A method for predicting relative motion in formation flight based on correlation coefficient fitting

Abstract

A method for predicting relative motion in formation flight based on correlation coefficient fitting is proposed. This method obtains relative navigation motion state data, calculates the correlation coefficient, and uses this coefficient to predict the relative distance of spacecraft in free motion. The method is simple in form, improves the accuracy of relative motion prediction, and is easy to implement in engineering, providing a technical reserve for acquiring guidance-related parameters of spacecraft in near-circular orbit formation scenarios.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft formation flight guidance and control, and relates to a method for predicting the relative motion of formation flight based on the fitting of prediction correlation coefficients. Background Technology

[0002] Long-duration formation flying of spacecraft in near-circular orbits is a prerequisite for completing tasks such as Earth interferometric imaging and high-precision gravity field measurement. Relative motion prediction is an essential computational step in formation flight guidance and control. In engineering, relative motion prediction typically uses the CW equation single-point extrapolation method. This method does not fully utilize existing relative navigation motion state data and has significant errors, making it difficult to meet the requirements of long-term configuration maintenance. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a formation flight relative motion prediction method based on prediction correlation coefficient fitting. This method can be used for relative motion prediction calculation in near-circular orbit formation scenarios. It can be calculated directly using existing relative navigation motion state data, has high accuracy, meets the requirements of long-term configuration maintenance, and is easy to implement in engineering.

[0004] The technical solution of this invention is:

[0005] A method for predicting the relative motion of formation flight based on correlation coefficient fitting includes:

[0006] Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, relative navigation motion state data is obtained;

[0007] Based on the obtained relative navigation motion state data, the prediction correlation coefficient is calculated by fitting.

[0008] The relative motion is predicted based on the correlation coefficient.

[0009] Preferably, the method for obtaining relative navigation motion state data based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system is as follows:

[0010] Assuming the main spacecraft remains in free motion during near-circular orbit formation flight, the following N+1 relative navigation motion state-related data are obtained from the spacecraft's relative navigation system based on the three-axis position data x(t), y(t), and z(t) of the spacecraft relative to the main spacecraft in the main spacecraft's orbital coordinate system collected at time t:

[0011]

[0012] Where t0 is the set start time, t k(k = 0, 1, 2, ..., N) represents the set time for acquiring relative navigation motion state related data, n(t k ) for t k The orbital angular velocity of the primary spacecraft at that moment, H xz (t k H y (t k ), Y xz (t k ), Y y (t k ) are respectively t k The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time.

[0013] Preferred, t k >t k-1 >…>t1>t0.

[0014] Preferred,

[0015] The main spacecraft's orbital coordinate system is: origin O o The main spacecraft's center of mass, O o Z o The axis points towards the Earth's center of mass, O o Y o The axis is perpendicular to O o Z o The axis points in the negative direction of the orbital angular velocity, O o X o Shaft and O o Z o O o Y o The axes form a right-handed coordinate system;

[0016] From the spacecraft's orbital coordinate system: origin O d To remove the spacecraft's center of mass, O d Z d The axis points towards the Earth's center of mass, O d Y d The axis is perpendicular to O d Z d The axis points in the negative direction of the orbital angular velocity, O d X d Shaft and O d Z d O d Y d The axes form a right-handed coordinate system.

[0017] Preferably, the specific method for calculating the predictive correlation coefficient is as follows:

[0018] 1) Set the in-plane fitting intermediate quantity matrix at time t0 In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector That is, P xz (t0) is a 4×4 matrix, Q xz (t0) is a 4×1 dimensional vector, P y (t0) is a 2×2 matrix, Q y (t0) is a 2×1 dimensional vector, H xz (t0), H y (t0), Y xz (t0), Y y (t0) represents the in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at time t0.

[0019] 2)t k At time k = 1, 2, ..., N

[0020]

[0021] Among them, H xz (t k H y (t k ), Y xz (t k ), Y y (t k ) are respectively t k The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time;

[0022] 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficients

[0023] 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variable ζ = [ζ1ζ2ζ3ζ4ζ5]. T Among them, the predicted out-of-plane relative position Y fity (t k )=[ζ1+ζ2(t k -t0)]sin[ζ3(t k -t0)+ζ4]+ζ5, the solution for optimizing the decision variables is obtained as

[0024] Preferably, if an iterative method is used to solve the optimization decision variables, the initial value of ζ is ζ0 = [ζ 01 ζ 02 ζ03 ζ 04 ζ 05 ] T satisfy ζ 02 =0, ζ 03 =n(t0), ζ 05 =0, n(t0) is the orbital angular velocity of the main spacecraft at time t0.

[0025] Preferably, the relative motion is predicted based on the prediction correlation coefficient, and the specified prediction time is t. pred The prediction method is as follows:

[0026]

[0027] Among them, Y predx (t pred ), Y predy (t pred ), Y predz (t pred These represent the three-axis positions of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. denoted as the three-axis velocities of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time, n(t) is the orbital angular velocity of the master spacecraft in the master spacecraft's orbital coordinate system at the current time, and t0 is the set start time.

[0028] A formation flight relative motion prediction system based on prediction correlation coefficient fitting includes a relative navigation motion state data acquisition module, a prediction correlation coefficient fitting calculation module, and a relative motion prediction module.

[0029] Relative navigation motion state data acquisition module: Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, it obtains relative navigation motion state data;

[0030] Predictive correlation coefficient fitting calculation module: Based on the obtained relative navigation motion state data, the predictive correlation coefficient is fitted and calculated;

[0031] Relative motion prediction module: Predicts relative motion based on the prediction correlation coefficient.

[0032] Preferably, the method for the prediction correlation coefficient fitting calculation module to fit and calculate the prediction correlation coefficient is as follows:

[0033] 1) Set the in-plane fitting intermediate quantity matrix at time t0 In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector That is, P xz(t0) is a 4×4 matrix, Q xz (t0) is a 4×1 dimensional vector, P y (t0) is a 2×2 matrix, Q y (t0) is a 2×1 dimensional vector, H xz (t0), H y (t0), Y xz (t0), Y y (t0) represents the in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at time t0.

[0034] 2)t k At time k = 1, 2, ..., N

[0035]

[0036] Among them, H xz (t k H y (t k ), Y xz (t k ), Y y (t k ) are respectively t k The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time;

[0037] 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficients

[0038] 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variable ζ = [ζ1 ζ2 ζ3 ζ4 ζ5] T Among them, the predicted out-of-plane relative position Y fity (t k )=[ζ1+ζ2(t k -t0)]sin[ζ3(t k -t0)+ζ4]+ζ5, the solution for optimizing the decision variables is obtained as

[0039] Preferably, the relative motion prediction module predicts the relative motion based on the prediction correlation coefficient, and the specified prediction time is t. pred The prediction method is as follows:

[0040]

[0041] Among them, Y predx(t pred ), Y predy (t pred ), Y predz (t pred These represent the three-axis positions of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. denoted as the three-axis velocities of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time, n(t) is the orbital angular velocity of the master spacecraft in the master spacecraft's orbital coordinate system at the current time, and t0 is the set start time.

[0042] The advantages of this invention compared to the prior art are:

[0043] (1) The relative motion prediction method of the present invention takes the relative motion state data obtained as the starting point, avoids the large calculation error caused by the single-point extrapolation method of CW equation, has high accuracy, and meets the requirements of long-term configuration maintenance.

[0044] (2) The relative motion prediction method of the present invention makes full use of the relative motion characteristics of near-circular orbits. By obtaining relative navigation motion state data, fitting and calculating the prediction correlation coefficient, and using the prediction correlation coefficient to predict the relative distance of the spacecraft in free motion state, it does not require complex theoretical analysis, has a flexible design concept, and is easy to implement in engineering. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the prediction process of this invention;

[0046] Figure 2 A schematic diagram of the relative position of the X-axis obtained using the dynamic simulation method (actual value), the CW single-point prediction method, and the method of the present invention;

[0047] Figure 3 This is a schematic diagram illustrating the error between the predicted X-axis relative position and the actual value using the CW single-point prediction method and the method of this invention.

[0048] Figure 4 A schematic diagram of the X-axis relative velocity obtained using the dynamic simulation method (actual value), the CW single-point prediction method, and the method of this invention;

[0049] Figure 5 This is a schematic diagram illustrating the error between the X-axis relative velocity predicted by the CW single-point prediction method and the method of this invention, and the actual value.

[0050] Figure 6 This is a schematic diagram of the relative position of the Y-axis obtained by the dynamic simulation method (actual value), the CW single-point prediction method, and the method of the present invention.

[0051] Figure 7This is a schematic diagram illustrating the error between the predicted relative position of the Y-axis and the actual value using the CW single-point prediction method and the method of this invention.

[0052] Figure 8 This diagram illustrates the relative Y-axis velocity obtained by the dynamic simulation method (actual value), the CW single-point prediction method, and the method of this invention.

[0053] Figure 9 This is a schematic diagram illustrating the error between the predicted Y-axis relative velocity and the actual value using the CW single-point prediction method and the method of this invention.

[0054] Figure 10 This is a schematic diagram of the relative Z-axis position obtained by the dynamic simulation method (actual value), the CW single-point prediction method, and the method of this invention.

[0055] Figure 11 This is a schematic diagram illustrating the error between the Z-axis relative position predicted by the CW single-point prediction method and the method of this invention, and the actual value.

[0056] Figure 12 This diagram illustrates the relative Z-axis velocity obtained by the dynamic simulation method (actual value), the CW single-point prediction method, and the method of this invention.

[0057] Figure 13 This is a schematic diagram illustrating the error between the Z-axis relative velocity predicted by the CW single-point prediction method and the method of this invention, and the actual value. Detailed Implementation

[0058] When spacecraft conduct long-duration formation flights, relative motion prediction is typically required to calculate appropriate formation maintenance control parameters when a predetermined threshold is triggered. In engineering practice, relative motion prediction often employs a single-point extrapolation method based on the CW equation, which does not fully utilize existing relative navigation motion state data and contains significant errors, making it difficult to meet the requirements for long-duration formation maintenance. To overcome these challenges, this invention proposes a relative motion prediction method based on prediction correlation coefficient fitting. By obtaining relative navigation motion state data, a prediction correlation coefficient is calculated through fitting, and this coefficient is used to predict the relative distance of the spacecraft in its free motion state. This method is simple in form, improves the calculation accuracy of relative motion prediction, and is easy to implement in engineering, providing a technical reserve for acquiring guidance-related parameters for spacecraft in near-circular orbit formation scenarios.

[0059] like Figure 1 As shown, the present invention provides a method for predicting the relative motion of formation flight based on prediction correlation coefficient fitting, the steps of which are as follows:

[0060] (1) Obtain relative navigation motion state data based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system.

[0061] The main spacecraft's orbital coordinate system is: origin O o The main spacecraft's center of mass, O o Z o The axis points towards the Earth's center of mass, O o Y o The axis is perpendicular to O o Z o The axis points in the negative direction of the orbital angular velocity, O o X o Shaft and O o Z o O o Y o The axes form a right-handed coordinate system;

[0062] From the spacecraft's orbital coordinate system: origin O d To remove the spacecraft's center of mass, O d Z d The axis points towards the Earth's center of mass, O d Y d The axis is perpendicular to O d Z d The axis points in the negative direction of the orbital angular velocity, O d X d Shaft and O d Z d O d Y d The axes form a right-handed coordinate system.

[0063] Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, the method for obtaining relative navigation motion state data is as follows:

[0064] Assuming the main spacecraft remains in free motion during near-circular orbit formation flight, the following N+1 relative navigation motion state-related data are obtained from the spacecraft's relative navigation system based on the three-axis position data x(t), y(t), and z(t) of the spacecraft relative to the main spacecraft in the main spacecraft's orbital coordinate system collected at time t:

[0065]

[0066] Where t0 is the set start time, t k (k = 0, 1, 2, ..., N) represents the set time for acquiring relative navigation motion state related data, t k >t k-1 >...>t1>t0, n(t k ) for t k The orbital angular velocity of the primary spacecraft at that moment, H xz (t k H y (t k ), Y xz(t k ), Y y (t k ) are respectively t k The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time.

[0067] (2) Calculate the prediction correlation coefficient based on the relative navigation motion state data obtained in step (1).

[0068] The specific method for calculating the predictive correlation coefficient is as follows:

[0069] 1) Set the in-plane fitting intermediate quantity matrix at time t0 In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector That is, P xz (t0) is a 4×4 matrix, Q xz (t0) is a 4×1 dimensional vector, P y (t0) is a 2×2 matrix, Q y (t0) is a 2×1 dimensional vector, H xz (t0), H y (t0), Y xz (t0), Y y (t0) represents the in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at time t0.

[0070] 2)t k At time k = 1, 2, ..., N

[0071]

[0072] Among them, H xz (t k H y (t k ), Y xz (t k ), Y y (t k ) are respectively t k The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time;

[0073] 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficients

[0074] 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variable ζ = [ζ1 ζ2 ζ3 ζ4 ζ5] T Among them, the predicted out-of-plane relative position Y fity (t k )=[ζ1+ζ2(t k -t0)]sin[ζ3(t k -t0)+ζ4]+ζ5, the solution for optimizing the decision variables is obtained as If an iterative approach is used to solve for the optimization decision variables, the initial value of ζ is ζ0 = [ζ 01 ζ 02 ζ 03 ζ 04 ζ 05 ] T satisfy ζ 02 =0, ζ 03 =n(t0), ζ 05 =0, n(t0) is the orbital angular velocity of the main spacecraft at time t0.

[0075] (3) Based on the prediction correlation coefficient in step (3), predict the relative motion.

[0076] The relative motion is predicted based on the correlation coefficient, and the specified prediction time is t. pred The prediction method is as follows:

[0077]

[0078] Among them, Y predx (t pred ), Y predy (t pred ), Y predz (t pred These represent the three-axis positions of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. denoted as the three-axis velocities of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time, n(t) is the orbital angular velocity of the master spacecraft in the master spacecraft's orbital coordinate system at the current time, and t0 is the set start time.

[0079] The present invention also provides a formation flight relative motion prediction system based on prediction correlation coefficient fitting, including a relative navigation motion state data acquisition module, a prediction correlation coefficient fitting calculation module, and a relative motion prediction module.

[0080] Relative navigation motion state data acquisition module: Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, it obtains relative navigation motion state data.

[0081] Predictive correlation coefficient fitting calculation module: Based on the obtained relative navigation motion state data, the predictive correlation coefficient is fitted and calculated.

[0082] Relative motion prediction module: Predicts relative motion based on the prediction correlation coefficient.

[0083] The method for calculating the predicted correlation coefficient using the correlation coefficient fitting calculation module is as follows:

[0084] 1) Set the in-plane fitting intermediate quantity matrix at time t0 In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector That is, P xz (t0) is a 4×4 matrix, Q xz (t0) is a 4×1 dimensional vector, P y (t0) is a 2×2 matrix, Q y (t0) is a 2×1 dimensional vector, H xz (t0), H y (t0), Y xz (t0), Y y (t0) represents the in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at time t0.

[0085] 2)t k At time k = 1, 2, ..., N

[0086]

[0087] Among them, H xz (t k H y (t k ), Y xz (t k ), Y y (t k ) are respectively t k-1 The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time;

[0088] 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficients

[0089] 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variable ζ = [ζ1 ζ2 ζ3 ζ4 ζ5] TAmong them, the predicted out-of-plane relative position Y fity (t k )=[ζ1+ζ2(t k -t0)]sin[ζ3(t k -t0)+ζ4]+ζ5, the solution for optimizing the decision variables is obtained as

[0090] The relative motion prediction module predicts relative motion based on the prediction correlation coefficient. Let the specified prediction time be t. pred The prediction method is as follows:

[0091]

[0092] Among them, Y predx (t pred ), Y predy (t pred ), Y predz (t pred These represent the three-axis positions of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. denoted as the three-axis velocities of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time, n(t) is the orbital angular velocity of the master spacecraft in the master spacecraft's orbital coordinate system at the current time, and t0 is the set start time.

[0093] Figure 1 Here is a block diagram of a formation flight relative motion prediction method based on prediction correlation coefficient fitting. The calculation example calculated according to steps (1) to (3) is as follows.

[0094] Consider two spacecraft flying in a near-circular orbit at an altitude of 500 km. The initial instantaneous elements of the master spacecraft are: semi-major axis 6878 km, eccentricity 0.001, orbital inclination 97.5°, right ascension of ascending node 326.3°, perigee argument 30°, and mean anomaly 0.01°. The initial instantaneous elements of the slave spacecraft are: semi-major axis 6877.98 km, eccentricity 0.0011, orbital inclination 97.505°, right ascension of ascending node 326.33°, perigee argument 30.001°, and mean anomaly 0°.

[0095] Starting from the initial time t0 = 10s, data is acquired every 500s, for a total of 13 times. The prediction correlation coefficient is calculated using the method of this invention, the CW single-point prediction method, and the dynamic simulation method, and the relative motion is predicted. Simultaneously, the errors between the position and velocity obtained by the method of this invention and the CW single-point prediction method and the dynamic simulation method are calculated, resulting in a schematic diagram of the relative position and velocity correlation along the XYZ axes, as shown below. Figures 2-13 As shown.

[0096] Depend on Figures 2-13 It can be seen that, compared with the single-point extrapolation method of CW equations, the present invention can guarantee the accuracy of relative motion prediction.

[0097] This invention obtains relative navigation motion state data, fits and calculates a prediction correlation coefficient, and uses this correlation coefficient to predict the relative distance of a spacecraft in free motion. The method of this invention can be used for relative motion prediction calculations in near-circular orbit formation scenarios, and can be performed directly using existing relative navigation motion state data, making it easy to implement in engineering.

[0098] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for predicting the relative motion of formation flight based on prediction correlation coefficient fitting, characterized in that, include: Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, relative navigation motion state data is obtained; Based on the obtained relative navigation motion state data, the prediction correlation coefficient is calculated by fitting. The relative motion is predicted based on the predicted correlation coefficient; The specific method for calculating the prediction correlation coefficient is as follows: 1) Settings In-time fitting intermediate quantity matrix In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector ,Right now for 3D matrix for 3D vector for 3D matrix for 3D vector , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time; 2) time, in, , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time; 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficient ; 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variables. Among them, the predicted out-of-plane relative position The solution for optimizing the decision variables is obtained as follows: .

2. The method for predicting relative motion of formation flight based on prediction correlation coefficient fitting according to claim 1, characterized in that, Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, the method for obtaining relative navigation motion state data is as follows: Assuming the main spacecraft remains in free motion throughout the near-circular orbit formation flight, the relative navigation system of the spacecraft will determine the course of the flight. The three-axis position data of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system are collected continuously. , , The following results were obtained: Relative navigation motion state related data: in, The set start time, The set time for collecting data related to the relative navigation motion state. for The orbital angular velocity of the main spacecraft at that moment, , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time.

3. The method for predicting relative motion of formation flight based on prediction correlation coefficient fitting according to claim 2, characterized in that, 。 4. The method for predicting relative motion of formation flight based on prediction correlation coefficient fitting according to claim 2, characterized in that, The main spacecraft's orbital coordinate system is: origin O o The main spacecraft's center of mass, O o Z o The axis points towards the Earth's center of mass, O o Y o The axis is perpendicular to O o Z o The axis points in the negative direction of the orbital angular velocity, O o X o Shaft and O o Z o O o Y o The axes form a right-handed coordinate system; From the spacecraft's orbital coordinate system: origin O d To remove the spacecraft's center of mass, O d Z d The axis points towards the Earth's center of mass, O d Y d The axis is perpendicular to O d Z d The axis points in the negative direction of the orbital angular velocity, O d X d Shaft and O d Z d O d Y d The axes form a right-handed coordinate system.

5. The method for predicting relative motion of formation flight based on prediction correlation coefficient fitting according to claim 1, characterized in that, If an iterative method is used to solve for the optimization decision variables initial value satisfy , , , , , for The orbital angular velocity of the main spacecraft at that moment.

6. The method for predicting relative motion of formation flight based on prediction correlation coefficient fitting according to claim 1, characterized in that, The relative motion is predicted based on the correlation coefficient. Let the specified prediction time be... The prediction method is as follows: in, , , These represent the three-axis positions of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. , , These represent the three-axis velocities of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. The orbital angular velocity of the main spacecraft in the main spacecraft's orbital coordinate system at the current moment. The set start time.

7. A formation flight relative motion prediction system based on prediction correlation coefficient fitting, characterized in that, It includes a relative navigation motion state data acquisition module, a prediction correlation coefficient fitting calculation module, and a relative motion prediction module; Relative navigation motion state data acquisition module: Based on the definitions of the master spacecraft orbital coordinate system and the slave spacecraft orbital coordinate system, it obtains relative navigation motion state data; Predictive correlation coefficient fitting calculation module: Based on the obtained relative navigation motion state data, the predictive correlation coefficient is fitted and calculated; Relative motion prediction module: Predicts relative motion based on the prediction correlation coefficient; The specific method for calculating the prediction correlation coefficient is as follows: 1) Settings In-time fitting intermediate quantity matrix In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector ,Right now for 3D matrix for 3D vector for 3D matrix for 3D vector , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time; 2) time, in, , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time; 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficient ; 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variables. Among them, the predicted out-of-plane relative position The solution for optimizing the decision variables is obtained as follows: .

8. The formation flight relative motion prediction system based on prediction correlation coefficient fitting according to claim 7, characterized in that, The method for calculating the predicted correlation coefficient using the correlation coefficient fitting calculation module is as follows: 1) Settings In-time fitting intermediate quantity matrix In-plane fitting of intermediate vector Out-of-plane fitting intermediate matrix Out-of-plane fitting intermediate vector ,Right now for 3D matrix for 3D vector for 3D matrix for 3D vector , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time; 2) time, in, , , , They are respectively The in-plane measurement matrix, out-of-plane measurement matrix, in-plane position, and out-of-plane position of the spacecraft relative to the host spacecraft in the host spacecraft's orbital coordinate system at any given time; 3) Calculate the in-plane intermediate fitting coefficients Out-of-plane intermediate fitting coefficient ; 4) Using the in-plane and out-of-plane intermediate fitting coefficients, under constraints... Next, solve for the optimal decision variables. Among them, the predicted out-of-plane relative position The solution for optimizing the decision variables is obtained as follows: .

9. A formation flight relative motion prediction system based on prediction correlation coefficient fitting according to claim 8, characterized in that, The relative motion prediction module predicts relative motion based on the prediction correlation coefficient. Let the specified prediction time be... The prediction method is as follows: in, , , These represent the three-axis positions of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. , , These represent the three-axis velocities of the slave spacecraft relative to the master spacecraft in the master spacecraft's orbital coordinate system at the predicted time. The orbital angular velocity of the main spacecraft in the main spacecraft's orbital coordinate system at the current moment. The set start time.

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