CN115876227B - On-orbit calibration method and system for intersatellite pointing of gravity satellite - Google Patents
On-orbit calibration method and system for intersatellite pointing of gravity satellite Download PDFInfo
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Abstract
本发明涉及一种重力卫星星间指向的在轨定标方法及系统，具体涉及地球物理测量技术领域。所述方法包括：根据KBR测距数据得到双星中各卫星的质心到天线相位中心矢量的模值；将观测数据带入星间测距理论模型得到双星的星间测距；计算双星的星间测距的残差；将双星间的星间测距、残差、双星的KBR测距数据和双星中各卫星的质心到天线相位中心矢量的模值代入观测方程进行求解得到双星的角度变化量；根据双星中各卫星的质心到天线相位中心矢量的模值和角度变化量完成重力卫星星间指向的在轨定标。本发明可对卫星实际在轨的双星指向变化进行标定，提高定标结果的准确度。
The present invention relates to an on-orbit calibration method and system for inter-satellite pointing of a gravity satellite, and specifically to the field of geophysical measurement technology. The method comprises: obtaining the modulus of the center of mass of each satellite in a binary satellite to the antenna phase center vector according to KBR ranging data; bringing the observation data into the inter-satellite ranging theoretical model to obtain the inter-satellite ranging of the binary satellite; calculating the residual of the inter-satellite ranging of the binary satellite; substituting the inter-satellite ranging, residual, KBR ranging data of the binary satellite and the modulus of the center of mass of each satellite in the binary satellite to the antenna phase center vector into the observation equation for solving to obtain the angular variation of the binary satellite; completing the on-orbit calibration of the inter-satellite pointing of the gravity satellite according to the modulus and angular variation of the center of mass of each satellite in the binary satellite to the antenna phase center vector. The present invention can calibrate the actual on-orbit pointing variation of the binary satellite, and improve the accuracy of the calibration result.
Description
Technical Field
The invention relates to the technical field of geophysical measurement, in particular to an on-orbit calibration method and system for orientation between gravity satellites.
Background
The inter-satellite pointing calibration of the gravity satellite is to check the alignment condition between two satellites, and is defined as the vector from the center of mass of the satellite to the phase center of the antennaRelative to the direction of the line of sightIncluded angle of (i.e.)
Wherein R SF→IRF is a rotation matrix from the satellite reference frame to the inertial frame, fig. 1 is a satellite reference frame (SF), and fig. 2 is an antenna phase center reference frame (KF) and line of sight reference frame (LOS). KF is that its origin of coordinates is located at the center of mass of the satellite, the x-axis direction is defined as pointing from the center of mass of the satellite to the phase center of the antenna, the z-axis direction is defined as vertically downward along the flight direction of the satellite, and the y-axis direction is determined by right-hand rule.
LOS, wherein the origin of coordinates is positioned at the center of mass of the satellite, the x-axis direction is the connecting line of the sight directions of the two centers of mass of the satellite, the z-axis direction points to the earth center, and the y-axis direction is determined according to the right-hand rule.
The line of sight reference frame is defined as:
Where j=1, 2 in the above equation, represents satellite j, The satellite 1 and satellite 2 centroid position vectors respectively,Representing the X component of satellite j (1 or 2) in the LOS coordinate system,Representing the Y component of satellite j (1 or 2) in the LOS coordinate system,The Z component of satellite j (1 or 2) in the LOS coordinate system is represented.
The antenna phase center reference frame is defined as:
Representing the X component of satellite j (1 or 2) in KF coordinate system, Representing satellite j (1 or 2 the Y component in KF coordinate system,Representing the Z component of satellite j (1 or 2) in the KF coordinate system, R SF→IRF represents the transformation matrix of the satellite reference system into the inertial system,Is the satellite centroid to antenna phase center vector. The satellite reference system coordinate axis coincides with the antenna phase center reference system.
The inter-satellite pointing requires smaller angular deviation, and the reasons are that the inter-satellite distance measurement observed quantity is influenced by the point shaking, and the multipath effect is formed by the fact that the microwave signal is reflected on the satellite surface for multiple times.
The existing inter-satellite pointing calibration method mostly adopts post-precision orbit and precision attitude data during stable operation of satellites to evaluate double-satellite pointing of the satellites, and cannot reflect real inter-satellite pointing conditions, so that calibration results are inaccurate.
Disclosure of Invention
The invention aims to provide an on-orbit calibration method and system for the orientation between gravity satellites, which can calibrate the actual on-orbit double-satellite orientation change of the satellites and improve the accuracy of on-orbit calibration results.
In order to achieve the above object, the present invention provides the following solutions:
An on-orbit calibration method for the orientation between gravity satellites comprises the following steps:
the method comprises the steps of obtaining observation data at a plurality of moments, wherein the observation data comprise angles of satellites, precise orbit determination data and KBR ranging data of double satellites, the angles of the satellites are determined according to a maneuvering scheme, and the angles are roll angles or pitch angles;
for any moment, obtaining a module value from the mass center of each satellite in the double satellites at the moment to an antenna phase center vector according to KBR ranging data at the moment;
Constructing an inter-satellite ranging theoretical model according to the observation data at the moment;
calculating the residual error of inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model;
Substituting the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the vector from the mass center of each satellite in the double satellites to the antenna phase center into an observation equation, and solving by using weighted least square estimation to obtain the angle variable quantity of the double satellites, wherein the angle variable quantity is a roll angle variable quantity or a pitch angle variable quantity.
An on-orbit targeting system for gravitational satellite inter-satellite pointing comprising:
the system comprises an acquisition module, a control module and a control module, wherein the acquisition module is used for acquiring observation data at a plurality of moments, wherein the observation data comprises the angle of a satellite, precise orbit determination data and KBR ranging data of double satellites, the angle of the satellite is determined according to a maneuvering scheme, and the angle is a roll angle or a pitch angle;
The double-star model value calculation module is used for obtaining the model value from the mass center of each satellite in the double star to the antenna phase center vector at any moment according to KBR ranging data at the moment;
The inter-satellite distance measurement calculation module is used for constructing an inter-satellite distance measurement theoretical model according to the observation data at the moment;
The residual calculation module is used for calculating the residual error of the inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model;
The change amount calculation module is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the vector from the mass center of each satellite in the double satellites to the antenna phase center into an observation equation, and solving by adopting weighted least square estimation to obtain the angle change amount of the double satellites, wherein the angle change amount is a roll angle change amount or a pitch angle change amount.
According to the specific embodiment of the invention, the method has the following technical effects that the method obtains the module value from the center of mass of each satellite in the double satellites to the antenna phase center vector according to KBR ranging data, constructs an inter-satellite ranging theoretical model according to observation data at the moment, calculates the residual error of inter-satellite ranging of the double satellites, substitutes the module value from the inter-satellite ranging, residual error and the KBR ranging data of each satellite in the double satellites and the center of mass of each satellite in the double satellites to the antenna phase center vector into an observation equation to solve to obtain the angle variation of the double satellites, and finishes on-orbit calibration of the orientation between gravity satellites according to the module value from the center of mass of each satellite in the double satellites to the antenna phase center vector, so that the actual on-orbit double-satellite orientation variation of the satellites can be calibrated, and the accuracy of the calibration result is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic SF diagram;
FIG. 2 is a schematic diagram of KF and LOS;
fig. 3 is a flowchart of an on-orbit calibration method for orientation between gravity satellites according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The technical scheme adopted by the invention is that the satellite double-star directional calibration is realized by a satellite directional maneuvering period searching method, in principle, ideal inter-star directional leads two satellite centroids and two antenna phase centers to be on the connecting line of the two satellite centroids, a conversion matrix from KF to LOS is recorded as R KF→LOS, which can be defined as R KF→LOS＝Rx(ψ)Ry(θ)Rz (phi), wherein the rotation matrix around x, y and z axes is respectively expressed by Rx (phi), R y (theta) and Rz (phi). R KF→LOS is the same as R SF→LOS. According toAndThe inter-satellite bearing calculation is γ= arccos (cos θcos Φ).
In an ideal case, the expected conversion matrix from the satellite coordinate system to the LOS coordinate system is R SF,d→LOS, in a real case, the estimated conversion matrix from the satellite coordinate system to the LOS coordinate system is R SF,e→LOS, which can be written as R SF,e→LOS＝RSF,d→LOS·RSF,e→SF,d, and then the calibration of the inter-satellite pointing is performed on the conversion matrix R SF,e→SF,d.
Let R SFj,e→SFj,d＝Rx(δψj)Ry(δθj)Rz(δφj), j=1, 2, the euler angles δψ j,δθj and δΦ j are the amounts to be calibrated. Subscript 11 of the R SFj,d→LOS,11 variable represents row 1 column of matrix 1, subscript 12 of the R SFj,d→LOSFj,12 variable represents row 2 column of matrix 1, and subscript 13 of the R SFj,d→LOSFj,13 variable represents row 3 column of matrix 1.
The inter-satellite bearing can be calculated at this time as cosγj＝RSFj,d→LOS,11cosδθjcosδφj+RSFj,d→LOSFj,12(-cosδψjsinδφj+sinδψjsinδθjcosδφj)+RSFj,d→LOSFj,13(sinδψjsinδφj+cosδψjsinδθjcosδφj)
When the euler angles δψ j,δθj and δΦ j are small, and R SFj,d→LOSFj,11＝1,RSFj,d→LOSFj,12＝0,RSFj,d→LOSFj,13 =0, there is therefore
The following study uses maneuver to perform inter-satellite pointing calibration, namely, KBR data gives the distance between two phase centers, and the distance between the two phase centers, namely, the distance between two satellites, can be modeled
Wherein, the AndThe position vectors of the phase centers of the satellite 1 and satellite 2 antennas in an inertial system are respectively, R br is the system difference, and R nr is the ranging noise. The position vector of the antenna phase center in the inertial frame can be expressed as:
And Here, theAndThe position vectors of the centroids of satellite 1 and satellite 2 in the inertial frame,For the representation of the position vector of the KBR antenna phase center relative to the satellite j centroid on satellite j in the satellite j body coordinate system, R SFj→IRF (j=1, 2) is the transformation matrix from the satellite j coordinate system into the inertial system. Recording device In calculating L 12, one can compareMeanwhile, the satellite inertial coordinate system is converted into an LOS coordinate system of the satellite 1, and is marked as LOSF1, and R IRF→LOSF1 represents a conversion matrix from the satellite inertial coordinate system to the satellite 1LOS coordinate system; is the distance from the satellite 2 antenna phase center to the centroid; is the distance from the satellite 1 antenna phase center to the centroid, Recording device Accurate to the order of 1 micrometer, can obtainWhere E is a 3-dimensional identity matrix, Is the error factor of the inter-star distance vector, r 12 is the centroid distance between the two stars; is the x component of satellite 1 in the LOS coordinate system and delta is the measurement error. Because in the LOSF1 coordinate system, Therefore, there are:
Refers to the velocity vector of satellite j under the inertial frame; Position vector of satellite j under inertial frame.
When the maneuvering scheme is designed and the satellite attitude is changed, the following steps are obtained:
R SFj→LOSF1＝RSFj,d→LOSF1RSFj,e→SFj,dRSFj,t→SFj,d, where R SFj,t→SFj,d is a maneuver-induced satellite attitude change, defined as using euler angles ψ j,θj and Φ j:
RSFj,t→SFj,d＝Rx(ψj)Ry(θj)Rz(φj),j=1,2。
in the ideal case of a combination of the above-mentioned, R SF1,d→LOSF1 = E, and, At this time, if the reference relationship is definedAnd linear approximation of R SFj,e→SFj,d yields:
The product can be obtained by the method,
Let phi be the satellite roll angle, θ be the satellite pitch angle, ψ be the satellite yaw angle, Φ 1 be the roll angle of satellite A, φ 2 be the roll angle of satellite B, θ 1 be the pitch angle of satellite A, θ 2 be the pitch angle of satellite B, ψ 1 be the yaw angle of satellite A, ψ 2 be the yaw angle of satellite B, the design of the periodic maneuver comprises the following four basic maneuvers according to GRACE mission experience:
① A specific moment is generated by an attitude control system on the satellite, so that the satellite a maneuvers in the yaw direction in the following manner: Phi 10 is the satellite maneuver initial offset angle;
Is the satellite maneuver offset amplitude.
The phase observations under this maneuver are sensitive to the antenna center component of satellite A along the roll and pitch axes, denoted as MA, under which the other Euler angles are
ψ1＝θ1＝ψ2＝θ2＝φ2=0。
② Similar to ①, this motorized control satellite a is motorized in the pitch direction, in the following manner:
The phase observations under this maneuver are sensitive to the antenna center component of satellite A along the roll and yaw axes, denoted MB under which the other Euler angles are
ψ1＝φ1＝ψ2＝θ2＝φ2=0。
③ Similar to ①, this motorized control satellite B is motorized in the yaw direction, in the following manner:
The phase observations under this maneuver are sensitive to the antenna center component of satellite B along the roll and pitch axes, denoted as MC under which the other euler angles are
ψ1＝θ1＝φ1＝ψ2＝θ2=0。
④ Similar to ③, this motorized control satellite B is motorized in the pitch direction, in the following manner:
The phase observations under this maneuver are sensitive to the antenna center components of satellite B along the roll and yaw axes, denoted as MD, under which other euler angles are found
ψ1＝θ1＝φ1＝ψ2＝φ2=0。
In the motor scheme MA, there are
Calculating partial derivatives of
In the maneuver MB, there are
Partial derivative of
In the motor scheme MC, there are
Partial derivative of
In the motor scheme MD, there are
Partial derivative of
From the partial derivative calculations above, each scheme may estimate different parameters, as shown in Table 1.
Table 1 whether the table (can:. V. And cannot:. X) can be estimated in different schemes for different parameters
In summary, the embodiment of the present invention provides an on-orbit calibration method for orientation between gravity satellites, as shown in fig. 3, including:
step 101, acquiring observation data at a plurality of moments, wherein the observation data comprise angles of satellites, precise orbit determination data and KBR ranging data of double satellites, the angles of the satellites are determined according to a maneuvering scheme, and the angles are roll angles or pitch angles.
102, For any moment, obtaining a module value from the mass center of each satellite in the double satellites at the moment to an antenna phase center vector according to KBR ranging data at the moment.
And 103, constructing an inter-satellite ranging theoretical model according to the observation data at the moment.
104, Calculating the residual error of inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model, and obtaining after MA maneuver of the satellitesAndBy means ofThe inter-satellite residual is obtained.
The expression form of the inter-satellite distance measurement theoretical model is according to the formula Is obtained by pushing, and can be obtained according to an inter-satellite ranging theory model by utilizing a Taylor formulaThis method is well known.
And 105, substituting inter-satellite ranging, residual errors, KBR ranging data of the double satellites and a module value of a vector from the mass center of each satellite in the double satellites to the phase center of an antenna into an observation equation, and solving by using weighted least square estimation to obtain an angle variation of the double satellites, wherein the angle variation is a roll angle variation or pitch angle variation, and the on-orbit calibration of the orientation between gravity satellites can be completed according to the module value and the angle variation of the vector from the mass center of each satellite in the double satellites to the phase center of the antenna.
In practical application, the acquiring the observation data at a plurality of moments specifically includes:
And when the maneuvering scheme is that the first satellite in the double satellites runs in the yaw direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the first satellite at a plurality of moments.
And when the maneuvering scheme is that a first satellite in the double satellites runs in the pitching direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitching angle of the first satellite at a plurality of moments.
And when the maneuvering scheme is that a second satellite in the double satellites runs in the yaw direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the second satellite at a plurality of moments.
And when the maneuvering scheme is that a second satellite in the double satellites runs in the pitching direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitching angle of the second satellite at a plurality of moments.
In practical application, the obtaining the module value from the center of mass of each satellite in the double satellites at the moment to the antenna phase center vector according to the KBR ranging data at the moment specifically includes:
And calculating the sum of a reference value d pc10 of the module value from the centroid of the first satellite to the antenna phase center vector in the double satellites and a variation delta d pc1 of the module value from the centroid of the first satellite to the antenna phase center vector to obtain a module value d pc1 of the module value from the centroid of the first satellite to the antenna phase center vector.
And calculating the sum of a reference value d pc20 of the module value from the mass center of the second satellite to the antenna phase center vector in the double satellites and the variation delta d pc2 of the module value from the mass center of the second satellite to the antenna phase center vector to obtain a module value d pc2 of the module value from the mass center of the second satellite to the antenna phase center vector.
In practical application, the inter-satellite ranging theory model specifically comprises:
When the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is that Wherein L 12 is inter-satellite ranging between two satellites, r 12 is precise orbit determination data, d pc20 is a reference value from the centroid of the second satellite to the model value of the antenna phase center vector, d pc10 is a reference value from the centroid of the first satellite to the model value of the antenna phase center vector, and phi 1 is the roll angle of the first satellite.
When the maneuvering scheme is that the first satellite in the double satellites runs in the pitching direction, the inter-satellite ranging theory model is thatWherein θ 1 is the pitch angle of the first satellite.
When the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is thatWherein phi 2 is the roll angle of the second satellite.
When the maneuvering scheme is to make the second satellite in the double satellites run in the pitching direction, the inter-satellite ranging theory model is thatWherein θ 2 is the pitch angle of the second satellite.
In practical application, substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the modulus value from the mass center of each satellite in the double satellites to the antenna phase center vector into an observation equation, and solving by using weighted least square estimation to obtain the angle variation of the double satellites specifically comprises the following steps:
When the maneuvering scheme is that the first satellite in the double satellites runs in the yaw direction, the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to the antenna phase center vector are substituted into an observation equation, and the roll angle variation quantity of the double satellites is obtained by solving through weighted least square estimation.
When the maneuvering scheme is that the first satellite in the double satellites runs in the pitching direction, the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to the antenna phase center vector at all moments are substituted into an observation equation, and weighted least square estimation is adopted to solve to obtain the pitch angle variation of the double satellites.
When the maneuvering scheme is that the second satellite in the double satellites runs in the yaw direction, the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to the antenna phase center vector are substituted into an observation equation, and the roll angle variation quantity of the double satellites is obtained by solving through weighted least square estimation.
When the maneuvering scheme is that the second satellite in the double satellites runs in the pitching direction, the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to the antenna phase center vector at all moments are substituted into an observation equation, and weighted least square estimation is adopted to solve to obtain the pitch angle variation of the double satellites.
Aiming at the method, the embodiment of the invention provides an on-orbit calibration system for the orientation between gravity satellites, which comprises the following steps:
the system comprises an acquisition module, a control module and a control module, wherein the acquisition module is used for acquiring observation data at a plurality of moments, the observation data comprise angles of satellites, precise orbit determination data and KBR ranging data of double satellites, the angles of the satellites are determined according to a maneuvering scheme, and the angles are roll angles or pitch angles.
And the double-star model value calculation module is used for obtaining the model value from the mass center of each satellite in the double star to the antenna phase center vector at any moment according to the KBR ranging data at the moment.
And the inter-satellite distance measurement calculation module is used for constructing an inter-satellite distance measurement theoretical model according to the observation data at the moment.
And the residual calculation module is used for calculating the residual of the inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model.
The change amount calculation module is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the vector from the mass center of each satellite in the double satellites to the antenna phase center into an observation equation, and solving by adopting weighted least square estimation to obtain the angle change amount of the double satellites, wherein the angle change amount is a roll angle change amount or a pitch angle change amount.
As an optional implementation manner, the acquiring module specifically includes:
And the MA acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the first satellite at a plurality of moments when the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction.
And the MB acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitch angle of the first satellite at a plurality of moments when the maneuvering scheme is that the first satellite in the double satellites operates in the pitch direction.
And the MC acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the second satellite at a plurality of moments when the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction.
And the MD acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitch angle of the second satellite at a plurality of moments when the maneuvering scheme is that the second satellite in the double satellites operates in the pitch direction.
As an optional implementation manner, the double-star model value calculating module specifically includes:
And the module value calculation unit of the first satellite is used for calculating the sum of the reference value of the module value from the centroid of the first satellite to the antenna phase center vector in the double satellites and the variation quantity of the module value from the centroid of the first satellite to the antenna phase center vector to obtain the module value from the centroid of the first satellite to the antenna phase center vector.
And the module value calculation unit of the second satellite is used for calculating the sum of the reference value of the module value from the mass center of the second satellite to the antenna phase center vector in the double satellites and the variation quantity of the module value from the mass center of the second satellite to the antenna phase center vector to obtain the module value from the mass center of the second satellite to the antenna phase center vector.
As an optional implementation manner, the inter-satellite ranging theory model specifically includes:
When the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is that Wherein L 12 is inter-satellite ranging between two satellites, r 12 is precise orbit determination data, d pc20 is a reference value from the centroid of the second satellite to the model value of the antenna phase center vector, d pc10 is a reference value from the centroid of the first satellite to the model value of the antenna phase center vector, and phi 1 is the roll angle of the first satellite.
When the maneuvering scheme is that the first satellite in the double satellites runs in the pitching direction, the inter-satellite ranging theory model is thatWherein θ 1 is the pitch angle of the first satellite.
When the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is thatWherein phi 2 is the roll angle of the second satellite.
When the maneuvering scheme is to make the second satellite in the double satellites run in the pitching direction, the inter-satellite ranging theory model is thatWherein θ 2 is the pitch angle of the second satellite.
As an optional implementation manner, the variation calculating module specifically includes:
And the MA variation calculation unit is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites under all moments into an observation equation when the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction, and solving by adopting weighted least square estimation to obtain the roll angle variation of the double satellites.
And the MB variation calculation unit is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites under all moments into an observation equation when the maneuvering scheme is that the first satellite in the double satellites operates in the pitching direction, and solving by adopting weighted least square estimation to obtain the pitch angle variation of the double satellites.
And the MC variation calculation unit is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the center-of-mass-to-antenna phase center vector of each satellite in the double satellites into an observation equation when the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction, and solving by adopting weighted least square estimation to obtain the roll angle variation of the double satellites.
And the MD variation calculation unit is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites under all moments into an observation equation when the maneuvering scheme is that the second satellite in the double satellites operates in the pitching direction, and solving by adopting weighted least square estimation to obtain the pitch angle variation of the double satellites.
The embodiment of the invention provides a more specific on-orbit calibration method for the orientation between gravity satellites.
Firstly, performing MA maneuvering scheme pointing calculation;
The maneuver map MA may estimate the parameter d pc1,δφ1,dpc2,δφ2. Note d pc1＝dpc10+δdpc1,dpc2＝dpc20+δdpc2, where d pc10 and d pc20 are references to d pc1 and d pc2, respectively. The estimation algorithm is:
S1, reading in KBR ranging data and obtaining d pc20、dpc10. The KBR ranging data file contains d pc20、dpc10.
S2, reading in precise orbit determination data, obtaining r 12, and constructing an inter-satellite distance measurement theoretical model
Wherein the method comprises the steps of
S3, calculating residual error y (t) of the inter-satellite ranging L 12.
S4, determining an estimation model, and establishing an observation equation. And fitting a residual error generated by precise orbit determination by using a 4-order polynomial. Establishing an observation equation
Wherein the method comprises the steps of
p4(t)＝a0+a1t+a2t2+a3t3+a4t4
Let the parameter vector to be estimated be
The observation equation can be written as
Wherein the method comprises the steps of
H(t)=(Hpoly(t)Hvip(t))
Hpoly(t)＝(1,t,t2,t3,t4
Partial derivative in the aboveAnd
Centralizing all observations, assuming N observations, defining
The observation equation can be written as
S5, solving and calculating the above by using weighted least square estimation to obtainParameters.
The estimated covariance matrix is (H TWH)-1.
Here the least squares estimation is finalAnd the parameters can realize the estimation of the double-star roll angle variation delta phi 1,δφ2.
Secondly, carrying out MB maneuvering scheme pointing calculation;
the maneuver scheme MB may estimate the parameter d pc1,δθ1,dpc2,δθ2. The estimation algorithm is as follows:
s1, reading in KBR ranging data and obtaining d pc20、dpc10.
S2, reading in precise orbit determination data, obtaining r 12, and constructing an inter-satellite distance measurement theoretical model
Wherein the method comprises the steps of
S3, calculating residual error y (t) of the inter-satellite ranging L 12.
S4, determining an estimation model, and establishing an observation equation. And fitting a residual error generated by precise orbit determination by using a 4-order polynomial. Establishing an observation equation
Wherein the method comprises the steps of
p4(t)=a0+a1t+a2t2+a3t3+a4t4
Let the parameter vector to be estimated be
The observation equation can be written as
Wherein the method comprises the steps of
H(t)=(Hpoly(t)Hvip(t))
Hpoly(t)＝(1,t,t2,t3,t4)
Partial derivative in the aboveAndCentralizing all observations, assuming N observations, defining
The observation equation can be written as
S5, solving and calculating the above by using weighted least square estimation to obtainParameters.
The estimated covariance matrix is (H TWH)-1.
Here the least squares estimation is finalAnd the parameters can realize the estimation of the change quantity delta theta 1,δθ2 of the double-star pitch angle.
Thirdly, performing MC maneuver scheme pointing calculation;
The maneuver version MC may estimate the parameter d pc1,δφ1,dpc2,δφ2. The estimation algorithm is as follows:
s1, reading in KBR ranging data and obtaining d pc20、dpc10.
S2, reading in precise orbit determination data, obtaining r 12, and constructing an inter-satellite distance measurement theoretical model
Wherein the method comprises the steps of
S3, calculating residual error y (t) of the inter-satellite ranging L 12.
S4, determining an estimation model, and establishing an observation equation. And fitting a residual error generated by precise orbit determination by using a 4-order polynomial. Establishing an observation equation
Wherein the method comprises the steps of
p4(t)＝a0+a1t+a2t2+a3t3+a4t4
Let the parameter vector to be estimated be
The observation equation can be written as
Wherein the method comprises the steps of
H(t)=(Hpoly(t)Hvip(t))
Hpoly(t)＝(1,t,t2,t3,t4
Partial derivative in the aboveAndCentralizing all observations, assuming N observations, defining
The observation equation can be written as
S5, solving and calculating the above by using weighted least square estimation to obtainParameters.
The estimated covariance matrix is (H TWH)-1.
Here the least squares estimation is finalAnd the parameters can realize the estimation of the double-star roll angle variation delta phi 1,δφ2.
Fourthly, performing MD maneuvering scheme pointing calculation;
the maneuver MD may estimate the parameter d pc1,δθ1,dpc2,δθ2. The estimation algorithm is as follows:
s1, reading in KBR ranging data and obtaining d pc20、dpc10.
S2, reading in precise orbit determination data, obtaining r 12, and constructing an inter-satellite distance measurement theoretical model
Wherein the method comprises the steps of
S3, calculating residual error y (t) of the inter-satellite ranging L 12.
S4, determining an estimation model, and establishing an observation equation. And fitting a residual error generated by precise orbit determination by using a 4-order polynomial. Establishing an observation equation
Wherein the method comprises the steps of
p4(t)＝a0+a1t+a2t2+a3t3+a4t4
Let the parameter vector to be estimated be
The observation equation can be written as
Wherein the method comprises the steps of
H(t)=(Hpoly(t)Hvip(t))
Hpoly(t)＝(1,t,t2,t3,t4)
Partial derivative in the aboveAnd
Centralizing all observations, assuming N observations, defining
The observation equation can be written as
S5, solving and calculating the above by using weighted least square estimation to obtainParameters.
The estimated covariance matrix is (H TWH)-1.
Here the least squares estimation is finalAnd the parameters can realize the estimation of the double-star roll angle variation delta theta 1,δθ2.
In the embodiment, the method is applied to simulation of actual measurement data provided by a GRACE Follow-On task as actual measurement data of measurement errors, and the data adopted by the simulation comprise 1B-level precise orbit determination data GNI B obtained On 1 st of 2018, 1B-level inter-phase center ranging data KBR1B and antenna phase center 1B-level calibration data VKB1B data.
The KBR1B data includes offset distance measurement, distance measurement change rate, distance measurement acceleration, time of flight correction, antenna phase center deviation correction and the like, and the time interval is 5 seconds in KBR1B data of the day of 2018, 6 months and 1 day. The inter-satellite distance and inter-satellite variability given by the precise orbit determination data GNI B obtained in 2018, month 6 and 1 in the GRACE Follow-On task, GNI B data contains satellite position and speed under the geocentric inertial system, and the time interval is 1 second.
(1) Three maneuvering periods simulation under condition of duration 1000s
First, simulation was carried out under three maneuver periods when the maneuver duration was 1000 s. The true value of the Yaw (Yaw) direction offset angle of satellite a is 1mrad. The absolute error of the estimated value and the theoretical value of the Yaw (Yaw) direction of the satellite A is calculated by repeating the experiment for 25 times, and from the experimental result, the absolute error percentage of the maneuvering scheme of 13 times 251s is smaller than that of the other two cases, the absolute error of the maneuvering period of 8 times 250s is smaller than that of the other two cases, and the absolute error percentage of the maneuvering scheme of 4 times 249s is smaller than that of the other two cases. Thus, different maneuver periods may have an impact on the results, compared to the worst 249s maneuver period, the best 251s maneuver period. Accordingly, subsequently, further simulations will be developed for 250s and 251s maneuver cycles, pointing to the targeting capability through simulation studies.
TABLE 2 simulation maneuver protocol MA maneuver parameter settings
| Motor deflection value (°) | Maneuver amplitude (°) | Maneuvering period(s) | Maneuvering duration(s) | |
| Case 1 | 2 | 1 | 249 | 1000 |
| Case 2 | 2 | 1 | 250 | 1000 |
| Case 3 | 2 | 1 | 251 | 1000 |
(2) The ability to resolve different pointing offset angles for the duration of the maneuver at 1000s, at 249s,250s, and 251s maneuver periods, and simultaneously the phase center vector magnitude.
The pointing bias calibration has a certain capability in view of data quality limitations. The following true values for the direction deviation angle are respectively 1mrad,0.5mrad,0.1mrad,0.05mrad and 0.01 and (5) carrying out calculation quality evaluation at mrad. For each pointing deviation value, consider the maneuver duration of 1000s, and maneuver period of different magnitudes for pointing deviation angle solvency under three conditions of 249s,250s and 251s respectively. 6 simulation results were performed. From these simulation results, the solution error was less than 10% for all three maneuver periods with a true value of 1 mrad. At a true value of 0.5mrad, the maneuver period is 249s, and the estimated and true value deviation is between 11.7% and 29.2%. The maneuver period was 250s, the estimated and true deviations were between 1.7% and 18.7%, and in four cases less than 10%. The maneuver period was 251s, the estimated and true value deviation was between 0.3% and 12.7%, and less than 10% in four cases. At a true value of 0.1mrad, the estimation results were poor, with the best results at a maneuver period of 251 s. The estimated and true value deviations were between 6.2% and 60.2% for a maneuver period of 251s, and were greater than 10% in five cases. When the deviation angle true value is 0.05mrad and 0.01mrad, the resolution accuracy is worse. To sum up, with a true value of 0.5mrad, with a maneuver period of 251s, it is barely possible to achieve an absolute error of the estimated value and the offset value close to 10%, indicating that the pointing angle offset cannot be too small under absolute calibration. In general, the resolution is poor when the pointing deviation truth value is less than 1mrad, with 251s maneuver period scheme estimation accuracy being best.
(3) The ability to resolve different pointing offset angles for the duration of the maneuver of 1000s, for the maneuver periods of 247 s,250s and 251s, does not resolve the phase center vector magnitude.
The following true values for the direction deviation angle are respectively 1mrad,0.5mrad,0.1mrad,0.05mrad and 0.01 and (5) carrying out calculation quality evaluation at mrad. For each pointing deviation value, consider the maneuver duration of 1000s, and maneuver period of different magnitudes for pointing deviation angle solvency under three conditions of 249s,250s and 251s respectively. 6 simulation results were performed. From these simulation results, it can be seen that the solution error is less than 7% for all three maneuver periods at a true value of 1 mrad. At a true value of 0.5mrad, the estimated value deviates from the true value by within 7% for maneuvering periods 249s and 250 s. The maneuver period is 251s, and the deviation between the estimated value and the true value is about 10%. At true values of 0.1mrad,0.05mrad and 0.01mrad, the resolution becomes poor, exceeding 10%. To sum up, with a true value of 0.5mrad, it is barely possible to achieve an absolute error of the estimated value and the deviation value close to 10% by using the schemes with the maneuvering period of 249s and 250s, which means that the true value of the pointing angle deviation value cannot be too small under absolute calibration. In general, the resolution is poor when the pointing deviation truth value is less than 0.5mrad, where 249s maneuver period scheme estimation accuracy is best, and 250s maneuver period scheme estimation accuracy may also be less than 7%.
From the above experimental results, when the phase center amplitude and the directional deviation angle are simultaneously calculated, the directional deviation angle is smaller than 1mrad, and the result of the calculation is poor. If, in order to be able to resolve smaller pointing deviation angles, for example 0.5mrad, a motor duration of 3000s is advantageously used. In general, however, resolving 1mrad of the pointing offset angle can ensure the resolving accuracy.
The method has the advantages that the pointing periodic swing is realized through satellite maneuver, the inter-satellite pointing observation data are obtained, the inter-satellite pointing is estimated, and the situation that the conventional method cannot truly and accurately reflect the double-satellite pointing can be avoided, so that the accurate double-satellite pointing control condition parameters of satellites are obtained, and the accuracy of the on-orbit calibration result is improved.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, which are intended to facilitate an understanding of the principles and concepts of the invention and are to be varied in scope and detail by persons of ordinary skill in the art based on the teachings herein. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (10)
1. An on-orbit calibration method for the orientation between gravity satellites is characterized by comprising the following steps:
the method comprises the steps of obtaining observation data at a plurality of moments, wherein the observation data comprise angles of satellites, precise orbit determination data and KBR ranging data of double satellites, the angles of the satellites are determined according to a maneuvering scheme, and the angles are roll angles or pitch angles;
for any moment, obtaining a module value from the mass center of each satellite in the double satellites at the moment to an antenna phase center vector according to KBR ranging data at the moment;
Constructing an inter-satellite ranging theoretical model according to the observation data at the moment;
calculating the residual error of inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model;
Substituting the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the vector from the mass center of each satellite in the double satellites to the antenna phase center into an observation equation, and solving by using weighted least square estimation to obtain the angle variable quantity of the double satellites, wherein the angle variable quantity is a roll angle variable quantity or a pitch angle variable quantity.
2. The on-orbit calibration method for the orientation between gravity satellites according to claim 1, wherein the acquiring the observation data at a plurality of moments specifically comprises:
When the maneuvering scheme is that a first satellite in a double satellite runs in a yaw direction, acquiring the precise orbit determination data, KBR ranging data of the double satellite and a roll angle of the first satellite at a plurality of moments;
When the maneuvering scheme is that a first satellite in a double satellite runs in a pitching direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellite and the pitching angle of the first satellite at a plurality of moments;
When the maneuvering scheme is that a second satellite in the double satellites runs in a yaw direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the second satellite at a plurality of moments;
And when the maneuvering scheme is that a second satellite in the double satellites runs in the pitching direction, acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitching angle of the second satellite at a plurality of moments.
3. The on-orbit calibration method for the orientation between gravity satellites according to claim 1, wherein the obtaining the module value of the vector from the center of mass of each satellite in the double satellites to the phase center of the antenna at the moment according to the KBR ranging data at the moment specifically comprises:
Calculating the sum of the reference value of the module value from the centroid of the first satellite to the antenna phase center vector in the double satellites and the variation quantity from the centroid of the first satellite to the module value of the antenna phase center vector to obtain the module value from the centroid of the first satellite to the antenna phase center vector;
And calculating the sum of the reference value of the module value from the mass center of the second satellite to the antenna phase center vector in the double satellites and the variation quantity from the mass center of the second satellite to the module value of the antenna phase center vector to obtain the module value from the mass center of the second satellite to the antenna phase center vector.
4. The on-orbit calibration method for the orientation between gravity satellites according to claim 2, wherein the inter-satellite ranging theoretical model is specifically:
When the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is that Wherein L 12 is inter-satellite ranging between two satellites, r 12 is precise orbit determination data, d pc20 is a reference value from the centroid of the second satellite to the model value of the antenna phase center vector, d pc10 is a reference value from the centroid of the first satellite to the model value of the antenna phase center vector, and phi 1 is the roll angle of the first satellite;
When the maneuvering scheme is that the first satellite in the double satellites runs in the pitching direction, the inter-satellite ranging theory model is that Wherein, θ 1 is the pitch angle of the first satellite;
When the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is that Wherein phi 2 is the roll angle of the second satellite;
When the maneuvering scheme is to make the second satellite in the double satellites run in the pitching direction, the inter-satellite ranging theory model is that Wherein θ 2 is the pitch angle of the second satellite.
5. The on-orbit calibration method for the orientation between the gravity satellites according to claim 2, wherein the substitution of the inter-satellite ranging between the double satellites, the residual error, the KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites into the observation equation, and the solution by using weighted least square estimation to obtain the angle variation of the double satellites specifically comprises the following steps:
when the maneuvering scheme is that a first satellite in the double satellites runs in a yaw direction, substituting the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and a module value of a center of mass of each satellite in the double satellites to an antenna phase center vector into an observation equation, and solving by adopting weighted least square estimation to obtain a roll angle variation quantity of the double satellites;
When the maneuvering scheme is that a first satellite in the double satellites runs in the pitching direction, substituting the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to an antenna phase center vector into an observation equation, and solving by adopting weighted least square estimation to obtain the pitch angle variation of the double satellites;
When the maneuvering scheme is that a second satellite in the double satellites runs in the yaw direction, substituting the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to an antenna phase center vector into an observation equation, and solving by adopting weighted least square estimation to obtain the roll angle variation quantity of the double satellites;
When the maneuvering scheme is that the second satellite in the double satellites runs in the pitching direction, the inter-satellite ranging, the residual error, KBR ranging data of the double satellites and the modular value of the center of mass of each satellite in the double satellites to the antenna phase center vector at all moments are substituted into an observation equation, and weighted least square estimation is adopted to solve to obtain the pitch angle variation of the double satellites.
6. An on-orbit targeting system for gravitational satellite inter-satellite pointing comprising:
the system comprises an acquisition module, a control module and a control module, wherein the acquisition module is used for acquiring observation data at a plurality of moments, wherein the observation data comprises the angle of a satellite, precise orbit determination data and KBR ranging data of double satellites, the angle of the satellite is determined according to a maneuvering scheme, and the angle is a roll angle or a pitch angle;
The double-star model value calculation module is used for obtaining the model value from the mass center of each satellite in the double star to the antenna phase center vector at any moment according to KBR ranging data at the moment;
The inter-satellite distance measurement calculation module is used for constructing an inter-satellite distance measurement theoretical model according to the observation data at the moment;
The residual calculation module is used for calculating the residual error of the inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model;
The change amount calculation module is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the vector from the mass center of each satellite in the double satellites to the antenna phase center into an observation equation, and solving by adopting weighted least square estimation to obtain the angle change amount of the double satellites, wherein the angle change amount is a roll angle change amount or a pitch angle change amount.
7. The on-orbit calibration system for the orientation between gravitational satellites according to claim 6, wherein the acquisition module comprises:
The MA acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the first satellite at a plurality of moments when the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction;
The MB acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitch angle of the first satellite at a plurality of moments when the maneuvering scheme is that the first satellite in the double satellites operates in the pitch direction;
The MC acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the roll angle of the second satellite at a plurality of moments when the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction;
and the MD acquisition unit is used for acquiring the precise orbit determination data, the KBR ranging data of the double satellites and the pitch angle of the second satellite at a plurality of moments when the maneuvering scheme is that the second satellite in the double satellites operates in the pitch direction.
8. The on-orbit calibration system for the orientation between gravity satellites according to claim 6, wherein the double-star model calculation module specifically comprises:
A module value calculating unit of the first satellite, configured to calculate a sum of a reference value of a module value from a centroid of the first satellite to an antenna phase center vector in the double satellites and a variation amount from the centroid of the first satellite to the module value of the antenna phase center vector to obtain a module value from the centroid of the first satellite to the antenna phase center vector;
and the module value calculation unit of the second satellite is used for calculating the sum of the reference value of the module value from the mass center of the second satellite to the antenna phase center vector in the double satellites and the variation quantity of the module value from the mass center of the second satellite to the antenna phase center vector to obtain the module value from the mass center of the second satellite to the antenna phase center vector.
9. The on-orbit calibration system for the orientation of gravity satellites according to claim 7, wherein the inter-satellite ranging theoretical model is specifically:
When the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is that Wherein L 12 is inter-satellite ranging between two satellites, r 12 is precise orbit determination data, d pc20 is a reference value from the centroid of the second satellite to the model value of the antenna phase center vector, d pc10 is a reference value from the centroid of the first satellite to the model value of the antenna phase center vector, and phi 1 is the roll angle of the first satellite;
When the maneuvering scheme is that the first satellite in the double satellites runs in the pitching direction, the inter-satellite ranging theory model is that Wherein, θ 1 is the pitch angle of the first satellite;
When the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction, the inter-satellite ranging theory model is that Wherein phi 2 is the roll angle of the second satellite;
When the maneuvering scheme is to make the second satellite in the double satellites run in the pitching direction, the inter-satellite ranging theory model is that Wherein θ 2 is the pitch angle of the second satellite.
10. The on-orbit calibration system for the orientation between gravity satellites according to claim 7, wherein the variation calculation module comprises:
The MA variation amount calculation unit is used for substituting the inter-satellite ranging between the double satellites, the residual error, KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites under all moments into an observation equation when the maneuvering scheme is that the first satellite in the double satellites operates in the yaw direction, and solving by adopting weighted least square estimation to obtain the roll angle variation amount of the double satellites;
The MB variation amount calculation unit is used for substituting the inter-satellite ranging between the double satellites, the residual error, KBR ranging data of the double satellites and the module value of the center of mass of each satellite in the double satellites to an antenna phase center vector into an observation equation when the maneuvering scheme is that the first satellite in the double satellites runs in the pitching direction, and solving by adopting weighted least square estimation to obtain the pitch angle variation amount of the double satellites;
The MC variation calculation unit is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites under all moments into an observation equation when the maneuvering scheme is that the second satellite in the double satellites operates in the yaw direction, and solving by adopting weighted least square estimation to obtain the roll angle variation of the double satellites;
And the MD variation calculation unit is used for substituting the inter-satellite ranging, the residual error, the KBR ranging data of the double satellites and the module value of the center of mass to antenna phase center vector of each satellite in the double satellites under all moments into an observation equation when the maneuvering scheme is that the second satellite in the double satellites operates in the pitching direction, and solving by adopting weighted least square estimation to obtain the pitch angle variation of the double satellites.
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