An In-orbit Calibration Method and System for Inter-satellite Pointing of Gravity Satellites

Abstract

The present invention relates to an on-orbit calibration method and system for the inter-satellite pointing of gravity satellites, and specifically relates to the technical field of geophysical measurement. The method includes: obtaining the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center according to the KBR ranging data; bringing the observation data into the inter-satellite ranging theoretical model to obtain the inter-satellite ranging of the double satellites; calculating the residual of the inter-satellite ranging of the double satellites; substituting the inter-satellite ranging between the double satellites, the residual, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center into the observation equation to solve for the angular change amount of the double satellites; and completing the on-orbit calibration of the inter-satellite pointing of the gravity satellites according to the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center and the angular change amount. The present invention can calibrate the change in the inter-satellite pointing of the satellites in actual orbit, and improve the accuracy of the calibration result.

Description

Technical Field

[0001] The present invention relates to the technical field of geophysical measurement, and particularly to an on-orbit calibration method and system for inter-satellite pointing of a gravity satellite. Background Art

[0002] The calibration of the inter-satellite pointing of a gravity satellite is to check the alignment between the two satellites, which is defined as the angle between the vector from the satellite's center of mass to the antenna phase center relative to the line-of-sight direction i.e.,

[0003]

[0004] wherein, R SF→IRF is the rotation matrix from the satellite reference coordinate system to the inertial system, Figure 1 is the satellite reference frame (SF), Figure 2 is the antenna phase center reference coordinate system (KF) and the line-of-sight reference coordinate system (LOS). KF: Its coordinate origin is located at the satellite's center of mass, the x-axis direction is defined as pointing from the satellite's center of mass to the antenna phase center, the z-axis direction is defined as vertically downward along the satellite's flight direction, and the y-axis direction is determined by the right-hand rule.

[0005] LOS: Its coordinate origin is located at the satellite's center of mass, the x-axis direction is the line connecting the line-of-sight directions of the two satellite centers of mass, the z-axis direction points to the center of the earth, and the y-axis direction is determined by the right-hand rule.

[0006] The line-of-sight reference coordinate system is defined as:

[0007]

[0008]

[0009]

[0010] wherein, in the above formula, j = 1, 2, representing satellite j, are the position vectors of the centers of mass of satellite 1 and satellite 2 respectively, represents the X component of satellite j (1 or 2) in the LOS coordinate system, represents the Y component of satellite j (1 or 2) in the LOS coordinate system, represents the Z component of satellite j (1 or 2) in the LOS coordinate system.

[0011] The antenna phase center reference coordinate system is defined as:

[0012]

[0013]

[0014]

[0015] Denotes the X - component of satellite j (1 or 2) in the KF coordinate system, Denotes the Y - component of satellite j (1 or 2) in the KF coordinate system, Denotes the Z - component of satellite j (1 or 2) in the KF coordinate system, R SF→IRF Denotes the transformation matrix from the satellite reference frame to the inertial frame, Is the vector from the satellite's center of mass to the antenna phase center. The coordinate axes of the satellite reference frame are consistent with those of the antenna phase center reference frame.

[0016]

[0017] The angular deviation requirements for inter - satellite pointing are relatively small, and there are two reasons: one is that the pointing jitter affects the inter - satellite ranging observation; the other is the multipath effect formed by multiple reflections of microwave signals on the satellite surface.

[0018] Most of the existing inter - satellite pointing calibration methods use the post - mission precise orbit and precise attitude data during the stable operation of the satellite to evaluate the two - satellite pointing of the satellite. This method cannot reflect the real inter - satellite pointing situation, resulting in inaccurate calibration results. Summary of the Invention

[0019] The purpose of the present invention is to provide an on - orbit calibration method and system for the inter - satellite pointing of gravity satellites, which can calibrate the change of the two - satellite pointing of the satellite during actual on - orbit operation and improve the accuracy of the on - orbit calibration result.

[0020] To achieve the above - mentioned purpose, the present invention provides the following solutions:

[0021] An on - orbit calibration method for the inter - satellite pointing of gravity satellites, comprising:

[0022] Obtain observation data at multiple moments; the observation data includes the angles of the satellite, precise orbit determination data, and KBR ranging data of the two - satellite; the angles of the satellite are determined according to the maneuvering plan; the angles are roll angles or pitch angles;

[0023] For any moment, obtain the modulus value of the vector from the center of mass of each satellite in the two - satellite at the moment to the antenna phase center according to the KBR ranging data at the moment;

[0024] Construct an inter - satellite ranging theoretical model according to the observation data at the moment;

[0025] Calculate the residual of the inter - satellite ranging of the two - satellite at the moment according to the inter - satellite ranging theoretical model;

[0026] Substitute the inter-satellite ranging between the two satellites at all times, the residuals, the KBR ranging data of the two satellites, and the magnitudes of the vectors from the centroid of each satellite in the two satellites to the antenna phase center into the observation equation, and use weighted least squares estimation to solve for the angular change of the two satellites; the angular change is the roll angle change or the pitch angle change.

[0027] An in-orbit calibration system for the inter-satellite pointing of a gravity satellite, comprising:

[0028] An acquisition module, configured to acquire observation data at multiple times; the observation data includes the angles of the satellites, precise orbit determination data, and KBR ranging data of the two satellites; the angles of the satellites are determined according to the maneuvering plan; the angles are the roll angle or the pitch angle;

[0029] A two-satellite magnitude calculation module, configured to, for any given time, obtain the magnitudes of the vectors from the centroid of each satellite in the two satellites to the antenna phase center at the given time according to the KBR ranging data at the given time;

[0030] An inter-satellite ranging calculation module, configured to construct an inter-satellite ranging theoretical model according to the observation data at the given time;

[0031] A residual calculation module, configured to calculate the residuals of the inter-satellite ranging of the two satellites at the given time according to the inter-satellite ranging theoretical model;

[0032] A change amount calculation module, configured to substitute the inter-satellite ranging between the two satellites at all times, the residuals, the KBR ranging data of the two satellites, and the magnitudes of the vectors from the centroid of each satellite in the two satellites to the antenna phase center into the observation equation, and use weighted least squares estimation to solve for the angular change of the two satellites; the angular change is the roll angle change or the pitch angle change.

[0033] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: The present invention obtains the magnitudes of the vectors from the centroid of each satellite in the two satellites to the antenna phase center according to the KBR ranging data; constructs an inter-satellite ranging theoretical model according to the observation data at the given time; calculates the residuals of the inter-satellite ranging of the two satellites; substitutes the inter-satellite ranging between the two satellites, the residuals, the KBR ranging data of the two satellites, and the magnitudes of the vectors from the centroid of each satellite in the two satellites to the antenna phase center into the observation equation for solution to obtain the angular change of the two satellites; completes the in-orbit calibration of the inter-satellite pointing of the gravity satellite according to the magnitudes of the vectors from the centroid of each satellite in the two satellites to the antenna phase center and the angular change, can calibrate the actual in-orbit change of the two-satellite pointing of the satellite, and improves the accuracy of the calibration result. Description of the Drawings

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0035] Figure 1 It is a schematic diagram of SF;

[0036] Figure 2 It is a schematic diagram of KF and LOS;

[0037] Figure 3 It is a flowchart of an on-orbit calibration method for inter-satellite pointing of a gravity satellite provided by an embodiment of the present invention. Detailed implementation manners

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0039] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific implementation manners.

[0040] The technical solution adopted by the present invention is to realize the inter-satellite pointing calibration of the satellite through the satellite pointing maneuver cycle search method. In principle, the ideal inter-satellite pointing makes the centers of mass of the two satellites and the phase centers of the two antennas on the line connecting the centers of mass of the two satellites. Denote the transformation matrix from KF to LOS as R KF→LOS , which can be defined as: R KF→LOS = R x (ψ)R y (θ)R z (φ), where the rotation matrices around the x, y, and z axes are represented by Rx(ψ), R y (θ), Rz(φ) respectively. R KF→LOS and R SF→LOS are the same. According to and the inter-satellite pointing calculation is obtained as: γ = arccos(cosθcosφ).

[0041] Assume that in the ideal case, the expected transformation matrix from the satellite coordinate system to the LOS coordinate system is R SF,d→LOS , and in the actual case, the estimated transformation matrix from the satellite coordinate system to the LOS coordinate system is R SF,e→LOS, can be written as R SF,e→LOS = R SF,d→LOS ·R SF,e→SF,d , then the content of inter-satellite pointing calibration is to calibrate the transformation matrix R SF,e→SF,d .

[0042] Let R SFj,e→SFj,d = R x (δψ j )R y (δθ j )R z (δφ j ), j = 1, 2, then the Euler angles δψ j , δθ j and δφ j are the quantities to be calibrated. The subscript 11 of the R SFj,d→LOS,11 variable represents the 1st row and 1st column of the matrix; the subscript 12 of the R SFj,d→LOSFj,12 variable represents the 1st row and 2nd column of the matrix, and the subscript 13 of the R SFj,d→LOSFj,13 variable represents the 1st row and 3rd column of the matrix.

[0043] The inter-satellite pointing can be calculated as cosγ j = R SFj,d→LOS,11 cosδθ j cosδφ j + R SFj,d→LOSFj,12 (-cosδψ j sinδφ j + sinδψ j sinδθ j cosδφ j ) + R SFj,d→LOSFj,13 (sinδψ j sinδφ j + cosδψ j sinδθ j cosδφ j )

[0044] When the Euler angles δψ j , δθ j and δφ j are small quantities, and R SFj,d→LOSFj,11 = 1, R SFj,d→LOSFj,12 = 0, R SFj,d→LOSFj,13 = 0, so there is

[0045] Next, study the use of maneuvers to carry out inter-satellite pointing calibration: The KBR data gives the distance between two phase centers, which can be modeled as the distance between two phase centers, that is, the distance between two satellites

[0046] Among them, and They are the position vectors of the antenna phase centers of Satellite 1 and Satellite 2 in the inertial system, respectively, R br is the systematic difference, R nr is the ranging noise. The position vector of the antenna phase center in the inertial system can be expressed as:

[0047] and where and are the position vectors of the mass centers of Satellite 1 and Satellite 2 in the inertial system, respectively, is the representation in the body coordinate system of Satellite j of the position vector of the KBR antenna phase center relative to the mass center of Satellite j, R SFj→IRF (j = 1, 2) is the transformation matrix from the coordinate system of Satellite j to the inertial system. Denote When calculating L 12 , can be transformed to the LOS coordinate system of Satellite 1 simultaneously, denoted as LOSF1, R IRF→LOSF1 represents the transformation matrix from the satellite inertial coordinate system to the LOS coordinate system of Satellite 1; is the distance from the antenna phase center of Satellite 2 to the mass center; is the distance from the antenna phase center of Satellite 1 to the mass center, Denote Accurate to the order of 1 micron, we can obtain where E is the 3D identity matrix, is the error factor of the inter-satellite distance vector, r 12 is the mass center distance between the two satellites; is the x component of Satellite 1 in the LOS coordinate system; δ is the measurement error. Since in the LOSF1 coordinate system, therefore, we have:

[0048]

[0049]

[0050]

[0051] refers to the velocity vector of Satellite j in the inertial system; the position vector of Satellite j in the inertial system.

[0052] When designing a maneuvering plan and changing the satellite attitude, we can obtain:

[0053] RSFj→LOSF1 = R SFj,d→LOSF1 R SFj,e→SFj,d R SFj,t→SFj,d , where, R SFj,t→SFj,d is the satellite attitude change caused by maneuvering, and using the Euler angles ψ j , θ j and φ j , it is defined as:

[0054] R SFj,t→SFj,d = R x (ψ j )R y (θ j )R z (φ j ), j = 1, 2.

[0055] Ideally, R SF1,d→LOSF1 = E, At this time, if the reference relationship is defined and a linear approximation is made to R SFj,e→SFj,d , the following is obtained:

[0056]

[0057] It is obtained that

[0058]

[0059] Let φ be the satellite roll angle, θ be the satellite pitch angle, ψ be the satellite yaw angle, φ1 represent the roll angle of satellite A, φ2 represent the roll angle of satellite B, θ1 represent the pitch angle of satellite A, θ2 represent the pitch angle of satellite B, ψ1 represent the yaw angle of satellite A, and ψ2 represent the yaw angle of satellite B. According to the GRACE mission experience, the design of the periodic maneuvering scheme includes the following four basic maneuvering schemes:

[0060] ① By generating a specific torque through the attitude control system on the satellite, satellite A maneuvers in the yaw direction in the following manner: φ 10 is the initial offset angle of satellite maneuvering;

[0061] is the offset amplitude of satellite maneuvering.

[0062] Under this maneuvering scheme, the phase observation is sensitive to the antenna center components of satellite A along the rolling axis and the pitch axis. This scheme is denoted as MA. Under scheme MA, the other Euler angles

[0063] ψ1 = θ1 = ψ2 = θ2 = φ2 = 0.

[0064] ② Similar to ①, the difference is that this maneuver controls satellite A in the pitch direction in the following manner:

[0065] Under this maneuvering scheme, the phase observation is sensitive to the antenna center components of satellite A along the roll axis and the yaw axis. This scheme is denoted as MB. Under scheme MB, the other Euler angles

[0066] ψ1 = φ1 = ψ2 = θ2 = φ2 = 0.

[0067] ③ Similar to ①, the difference is that this maneuver controls satellite B in the yaw direction and maneuvers in the following manner:

[0068] Under this maneuvering scheme, the phase observation is sensitive to the antenna center components of satellite B along the roll axis and the pitch axis. This scheme is denoted as MC. Under scheme MC, the other Euler angles

[0069] ψ1 = θ1 = φ1 = ψ2 = θ2 = 0.

[0070] ④ Similar to ③, the difference is that this maneuver controls satellite B in the pitch direction and maneuvers in the following manner:

[0071] Under this maneuvering scheme, the phase observation is sensitive to the antenna center components of satellite B along the roll axis and the yaw axis. This scheme is denoted as MD. Under scheme MD, the other Euler angles

[0072] ψ1 = θ1 = φ1 = ψ2 = φ2 = 0.

[0073] In maneuvering scheme MA, there is

[0074]

[0075]

[0076]

[0077]

[0078] Calculating the partial derivatives, there are

[0079]

[0080]

[0081]

[0082]

[0083] In maneuvering scheme MB, there is

[0084]

[0085]

[0086]

[0087]

[0088] The partial derivative is

[0089]

[0090]

[0091]

[0092]

[0093] In the maneuvering plan MC, there are

[0094]

[0095]

[0096]

[0097]

[0098] The partial derivative is

[0099]

[0100]

[0101]

[0102]

[0103] In the maneuvering plan MD, there are

[0104]

[0105]

[0106]

[0107]

[0108] The partial derivative is

[0109]

[0110]

[0111]

[0112]

[0113] As can be seen from the above partial derivative calculations, each scheme can estimate different parameters, as shown in Table 1.

[0114] Table 1 Estimability of Different Parameters in Different Schemes (Yes: √, No: ×)

[0115]

[0116]

[0117] In summary, the embodiment of the present invention provides an on-orbit calibration method for the inter-satellite pointing of a gravity satellite, as Figure 3 shown, including:

[0118] Step 101: Obtain observation data at multiple moments; the observation data includes the angles of the satellites, precise orbit determination data, and KBR ranging data of the double satellites; the angles of the satellites are determined according to the maneuvering scheme; the angles are roll angles or pitch angles.

[0119] Step 102: For any moment, obtain the modulus of the vector from the center of mass of each satellite in the double satellites at the moment to the antenna phase center according to the KBR ranging data at the moment.

[0120] Step 103: Construct an inter-satellite ranging theoretical model according to the observation data at the moment.

[0121] Step 104: Calculate the residual of the inter-satellite ranging of the double satellites at the moment according to the inter-satellite ranging theoretical model. After the satellite performs a MA maneuver, and Using the inter-satellite distance residual can be obtained.

[0122] The expression form of the inter-satellite ranging theoretical model is derived according to the formula Using the Taylor formula, this method is well-known.

[0123] Step 105: Substitute the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the center of mass of each satellite in the double satellites to the antenna phase center at all moments into the observation equation, and use weighted least squares estimation to solve for the angular change of the double satellites; the angular change is the roll angle change or the pitch angle change, and the on-orbit calibration of the inter-satellite pointing of the gravity satellite can be completed according to the modulus of the vector from the center of mass of each satellite in the double satellites to the antenna phase center and the angular change.

[0124] In practical applications, the obtaining of the observation data at multiple moments specifically includes:

[0125] When the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, the precise orbit determination data, the KBR ranging data of the double satellites, and the roll angle of the first satellite at multiple moments are obtained.

[0126] When the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, the precise orbit determination data, the KBR ranging data of the double satellites, and the pitch angle of the first satellite at multiple moments are obtained.

[0127] When the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction, the precise orbit determination data, the KBR ranging data of the double satellites, and the roll angle of the second satellite at multiple moments are obtained.

[0128] When the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction, the precise orbit determination data, the KBR ranging data of the double satellites, and the pitch angle of the second satellite at multiple moments are obtained.

[0129] In practical applications, the obtaining of the modulus of the vector from the center of mass of each satellite in the double satellites to the antenna phase center at the moment based on the KBR ranging data at the moment specifically includes:

[0130] Calculating the reference value d of the modulus of the vector from the center of mass of the first satellite in the double satellites to the antenna phase center pc10 and the change amount δd of the modulus of the vector from the center of mass of the first satellite to the antenna phase center pc1 and summing them to obtain the modulus d of the vector from the center of mass of the first satellite to the antenna phase center pc1 .

[0131] Calculating the reference value d of the modulus of the vector from the center of mass of the second satellite in the double satellites to the antenna phase center pc20 and the change amount δd of the modulus of the vector from the center of mass of the second satellite to the antenna phase center pc2 and summing them to obtain the modulus d of the vector from the center of mass of the second satellite to the antenna phase center pc2 .

[0132] In practical applications, the inter-satellite ranging theoretical model is specifically:

[0133] When the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, the inter-satellite ranging theoretical model is where L 12 is the inter-satellite ranging between the double satellites, r 12Precision orbit determination data, d pc20 is the reference value of the modulus of the vector from the centroid of the second satellite to the antenna phase center, d pc10 is the reference value of the modulus of the vector from the centroid of the first satellite to the antenna phase center, and φ1 is the roll angle of the first satellite.

[0134] When the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ1 is the pitch angle of the first satellite.

[0135] When the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction, the inter-satellite ranging theoretical model is where φ2 is the roll angle of the second satellite.

[0136] When the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ2 is the pitch angle of the second satellite.

[0137] In practical applications, substituting the inter-satellite ranging between the double satellites at all times, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center into the observation equation, and using weighted least squares estimation to solve to obtain the angular change amount of the double satellites, specifically including:

[0138] When the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, substitute the inter-satellite ranging between the double satellites at all times, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center into the observation equation, and use weighted least squares estimation to solve to obtain the roll angle change amount of the double satellites.

[0139] When the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, substitute the inter-satellite ranging between the double satellites at all times, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center into the observation equation, and use weighted least squares estimation to solve to obtain the pitch angle change amount of the double satellites.

[0140] When the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction, substitute the inter-satellite ranging between the double satellites at all times, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center into the observation equation, and use weighted least squares estimation to solve to obtain the roll angle change amount of the double satellites.

[0141] When the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction, the inter-satellite ranging between the double satellites at all times, the residuals, the KBR ranging data of the double satellites, and the magnitudes of the vectors from the center of mass of each satellite in the double satellites to the antenna phase center are substituted into the observation equation, and the weighted least squares estimation is used to solve for the change in the pitch angle of the double satellites.

[0142] For the above method, an embodiment of the present invention provides an on-orbit calibration system for the inter-satellite pointing of a gravity satellite, including:

[0143] An acquisition module, configured to acquire observation data at multiple times; the observation data includes the angles of the satellites, precise orbit determination data, and the KBR ranging data of the double satellites; the angles of the satellites are determined according to the maneuvering plan; the angles are roll angles or pitch angles.

[0144] A double-satellite magnitude calculation module, configured to, for any one time, obtain the magnitudes of the vectors from the center of mass of each satellite in the double satellites to the antenna phase center at the time according to the KBR ranging data at the time.

[0145] An inter-satellite ranging calculation module, configured to construct an inter-satellite ranging theoretical model according to the observation data at the time.

[0146] A residual calculation module, configured to calculate the residuals of the inter-satellite ranging of the double satellites at the time according to the inter-satellite ranging theoretical model.

[0147] A change amount calculation module, configured to substitute the inter-satellite ranging between the double satellites at all times, the residuals, the KBR ranging data of the double satellites, and the magnitudes of the vectors from the center of mass of each satellite in the double satellites to the antenna phase center into the observation equation, and use the weighted least squares estimation to solve for the change in the angle of the double satellites; the change in the angle is the change in the roll angle or the change in the pitch angle.

[0148] As an optional implementation manner, the acquisition module specifically includes:

[0149] An MA acquisition unit, configured to, when the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, acquire the precise orbit determination data, the KBR ranging data of the double satellites, and the roll angle of the first satellite at multiple times.

[0150] An MB acquisition unit, configured to, when the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, acquire the precise orbit determination data, the KBR ranging data of the double satellites, and the pitch angle of the first satellite at multiple times.

[0151] The MC acquisition unit is configured to acquire the precise orbit determination data, the KBR ranging data of the double satellites, and the roll angle of the second satellite at multiple moments when the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction.

[0152] The MD acquisition unit is configured to acquire the precise orbit determination data, the KBR ranging data of the double satellites, and the pitch angle of the second satellite at multiple moments when the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction.

[0153] As an optional implementation manner, the double - satellite modulus calculation module specifically includes:

[0154] The modulus calculation unit of the first satellite is configured to calculate the sum of the reference value of the modulus of the vector from the centroid of the first satellite in the double satellites to the antenna phase center and the change amount of the modulus of the vector from the centroid of the first satellite to the antenna phase center to obtain the modulus of the vector from the centroid of the first satellite to the antenna phase center.

[0155] The modulus calculation unit of the second satellite is configured to calculate the sum of the reference value of the modulus of the vector from the centroid of the second satellite in the double satellites to the antenna phase center and the change amount of the modulus of the vector from the centroid of the second satellite to the antenna phase center to obtain the modulus of the vector from the centroid of the second satellite to the antenna phase center.

[0156] As an optional implementation manner, the inter - satellite ranging theoretical model is specifically:

[0157] When the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, the inter - satellite ranging theoretical model is where L 12 is the inter - satellite ranging between the double satellites, r 12 is the precise orbit determination data, d pc20 is the reference value of the modulus of the vector from the centroid of the second satellite to the antenna phase center, d pc10 is the reference value of the modulus of the vector from the centroid of the first satellite to the antenna phase center, and φ1 is the roll angle of the first satellite.

[0158] When the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, the inter - satellite ranging theoretical model is where θ1 is the pitch angle of the first satellite.

[0159] When the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction, the inter - satellite ranging theoretical model is where φ2 is the roll angle of the second satellite.

[0160] When the maneuvering scheme is to make the second satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ2 is the pitch angle of the second satellite.

[0161] As an alternative implementation manner, the variation calculation module specifically includes:

[0162] MA variation calculation unit, which is used for when the maneuvering scheme is to make the first satellite in the double satellites operate in the yaw direction, substituting the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all times into the observation equation, and using weighted least squares estimation to solve for the roll angle variation of the double satellites.

[0163] MB variation calculation unit, which is used for when the maneuvering scheme is to make the first satellite in the double satellites operate in the pitch direction, substituting the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all times into the observation equation, and using weighted least squares estimation to solve for the pitch angle variation of the double satellites.

[0164] MC variation calculation unit, which is used for when the maneuvering scheme is to make the second satellite in the double satellites operate in the yaw direction, substituting the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all times into the observation equation, and using weighted least squares estimation to solve for the roll angle variation of the double satellites.

[0165] MD variation calculation unit, which is used for when the maneuvering scheme is to make the second satellite in the double satellites operate in the pitch direction, substituting the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all times into the observation equation, and using weighted least squares estimation to solve for the pitch angle variation of the double satellites.

[0166] The embodiment of the present invention provides a more specific on-orbit calibration method for the inter-satellite pointing of gravity satellites.

[0167] The first step is to perform the pointing calculation of the maneuvering scheme of MA;

[0168] The estimable parameters of the maneuvering scheme MA are d pc1 , δφ1, d pc2 , δφ2. Denote d pc1 = d pc10 + δd pc1 , d pc2 = dpc20 +δd pc2 , where d pc10 and d pc20 are the reference values of d pc1 and d pc2 respectively. Then the estimation algorithm is as follows:

[0169] S1. Read in the KBR ranging data to obtain d pc20 , d pc10 . The KBR ranging data file contains d pc20 , d pc10 .

[0170] S2. Read in the precise orbit determination data to obtain r 12 , and construct the inter-satellite ranging theoretical model

[0171]

[0172] where

[0173]

[0174] S3. Calculate the residual y(t) of the inter-satellite ranging L 12 .

[0175] S4. Determine the estimation model and establish the observation equation. Use a fourth-order polynomial to fit the residual generated by precise orbit determination. Establish the observation equation

[0176]

[0177] where

[0178] p4(t) = a0 + a1t + a2t 2 + a3t 3 + a4t 4

[0179] Let the vector of parameters to be estimated be

[0180]

[0181] The observation equation can be written as

[0182]

[0183] where

[0184] H(t) = (H poly (t) H vip (t))

[0185] H poly (t) = (1, t, t 2 , t 3 , t 4

[0186]

[0187] In the above formula, the partial derivative and

[0188] Collect all the observed values. Assuming there are N observations, define

[0189]

[0190] The observation equation can be written as

[0191]

[0192] S5. Use weighted least squares estimation to solve and calculate the above formula, and the following can be obtained parameters.

[0193]

[0194] The estimated covariance matrix is (H T WH) -1 .

[0195] Here are the final parameters of the least squares estimation, which can be used to estimate the changes in the roll angles of the two stars, δφ1 and δφ2.

[0196] Second, perform the pointing calculation of the maneuvering plan of MB;

[0197] The maneuvering plan MB can estimate the parameters d pc1 , δθ1, d pc2 , δθ2. The estimation algorithm is as follows:

[0198] S1. Read in the KBR ranging data to obtain d pc20 , d pc10 .

[0199] S2. Read in the precise orbit determination data to obtain r 12 , and construct the inter-satellite ranging theoretical model

[0200]

[0201] where

[0202]

[0203] S3. Calculate the residual y(t) of the inter-satellite ranging L 12 .

[0204] S4. Determine the estimation model and establish the observation equation. Use a 4th-order polynomial to fit the residuals generated by precise orbit determination. Establish the observation equation

[0205]

[0206] where

[0207] p4(t) = a0 + a1t + a2t 2 + a3t 3 + a4t 4

[0208] Let the vector of parameters to be estimated be

[0209]

[0210] The observation equation can be written as

[0211]

[0212] where

[0213] H(t) = (H poly (t)H vip (t))

[0214] H poly (t) = (1, t, t 2 , t 3 , t 4 )

[0215]

[0216] In the above equation, the partial derivatives and Pool all the observed values. Assuming there are N observations, define

[0217]

[0218] The observation equation can be written as

[0219]

[0220] S5. Solve and calculate the above equation using weighted least squares estimation to obtain parameters.

[0221]

[0222] The estimated covariance matrix is (H T WH) -1 .

[0223] Here are the final parameters of the least squares estimation, which can be used to estimate the changes in the pitch angles of the two stars, δθ1 and δθ2.

[0224] Step 3: Calculate the pointing of the maneuver plan of MC;

[0225] The maneuver plan MC can estimate the parameters d pc1 , δφ1, d pc2 , δφ2. The estimation algorithm is as follows:

[0226] S1. Read in the KBR ranging data to obtain d pc20 , d pc10 .

[0227] S2. Read in the precise orbit determination data to obtain r 12 , and construct the inter-satellite ranging theoretical model

[0228]

[0229] where

[0230]

[0231] S3. Calculate the residual y(t) of the inter-satellite ranging L 12 .

[0232] S4. Determine the estimation model and establish the observation equation. Use a 4th-order polynomial to fit the residuals generated by precise orbit determination. Establish the observation equation

[0233]

[0234] where

[0235] p4(t) = a0 + a1t + a2t 2 + a3t 3 + a4t 4

[0236] Let the vector of parameters to be estimated be

[0237]

[0238] The observation equation can be written as

[0239]

[0240] where

[0241] H(t) = (H poly (t)H vip (t))

[0242] H poly (t) = (1, t, t 2 , t 3 , t 4

[0243]

[0244] In the above formula, the partial derivative and Collect all the observed values. Assume there are N observations, and define

[0245]

[0246] The observation equation can be written as

[0247]

[0248] S5. Use weighted least squares estimation to solve and calculate the above formula, and the following can be obtained parameters.

[0249]

[0250] The estimated covariance matrix is (H T WH) -1 .

[0251] Here are the final parameters of the least squares estimation, which can be used to estimate the changes in the roll angles of the two stars, δφ1 and δφ2.

[0252] Step 4: Calculate the pointing of the maneuvering plan of MD;

[0253] The maneuvering plan MD can estimate the parameters d pc1 , δθ1, d pc2 , δθ2. The estimation algorithm is as follows:

[0254] S1. Read in the KBR ranging data to obtain d pc20 , d pc10 .

[0255] S2. Read in the precise orbit determination data to obtain r 12 , and construct the inter-satellite ranging theoretical model

[0256]

[0257] where

[0258]

[0259] S3. Calculate the residual y(t) of the inter-satellite ranging L 12 .

[0260] S4. Determine the estimation model and establish the observation equation. Use a 4th-order polynomial to fit the residuals generated by precise orbit determination. Establish the observation equation

[0261]

[0262] where

[0263] p4(t) = a0 + a1t + a2t 2 + a3t 3 + a4t 4

[0264] Let the vector of parameters to be estimated be

[0265]

[0266] The observation equation can be written as

[0267]

[0268] where

[0269] H(t) = (H poly (t)H vip (t))

[0270] H poly (t) = (1, t, t 2 , t 3 , t 4 )

[0271]

[0272] In the above equation, the partial derivatives and

[0273] Collect all the observed values. Assuming there are N observations, define

[0274]

[0275] The observation equation can be written as

[0276]

[0277] S5. Solve and calculate the above equation using weighted least squares estimation, and the parameters can be obtained.

[0278]

[0279] The estimated covariance matrix is (H T WH) -1 .

[0280] Here are the final parameters of the least squares estimation, which can be used to estimate the changes in the double-star roll angles δθ1 and δθ2.

[0281] In this embodiment, the above method is applied to the measured data provided by the GRACE Follow-On mission as the measured data of measurement error for simulation. The data used in this simulation includes the 1B-level precise orbit determination data GNI1B obtained on June 1, 2018, the ranging data KBR1B between 1B-level phase centers, and the 1B-level calibration data VKB1B of the antenna phase center.

[0282] Among the KBR1B data, there are ranging biases, ranging rate of change, ranging acceleration, flight time correction, and antenna phase center bias correction, etc. The KBR1B data on June 1, 2018, has a time interval of 5 seconds. The inter-satellite distance and the rate of change of the inter-satellite distance given by the precise orbit determination data GNI1B obtained on June 1, 2018, in the GRACE Follow-On mission. Among the GNI1B data, there are the satellite positions and velocities in the geocentric inertial system, with a time interval of 1 second.

[0283] (1) Simulations of three maneuver periods in the case of a duration of 1000s

[0284] First, simulations are carried out for three maneuver periods when the maneuver duration is 1000s. The true value of the deviation angle of satellite A in the yaw direction is 1 mrad. 25 repeated experiments are conducted. The absolute error between the estimated value and the theoretical value of the yaw direction of satellite A is calculated. From the experimental results, it can be obtained that the percentage of the absolute error of the 13-time maneuver plan with a period of 251s is less than the other two cases, the absolute value error of the 8-time maneuver period of 250s is less than the other two cases, and the percentage of the absolute error of the 4-time maneuver plan with a period of 249s is less than the other two cases. Therefore, different maneuver periods will have an impact on the results. Comparatively speaking, the 249s maneuver period is the worst, and the 251s maneuver period is the best. Therefore, subsequently, further simulations will be carried out for the 250s and 251s maneuver periods to study the pointing calibration ability through simulation.

[0285] Table 2 Simulation maneuver plan MA maneuver parameter settings

[0286] Maneuvering offset (°) Maneuvering 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

[0287] (2) The ability to solve different pointing deviation angles in the case of a 1000s maneuver duration for the 249s, 250s, and 251s maneuver periods, and simultaneously solve the amplitude of the phase center vector.

[0288] Considering the data quality limitations, the pointing deviation calibration has a certain ability. The following conducts the solution quality assessment when the true values of the pointing deviation angles are 1 mrad, 0.5 mrad, 0.1 mrad, 0.05 mrad, and 0.01 mrad respectively. For each true value of the pointing deviation, consider the maneuvering duration of 1000 s and the solution ability of different magnitudes of the pointing deviation angles in three cases where the maneuvering periods are 249 s, 250 s, and 251 s respectively. Six simulation results are obtained. From these simulation results, when the true value is 1 mrad, in the three cases of the maneuvering periods, the solution errors are all less than 10%. When the true value is 0.5 mrad, for the maneuvering period of 249 s, the deviation between the estimated value and the true value is between 11.7% and 29.2%. For the maneuvering period of 250 s, the deviation between the estimated value and the true value is between 1.7% and 18.7%, and in four cases it is less than 10%. For the maneuvering period of 251 s, the deviation between the estimated value and the true value is between 0.3% and 12.7%, and in four cases it is less than 10%. When the true value is 0.1 mrad, the estimation results are poor, and among them, when the maneuvering period is 251 s, the result is the best. When the maneuvering period is 251 s, the deviation between the estimated value and the true value is between 6.2% and 60.2%, and in five cases it is greater than 10%. When the true value of the deviation angle is 0.05 mrad and 0.01 mrad, the solution accuracy is even worse. To sum up, when the true value is 0.5 mrad, using the maneuvering period of 251 s, it is barely possible to make the absolute error between the estimated value and the deviation value close to 10%, indicating that the pointing angle deviation value under absolute calibration cannot be too small. Generally speaking, when the true value of the pointing deviation is less than 1 mrad, the solution accuracy is poor, and among them, the estimation accuracy of the 251 s maneuvering period scheme is the best.

[0289] (3) The ability to solve different pointing deviation angles in the cases of 249 s, 250 s, and 251 s maneuvering periods with a maneuvering duration of 1000 s, without solving the amplitude of the phase center vector.

[0290] The following is to conduct a solution quality assessment when the true values of the pointing deviation angle are 1 mrad, 0.5 mrad, 0.1 mrad, 0.05 mrad, and 0.01 mrad respectively. For each true value of the pointing deviation, considering the maneuvering duration of 1000 s, the solution capabilities for different magnitudes of the pointing deviation angle are considered under three cases where the maneuvering periods are 249 s, 250 s, and 251 s respectively. Six simulation results are obtained. From these simulation results, it can be seen that when the true value is 1 mrad, under the three cases of the maneuvering period, the solution errors are all less than 7%. When the true value is 0.5 mrad, in the cases where the maneuvering periods are 249 s and 250 s, the deviation between the estimated value and the true value is within 7%. When the maneuvering period is 251 s, the deviation between the estimated value and the true value is about 10%. When the true values are 0.1 mrad, 0.05 mrad, and 0.01 mrad, the solution accuracy deteriorates and exceeds 10%. In summary, when the true value is 0.5 mrad, by using the schemes with the maneuvering periods of 249 s and 250 s, it is barely possible to make the absolute error between the estimated value and the deviation value close to 10%, indicating that the true value of the pointing angle deviation under absolute calibration cannot be too small. Generally speaking, when the true value of the pointing deviation is less than 0.5 mrad, the solution accuracy is poor. Among them, the estimation accuracy of the 249 s maneuvering period scheme is the best, and the estimation accuracy of the 250 s maneuvering period scheme can also be less than 7%.

[0291] From the above experimental results, it can be obtained that when simultaneously solving the phase center amplitude and the pointing deviation angle, when the pointing deviation angle is less than 1 mrad, the solution result is poor. If in order to solve a smaller pointing deviation angle, such as 0.5 mrad, it is advisable to adopt a maneuvering duration of 3000 s. However, generally speaking, the solution accuracy can be guaranteed when solving the 1 mrad pointing deviation angle.

[0292] The beneficial effect of the present invention is to achieve a periodic swing of the pointing through satellite maneuvering, obtain the inter-satellite pointing observation data, estimate the inter-satellite pointing of the satellite, which can avoid the traditional method that cannot truly and accurately reflect the pointing situation of the double satellites, thereby obtaining the accurate parameters of the double-satellite pointing control situation of the satellite and improving the accuracy of the on-orbit calibration result.

[0293] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0294] In this article, specific examples are used to illustrate the principles and implementation modes of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation modes and application scopes. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. An on-orbit calibration method for inter-satellite pointing of a gravity satellite, characterized in that, Including: Obtaining observation data at multiple moments; The observation data includes the angle of the satellite, precise orbit determination data, and KBR ranging data of the double star; the angle of the satellite is determined according to the maneuvering plan; the angle is the roll angle or the pitch angle; For any moment, according to the KBR ranging data at the moment, obtain the modulus of the vector from the centroid of each satellite in the double star to the antenna phase center at the moment; Construct an inter-satellite ranging theoretical model according to the observation data at the moment; Calculate the residual of the inter-satellite ranging of the double star at the moment according to the inter-satellite ranging theoretical model; Substitute the inter-satellite ranging between the double stars, the residual, the KBR ranging data of the double star, and the modulus of the vector from the centroid of each satellite in the double star to the antenna phase center at all moments into the observation equation, and use weighted least squares estimation to solve for the angle change of the double star; the angle change is the roll angle change or the pitch angle change.

2. The on-orbit calibration method for inter-satellite pointing of a gravity satellite according to claim 1, wherein The obtaining of the observation data at multiple moments specifically includes: When the maneuvering plan is to make the first satellite in the double star run in the yaw direction, obtain the precise orbit determination data, the KBR ranging data of the double star, and the roll angle of the first satellite at multiple moments; When the maneuvering plan is to make the first satellite in the double star run in the pitch direction, obtain the precise orbit determination data, the KBR ranging data of the double star, and the pitch angle of the first satellite at multiple moments; When the maneuvering plan is to make the second satellite in the double star run in the yaw direction, obtain the precise orbit determination data, the KBR ranging data of the double star, and the roll angle of the second satellite at multiple moments; When the maneuvering plan is to make the second satellite in the double star run in the pitch direction, obtain the precise orbit determination data, the KBR ranging data of the double star, and the pitch angle of the second satellite at multiple moments.

3. The on-orbit calibration method for inter-satellite pointing of a gravity satellite according to claim 1, wherein The obtaining of the modulus of the vector from the centroid of each satellite in the double star to the antenna phase center at the moment according to the KBR ranging data at the moment specifically includes: Calculate the sum of the reference value of the modulus of the vector from the centroid of the first satellite in the double star to the antenna phase center and the change amount of the modulus of the vector from the centroid of the first satellite to the antenna phase center to obtain the modulus of the vector from the centroid of the first satellite to the antenna phase center; Calculate the sum of the reference value of the modulus of the vector from the centroid of the second satellite in the double star to the antenna phase center and the change amount of the modulus of the vector from the centroid of the second satellite to the antenna phase center to obtain the modulus of the vector from the centroid of the second satellite to the antenna phase center.

4. A method for on-orbit calibration of the inter-satellite pointing of a gravity satellite according to claim 2, characterized in that, The inter-satellite ranging theoretical model is specifically: When the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, the inter-satellite ranging theoretical model is where L 12 is the inter-satellite ranging between the double satellites, r 12 is the precise orbit determination data, d pc20 is the reference value of the modulus of the vector from the centroid of the second satellite to the antenna phase center, d pc10 is the reference value of the modulus of the vector from the centroid of the first satellite to the antenna phase center, and φ1 is the roll angle of the first satellite; When the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ1 is the pitch angle of the first satellite; When the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction, the inter-satellite ranging theoretical model is where φ2 is the roll angle of the second satellite; When the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ2 is the pitch angle of the second satellite.

5. A method for on-orbit calibration of the inter-satellite pointing of a gravity satellite according to claim 2, characterized in that, The substituting of the inter-satellite ranging between the double stars, the residual, the KBR ranging data of the double star, and the modulus of the vector from the centroid of each satellite in the double star to the antenna phase center at all moments into the observation equation, and using weighted least squares estimation to solve for the angle change of the double star specifically includes: When the maneuvering plan is to make the first satellite in the double - satellite system operate in the yaw direction, the inter - satellite ranging between the double - satellites at all times, the residuals, the KBR ranging data of the double - satellites, and the magnitudes of the vectors from the center - of - mass of each satellite in the double - satellites to the antenna phase center are substituted into the observation equation, and weighted least - squares estimation is used to solve for the roll - angle change of the double - satellites; When the maneuvering plan is to make the first satellite in the double - satellite system operate in the pitch direction, the inter - satellite ranging between the double - satellites at all times, the residuals, the KBR ranging data of the double - satellites, and the magnitudes of the vectors from the center - of - mass of each satellite in the double - satellites to the antenna phase center are substituted into the observation equation, and weighted least - squares estimation is used to solve for the pitch - angle change of the double - satellites; When the maneuvering plan is to make the second satellite in the double - satellite system operate in the yaw direction, the inter - satellite ranging between the double - satellites at all times, the residuals, the KBR ranging data of the double - satellites, and the magnitudes of the vectors from the center - of - mass of each satellite in the double - satellites to the antenna phase center are substituted into the observation equation, and weighted least - squares estimation is used to solve for the roll - angle change of the double - satellites; When the maneuvering plan is to make the second satellite in the double - satellite system operate in the pitch direction, the inter - satellite ranging between the double - satellites at all times, the residuals, the KBR ranging data of the double - satellites, and the magnitudes of the vectors from the center - of - mass of each satellite in the double - satellites to the antenna phase center are substituted into the observation equation, and weighted least - squares estimation is used to solve for the pitch - angle change of the double - satellites.

6. An on-orbit calibration system for inter-satellite pointing of a gravity satellite, characterized in that It includes: An acquisition module, configured to acquire observation data at multiple times; The observation data includes the angles of the satellites, precise orbit - determination data, and the KBR ranging data of the double - satellites; the angles of the satellites are determined according to the maneuvering plan; the angles are roll angles or pitch angles; A double - satellite magnitude calculation module, configured to, for any given time, obtain the magnitudes of the vectors from the center - of - mass of each satellite in the double - satellites to the antenna phase center at the given time according to the KBR ranging data at the given time; An inter - satellite ranging calculation module, configured to construct an inter - satellite ranging theoretical model according to the observation data at the given time; A residual calculation module, configured to calculate the residuals of the inter - satellite ranging of the double - satellites at the given time according to the inter - satellite ranging theoretical model; A change - amount calculation module, configured to substitute the inter - satellite ranging between the double - satellites at all times, the residuals, the KBR ranging data of the double - satellites, and the magnitudes of the vectors from the center - of - mass of each satellite in the double - satellites to the antenna phase center into the observation equation, and use weighted least - squares estimation to solve for the angle change of the double - satellites; the angle change is the roll - angle change or the pitch - angle change.

7. The on-orbit calibration system for inter-satellite pointing of a gravity satellite according to claim 6, wherein, The acquisition module specifically includes: An MA acquisition unit, configured to, when the maneuvering plan is to make the first satellite in the double - satellite system operate in the yaw direction, acquire the precise orbit - determination data, the KBR ranging data of the double - satellites, and the roll angle of the first satellite at multiple times; The MB acquisition unit is used to obtain the precise orbit determination data, the KBR ranging data of the double satellites, and the pitch angle of the first satellite at multiple moments when the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction. The MC acquisition unit is used to obtain the precise orbit determination data, the KBR ranging data of the double satellites, and the roll angle of the second satellite at multiple moments when the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction. The MD acquisition unit is used to obtain the precise orbit determination data, the KBR ranging data of the double satellites, and the pitch angle of the second satellite at multiple moments when the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction.

8. An in-orbit calibration system for gravitational satellite inter-satellite pointing according to claim 6, characterized in that The double-satellite modulus calculation module specifically includes: The modulus calculation unit of the first satellite is used to calculate the sum of the reference value of the modulus of the vector from the centroid of the first satellite in the double satellites to the antenna phase center and the change amount of the modulus of the vector from the centroid of the first satellite to the antenna phase center to obtain the modulus of the vector from the centroid of the first satellite to the antenna phase center. The modulus calculation unit of the second satellite is used to calculate the sum of the reference value of the modulus of the vector from the centroid of the second satellite in the double satellites to the antenna phase center and the change amount of the modulus of the vector from the centroid of the second satellite to the antenna phase center to obtain the modulus of the vector from the centroid of the second satellite to the antenna phase center.

9. The on-orbit calibration system for inter-satellite pointing of a gravity satellite according to claim 7, wherein, The inter-satellite ranging theoretical model is specifically: When the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction, the inter-satellite ranging theoretical model is where L 12 is the inter-satellite ranging between the double satellites, r 12 is the precise orbit determination data, d pc20 is the reference value of the modulus of the vector from the center of mass of the second satellite to the antenna phase center, d pc10 is the reference value of the modulus of the vector from the center of mass of the first satellite to the antenna phase center, and φ1 is the roll angle of the first satellite; When the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ1 is the pitch angle of the first satellite; When the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction, the inter-satellite ranging theoretical model is where φ2 is the roll angle of the second satellite; When the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction, the inter-satellite ranging theoretical model is where θ2 is the pitch angle of the second satellite.

10. A on-orbit calibration system for gravitational satellite inter-satellite pointing according to claim 7, characterized in that, The change amount calculation module specifically includes: The MA change amount calculation unit is used to substitute the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all moments into the observation equation and use weighted least squares estimation to solve for the roll angle change amount of the double satellites when the maneuvering plan is to make the first satellite in the double satellites operate in the yaw direction. The MB change amount calculation unit is used to substitute the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all moments into the observation equation and use weighted least squares estimation to solve for the pitch angle change amount of the double satellites when the maneuvering plan is to make the first satellite in the double satellites operate in the pitch direction. The MC change amount calculation unit is used to substitute the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the modulus of the vector from the centroid of each satellite in the double satellites to the antenna phase center at all moments into the observation equation and use weighted least squares estimation to solve for the roll angle change amount of the double satellites when the maneuvering plan is to make the second satellite in the double satellites operate in the yaw direction. The MD change calculation unit is configured to, when the maneuvering plan is to make the second satellite in the double satellites operate in the pitch direction, substitute the inter-satellite ranging between the double satellites, the residuals, the KBR ranging data of the double satellites, and the magnitudes of the vectors from the center of mass of each satellite in the double satellites to the antenna phase center at all times into the observation equation, and use weighted least squares estimation to solve for the pitch angle change of the double satellites.

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