station is finally calculated according to earth rotation information, earth ellipsoid information, the precession of the equinoxes and nutating matrix Degree information is simultaneously sent to data comparing module;Data comparing module believes the earth station of earth station's latitude and longitude information and theoretical bookbinding Breath is compared, and the tracking error of Shuo Chuan antenna tracking earth station is calculated, if the tracking error is less than the threshold value of setting, Then think that number passes antenna and is directed to accurately track earth station;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track earth station.
2. a kind of spacecraft passes antenna with number and accurately tracks earth station's test verification method, it is characterised in that comprise the following steps that
(1) remote control system to send the motor-driven control instruction of satellite;
(2) control subsystem calculates number in real time and passes antenna directional angle according to the track of satellite, the attitude of satellite and earth station's information Degree, and be sent to number and pass antenna control module, number passes antenna control module according to calculated antenna directional angle, and driving number passes day Line is directed toward earth station;
(3) satellite dynamics module receives executing agency's information on star, emulates to satellite dynamics, and exports true The attitude of satellite, orbit information, and it is sent to Shuo Chuan antenna tracking earth station computing module;
(4) latitude and longitude information of earth station is calculated and is sent to data comparing module, specifically:
Posture of the Shuo Chuan antenna tracking earth station's computing module according to satellite, orbit information calculate number and pass antenna in inertial space In direction, then according to the orbital position of satellite, earth ellipsoid information and earth station's elevation information be calculated the earth's core to ground Direction of the face station vector in inertial space, finally according to earth rotation information, earth ellipsoid information, the precession of the equinoxes and nutating matrix meter It calculates the latitude and longitude information for obtaining earth station and is sent to data comparing module;
(5) earth station's latitude and longitude information is compared data comparing module with earth station's information of theory bookbinding, is calculated The tracking error of Shuo Chuan antenna tracking earth station, if the error is less than specified threshold value, then it is assumed that number passes antenna and is directed to Accurate tracking earth station;Otherwise, then it is assumed that number, which passes antenna, cannot accurately track earth station.
3. a kind of spacecraft according to claim 2 passes antenna with number and accurately tracks earth station's test verification method, special Sign is: the step (4) the specific implementation process is as follows:
(2a) related data updates;
(2b) number passes antenna pointing vector and calculates;
(2c) iterates to calculate the latitude and longitude information that number passes the earth station that antenna is directed toward.
4. a kind of spacecraft according to claim 3 passes antenna with number and accurately tracks earth station's test verification method, special Sign is: what related data updated in the step (2a) is implemented as follows:
The time and orbit information of (2a1) according to satellite calculate the Greenwich sidereal time angle for obtaining sub-satellite point position LamdaG0;
(2a2) updates antenna pointing angle azimuth angle alpha and pitch angle β.
5. a kind of spacecraft according to claim 3 passes antenna with number and accurately tracks earth station's test verification method, special Sign is: step (2b) number passes the detailed process that antenna pointing vector calculates are as follows:
(2b1) is calculated according to the time of satellite, posture information, orbit information and is obtained satellite health coordinate system relative to inertial system Transition matrix CibAnd position vector of the satellite in inertial system
(2b2) installs Matrix C according to updated antenna pointing angle α, β, antennaab, antenna installation deviation Matrix CarbAnd conversion Matrix Cib, calculate the antenna for obtaining and indicating in inertial system and be directed toward
6. a kind of spacecraft according to claim 3 passes antenna with number and accurately tracks earth station's test verification method, special Sign is: iterative calculation number passes the specific implementation of the latitude and longitude information for the earth station that antenna is directed toward such as in the step (2c) Under:
(2c1) is directed toward according to antennaWith position vector of the satellite in inertial systemIt calculates and swears with obtaining antenna vector and star Angle between amount:
(2c2) calculates the angle theta for obtaining earth station's vector and satellite to earth station's vectorsERelevant formula are as follows:
SsE=sin (θsE)=rssin(θsa)/rE0
WhereinE is eccentricity of the earth, REFor earth radius,For ground The latitude at face station, initial value 0,Position of the rs satellite in inertial system;
As the S of calculatingsEThere are when following situations, it may occur in which a variety of situations:
When | SsE| when >=1, illustrates that antenna is directed toward at this time and the earth is without intersection point, set longitude, the latitude E of earth stationλIt is 0, And stop the calculating of this period, and jump back to the calculating that (2a) carries out next period;
When | SsE| when < 1, illustrate that antenna direction has earth station at this time, with calculating earth station's vector at this time and star the folder between vector Angle θrErsAre as follows:
θrErssEsa
θsE=sin-1(SsE)
(2c3) is according to θsE、θrErsWith position r of the satellite in inertial systems, calculate the vector for obtaining earth station to satellite
(2c4) is according to satellite vectorWithIt calculates and obtains earth station's vectorAre as follows:
(2c5) consolidates earth station's vector median filters to the earth according to the Greenwich sidereal time angle LamdaG0 of sub-satellite point position Even in coordinate system;
(2c6) calculates earth station's longitude and latitude E according to earth station's vector in terrestrial coordinate systemλAnd to the longitude and latitude of earth station Degree carries out the precession of the equinoxes and the compensation of nutating item;
(2c7) willIt brings into step (2c2), computes repeatedly to step (2c6), until calculatedWith last computation 'sDifference is less than the threshold value of setting, then Eλ(n)、As earth station's final longitude and latitude value.
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