CN113447957A - Vibration eliminating algorithm for high-precision real-time satellite orbit instantaneous semi-major axis - Google Patents

Vibration eliminating algorithm for high-precision real-time satellite orbit instantaneous semi-major axis Download PDF

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CN113447957A
CN113447957A CN202110693056.XA CN202110693056A CN113447957A CN 113447957 A CN113447957 A CN 113447957A CN 202110693056 A CN202110693056 A CN 202110693056A CN 113447957 A CN113447957 A CN 113447957A
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orbit
satellite
major axis
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CN113447957B (en
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陈培
程乙洲
贾振俊
耿铖
孙秀聪
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Beihang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
    • G01S19/08—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing integrity information, e.g. health of satellites or quality of ephemeris data
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/242—Orbits and trajectories

Abstract

The invention provides a satellite orbit semimajor axis vibration eliminating scheme based on discrete Fourier transform and least square fitting, constructs a vibration eliminating semimajor axis calculation method suitable for satellite orbit phase control, establishes a method combining orbit prediction, numerical averaging and numerical fitting, and further designs a high-precision real-time satellite orbit semimajor axis vibration eliminating algorithm. The method adopts the concepts of numerical averaging and numerical fitting, and gives a primary vibration elimination semimajor axis by utilizing the numerical averaging; and further de-oscillating by using a discrete Fourier transform and numerical fitting method. The specific implementation method of the invention is that an orbit dynamics model is utilized to carry out orbit prediction, so as to obtain the high-precision absolute position and speed information of the satellite in a sufficiently long time period, finally the instantaneous semimajor axis of the satellite orbit is obtained by calculation, and the instantaneous semimajor axis in a certain period is utilized to obtain the primary vibration elimination semimajor axis by using numerical value average; extracting the natural frequency of residual short-period oscillation by discrete Fourier transform; and finally, calculating to obtain the satellite orbit vibration-removing average semimajor axis by using a numerical fitting method according to the residual short-period oscillation natural frequency. The invention has the advantages of high navigation precision and good real-time performance.

Description

Vibration eliminating algorithm for high-precision real-time satellite orbit instantaneous semi-major axis
Technical Field
The invention provides a high-precision real-time satellite orbit instantaneous semi-major axis vibration elimination algorithm, which relates to lengthening an available orbit by orbit prediction in a short time under the condition that a satellite high-precision orbit is known in a certain time, averagely eliminating vibration of segmented numerical values of the orbit instantaneous semi-major axis for the first time, extracting residual short-period vibration natural frequency of the initial vibration elimination semi-major axis by discrete Fourier transform, fitting the numerical values of the initial vibration elimination semi-major axis, eliminating residual short-period vibration terms, keeping long-term terms and long-period terms, and finally obtaining the satellite orbit average semi-major axis after short-period vibration elimination. Belonging to the technical field of navigation.
Background
With the rapid development of the small satellite constellation technology, the small satellite constellation is valued by the aerospace major countries in the world. Pigeon group satellite (DOVE) constellation, developed by Planet Labs, USA. The small satellite formation uses CubeSat satellites with the volume of 3U (10cm multiplied by 30cm) and the weight of only 5.8Kg to form small satellite formation, can achieve the observation of 3m resolution of the earth, can traverse and shoot the earth once every day, and is very high in manufacturing cost if a traditional satellite constellation is used. The star link (StarLink) satellite constellation, developed by the well-known company SpaceX, which projects more than ten thousand microsatellites to be transmitted before 2024, constitutes a satellite constellation. According to SpaceX, if everything goes well, the constellation of star-linked satellites will provide a low-cost Internet connection task and will not be limited by geographical location, which will greatly promote the development of the Internet.
However, most satellite constellations face the problem of orbit phase maintenance, and generally the whole constellation needs to be maintained through orbit phase control. Assuming that the actual position of the satellite is a' and the satellite should be at the target position a, the included angle of the latitude argument between the satellite and the target position is α, the satellite needs to ensure that the α angle cannot be too large through the orbital phase control.
Generally, satellites maintain orbital phase by controlling the orbital semimajor axis. If the orbit semi-major axis of a satellite at an ideal position becomes larger, the orbit period of the satellite is increased, and the phase error of the satellite is larger and larger. Therefore, determining the semi-major axis of the satellite orbit becomes a serious issue for satellite phase control.
The instantaneous semi-major axis of the satellite can be divided into three parts, namely a long-term, a long-period term and a short-period oscillation term. The long term, which is mainly the orbit of the satellite under the influence of the earth central gravitational field, is a main component of the semi-major axis of the orbit, and the change of the long term has no period, and can drift gradually along with the time. Under the influence of the perturbation forces such as the global non-spherical gravity field, the sea tide and the earth tide caused by the deformation of the earth, the three-body attraction force caused by the sun and the moon, the atmospheric resistance, the sunlight pressure and the like, the semi-long axis of the orbit can generate a short period oscillation item and a long period item. The long period term of the satellite orbit semi-major axis means that the actual orbit semi-major axis slowly and periodically changes along with time, and is obvious after a long period; the short-period oscillation of the semi-major axis of the satellite orbit refers to that the semi-major axis of the orbit rapidly oscillates back and forth around a value, and the period is relatively short.
At present, the orbit of a low-orbit satellite is generally determined by a GNSS orbit determination technology, and a semi-major axis of the satellite orbit is obtained. The GNSS is generally called a Global Navigation Satellite System (Global Navigation Satellite System), and includes GPS in the united states, GLONASS in russia, Galileo in europe, and beidou in china, and the like. This is a system that can provide a spatial and temporal reference for the user. With the development of GNSS systems, there are more and more low-orbit satellites using GNSS-based satellite precision orbit determination technology.
However, with GNSS orbit determination, only the instantaneous semi-major axis of the low-orbit satellite orbit at each time can be obtained, which is quite disadvantageous for small satellite phase control. Since most of the time the purpose of satellite orbit phase control is to suppress long-term drift of satellite phase, i.e. long-term drift of the orbit semi-major axis, it is generally not desirable to deal with short-period oscillation of the satellite orbit semi-major axis, because the short-period oscillation term has less influence on the phase and the handling wastes much fuel, which is unacceptable for many satellites, especially for small satellites.
The short-period term of the orbit instantaneous semi-major axis, even though it has a small effect on the satellite phase, has a much larger effect on the instantaneous semi-major axis in the short term than the drift portion and the long-period term of the long-term. The orbit phase control system of the satellite determines whether to carry out orbit control according to the difference between the actual semi-major axis and the target semi-major axis. If the short-period oscillation items in the instantaneous semi-long axis are not eliminated, the control times of the orbit phase control system are far higher than the times which should be controlled, so that the fuel consumption is greatly improved, and the cost of the satellite is increased.
In summary, the invention provides a high-precision real-time satellite orbit semimajor axis vibration elimination algorithm, which obtains a high-precision orbit in a longer time period through short-time satellite orbit prediction under the condition that the high-precision orbit of a satellite in a certain time period is known, then performs orbit semimajor axis sectional averaging (primary vibration elimination), determines the residual short period oscillation natural frequency after primary vibration elimination through discrete Fourier transform, finally adopts a numerical fitting mode to remove the residual short period oscillation item in the primary vibration elimination semimajor axis, retains the long term item and the long period item, and finally obtains the satellite orbit average semimajor axis after short period oscillation elimination.
Disclosure of Invention
Objects of the invention
The invention aims to eliminate the short-period oscillation of the instantaneous semi-major axis of the satellite orbit and provide an effective feedback value for an orbit phase control system. The method includes the steps that under the condition that the high-precision orbit of a satellite is known within a certain time period, the high-precision orbit of a longer time is obtained through short-time satellite orbit prediction, then orbit semimajor axis sectional averaging (primary vibration elimination) is carried out, the residual short-period oscillation natural frequency after primary vibration elimination is determined through discrete Fourier transform, finally, a numerical fitting mode is adopted, the residual short-period oscillation item in the primary vibration elimination semimajor axis is removed, the long-term item and the long-period item are reserved, and finally the satellite orbit average semimajor axis after the short-period oscillation elimination is obtained. The method has the advantages of high precision and good real-time performance, and is suitable for a scene in which a satellite performs orbit phase control through an orbit semimajor axis.
(II) technical scheme
The implementation steps of the high-precision real-time orbit instantaneous semi-major axis vibration elimination algorithm are as follows:
the method comprises the following steps: obtaining high-precision orbit of satellite in certain time period
Step two: and (3) forecasting the orbit by using the orbit dynamics to obtain the satellite high-precision orbit in a longer time period.
The total external force of the satellite is F, the rotational angular velocity of the earth is omega, the position vector of the satellite in the WGS84 coordinate system is r, and then the kinetic equation of the satellite in the WGS84 coordinate system is
Figure BDA0003127427160000041
Where 2 ω × r is the coriolis acceleration, ω × (ω × r) is the centrifugal acceleration, and m is the mass of the satellite. F is the resultant external force of the satellite, including the gravity of the earth center, the non-spherical gravity field of the earth, the sea tide and the earth tide caused by the deformation of the earth, the three-body gravity caused by the sun and the moon, the atmospheric resistance, the sunlight pressure and other forces, wherein the gravity of the earth center is the most main force, and other forces can be regarded as small quantities.
The angular velocity vector of the earth is expressed in the WGS84 coordinate system
ω≈[0 0 7.292×10-5]Trad/s (2)
By numerical calculation of equation (1), t can be calculatedi-1Position velocity r of timei-1And vi-1And predicting to obtain satellite tiPosition velocity r of timeiAnd vi。
Step three: and (4) solving an instantaneous semi-major axis by using the instantaneous position speed.
At tiThe position and speed of the moment are
ri＝||ri|| (3)
vi＝||vi|| (4)
At tiInstantaneous semi-major axis of time is
Figure BDA0003127427160000051
Wherein a isiIs tiInstantaneous semi-major axis of time, G is the constant of universal gravitation, M is the central celestial (earth) mass, riIs tiPosition size of time, viIs tiThe velocity magnitude of the moment.
Step four: checking whether the instantaneous semi-major axis data of q N circles exist, and if not, repeating the steps two to three.
The value principle of the integer value N is as follows: the time for the satellite to rotate N revolutions around the earth is as close to 1 day as possible.
The value principle of the integer value q is as follows: typically 3 to 7, depending on the required accuracy adjustment. The larger the value is, the higher the precision of the vibration elimination semimajor axis obtained by the algorithm is, but the larger the required original data amount and calculated amount are.
Step five: and (4) carrying out sectional averaging on the instantaneous semi-major axis to obtain the primary vibration elimination semi-major axis. And calculating the initial vibration elimination semimajor axis after the numerical average of each segment (N circles around the earth) by using the instantaneous semimajor axis at each moment.
Note that there may be an overlapping portion between the segments (N turns). For example, the first segment may be taken to be the 1 st to nth turn, the second segment may be taken to be the 2 nd to N +1 th turn, the third segment may be taken to be the 3 rd to N +2 th turn, and so on. This is advantageous for increasing the data size of the initial oscillation-canceling semimajor axis after numerical averaging.
Assume that the sample point of the instantaneous semi-major axis in the mth segment (N circles) has NmThen the initial vibration-damping half-field axis after the numerical averaging of the mth segment (N-turn) is:
Figure BDA0003127427160000052
wherein
Figure BDA0003127427160000061
Is the first damping semimajor axis of the mth segment (N turns).
Calculate the initial vibration-damping semi-major axis after the numerical average of k segments (N circles)
Figure BDA0003127427160000062
Figure BDA0003127427160000063
Note that these k segments may coincide but are to completely cover all of the instantaneous semi-major axis data extracted in step four.
Step six: and (3) extracting the natural frequency of the residual short-period oscillation of the primary vibration-removing semimajor axis by discrete Fourier transform.
According to the segmented primary vibration elimination semimajor axis extracted in the step five
Figure BDA0003127427160000064
Performing discrete Fourier transform to extract three main residual short-period oscillation frequencies omega1、ω2、ω3。
Step seven: further reduction of semi-major axis oscillation using data fitting
Fitting function:
Figure BDA0003127427160000065
where τ is the argument in circles.
Wherein
Figure BDA0003127427160000066
For the fitted satellite primary derotation half-field axis, c + k1τ+k2τ2Is a polynomial function, represents the sum of the long-period term and the long-term of the semi-major axis, and is a required average term; the remaining part of the trigonometric function is a short period oscillation item which needs to be rejected. Omega1、ω2、ω3For the period of oscillation of the instantaneous semi-major axis, its specific value needs to be determined by discrete fourier transform before fitting. A in the formula (7)1、A2、A3、
Figure BDA0003127427160000067
Figure BDA0003127427160000068
k1、k2And c are parameters to be determined for fitting.
Fitting the object:
Figure BDA0003127427160000069
Figure BDA00031274271600000610
the fitting method comprises the following steps: the least squares method is adopted so that the error between equation (7) and the fitting object is minimized.
Assuming a fitting function of
f(τ)＝A1g1(τ,ξ)+A2g2(τ,ξ)+…+Algl(τ,ξ) (9)
A＝[A1 A2 ... Al]TAnd
Figure BDA0003127427160000071
to fit the determined parameters, combining equation (8) and equation (9), the parameters A and w are determined such that
Figure BDA0003127427160000072
Equation (10) is minimized, minF (A, ξ).
And (3) fitting results:
after removing the trigonometric function in the fitted polynomial, the remaining polynomial part is the semimajor axis after removing the short period oscillations.
Figure BDA0003127427160000073
The final result of the vibration-damping semimajor axis is
Figure BDA0003127427160000074
(III) advantages
The high-precision real-time satellite orbit vibration elimination algorithm provided by the invention has the advantages that:
firstly, the length of the available track is increased by using track forecast, and the real-time performance is improved.
The invention provides a vibration eliminating algorithm by utilizing the average addition fitting of the instantaneous semi-major axis in a certain period. The algorithm eliminates most short-period oscillation of the instantaneous semi-major axis, retains a long-term and a long-period term of the semi-major axis, and provides favorable conditions for phase control of the satellite.
Drawings
FIG. 1 is a flow chart of the steps of the present invention
Detailed Description
The implementation steps of the high-precision real-time orbit instantaneous semi-major axis vibration elimination algorithm are as follows:
the method comprises the following steps: obtaining high-precision orbit of satellite in certain time period
Step two: and (3) forecasting the orbit by using the orbit dynamics to obtain the satellite high-precision orbit in a longer time period.
The total external force of the satellite is F, the rotational angular velocity of the earth is omega, the position vector of the satellite in the WGS84 coordinate system is r, and then the kinetic equation of the satellite in the WGS84 coordinate system is
Figure BDA0003127427160000081
Where 2 ω × r is the coriolis acceleration, ω × (ω × r) is the centrifugal acceleration, and m is the mass of the satellite. F is the resultant external force of the satellite, including the gravity of the earth center, the non-spherical gravity field of the earth, the sea tide and the earth tide caused by the deformation of the earth, the three-body gravity caused by the sun and the moon, the atmospheric resistance, the sunlight pressure and other forces, wherein the gravity of the earth center is the most main force, and other forces can be regarded as small quantities.
The angular velocity vector of the earth is expressed in the WGS84 coordinate system
ω≈[0 0 7.292×10-5]Trad/s (13)
By numerical calculation of equation (1), t can be calculatedi-1Position velocity r of timei-1And vi-1And predicting to obtain satellite tiPosition velocity r of timeiAnd vi。
Step three: and (4) solving an instantaneous semi-major axis by using the instantaneous position speed.
At tiThe position and speed of the moment are
ri＝||ri|| (14)
vi＝||vi|| (15)
At tiInstantaneous semi-major axis of time is
Figure BDA0003127427160000082
Wherein a isiIs tiInstantaneous semi-major axis of time, G is the constant of universal gravitation, M is the central celestial (earth) mass, riIs tiPosition size of time, viIs tiThe velocity magnitude of the moment.
Step four: checking whether the instantaneous semi-major axis data of q N circles exist, and if not, repeating the steps two to three.
The value principle of the integer value N is as follows: the time for the satellite to rotate N revolutions around the earth is as close to 1 day as possible.
The value principle of the integer value q is as follows: typically 3 to 7, depending on the required accuracy adjustment. The larger the value is, the higher the precision of the vibration elimination semimajor axis obtained by the algorithm is, but the larger the required original data amount and calculated amount are.
Step five: and (4) carrying out sectional averaging on the instantaneous semi-major axis to obtain the primary vibration elimination semi-major axis. And calculating the initial vibration elimination semimajor axis after the numerical average of each segment (N circles around the earth) by using the instantaneous semimajor axis at each moment.
Note that there may be an overlapping portion between the segments (N turns). For example, the first segment may be taken to be the 1 st to nth turn, the second segment may be taken to be the 2 nd to N +1 th turn, the third segment may be taken to be the 3 rd to N +2 th turn, and so on. This is advantageous for increasing the data size of the initial oscillation-canceling semimajor axis after numerical averaging.
Assume that the sample point of the instantaneous semi-major axis in the mth segment (N circles) has NmThen the initial vibration-damping half-field axis after the numerical averaging of the mth segment (N-turn) is:
Figure BDA0003127427160000091
wherein
Figure BDA0003127427160000092
Is the first damping semimajor axis of the mth segment (N turns).
Calculate the initial vibration-damping semi-major axis after the numerical average of k segments (N circles)
Figure BDA0003127427160000093
Figure BDA0003127427160000094
Note that these k segments may coincide but are to completely cover all of the instantaneous semi-major axis data extracted in step four.
Step six: and (3) extracting the natural frequency of the residual short-period oscillation of the primary vibration-removing semimajor axis by discrete Fourier transform.
According to the segmented primary vibration elimination semimajor axis extracted in the step five
Figure BDA0003127427160000101
Performing discrete Fourier transform to extract three main residual short-period oscillation frequencies omega1、ω2、ω3。
Step seven: further reduction of semi-major axis oscillation using data fitting
Fitting function:
Figure BDA0003127427160000102
where τ is the argument in circles.
Wherein
Figure BDA0003127427160000103
For the fitted satellite primary derotation half-field axis, c + k1τ+k2τ2Is a polynomial function, represents the sum of the long-period term and the long-term of the semi-major axis, and is a required average term; the remaining part of the trigonometric function is a short period oscillation item which needs to be rejected. Omega1、ω2、ω3For the period of oscillation of the instantaneous semi-major axis, its specific value needs to be determined by discrete fourier transform before fitting. A in the formula (7)1、A2、A3、
Figure BDA0003127427160000104
Figure BDA0003127427160000105
k1、k2And c are parameters to be determined for fitting.
Fitting the object:
Figure BDA0003127427160000106
Figure BDA0003127427160000107
the fitting method comprises the following steps: the least squares method is adopted so that the error between equation (7) and the fitting object is minimized.
Assuming a fitting function of
f(τ)＝A1g1(τ,ξ)+A2g2(τ,ξ)+…+Algl(τ,ξ) (20)
A＝[A1 A2 ... Al]TAnd
Figure BDA0003127427160000108
to fit the determined parameters, combining equation (8) and equation (9), the parameters A and w are determined such that
Figure BDA0003127427160000109
Equation (10) is minimized, minF (A, ξ).
And (3) fitting results:
after removing the trigonometric function in the fitted polynomial, the remaining polynomial part is the semimajor axis after removing the short period oscillations.
Figure BDA0003127427160000111
The final result of the vibration-damping semimajor axis is
Figure BDA0003127427160000112

Claims (1)

1. A high-precision real-time satellite orbit instantaneous semi-major axis vibration elimination algorithm comprises the following steps:
the method comprises the following steps: and acquiring the high-precision orbit of the satellite within a certain time period.
Step two: and (3) forecasting the orbit by using the orbit dynamics to obtain the satellite high-precision orbit in a longer time period.
Step three: and (4) solving an instantaneous semi-major axis by using the instantaneous position speed.
Step four: checking whether the instantaneous semi-major axis data of q N circles exist, and if not, repeating the steps two to three.
The value principle of the integer value N is as follows: the time for the satellite to rotate N revolutions around the earth is as close to 1 day as possible.
The value principle of the integer value q is as follows: typically 3 to 7, depending on the required accuracy adjustment.
Step five: and (4) carrying out sectional averaging on the instantaneous semi-major axis to obtain the primary vibration elimination semi-major axis.
Step six: and (3) extracting the natural frequency of the residual short-period oscillation of the primary vibration-removing semimajor axis by discrete Fourier transform.
Step seven: semi-major axis oscillation is further reduced using data fitting.
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