CN116679327A - Antenna feed opportunistic electric axis calibration method based on fixed satellite - Google Patents

Antenna feed opportunistic electric axis calibration method based on fixed satellite Download PDF

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Publication number
CN116679327A
CN116679327A CN202310433693.2A CN202310433693A CN116679327A CN 116679327 A CN116679327 A CN 116679327A CN 202310433693 A CN202310433693 A CN 202310433693A CN 116679327 A CN116679327 A CN 116679327A
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azimuth
pitch angle
angle
antenna feed
calculating
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CN202310433693.2A
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Chinese (zh)
Inventor
刘迎喜
吴书猛
李崇林
王金林
伍捍东
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XI'AN HENGDA MICROWAVE TECHNOLOGY DEVELOPMENT CO LTD
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XI'AN HENGDA MICROWAVE TECHNOLOGY DEVELOPMENT CO LTD
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Priority to CN202310433693.2A priority Critical patent/CN116679327A/en
Publication of CN116679327A publication Critical patent/CN116679327A/en
Withdrawn legal-status Critical Current

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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
    • G01S19/24Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/27Acquisition or tracking or demodulation of signals transmitted by the system creating, predicting or correcting ephemeris or almanac data within the receiver
    • 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
    • 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
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42Determining position
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Power Engineering (AREA)
  • Variable-Direction Aerials And Aerial Arrays (AREA)

Abstract

The invention discloses an antenna feed opportunistic electric axis calibration method based on fixed satellites, which comprises the following steps: calculating a first azimuth angle and a first pitch angle in a geographic coordinate system of the antenna feed servo turntable according to the longitude of the antenna feed servo turntable and the longitude of the satellite; respectively calculating a second azimuth angle and a second pitch angle of the antenna feed servo turntable under a carrier coordinate system according to the first azimuth angle and the first pitch angle; calculating an azimuth error from the second azimuth; calculating a pitch angle error according to the second pitch angle; and (3) calibrating the azimuth angle of the antenna feed servo motor shaft according to the azimuth angle error by adopting a gradient descent method, and calibrating the pitch angle of the antenna feed servo motor shaft according to the pitch angle error. The method solves the problems that the existing antenna feed servo motor electric shaft calibration method is complex in operation and low in calibration accuracy.

Description

Antenna feed opportunistic electric axis calibration method based on fixed satellite
Technical Field
The invention belongs to the technical field of antenna feed servo, and particularly relates to an antenna feed servo electric axis calibration method based on fixed satellites.
Background
The antenna feeder of the low-orbit satellite tracking device is inconsistent with the zero position of an ideal calculated computer electric axis due to errors in transmission, so that recalibration operation is required. However, the conventional antenna feed opportunistic electric shaft calibration method is complex in operation and poor in calibration accuracy, so that the use effect of the method is seriously affected.
Disclosure of Invention
The invention aims to provide an antenna feed servo motor shaft calibration method based on a fixed satellite, which aims to solve the problems that the existing antenna feed servo motor shaft calibration method is complex in operation and low in calibration precision.
The invention adopts the following technical scheme:
the invention provides an antenna feed opportunistic electric axis calibration method based on fixed satellites, which comprises the following steps:
calculating a first azimuth angle and a first pitch angle in a geographic coordinate system of the antenna feed servo turntable according to the longitude of the antenna feed servo turntable and the longitude of the satellite;
respectively calculating a second azimuth angle and a second pitch angle of the antenna feed servo turntable under a carrier coordinate system according to the first azimuth angle and the first pitch angle;
calculating an azimuth error according to the second azimuth and a third azimuth, wherein the third azimuth is the azimuth corresponding to the strongest signal in one acquisition period; calculating a pitch angle error according to the second pitch angle and a third pitch angle, wherein the third pitch angle is a pitch angle corresponding to the strongest signal position in one acquisition period;
determining an azimuth increment in a gradient descent method according to the azimuth error, and determining a pitch angle increment in the gradient descent method according to the pitch angle error;
based on the azimuth angle increment and the pitch angle increment, the electromechanical shaft attitude of the antenna feed servo turntable is updated by adopting a gradient descent method.
Optionally, the calculating manner of the first azimuth angle and the first pitch angle in the geographic coordinate system of the antenna feed servo turntable according to the longitude of the antenna feed servo turntable and the longitude of the satellite is as follows:
where λ is the longitude of the satellite, λ n Longitude of the servo turntable for antenna, A is a first azimuth, R e Is the earth radius, h is the altitude of the satellite from sea level, and E is the first pitch angle.
Optionally, the calculating manner of calculating the second azimuth angle and the second pitch angle of the antenna feed servo turntable under the carrier coordinate system according to the first azimuth angle and the first pitch angle respectively is as follows:
wherein H is the sea angle of the antenna turntable, P is the pitch angle of the antenna turntable, R is the roll angle of the antenna turntable, A n For a second azimuth angle E n Is a second pitch angle.
Optionally, calculating the azimuth error from the second azimuth and the third azimuth comprises:
acquiring a third azimuth corresponding to the strongest signal in an acquisition period of the antenna feed servo turntable;
and calculating the difference between the second azimuth angle and the third azimuth angle to obtain an azimuth angle error.
Optionally, calculating the pitch angle error from the second pitch angle and the third pitch angle comprises:
acquiring a third pitch angle corresponding to the strongest signal position in one acquisition period of the antenna feed servo turntable;
and calculating the difference between the second pitch angle and the third pitch angle to obtain a pitch angle error.
Optionally, calibrating the azimuth of the antenna feed opportunity axis based on the azimuth error includes:
calculating azimuth increment according to azimuth error;
calculating an azimuth gradient according to the azimuth increment;
based on the azimuth gradient, the azimuth angle of the electromechanical axis of the antenna feed servo turntable is updated by adopting a gradient descent method.
Optionally, calibrating the pitch angle of the antenna feed opportunity shaft according to the pitch angle error includes:
calculating a pitch angle increment according to the pitch angle error;
calculating a pitch gradient according to the pitch angle increment;
based on the pitching gradient, a gradient descent method is adopted to update the pitching angle of the electromechanical shaft of the antenna feed servo turntable.
The beneficial effects of the invention are as follows: according to the longitude of the antenna feed servo turntable and the longitude of the satellite, the azimuth angle and the pitch angle of the antenna feed servo turntable under a geographic coordinate system and a carrier coordinate system are calculated respectively, compared with the traditional satellite attitude estimation and analysis method, the method is simpler in operation and high in calibration accuracy, the error accumulation of each link is avoided, the total azimuth angle error and the total pitch angle error under the carrier coordinate system are further calculated, the two errors are calibrated by adopting a gradient descent method, the calibration of the corresponding azimuth angle and the pitch angle of the antenna feed servo motor shaft is realized, and compared with the conventional calibration method of the antenna feed servo motor shaft, the method provided by the invention is simpler in operation and high in calibration accuracy, the calibration method is simplified, and the calibration time is shortened.
Drawings
FIG. 1 is a schematic diagram of steps of a method for calibrating an antenna feed servo motor based on a fixed satellite;
fig. 2 is a flowchart of calibration operation of an antenna feeder on the basis of a fixed satellite.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention provides an antenna feed opportunistic electric axis calibration method based on fixed satellites, which is shown in fig. 1 and combined with fig. 2, and comprises the following steps:
step 101, calculating a first azimuth angle and a first pitch angle in a geographic coordinate system of the antenna feed turntable according to the longitude of the antenna feed turntable and the longitude of a satellite;
in one embodiment, in the method for calibrating an antenna feeder and electric axis based on a fixed satellite provided by the present invention, related parameters of the antenna feeder and the satellite need to be acquired, and an angle of the antenna feeder and electric axis to be pointed to the satellite under a geographic coordinate system 0 error can be calculated directly according to a longitude of the antenna feeder and a longitude of the satellite, including: a first azimuth angle and a first pitch angle.
It should be noted that, before acquiring the relevant parameters of the antenna feed servo turntable and the satellite, the following steps are further performed, as shown in fig. 1, and specifically include: leveling the bottom of an antenna feed servo turntable through an inclinometer, and ensuring that the acquired initial data has 0 error under a geographic coordinate system; second, measuring antenna feed table information including the longitude lambda of the antenna feed table by GPS n Height h from sea level n And heading angle H; and thirdly, searching a fixed satellite with the same frequency band as the antenna feed servo antenna, and acquiring information of the satellite, wherein the information comprises longitude lambda of the satellite and height h from sea level.
Finally, according to the longitude lambda of the antenna feed servo turntable n Height h from sea level n And calculating a first angle azimuth A and a first pitch angle E of the antenna feed servo turntable, which are directed to the satellite in a geographic coordinate system, by the course angle H, the longitude lambda of the satellite and the altitude H from the sea level.
In this embodiment, the first azimuth angle and the first pitch angle of the antenna feed servo turntable pointing to the satellite in the geodetic coordinate system can be directly calculated according to the longitude of the antenna feed servo turntable, the longitude of the satellite and other parameters which can be directly obtained.
Step 102, respectively calculating a second azimuth angle and a second pitch angle of the antenna feed servo turntable under a carrier coordinate system according to the first azimuth angle and the first pitch angle;
in one embodiment, the coordinate conversion is further performed according to the calculated first azimuth angle and first pitch angle, so as to convert the first azimuth angle and first pitch angle in the geographic coordinate system into the second azimuth angle and second pitch angle in the carrier coordinate system.
Step 103, calculating an azimuth error according to the second azimuth and a third azimuth, wherein the third azimuth is the azimuth corresponding to the strongest signal in one acquisition period;
in one embodiment, to accurately calibrate the zero position of the azimuth of the antenna feed servo stage, the azimuth error in the carrier coordinate system needs to be calculated, specifically, the third azimuth A 'where the signal is maximum at this time is recorded' n Second azimuth angle A received from current time n Calculating azimuth angle error ΔA n =A′ n -A n Wherein A 'is' n Is a third azimuth angle in a carrier coordinate system, A n A second azimuth angle in the carrier coordinate system is received for the current time.
104, calculating a pitch angle error according to the second pitch angle and a third pitch angle, wherein the third pitch angle is a pitch angle corresponding to the strongest signal position in one acquisition period;
in one embodiment, in order to accurately calibrate the null position of the pitch angle of the antenna feed servo turntable, the pitch angle error in the carrier coordinate system needs to be calculated. Specifically, a third pitch angle E 'at which the signal is maximum at this time is recorded' n A second pitch angle E received from the current moment n And calculates a pitch angle error DeltaE n =E′ n -E n Wherein E 'is' n Is a third pitch angle under the carrier coordinate system, E n And receiving a second pitch angle in the carrier coordinate system for the current moment.
Step 105, determining an azimuth increment in the gradient descent method according to the azimuth error, and determining a pitch angle increment in the gradient descent method according to the pitch angle error;
in one embodiment, in order to adapt the method design using the gradient descent method, based on the calculated azimuth and pitch errors, an azimuth is set as an azimuth increment, which generally does not exceed the azimuth error at the calculation, and which can be set as follows, typically based on the number of iterations (3-5) of the algorithmFor example, iterating five times, the azimuth increment is 1/5 of the azimuth error; similarly, pitch angle increment is +.>
And 106, updating the electromechanical shaft posture of the antenna feed servo turntable by adopting a gradient descent method based on the azimuth angle increment and the pitch angle increment.
In one embodiment, in order to eliminate azimuth angle errors and pitch angle errors generated when calculating azimuth angles and pitch angles under different coordinate systems, respectively giving an azimuth angle increment and a pitch angle increment, and obtaining the azimuth angle of the next moment by calculating the sum of the initial value of the azimuth angle of the current moment and the azimuth angle increment; and simultaneously recording receiving levels corresponding to azimuth angles at two moments, obtaining azimuth gradients by calculating the difference value between the two moment level differences and the two moment azimuth angles, and according to a gradient descent method, until the azimuth gradients meet a preset minimum azimuth threshold value, wherein the azimuth angle obtained at the moment is an azimuth angle for controlling an antenna feed servo motor axis to point to the position where a satellite signal is maximum, so that the calibration of the azimuth angle of the antenna feed servo motor is realized. Similarly, firstly calculating the pitching gradient of the pitching angle, then adopting a gradient descent method until the pitching gradient meets a preset minimum pitching threshold value, and at the moment, controlling the antenna feed servo motor shaft to point to the pitching angle at the position where the satellite signal is maximum, updating the electromechanical shaft posture of the antenna feed servo turntable, and realizing the calibration of the pitching angle of the antenna feed servo turntable.
In one embodiment, the first azimuth and the first pitch angle in the geographic coordinate system of the antenna feed turntable are calculated according to the longitude of the antenna feed turntable and the longitude of the satellite by:
where λ is the longitude of the satellite, λ n Longitude of the servo turntable for antenna, A is a first azimuth, R e Is the earth radius, h is the altitude of the satellite from sea level, and E is the first pitch angle.
In one embodiment, the calculating manner of the second azimuth angle and the second pitch angle under the carrier coordinate system of the antenna feed servo turntable according to the first azimuth angle and the first pitch angle is as follows:
wherein H is the sea angle of the antenna turntable, P is the pitch angle of the antenna turntable, R is the roll angle of the antenna turntable, A n For a second azimuth angle E n Is a second pitch angle.
Optionally, calculating the azimuth error from the second azimuth and the third azimuth comprises:
acquiring a third azimuth corresponding to the strongest signal in an acquisition period of the antenna feed servo turntable;
and calculating the difference between the second azimuth angle and the third azimuth angle to obtain an azimuth angle error.
In one embodiment, a second azimuth A 'is recorded at which the signal is maximum' n Second azimuth angle A received from current time n Calculating azimuth angle error ΔA n =A′ n -A n Wherein A 'is' n For a second azimuth angle in the carrier coordinate system, A n Is the initial azimuth received at the current time.
Optionally, calculating the pitch angle error from the second pitch angle and the third pitch angle comprises:
acquiring a third pitch angle corresponding to the strongest signal position in one acquisition period of the antenna feed servo turntable;
and calculating the difference between the second pitch angle and the third pitch angle to obtain a pitch angle error.
In one embodiment, a third pitch angle E 'is recorded at which the signal is maximum' n A second pitch angle E received from the current moment n And calculates a pitch angle error DeltaE n =E′ n -E n Wherein E 'is' n Is a third pitch angle under the carrier coordinate system, E n And receiving a second pitch angle in the carrier coordinate system for the current moment.
Optionally, updating the electromechanical axis pose of the antenna feed servo stage using a gradient descent method based on the azimuth increment comprises:
calculating azimuth increment according to azimuth error;
calculating an azimuth gradient according to the azimuth increment;
based on the azimuth gradient, the azimuth angle of the electromechanical axis of the antenna feed servo turntable is updated by adopting a gradient descent method.
In one embodiment, the automatic calibration process for the orientation of the antenna feed opportunity electrical axis is as follows: receiving an initial azimuth angle A 1 Recording the corresponding receiving level as U A1 The method comprises the steps of carrying out a first treatment on the surface of the Setting an azimuth increment delta A of an antenna feed servo turntable according to the azimuth error, wherein the azimuth calibration is performed to eliminate the existing azimuth error, but to avoid calibrating the azimuth to be negative in practice, an azimuth increment is required to be reasonably set according to the calculated azimuth error, for example, the azimuth increment is 1/5 of the azimuth error; then adding the azimuth increment on the basis of the initial azimuth to obtain the azimuth of the next moment, for example: a is that 2 =A 1 +ΔA, where ΔA is the azimuthal increment, A 2 Azimuth for the next moment, and record the azimuth with A 2 Corresponding level U A2
Further calculating azimuth gradient based on azimuth incrementWherein A is 2 -A 1 =ΔA;
The azimuth angle of each moment is continuously updated along with the descending direction of the azimuth angle gradientK a Setting a constant for the first;
update A by performing the above steps 4 、A 5 Up toEpsilon is the first arbitrary decimal set, and the azimuth automatic calibration of the antenna feed servo motor shaft is completed.
Optionally, updating the electromechanical axis pose of the antenna feed servo turntable based on the pitch angle increment by using a gradient descent method comprises:
calculating a pitch angle increment according to the pitch angle error;
calculating a pitch gradient according to the pitch angle increment;
based on the pitching gradient, a gradient descent method is adopted to update the pitching angle of the electromechanical shaft of the antenna feed servo turntable.
In one embodiment, the pitch auto-calibration process is as follows: first, an initial pitch angle E is received 1 Recording the corresponding receiving level as U E1 The method comprises the steps of carrying out a first treatment on the surface of the The pitch angle increment delta E of an antenna feed servo turntable is preset according to the pitch angle error, and similarly, in order to avoid calibrating the pitch angle to be negative in practice, the pitch angle increment needs to be reasonably set according to the calculated pitch angle error, for example, the pitch angle increment is 1/5 of the pitch angle error; and then adding a pitch angle increment to the initial pitch angle to obtain the pitch angle at the next moment, for example: e (E) 2 =E 1 +ΔE, where ΔE is the pitch increment, E 2 For the pitch angle at the next moment, and record the pitch angle with E 2 Corresponding level U E2 The method comprises the steps of carrying out a first treatment on the surface of the Calculating pitch gradient on the basis of azimuth incrementWherein E is 2 -E 1 =ΔE;
Continuously updating the pitch angle at each moment along with the descending direction of the pitch angle gradientK e Setting a constant;
update E by executing the steps 4 、E 5 Up toEpsilon is any set decimal, and the azimuth automatic calibration of the antenna feed servo motor electric axis is completed at this time.

Claims (7)

1. An antenna feed opportunistic electric axis calibration method based on fixed satellites is characterized by comprising the following steps:
calculating a first azimuth angle and a first pitch angle of the antenna feed servo turntable in a geographic coordinate system according to the longitude of the antenna feed servo turntable and the longitude of a satellite;
respectively calculating a second azimuth angle and a second pitch angle of the antenna feed servo turntable under a carrier coordinate system according to the first azimuth angle and the first pitch angle;
calculating an azimuth angle error according to the second azimuth angle and a third azimuth angle, wherein the third azimuth angle is the azimuth angle corresponding to the strongest signal in one acquisition period; calculating a pitch angle error according to the second pitch angle and a third pitch angle, wherein the third pitch angle is a pitch angle corresponding to the strongest signal position in one acquisition period;
determining an azimuth increment in a gradient descent method according to the azimuth error, and determining a pitch angle increment in the gradient descent method according to the pitch angle error;
and updating the electromechanical shaft posture of the antenna feed servo turntable by adopting a gradient descent method based on the azimuth angle increment and the pitch angle increment.
2. The method of calibrating an antenna feed mechanism based on fixed satellites according to claim 1, wherein the first azimuth and the first pitch angle of the antenna feed mechanism in the geographic coordinate system are calculated according to the longitude of the antenna feed mechanism and the longitude of the satellites by:
where λ is the longitude of the satellite, λ n Longitude for the antenna feed servo turntable, A is the first azimuth, R e And the earth radius is h, the altitude of the satellite from the sea level is h, and E is the first pitch angle.
3. The method of calibrating an antenna feed opportunity axis based on fixed satellites of claim 2, wherein the calculating manner of calculating the second azimuth angle and the second pitch angle of the antenna feed opportunity table in the carrier coordinate system according to the first azimuth angle and the first pitch angle is as follows:
wherein H is the sea angle of the antenna feeding turntable, P is the pitch angle of the antenna feeding turntable, R is the roll angle of the antenna feeding turntable, A n For the second azimuth angle E n Is the second pitch angle.
4. The method of fixed satellite based antenna feed electric axis calibration of claim 1, wherein calculating an azimuth error from the second azimuth and third azimuth comprises:
acquiring the third azimuth corresponding to the strongest signal in one acquisition period of the antenna feed servo turntable;
and calculating the difference between the second azimuth angle and the third azimuth angle to obtain the azimuth angle error.
5. The method of fixed satellite based antenna feed electric axis calibration of claim 1, wherein calculating pitch angle errors from the second pitch angle and the third pitch angle comprises:
acquiring the third pitch angle corresponding to the strongest signal position in one acquisition period of the antenna feed servo turntable;
and calculating the difference value of the second pitch angle and the third pitch angle to obtain the pitch angle error.
6. The method of claim 1, wherein updating the electromechanical axis pose of the antenna feed servo stage using a gradient descent method based on the azimuth increment comprises:
calculating azimuth increment according to the azimuth error;
calculating an azimuth gradient according to the azimuth increment;
based on the azimuth gradient, updating the azimuth angle of the electromechanical axis of the antenna feed servo turntable by adopting a gradient descent method.
7. The method of claim 1, wherein updating the electromechanical axis pose of the antenna feed servo turntable using a gradient descent method based on the pitch angle increment comprises:
calculating a pitch angle increment according to the pitch angle error;
calculating a pitch gradient according to the pitch angle increment;
and updating the pitch angle of the electromechanical shaft of the antenna feed servo turntable by adopting a gradient descent method based on the pitch gradient.
CN202310433693.2A 2023-04-20 2023-04-20 Antenna feed opportunistic electric axis calibration method based on fixed satellite Withdrawn CN116679327A (en)

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