A satellite formation configuration control method based on historical navigation information

Abstract

This invention relates to a satellite formation configuration control method based on historical navigation information, comprising: calculating the x-axis and y-axis components of the relative inclination vector and the relative eccentricity vector between the slave and slave satellites at various time points based on the orbital elements of the master and slave satellites; obtaining the position and velocity state of the slave satellite in the local coordinate system of the master satellite; fitting the y-axis relative motion, the x-axis and y-axis components of the relative inclination vector, and the x-axis and y-axis components of the relative eccentricity vector of the slave satellite in the local coordinate system of the master satellite using the least squares method, and calculating the average relative orbital elements based on the fitting results; obtaining the target average relative orbital elements according to the designed satellite formation configuration, and then obtaining the average relative orbital element deviation; correcting the average relative orbital element deviation to initialize or reconstruct the satellite formation configuration. This method replaces the traditional method of converting instantaneous orbital elements to average orbital elements, which is complex in modeling and cumbersome in derivation.

Description

Technical Field

[0001] This invention relates to the field of satellite formation technology, and in particular to a satellite formation configuration control method based on historical navigation information. Background Technology

[0002] Satellite formations play a crucial role in Earth observation, deep space exploration, and communications. Formation missions must maintain a relative configuration to meet core mission requirements while also being able to dynamically reconfigure to adapt to environmental changes, mission adjustments, or satellite malfunctions. Therefore, achieving configuration maintenance and reconfiguration control of the formation is a critical issue. Currently, long-term autonomous formation missions primarily rely on average orbital elements design, making the determination of these elements a primary challenge. Two main methods exist for calculating the average orbital elements: one is a quasi-average orbital element determination method based on a filtering algorithm that considers J2 squared term compensation; the other provides a method for converting instantaneous orbital elements to average orbital elements considering J2 perturbations and atmospheric drag.

[0003] However, the conversion between instantaneous orbital elements and average orbital elements requires accurate dynamic modeling, and the derivation process is complex and demands high navigation accuracy. These requirements increase the implementation complexity of many formation missions, such as lunar formation missions, where the perturbation environment is complex, satellite navigation performance is low, and inter-satellite measurement payloads are affected by lighting conditions, leading to the loss of some navigation information. Therefore, a formation control method that relies on limited, low-precision navigation information needs to be proposed. Summary of the Invention

[0004] This invention proposes a satellite formation configuration control method based on historical navigation information for satellite formations with poor navigation accuracy or incomplete navigation information. It can perform least squares fitting and solution based on historical navigation data to obtain the average relative orbital elements of the slave satellites relative to the master satellite. This replaces the traditional method of converting instantaneous orbital elements to average orbital elements, which is complex and has a cumbersome derivation process. Furthermore, formation control is achieved based on the deviation of the average relative orbital elements. Moreover, the data fitting process can extract global features of the data and allows for the loss of some information.

[0005] This invention provides a satellite formation configuration control method based on historical navigation information, comprising:

[0006] The inertial coordinate states of the primary and secondary stars at various moments within a certain period of time are transformed to obtain the six orbital roots of the primary and secondary stars. Based on the six orbital roots of the primary and secondary stars, the x-axis and y-axis components of the relative inclination vector and the relative eccentricity vector between the secondary and primary stars at various moments are calculated.

[0007] By transforming the inertial coordinate states of the primary star and the secondary star at various moments within a certain period of time, the relative state of the secondary star in the local coordinate system of the primary star is obtained, thereby obtaining the position and velocity state of the secondary star in the local coordinate system of the primary star.

[0008] The least squares method was used to fit the relative motion of the slave star in the y-axis, the x-axis and y-axis components of the relative tilt vector, and the x-axis and y-axis components of the relative eccentricity vector in the local coordinate system of the master star. The average relative orbital elements were calculated based on the fitting results.

[0009] Based on the designed satellite formation configuration, the target's average relative orbital elements are obtained, and then the average relative orbital element deviation is obtained;

[0010] Correcting the mean relative orbital elements deviation is used to initialize or reconfigure satellite formation configurations.

[0011] Furthermore, the average relative orbital elements include the average relative inclination vector, the x-axis and y-axis components of the average relative eccentricity vector, and the average relative semi-major axis;

[0012] The target average relative orbital elements include the target average relative tilt vector, the x-axis and y-axis components of the target average relative eccentricity vector, and the target average relative semi-major axis.

[0013] Furthermore, the inertial frame states of the primary and secondary stars at various moments within a given time period are as follows: and ,in , The corresponding times are recorded as a time record matrix. T , ;

[0014] Convert the inertial coordinate state to orbital six-root numbers to obtain the orbital six-root numbers of the primary star at each time step. And the six roots of the star's orbit ,in , In the formula , , , , , and Let represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of the perigee, and true anomaly of the primary star at time i, respectively. , , , , , and Let represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of the perigee, and true anomaly of the follower star at time i, respectively.

[0015] according to and Calculate the relative eccentricity vector at each time point. x-axis components and y-axis components :

[0016] ,

[0017] Store the calculation results at different times and form a matrix. , ;

[0018] according to and Calculate the relative tilt vector at each time point. x-axis components and y-axis components :

[0019] ,

[0020] Store the calculation results at different times and form a matrix. , .

[0021] Furthermore, the x-axis and y-axis components of the relative tilt angle vector are fitted using the least squares method to extract the time recording matrix. T Calculate the orbital inclination and right ascension of the ascending node from the six orbital roots of the primary and secondary stars at different times, and calculate the x-axis and y-axis components of the average relative inclination vector, including:

[0022] use , The x-axis and y-axis components of the relative tilt angle vector are fitted using the least squares method in functional form to extract the time-recording matrix. T The orbital inclination of the primary and secondary stars at different times using the six-element number of their orbits. , Right ascension of ascending node , Calculate the x-axis component of the corresponding relative tilt angle vector. and the y-axis component of the relative tilt vector The values ​​are recorded in the matrix respectively. and Among them n The angular velocity of the main star's orbit;

[0023] Calculate the time record matrix TAt different times and Values ​​and record them in a matrix A In, the matrix A Each row contains three elements ;

[0024] According to the matrix , sum matrix A The constant can be obtained using the following formula. , , and , , :

[0025] ,

[0026] Furthermore, the x-axis and y-axis components of the average relative tilt vector are obtained as follows: , .

[0027] Furthermore, the x-axis and y-axis components of the relative eccentricity vector are fitted using the least squares method to extract the time-recording matrix. T The eccentricity and perigee argument of the orbital six roots of the primary and secondary stars at different times are used to calculate the x-axis and y-axis components of the average relative eccentricity vector, including:

[0028] use , The least squares method is used to fit the x-axis and y-axis components of the relative eccentricity vector in functional form to extract the time-recording matrix. T Eccentricity of the orbital six-root number of the primary and secondary stars at different times , and near-lunar point argument , Calculate the x-axis component of the corresponding relative eccentricity vector. and the y-axis component of the relative eccentricity vector The values ​​are recorded in the matrix respectively. and Among them n The angular velocity of the main star's orbit;

[0029] Calculate the time record matrix T At different times and Values ​​and record them in a matrix A In, where the matrix A Each row contains three elements ;

[0030] According to the matrix , sum matrix A The constant can be obtained using the following formula. , , and , , :

[0031] ,

[0032] Furthermore, the x-axis and y-axis components of the average relative eccentricity vector are obtained as follows: , .

[0033] Furthermore, based on the linearized expression of the relative motion in the y-direction, the relative motion of the slave star in the local coordinate system of the master star is fitted using the least squares method, and the time record matrix is ​​extracted. T The relative motion values ​​of the secondary star in the y-direction in the local coordinate system of the primary star at different times The average change in distance along the y-axis is calculated based on the relative motion relationship along the y-axis, and then the average relative semi-major axis is calculated, including:

[0034] use The linearized expression of the y-axis relative motion in functional form is used to fit the y-axis relative motion of the slave star in the local coordinate system of the master star using the least squares method, and the time record matrix is ​​extracted. T The relative motion values ​​in the y-direction at different times And recorded as a matrix Y By calculating the time record matrix T At different times and Values ​​and record them in a matrix A In, where the matrix A Each row contains four elements ,in n The angular velocity of the main star's orbit;

[0035] According to the matrix Y sum matrix A The constant can be obtained using the following formula. , , and :

[0036] ,

[0037] Based on the relative motion relationship in the y-direction Calculate the average change in distance in the y-direction Then the average relative semi-major axis is calculated. :

[0038] ,

[0039] In the formula, P The orbital period of the main star, k is the calculation period. Time intervals of the track, This represents the amplitude of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the constant deviation of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the coefficient of the long-term term of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This indicates the phase of the relative motion of the star in the x-direction within the local coordinate system of the primary star. This indicates the initial mean latitude argument of the primary star.

[0040] Furthermore, the average relative orbital element deviation includes the x-axis component of the average relative inclination vector deviation. and y-axis components x-axis component of the average relative eccentricity vector deviation and y-axis components and mean relative semi-major axis deviation ;

[0041] For a planar formation configuration, the target's average relative tilt vector is 0, therefore .

[0042] Furthermore, based on the average relative orbital element deviation, a four-pulse method is used for correction. The correction order is as follows: first, a normal pulse is used to correct the x-axis and y-axis components of the average relative tilt vector deviation; second, a radial pulse is used to correct the x-axis and y-axis components of the average relative eccentricity vector deviation; and finally, two tangential pulses are used to correct the average relative semi-major axis deviation.

[0043] Furthermore, it also includes determining the equations of motion of the secondary star relative to the primary star, including:

[0044] The relative orbital six-roots number, represented by a non-singular orbital six-root, is defined in the following form:

[0045] ,

[0046] In the formula, the subscript c represents the primary star, and the subscript d represents the secondary star. , , , , These represent the semi-major axis of the orbit, eccentricity, orbital inclination, right ascension of the ascending node, and argument of the perigee, respectively. u The argument of latitude is denoted by , and its value is . ,M For the angle of near point, Indicates the average relative semi-major axis, Indicates relative equal right axle. These represent the average relative eccentricity vectors. x-axis and y-axis components, These represent the average relative tilt angle vectors. The x-axis and y-axis components;

[0047] The equations of motion of the secondary star relative to the primary star are expressed using relative orbital elements:

[0048] ,

[0049] In the formula, x, y, and z are the position coordinates of the slave star in the local coordinate system of the master star. n The angular velocity of the main star's orbit. The initial mean latitude argument of the main star,

[0050] ,

[0051] In the formula, Indicates the semi-major axis of the primary star's orbit. This represents the amplitude of the relative motion of the secondary star in the x-direction within the local coordinate system of the primary star. This represents the constant deviation of the relative motion of the satellite in the x-direction within the local coordinate system of the primary star. This represents the amplitude of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the constant deviation of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the coefficient of the long-term term of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the amplitude of the relative motion of the satellite in the z-direction within the local coordinate system of the primary star. This indicates the phase of the relative motion of the star in the x-direction within the local coordinate system of the primary star. It represents the phase of the relative motion of the satellite in the z-direction within the local coordinate system of the primary star.

[0052] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the steps of a satellite formation configuration control method based on historical navigation information.

[0053] The present invention has at least the following beneficial effects:

[0054] The satellite formation configuration control method based on historical navigation information of the present invention performs least squares fitting solution based on historical navigation data, and calculates the average relative orbital elements of the slave satellites relative to the master satellites based on the fitting results, replacing the traditional method of converting instantaneous orbital elements into average orbital elements which is complex in modeling and cumbersome in derivation.

[0055] The least squares method was used to fit the relative motion of the slave star in the y-axis, the x-axis and y-axis components of the relative tilt vector, and the x-axis and y-axis components of the relative eccentricity vector in the local coordinate system of the master star. The data fitting process can extract global features of the data and allows for the loss of some information.

[0056] This method has low requirements for the navigation system and is also applicable to elliptical orbits, thus having practical engineering value. Attached Figure Description

[0057] To further illustrate the above and other advantages and features of the various embodiments of the present invention, a more specific description of the embodiments of the invention will be presented with reference to the accompanying drawings. It is to be understood that these drawings depict only typical embodiments of the invention and are therefore not intended to limit its scope. In the drawings, identical or corresponding parts will be indicated by identical or similar reference numerals for clarity.

[0058] Figure 1 A flowchart of a satellite formation configuration control method based on historical navigation information according to an embodiment of the present invention is shown.

[0059] Figure 2 A relative motion fitting diagram in the y-direction according to an embodiment of the present invention is shown.

[0060] Figure 3 A relative tilt angle vector fitting diagram is shown according to an embodiment of the present invention.

[0061] Figure 4 A relative eccentricity vector fitting diagram is shown according to an embodiment of the present invention.

[0062] Figure 5 A graph showing the change of the x-direction movement distance over time according to an embodiment of the present invention is shown.

[0063] Figure 6 A graph showing the change of the y-direction movement distance over time according to an embodiment of the present invention is shown.

[0064] Figure 7 A graph showing the change of the z-direction motion distance over time according to an embodiment of the present invention is shown. Detailed Implementation

[0065] It should be noted that the components in the accompanying drawings may be shown exaggerated for illustrative purposes and may not be to scale.

[0066] In this invention, the various embodiments are merely intended to illustrate the solutions of the invention and should not be construed as limiting.

[0067] In this invention, unless otherwise specified, the quantifiers “a” and “one” do not exclude scenarios involving multiple elements.

[0068] It should also be noted that, in the embodiments of the present invention, only a portion of the parts or components may be shown for clarity and simplicity. However, those skilled in the art will understand that, under the teachings of the present invention, the required parts or components can be added as needed for specific scenarios.

[0069] It should also be noted that within the scope of this invention, the terms "same", "equal", and "equal to" do not mean that the two values ​​are absolutely equal, but allow for a certain reasonable error. In other words, the terms also cover "substantially the same", "substantially equal", and "substantially equal to".

[0070] It should also be noted that in the description of this invention, the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not explicitly or implicitly suggest that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0071] Furthermore, the embodiments of the present invention describe the process steps in a specific order. However, this is only for the convenience of distinguishing each step, and is not a limitation on the order of each step. In different embodiments of the present invention, the order of each step can be adjusted according to the process.

[0072] Figure 1 A flowchart of a satellite formation configuration control method based on historical navigation information according to an embodiment of the present invention is shown.

[0073] like Figure 1 As shown, a satellite formation configuration control method based on historical navigation information includes:

[0074] Step 1: Determine the equation of motion of the secondary star relative to the primary star.

[0075] The relative orbital six-roots number, represented by a non-singular orbital six-root, is defined in the following form:

[0076] ,

[0077] In the formula, the subscript c represents the primary star, and the subscript d represents the secondary star. , , , , These represent the semi-major axis of the orbit, eccentricity, orbital inclination, right ascension of the ascending node, and argument of the perigee, respectively. u The argument of latitude is denoted by , and its value is . , M For the angle of near point, Indicates the average relative semi-major axis, Indicates relative equal right axle. These represent the average relative eccentricity vectors. x-axis and y-axis components, These represent the average relative tilt angle vectors. The x-axis and y-axis components.

[0078] The equations of motion of the secondary star relative to the primary star are expressed using relative orbital elements:

[0079] ,

[0080] In the formula, x, y, and z are the position coordinates of the slave star in the local coordinate system of the master star. n The angular velocity of the main star's orbit. The initial mean latitude argument of the main star,

[0081] ,

[0082] In the formula, Indicates the semi-major axis of the primary star's orbit. This represents the amplitude of the relative motion of the secondary star in the x-direction within the local coordinate system of the primary star. This represents the constant deviation of the relative motion of the satellite in the x-direction within the local coordinate system of the primary star. This represents the amplitude of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the constant deviation of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the coefficient of the long-term term of the relative motion of the secondary star in the y-direction within the local coordinate system of the primary star. This represents the amplitude of the relative motion of the satellite in the z-direction within the local coordinate system of the primary star. This indicates the phase of the relative motion of the star in the x-direction within the local coordinate system of the primary star. It represents the phase of the relative motion of the satellite in the z-direction within the local coordinate system of the primary star.

[0083] Step 2: Obtain the orbital root numbers of the primary and secondary stars by state transformation from the inertial coordinate states of the primary and secondary stars at various times within a certain period of time. Calculate the x-axis and y-axis components of the relative inclination vector and the relative eccentricity vector between the secondary and primary stars at various times based on the orbital root numbers of the primary and secondary stars.

[0084] The navigation system obtains the inertial frame states of the primary and secondary stars at various moments within a given time period, as follows: and ,in , The corresponding time record is a time record matrix. T ( ).

[0085] Inertial coordinate state refers to the satellite's orbital state in an inertial coordinate system, which includes parameters such as position and velocity.

[0086] Convert the inertial coordinate state to orbital six-root numbers to obtain the orbital six-root numbers of the primary star at each time step. And the six roots of the star's orbit ,in , In the formula , , , , , and Let represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of the perigee, and true anomaly of the primary star at time i, respectively. ,in , , , , and Let represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of the perigee, and true anomaly of the follower star at time i, respectively.

[0087] according to and Calculate the relative eccentricity vector at the corresponding time. x-axis components and y-axis components :

[0088] ,

[0089] Store the calculation results at different times and form a matrix. , ;

[0090] according to and Calculate the relative tilt vector at each time point. x-axis components and y-axis components :

[0091] ,

[0092] Store the calculation results at different times and form a matrix. , .

[0093] Step 3: Transform the inertial coordinate states of the primary star and the secondary star at various moments within a certain period of time to obtain the relative state of the secondary star in the local coordinate system of the primary star, thereby obtaining the position and velocity state of the secondary star in the local coordinate system of the primary star.

[0094] The relative state of the slave star in the local coordinate system of the primary star is obtained by transforming the inertial coordinate states of the primary star and the slave star. In the formula The relative state includes the position and velocity state of the slave star in the local coordinate system of the master star.

[0095] Step 4: Use the least squares method to fit the relative motion of the slave star in the y-direction, the x-axis and y-axis components of the relative inclination vector, and the x-axis and y-axis components of the relative eccentricity vector in the local coordinate system of the master star, and calculate the average relative orbital elements based on the fitting results.

[0096] The average relative orbital elements include the average relative inclination vector, the x-axis and y-axis components of the average relative eccentricity vector, and the average relative semi-major axis.

[0097] The least squares method was used to fit the x-axis and y-axis components of the relative tilt vector, and the average x-axis and y-axis components of the relative tilt vector were calculated based on the fitting results. The least squares method was also used to fit the x-axis and y-axis components of the relative eccentricity vector, and the average x-axis and y-axis components of the relative eccentricity vector were calculated based on the fitting results. The least squares method was used to fit the relative motion of the slave star in the y-direction in the local coordinate system of the master star, and the average relative semi-major axis was calculated based on the fitting results.

[0098] Step 4.1: Perform least squares fitting on the x-axis and y-axis components of the relative tilt angle vector to extract the time recording matrix. T Calculate the orbital inclination and right ascension of the ascending node from the six orbital roots of the primary and secondary stars at different times, and calculate the x-axis and y-axis components of the average relative inclination vector, including:

[0099] use , The x-axis and y-axis components of the relative tilt angle vector are fitted using the least squares method in functional form to extract the time-recording matrix. T The orbital inclination of the primary and secondary stars at different times using the six-element number of their orbits. , Right ascension of ascending node , Calculate the x-axis component of the corresponding relative tilt angle vector. and the y-axis component of the relative tilt vector The values ​​are recorded in the matrix respectively. and middle;

[0100] Calculate the time record matrix T At different times and Values ​​and record them in a matrix A In, where the matrix A Each row contains three elements ;

[0101] According to the matrix , sum matrix A The constant can be obtained using the following formula. , , and , , :

[0102] ,

[0103] Furthermore, the x-axis and y-axis components of the average relative tilt vector are obtained as follows: , .

[0104] Step 4.2: Perform least squares fitting on the x-axis and y-axis components of the relative eccentricity vector to extract the time recording matrix. T Calculate the x-axis and y-axis components of the average relative eccentricity vector by taking the eccentricity and perigee argument of the orbital six roots of the primary and secondary stars at different times.

[0105] use , The least squares method is used to fit the x-axis and y-axis components of the relative eccentricity vector in functional form to extract the time-recording matrix. T Eccentricity of the orbital six-root number of the primary and secondary stars at different times , and near-lunar point argument , Calculate the x-axis component of the corresponding relative eccentricity vector. and the y-axis component of the relative eccentricity vector The values ​​are recorded in the matrix respectively. and In the middle. By calculating the time record matrix. T At different times and Values ​​and record them in a matrix A In, where the matrix A Each row contains three elements According to the matrix , sum matrix A The following formula can be used to obtain the result. , , and , , :

[0106] ,

[0107] Furthermore, the x-axis and y-axis components of the average relative eccentricity vector can be obtained as follows: , .

[0108] Step 4.3: Based on the linearized expression of the relative motion in the y-direction, perform least squares fitting on the relative motion in the y-direction of the slave star in the local coordinate system of the master star, and extract the time record matrix. T The relative motion values ​​of the secondary star in the y-direction in the local coordinate system of the primary star at different times The average change in distance in the y-direction is calculated based on the relative motion relationship in the y-direction, and then the average relative semi-major axis is calculated.

[0109] use The linearized expression of the y-axis relative motion in functional form is used to fit the y-axis relative motion of the slave star in the local coordinate system of the master star using the least squares method, and the time record matrix is ​​extracted. T The relative motion values ​​in the y-direction at different times And recorded as matrix Y, the time-recording matrix is ​​calculated. T At different times and Values ​​and record them in a matrix A In, where the matrix A Each row contains four elements Based on matrix Y and A The following formula can be used to obtain the result. , , and :

[0110] ,

[0111] Based on the relative motion relationship in the y-direction The average change in distance in the y-direction can be calculated. Therefore, the average relative semi-major axis can be calculated. :

[0112] ,

[0113] In the formula, P The orbital period of the main star, k is the calculation period. The time interval of the track.

[0114] Step 5: Based on the designed satellite formation configuration, obtain the target average relative orbital elements and the average relative orbital element deviation.

[0115] For different satellite formation configurations, the corresponding average relative orbital elements of the target may be different. By selecting the satellite formation configuration, the average relative orbital elements of the target can be determined.

[0116] The target average relative orbital elements include the target average relative tilt vector, the x-axis and y-axis components of the target average relative eccentricity vector, and the target average relative semi-major axis.

[0117] The mean relative orbital element deviation includes the x-axis component of the mean relative inclination vector deviation. and y-axis components x-axis component of the average relative eccentricity vector deviation and y-axis components and mean relative semi-major axis deviation .

[0118] For a planar formation configuration, the target's average relative tilt vector is 0, therefore we have .

[0119] Step 6: Correct the average relative orbital element deviation to initialize or reconstruct the satellite formation configuration. Specifically, a four-pulse method is used to correct the x-axis and y-axis components of the average relative inclination vector deviation, the x-axis and y-axis components of the average relative eccentricity vector deviation, and the average relative semi-major axis deviation to initialize or reconstruct the satellite formation configuration.

[0120] A four-pulse method is used for correction, with the following order: first, a normal pulse is used to correct the x-axis and y-axis components of the average relative tilt vector deviation; second, a radial pulse is used to correct the x-axis and y-axis components of the average relative eccentricity vector deviation; and finally, two tangential pulses are used to correct the average relative semi-axis deviation. The correction pulse magnitudes and control phases are as follows:

[0121] ,

[0122] in, The normal pulse size, Radial pulse size, The pulse size for the first tangential correction. The pulse size for the second tangential correction. The argument of the primary star at the mean latitude when the normal pulse is applied. The radial pulse is the argument of the primary star at its mean latitude. The semi-major axis of the primary star's orbit, The orbital angular velocity of the main star.

[0123] The four-pulse correction precisely corrects the three core parameters that determine the configuration: relative inclination vector, relative eccentricity vector, and relative semi-major axis. This ensures that the corrected orbital elements perfectly match the relative orbital elements of the target satellite formation configuration. This correction process can directly achieve the initialization or reconstruction of the satellite formation configuration.

[0124] For planar formation configurations, the theoretical value of the average relative inclination vector is 0. When the average relative inclination vector is not 0, it indicates a deviation, which is the average relative inclination vector deviation. This deviation is the average relative inclination vector deviation.

[0125] The satellite formation configuration control method of the present invention mainly comprises the following three parts:

[0126] 1) Historical navigation data processing

[0127] Based on the inertial coordinate states of the primary and secondary stars recorded at different times, the orbital six roots are obtained through state transformation, and the relative eccentricity vector and relative inclination vector between the secondary and primary stars at the corresponding times are calculated. The relative state of the secondary star in the primary star's LVLH coordinate system is then obtained from the inertial coordinate states of the primary and secondary stars.

[0128] 2) Solving for the average relative orbital element deviation using least squares fitting

[0129] The least squares method was used to fit the relative motion in the y-direction, the relative eccentricity vector, and the relative tilt vector, respectively. The average relative semi-major axis can be obtained by further solving the linearized expression of the relative motion in the y-direction. The average relative eccentricity vector and the average relative tilt vector are directly obtained from the constant terms of the fitting results.

[0130] 3) Correction for relative orbital element deviation

[0131] Based on the obtained average relative orbital elements and the target average relative orbital elements, the correction amount can be obtained. , , , and The four-pulse method is used to correct the average relative tilt vector deviation, the average relative eccentricity vector deviation, and the average relative semi-axis deviation in sequence.

[0132] The satellite formation configuration control method of this invention is designed for satellite formations with poor navigation accuracy or incomplete navigation information. It can obtain the average relative orbital element deviation of the formation satellites by fitting historical navigation data, replacing the traditional method of converting instantaneous orbital elements to average orbital elements, which is complex in modeling and cumbersome in derivation. This allows for formation control based on the relative orbital element deviation. The method is also applicable to elliptical orbit formations.

[0133] Figure 2 A relative motion fitting diagram in the y-direction according to an embodiment of the present invention is shown. Figure 3 A relative tilt angle vector fitting diagram is shown according to an embodiment of the present invention. Figure 4 A relative eccentricity vector fitting diagram is shown according to an embodiment of the present invention. Figure 5 A graph showing the change of the x-direction movement distance over time according to an embodiment of the present invention is shown. Figure 6 A graph showing the change of the y-direction movement distance over time according to an embodiment of the present invention is shown. Figure 7 A graph showing the change of the z-direction motion distance over time according to an embodiment of the present invention is shown.

[0134] The method of this invention can achieve configuration maintenance and reconfiguration control of elliptical orbit satellite formations based on historical navigation information.

[0135] Taking the initialization and reconstruction of a linear formation configuration at an altitude of 300km on the moon as an example, it is necessary to initialize a linear formation configuration with the main star in front and the follower stars behind at a distance of 110km, and then reconstruct the configuration with a distance from 110km to 20km after initialization.

[0136] The initial orbital six-root parameters for the primary and secondary stars:

[0137] Main Star: , , , , , ;

[0138] From the stars: , , , , , .

[0139] Considering the inertial state, the position navigation error is [1.867, 2.067, 1.767] km (3σ), and the velocity navigation error is [1.6e-3, 1.8e-3, 1.6e-3] km / s (3σ). The least squares fitting method is used to fit the relative y-axis motion, relative tilt vector, and relative eccentricity vector calculated under the navigation states of the primary and secondary stars. The fitting results are... Figures 2 to 4 As shown. From Figures 2 to 4 It can be seen that the fitted values ​​of the relative motion in the y-direction are relatively close to the actual values, and the fitted average values ​​of the relative tilt vector and the relative eccentricity vector are also relatively close to the actual values. This indicates that even with large navigation errors, the least squares fitting method can still obtain relatively accurate average motion information.

[0140] Based on the configuration requirements of linear formation, the target's average relative tilt vector is: The target average relative eccentricity vector is By combining the above fitting results to obtain the current average relative orbital element deviation, the required correction amount can be determined. A four-pulse correction method was used for linear formation initialization at a distance of 110 km and configuration reconstruction at a distance of 20 km, with the following results: Figures 5 to 7 As shown. From Figures 5 to 7 It can be seen that during the initialization of the formation at a distance of 110km, corrections were made for the relative tilt vector deviation, relative eccentricity vector deviation, and relative semi-major axis deviation.

[0141] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the steps of a satellite formation configuration control method based on historical navigation information.

[0142] While some embodiments of the present invention have been described in this application, those skilled in the art will understand that these embodiments are merely illustrative. Numerous variations, alternatives, and improvements will arise in those skilled in the art under the teachings of this invention without departing from its scope. The appended claims are intended to define the scope of the invention and thereby cover methods and structures within the scope of the claims themselves and their equivalents.

Claims

1. A satellite formation configuration control method based on historical navigation information, characterized by, The inertial coordinate state of the primary satellite and the slave satellite at each time point in a period of time is converted by state transition to obtain the orbital six elements of the primary satellite and the slave satellite, and the x-axis and y-axis components of the relative inclination vector and the x-axis and y-axis components of the relative eccentricity vector of the slave satellite relative to the primary satellite at each time point are calculated according to the orbital six elements of the primary satellite and the slave satellite, wherein: The relative motion of the slave satellite in the y direction of the local coordinate system of the primary satellite, the x-axis and y-axis components of the relative inclination vector, and the x-axis and y-axis components of the relative eccentricity vector are fitted by using the least square method, and the average relative orbital elements are calculated based on the fitting results, wherein: The inertial system states of the master star and the slave star at various time instants within a period of time are respectively and wherein , The corresponding time instants are recorded as a time instant recording matrix T , ; Convert the inertial coordinate state into the orbital elements to obtain the orbital elements of the primary star at each time and the orbital elements of the secondary star wherein , , in the formula , , , , , and respectively represent the orbital semi-major axis, eccentricity, orbital inclination, longitude of the ascending node, argument of perigee and true anomaly of the primary star at the i-th time; , , , , , and respectively represent the orbital semi-major axis, eccentricity, orbital inclination, longitude of the ascending node, argument of perigee and true anomaly of the secondary star at the i-th time; According to and the x-axis component of the relative eccentricity vector and the y-axis component of the relative eccentricity vector at each instant of time : ， Storing and forming a matrix of the calculation results at different times , ; According to and the x-axis component of the relative tilt vector and the y-axis component of the relative tilt vector at each time instant : ， The calculation results at different times are stored and form a matrix , ; the inertial coordinate state of the primary star and the slave star at each time in a period of time is converted through the coordinate system to obtain the relative state of the slave star in the local coordinate system of the primary star, so as to obtain the position and speed state of the slave star in the local coordinate system of the primary star; According to the designed satellite formation configuration, the target average relative orbital elements are obtained, and then the average relative orbital element deviation is obtained; The x-axis and y-axis components of the relative inclination vector are fitted by least square method to extract the time record matrix T The orbit inclination and the ascending node right ascension of the primary star and the secondary star in the orbit elements at different moments are calculated to obtain the x-axis component and the y-axis component of the average relative inclination vector, including: Adopting , function form respectively to the x axis, y axis component of relative inclination vector carries on least square method fitting, extracts the time record matrix T under different time in the orbit inclination in the orbit six root number of main star and satellite star , and ascending node right ascension , , calculates the x axis component of corresponding relative inclination vector And the y axis component of relative inclination vector Value, and records to matrix And respectively, wherein n It is the orbit angular velocity of main star motion. By calculating the time record matrix T at different times and values and record to the matrix A , wherein the matrix A each row includes three elements ; According to the matrix , and the matrix A , the constants , , and , , can be obtained by the following equations: ， Further, the x-axis and y-axis components of the average relative inclination vector are respectively , ; The average relative orbital element deviation is corrected to initialize or reconstruct the satellite formation configuration. The average relative orbital elements include the average relative inclination vector, the x-axis and y-axis components of the average relative eccentricity vector, and the average relative semi-major axis; 2. The method of controlling formation of satellites in accordance with claim 1, wherein, The target average relative orbital elements include the target average relative inclination vector, the x-axis and y-axis components of the target average relative eccentricity vector, and the target average relative semi-major axis. According to the average relative orbital element deviation, the four-pulse method is used for correction, and the correction sequence is as follows: first, the x-axis and y-axis components of the average relative inclination vector deviation are corrected by using the normal pulse, second, the x-axis and y-axis components of the average relative eccentricity vector deviation are corrected by using the radial pulse, and finally, the average relative semi-major axis deviation is corrected by using two tangential pulses.

3. The method of controlling formation of satellites in accordance with claim 1, wherein, The x-axis and y-axis components of the relative eccentricity vector are fitted by least squares to extract the time record matrix T The eccentricity and the argument of perigee of the primary star and the secondary star at different times are calculated, and the x-axis component and the y-axis component of the average relative eccentricity vector are calculated, including: Adopting , function form respectively to the x axis, y axis component of relative eccentricity vector carries on least square method fitting, extracts the eccentricity in the primary star and the secondary star's orbit six roots in the time record matrix T under different time , and perigee amplitude angle , , calculates the x axis component of corresponding relative eccentricity vector And the y axis component of relative eccentricity vector Value, and records to matrix And respectively, wherein n It is the orbit angular velocity of primary star motion; By calculating the time record matrix T at different times and values and record to the matrix A , wherein the matrix A each row of the matrix includes three elements ; According to the matrix , and the matrix A , the constants , , and , , can be obtained by the following equations: , and further obtaining x-axis and y-axis components of the average relative eccentricity vector as , .

4. The method of controlling formation of satellites in accordance with claim 1, wherein, The y-direction relative motion of the satellite in the local coordinate system of the main satellite is least square fitted based on the linearized expression of the y-direction relative motion, and a time record matrix is extracted T The y-direction relative motion values of the satellite in the local coordinate system of the main satellite at different moments The average change amount of the y-direction distance is calculated according to the y-direction relative motion relationship, and then the average relative semi-major axis is calculated. Adopting The y-direction relative motion linearization expression in the function form carries out least square fitting on the y-direction relative motion of the satellite in the local coordinate system of the main satellite, extracts the time record matrix T The y-direction relative motion values at different times in the matrix And records as the matrix Y The values of T and at different times in the time record matrix are calculated and recorded into the matrix A , wherein each row of the matrix A includes four elements , wherein n is the orbit angular velocity of the main satellite According to the matrix Y and the matrix A , the constant , , and can be obtained by the following formula ， According to the relative motion relationship in the y direction Calculate the average change of the y direction distance , and then calculate the average relative semi-major axis : ， wherein P is the primary star orbital period, k is the computed interval orbit number, represents the y-direction relative motion amplitude of the secondary star in the primary star local coordinate system, represents the y-direction relative motion constant bias of the secondary star in the primary star local coordinate system, represents the y-direction relative motion long-term term coefficient of the secondary star in the primary star local coordinate system, represents the x-direction relative motion phase of the secondary star in the primary star local coordinate system, represents the initial amplitude of the primary star's declination.

5. The method of controlling formation of a satellite constellation based on historical navigation information according to claim 2, wherein, The average relative orbit root mean square deviation comprises the x-axis component of the average relative inclination vector deviation and the y-axis component , the x-axis component of the average relative eccentricity vector deviation and the y-axis component and the average relative semi-major axis deviation ; For the planar formation configuration, the target average relative inclination vector is 0, so .

6. The method of controlling formation of a satellite constellation based on historical navigation information according to claim 5, wherein, It also includes determining the motion equation of the slave satellite relative to the primary satellite, including:

7. The method of controlling formation of a satellite constellation based on historical navigation information according to claim 1, wherein, The relative orbital six elements expressed in the form of non-singular orbital six elements are defined as follows: The motion equation of the slave satellite relative to the primary satellite is expressed by using the relative orbital elements: ， wherein the subscript c denotes the primary star and the subscript d denotes the secondary star, , , , , denote the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the argument of perigee, respectively, u is the argument of the latitude, which has the value , M is the mean anomaly, denotes the mean relative semi-major axis, denotes the relative mean anomaly, denote the x-axis, y-axis components of the mean relative eccentricity vector , denote the x-axis, y-axis components of the mean relative inclination vector .

8. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the satellite formation configuration control method based on historical navigation information according to any one of claims 1-7. ， where x, y, z are the position coordinates of the satellite in the local coordinate system of the primary satellite, n is the angular velocity of the orbit of the primary satellite, is the initial azimuth of the primary satellite's latitude ， wherein a denotes the semi-major axis of the orbit of the primary star, denotes the amplitude of the x-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the constant offset of the x-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the amplitude of the y-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the constant offset of the y-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the long-term coefficient of the y-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the amplitude of the z-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the phase of the x-wise relative motion of the secondary star in the local coordinate system of the primary star, denotes the phase of the z-wise relative motion of the secondary star in the local coordinate system of the primary star. ​

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