A satellite formation configuration control method based on inter-satellite measurement information

Abstract

This invention relates to a satellite formation configuration control method based on inter-satellite measurement information, comprising: obtaining the distance and orientation information of each slave satellite in the local coordinate system of the host satellite, and directly calculating the position vector information of the slave satellites relative to the host satellite based on geometric relationships; performing data fitting processing on the position vector information of the slave satellites relative to the host satellite, and calculating the average relative orbital elements by combining the relative motion equations of the slave satellites relative to the host satellite; determining the target average relative orbital elements based on the target satellite formation configuration, and determining the average relative orbital element deviation based on the average relative orbital elements and the target average relative orbital elements; and correcting the average relative orbital element deviation, thereby regulating the long-term relative motion amplitude and orbital trajectory of the slave satellites relative to the host satellite in and out of the orbital plane, and performing configuration maintenance and reconstruction control of the satellite formation. The satellite formation configuration control method of this invention can be applied to satellite formations without navigation systems.

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 inter-satellite measurement information. Background Technology

[0002] Satellite formations can overcome the limitations of single satellites to achieve functions that are difficult to accomplish using traditional methods, playing an increasingly important and irreplaceable role in several key areas. Satellite formations need to overcome the influence of complex orbital perturbations and space environment disturbances to ensure relative stability of inter-satellite positions. Furthermore, they must possess the ability to autonomously and flexibly switch between different space configurations in orbit to adapt to diverse mission requirements. Therefore, maintaining and reconfiguring satellite formation configurations is the core key to realizing the enormous potential of satellite formation technology and achieving complex space mission objectives. Currently, satellite formation configuration maintenance and reconfiguration are mainly based on navigation information control. One existing method is to adopt a progressive control approach to achieve lunar highly elliptical orbit formation flight control, taking into account the impact of navigation errors. Another method is InSAR satellite formation configuration maintenance control, which considers relative navigation errors. However, for satellite formations without a navigation system or with an unstable navigation system, control methods based on navigation information are no longer applicable. Summary of the Invention

[0003] To address at least some of the problems mentioned above in the prior art, the present invention provides a satellite formation configuration control method based on inter-satellite measurement information, comprising the following steps:

[0004] The distance and orientation information of each slave star is measured by the primary star to obtain the distance and orientation information of each slave star in the local coordinate system of the primary star, and the position vector information of the slave star relative to the primary star is directly calculated based on the geometric relationship;

[0005] The position vector information of the secondary star relative to the primary star is subjected to data fitting processing, and the average relative orbital elements are calculated by combining the relative motion equations of the secondary star relative to the primary star.

[0006] The target average relative orbital elements are determined based on the target satellite formation configuration, and the average relative orbital element deviation is determined based on the average relative orbital elements and the target average relative orbital elements; and

[0007] By correcting the mean relative orbital element deviation, the long-term relative motion amplitude and orbital trajectory of the satellite relative to the host satellite within and outside the orbital plane are controlled, thereby maintaining and reconfiguring the satellite formation configuration.

[0008] Furthermore, it also includes determining the equations of motion of the secondary star relative to the primary star, including:

[0009] The non-singular orbital elements are defined as:

[0010] ,

[0011] In the formula, and These are the two components of the eccentricity vector. u The angle of latitude. , , , , and These represent the satellite's semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and mean perigee, respectively.

[0012] definition This represents the six-element number of the relative orbit of the secondary star to the primary star, according to the definition of non-singular orbital elements. It can be represented in the following form:

[0013] ,

[0014] In the formula, the subscript c Indicates the primary star, subscript d Indicates from the star, Indicates the average relative semi-major axis, Indicates relative equal right axle. Represents the average relative eccentricity vector x-axis and y-axis components, Represents the average relative tilt vector The x-axis and y-axis components;

[0015] The equations of motion of the star relative to the primary star are expressed in the form of six relative orbital roots:

[0016] ,

[0017] In the formula, n The angular velocity of the main star's orbit. The initial mean latitude argument of the main star, t Let x, y, and z be the time, and x, y, and z be the position coordinates of the slave star in the local coordinate system of the master star.

[0018] ,

[0019] in, 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 long-term relative motion coefficient of the orbital trajectory of the secondary star in 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.

[0020] Furthermore, when the distance between the secondary star and the primary star is measured in the primary star's LVLH coordinate system... L and direction information At that time, the position vector of the secondary star relative to the primary star can be directly calculated based on geometric relationships, as shown in the following formula:

[0021] ,

[0022] Through multiple measurements, a series of positional information of the secondary star relative to the primary star was obtained, and this information was stored as a positional data matrix. The x-axis motion data matrix y-axis motion data matrix z-axis motion data matrix The times corresponding to the measured data are recorded as a time record matrix T. .

[0023] Furthermore, the average relative orbital elements include the x-axis and y-axis components of the average relative inclination vector and the average relative eccentricity vector, as well as the average relative semi-major axis;

[0024] The position vector information of the secondary star relative to the primary star is subjected to data fitting processing, and combined with the relative motion equations of the secondary star relative to the primary star, the average relative orbital elements are calculated, including:

[0025] The least-squares fit is performed on the z-axis motion data matrix Z and the time record matrix T of the slave star relative to the master star, and the average relative tilt vector is calculated by combining the z-axis motion expression in the equation of motion of the slave star relative to the master star.

[0026] Least square fitting is performed on the x-axis motion data matrix X and the time record matrix T of the slave star relative to the master star, and the x-axis and y-axis components of the average relative eccentricity vector are calculated by combining the x-axis motion expression in the equation of motion of the slave star relative to the master star.

[0027] The least-squares fit is performed on the y-axis motion data matrix Y and the time record matrix T of the slave star relative to the master star, and the average relative semi-major axis is calculated by combining the y-axis motion expression in the equation of motion of the slave star relative to the master star.

[0028] Furthermore, least-squares fitting is performed on the z-axis motion data matrix Z and the time record matrix T of the slave star relative to the master star, and the average relative tilt vector is calculated by combining the z-axis motion expression in the equation of motion of the slave star relative to the master star, including:

[0029] use The least-squares fit is performed on the z-axis motion data matrix Z and the time record matrix T of the satellite relative to the host star in functional form;

[0030] Based on the z-direction motion expression in the equation of motion of the secondary star relative to the primary star The following correspondence was obtained:

[0031] ,

[0032] according to When the relative motion amplitude in the z-direction Given the value, the mean relative tilt angle vector magnitude can be obtained by solving. ;

[0033] Least-squares fitting is performed on the x-axis motion data matrix X and the time record matrix T of the secondary star relative to the primary star. The x-axis and y-axis components of the average relative eccentricity vector are then calculated using the x-axis motion expression in the secondary star's equation of motion relative to the primary star.

[0034] use The least-squares fit is performed on the x-axis motion data matrix X and the time record matrix T of the secondary star relative to the primary star in functional form, resulting in the x-axis motion expression. The corresponding relationships are as follows:

[0035] ,

[0036] according to , The expression yields:

[0037] ,

[0038] when , semi-major axis of primary star orbit Initial mean latitude argument of the primary star Given the values, determine the x-axis and y-axis components of the average relative eccentricity vector. , :

[0039] .

[0040] Furthermore, least-squares fitting is performed on the y-axis motion data matrix Y and the time record matrix T of the secondary star relative to the primary star, and the average relative semi-major axis is calculated by combining the y-axis motion expression in the equation of motion of the secondary star relative to the primary star, including:

[0041] use The least-squares fit is performed on the y-axis motion data matrix Y of the slave star relative to the master star and the time record matrix T in functional form;

[0042] Based on the expression for relative motion in the y-direction The following correspondence was obtained:

[0043] ,

[0044] Calculate the y-direction distance at the same latitude argument of track interval k based on the relative motion relationship in the y-direction:

[0045] ,

[0046] In the formula, P is the orbital period of the principal star. , k For calculation Time intervals of the track, n The angular velocity of the main star's orbit. This represents the initial time of the y-axis fitting. express Moment y Towards the average motion value, express Moment y Towards the average motion value;

[0047] according to , The average change in motion in the y-direction is calculated as follows:

[0048] ;

[0049] The average relative semi-major axis is obtained from the above formula. :

[0050] ;

[0051] The average relative semi-major axis deviation is obtained based on the corresponding relationship. :

[0052] .

[0053] Furthermore, 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;

[0054] The average relative orbital element deviation includes the x-axis and y-axis components of the average relative inclination vector deviation, the average relative eccentricity vector deviation, and the average relative semi-major axis deviation.

[0055] Furthermore, the four-pulse method is used to correct the average relative inclination vector deviation in the average relative orbital element deviation, thereby controlling the relative motion amplitude of the slave star relative to the master star outside the orbital plane, including:

[0056] When adjusting the relative motion amplitude of the slave star to the master star outside its orbital plane, the x-axis component of the average relative tilt vector deviation is used as the normal pulse. and y-axis components Corrections are made to regulate the out-of-plane relative motion amplitude of the slave star relative to the master star. The formulas for calculating the normal pulse magnitude and the applied control phase are as follows:

[0057] ,

[0058] in, Indicates the magnitude of the normal phase pulse. Indicates the application of control phase, This represents the angular velocity of the primary star's orbit. This represents the amplitude of relative motion in the z-direction. It represents the phase of the relative motion of the satellite in the z-direction within the local coordinate system of the primary star.

[0059] Furthermore, the four-pulse method is used to correct the average relative eccentricity vector deviation in the average relative orbital element deviation, thereby controlling the relative motion amplitude of the slave star relative to the master star within the orbital plane, including:

[0060] When adjusting the relative motion amplitude of the slave star within the orbital plane of the master star, the radial pulse is used to measure the x-axis component of the relative eccentricity vector deviation. and y-axis components Corrections are made to regulate the amplitude of the relative motion between the slave star and the master star within their orbital plane. The formulas for calculating the radial pulse magnitude and the applied control phase are as follows:

[0061] ,

[0062] in, Indicates the radial pulse size. Indicates the application of control phase, This represents the angular velocity of the primary star's orbit. This represents the semi-major axis of the primary star's orbit.

[0063] Furthermore, the four-pulse method is used to correct the average relative semi-major axis deviation in the average relative orbital element deviation, thereby controlling the long-term relative motion of the satellite's orbital trajectory relative to the host star, including:

[0064] When controlling the long-term relative motion of the orbital trajectory, the average relative semi-major axis deviation is adjusted independently without changing the average relative eccentricity vector. The average relative semi-major axis deviation is corrected using two tangential pulses, with the phases of the two pulse corrections being... and The jet volume and jet direction are the same for both tangential pulse corrections. The formula for calculating the magnitude of the tangential pulse corresponding to a single jet is as follows:

[0065] .

[0066] The present invention has at least the following beneficial effects:

[0067] The satellite formation configuration control method of this invention is applicable to satellite formations without navigation systems. Utilizing the stable, high-precision, and high-frequency characteristics of inter-satellite ranging and angular measurement, the method directly calculates the position vector information of the slave satellite relative to the host satellite using inter-satellite ranging and angular measurement information. Data fitting processing is performed on the position vector information of the slave satellite relative to the host satellite, and combined with the relative motion equations of the slave satellite relative to the host satellite, the average relative orbital elements are calculated. Based on the average relative orbital elements and the target average relative orbital elements, the deviation of the average relative orbital elements is determined, and then corrected using a four-pulse method. This allows for the long-term relative motion amplitude and orbital trajectory of the slave satellite relative to the host satellite within and outside the orbital plane, enabling configuration maintenance and reconfiguration control of the satellite formation. This method is applicable to satellite formations without navigation systems or with unstable navigation systems and has practical engineering application value. Attached Figure Description

[0068] 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.

[0069] Figure 1 A flowchart of a satellite formation configuration control method based on inter-satellite measurement information according to an embodiment of the present invention is shown.

[0070] Figure 2 A graph showing the relative semi-major axis actual value and average value over time is shown according to an embodiment of the present invention.

[0071] Figure 3 The diagram shows the actual value and average value of the relative eccentricity vector over time, according to an embodiment of the present invention.

[0072] Figure 4The actual value and average value-time variation of the relative tilt vector magnitude are shown according to an embodiment of the present invention.

[0073] Figure 5 A graph showing the x-direction movement distance as a function of time during formation configuration initialization according to an embodiment of the present invention is shown.

[0074] Figure 6 A graph showing the change of the y-direction movement distance over time during formation configuration initialization according to an embodiment of the present invention is shown.

[0075] Figure 7 The diagram shows the variation of the z-direction motion distance over time during formation initialization according to an embodiment of the present invention.

[0076] Figure 8 A graph showing the relative half-major axis-time variation of formation configuration initialization according to an embodiment of the present invention is shown.

[0077] Figure 9 A graph showing the relative eccentricity-time variation during formation configuration initialization according to an embodiment of the present invention is shown.

[0078] Figure 10 A graph showing the relative tilt angle-time variation during formation configuration initialization according to an embodiment of the present invention is shown.

[0079] Figure 11 A graph showing the relative ascending node right ascension-time variation for formation configuration initialization according to an embodiment of the present invention is shown.

[0080] Figure 12 A perigee argument-time variation diagram is shown for formation configuration initialization according to an embodiment of the present invention.

[0081] Figure 13 A graph showing the relative latitude angle versus time variation during formation configuration initialization according to an embodiment of the present invention is shown.

[0082] Figure 14 The diagram shows the variation of the x-direction movement distance maintained by the formation configuration according to an embodiment of the present invention over time.

[0083] Figure 15 A graph showing the change over time in the y-direction movement distance maintained by a formation configuration according to an embodiment of the present invention is shown.

[0084] Figure 16 The diagram shows the z-direction movement distance maintained by the formation configuration according to an embodiment of the present invention as a function of time. Detailed Implementation

[0085] It should be noted that the components in the accompanying drawings may be shown exaggerated for illustrative purposes and may not be to scale.

[0086] In this invention, the various embodiments are merely intended to illustrate the solutions of the invention and should not be construed as limiting.

[0087] In this invention, unless otherwise specified, the quantifiers “a” and “one” do not exclude scenarios involving multiple elements.

[0088] 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.

[0089] 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".

[0090] 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.

[0091] 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.

[0092] Figure 1 A flowchart of a satellite formation configuration control method based on inter-satellite measurement information according to an embodiment of the present invention is shown.

[0093] like Figure 1 As shown, a satellite formation configuration control method based on inter-satellite measurement information includes the following steps:

[0094] Step 1: The primary star measures the distance and orientation of the secondary stars to obtain the distance L and orientation information of each secondary star in the primary star's local coordinate system (primary star LVLH coordinate system). The position vector information of the secondary star relative to the primary star is obtained directly by solving the geometric relationship.

[0095] In the central celestial inertial coordinate system, the six orbital elements describing a satellite's position are defined as follows: , , , , and Let represent the satellite's semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and mean perigee, respectively. Considering the singularity caused by small eccentricities in circular or near-circular orbits, the non-singular orbital elements are defined as:

[0096] (1),

[0097] In the formula, and These are the two components of the eccentricity vector, where u is the horizontal latitude argument.

[0098] definition This represents the six-element number of the relative orbital path of the secondary star to the primary star, according to the definition of non-singular orbital elements mentioned above. It can be represented in the following form:

[0099] (2),

[0100] In the formula, the subscript c represents the primary star, and the subscript d represents the secondary star. Indicates the average relative semi-major axis, Indicates relative equal right axle. Represents the average relative eccentricity vector x-axis and y-axis components, Represents the average relative tilt vector The x-axis and y-axis components.

[0101] The equation of motion of the star relative to the primary star can be expressed in the form of the six roots of the relative orbit as follows:

[0102] (3),

[0103] In the formula, n The angular velocity of the main star's orbit. The initial mean latitude argument of the main star, t Let x, y, and z be the time, and x, y, and z be the position coordinates of the slave star in the LVLH coordinate system of the primary star.

[0104] (4),

[0105] in, 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 long-term relative motion coefficient of the orbital trajectory of the secondary star in 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.

[0106] When the distance L and direction information between the slave star and the primary star are measured in the primary star's local coordinate system at a fixed frequency, When the position vector of the secondary star relative to the primary star can be directly calculated based on geometric relationships, as shown in the following formula:

[0107] (5),

[0108] By taking multiple measurements, a series of positional information of the secondary star relative to the primary star can be obtained and stored as a positional data matrix. The x-axis motion data matrix y-axis motion data matrix z-axis motion data matrix The times corresponding to the measured data are recorded as a time record matrix T. .

[0109] Based on the stored data, the average relative orbital elements can be calculated.

[0110] Step 2: The least squares method is used to fit the position vector information of the secondary star relative to the primary star, and the average relative orbital elements are calculated by combining the relative motion equations of the secondary star relative to the primary star. The average relative orbital elements include the x-axis and y-axis components of the average relative inclination vector and the average relative eccentricity vector, as well as the average relative semi-major axis.

[0111] Step 2.1: Perform least-squares fitting on the z-axis motion data matrix Z and the time record matrix T of the slave star relative to the master star, and calculate the average relative tilt vector by combining the z-axis motion expression in the equation of motion of the slave star relative to the master star. The specific calculation is as follows:

[0112] use A least-squares fit is performed on the z-axis motion data matrix Z and the time record matrix T of the slave star relative to the master star in functional form. This is based on the z-axis motion expression in the equation of motion of the slave star relative to the master star. The following correspondence can be obtained:

[0113] (6),

[0114] according to When the relative motion amplitude in the z-direction Given the value, the magnitude of the average relative tilt vector deviation of out-of-plane quantities can be obtained by solving. .

[0115] Step 2.2 involves performing least-squares fitting on the x-axis motion data matrix Z and the time record matrix T of the slave star relative to the master star, and then calculating the x-axis and y-axis components of the average relative eccentricity vector using the x-axis motion expression in the equation of motion of the slave star relative to the master star. The specific calculation process is as follows:

[0116] use The least-squares fit is performed on the x-axis motion data matrix X and the time record matrix T of the secondary star relative to the primary star in functional form, resulting in the x-axis motion expression. The corresponding relationships can be obtained as follows:

[0117] (7),

[0118] according to , The expression yields:

[0119] (8),

[0120] when , semi-major axis of the primary star's orbit Initial mean latitude argument of the primary star When the values ​​are known, the x-axis and y-axis components of the average relative eccentricity vector can be obtained according to equations (7) and (8). , :

[0121] (9).

[0122] Step 2.3 involves performing least-squares fitting on the y-axis motion data matrix Y and the time record matrix T of the slave star relative to the master star, and then calculating the average relative semi-major axis using the y-axis motion expression in the equation of motion of the slave star relative to the master star. The specific calculation process is as follows:

[0123] use The least-squares fit is performed on the y-axis motion data matrix Y and the time record matrix T of the slave star relative to the master star in functional form, resulting in the y-axis relative motion expression. The following correspondence can be obtained:

[0124] (10)

[0125] Based on the relative motion relationship in the y-direction, the y-direction distance at the same latitude argument of track interval k is calculated as follows:

[0126] (11),

[0127] In the formula, P is the orbital period of the principal star. , k For calculation Time intervals of the track, n The angular velocity of the main star's orbit. This represents the initial time of the y-axis fitting. express Moment y Towards the average motion value, express Moment y Towards the average motion value.

[0128] according to , The average change in motion in the y-direction can be calculated:

[0129] (12);

[0130] The average semi-major axis can be obtained from the above formula. :

[0131] (13)

[0132] According to the correspondence of equation (10), the average relative semi-major axis can be obtained based on the fitting results. :

[0133] (14).

[0134] For a planar bounded linear formation configuration, the theoretical values ​​of the average relative semi-major axis, average relative inclination vector, and average relative eccentricity vector are all 0. When the average relative inclination vector is not 0, it indicates a deviation, specifically an average relative inclination vector deviation. In this case, the average relative inclination vector deviation is the mean relative inclination vector deviation. Ideally, the relative inclination vector deviation is 0, meaning the orbits of the secondary star and the primary star are coplanar. When the average relative semi-major axis is not 0, this mean relative semi-major axis deviation is the mean relative semi-major axis deviation. When the average relative eccentricity vector is not 0, this mean relative eccentricity vector deviation is the mean relative eccentricity vector deviation.

[0135] Step 3: Determine the target average relative orbital elements based on the target satellite formation configuration, and determine the average relative orbital element deviation based on the average relative orbital elements and the target average relative orbital elements.

[0136] For different satellite formation configurations, the corresponding target average relative orbital elements may be different. Once the satellite formation configuration is selected, the target average relative orbital elements can be determined. 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.

[0137] 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 .

[0138] For a planar formation configuration, the target's average relative tilt vector is 0, therefore we have .

[0139] Step 4: The four-pulse method is used to correct the average relative orbital element deviation, thereby controlling the long-term relative motion amplitude and orbital trajectory of the satellite relative to the host satellite within and outside the orbital plane, and performing configuration maintenance and reconstruction control of the satellite formation.

[0140] The four-pulse method is used to correct the x-axis and y-axis components of the average relative tilt vector deviation, the x-axis and y-axis components of the average relative eccentricity vector deviation, and the average relative semi-major axis deviation.

[0141] The specific correction process is as follows:

[0142] Step 4.1: When adjusting the amplitude of the out-of-plane (z-direction) relative motion of the slave star relative to the master star, the x-axis and y-axis components of the average relative tilt vector deviation are corrected by using the normal pulse, so as to adjust the amplitude of the out-of-plane relative motion of the slave star relative to the master star.

[0143] In other words, corrections can be made using a normal velocity increment (i.e., a pulse thrust along the Y-axis of the LVLH coordinate system (perpendicular to the primary star's orbital plane) at a specific latitude argument (control phase). The specific formulas for calculating the normal pulse size (velocity increment) and the applied control phase (latitude argument) are as follows:

[0144] (15)

[0145] in, Indicates the magnitude of the normal phase pulse. Indicates the application of control phase, This represents the angular velocity of the primary star's orbit. This represents the amplitude of relative motion in the z-direction. It represents the phase of the relative motion of the satellite in the z-direction within the local coordinate system of the primary star.

[0146] Step 4.2: When adjusting the relative motion amplitude of the slave star relative to the master star within the orbital plane (x, y directions), the x-axis component of the radial pulse average relative eccentricity vector deviation is used. and y-axis components Corrections are made to regulate the amplitude of the relative motion of the secondary star within the orbital plane of the primary star.

[0147] In other words, control is achieved through a radial velocity increment at a specific latitudinal argument (control phase). The specific formulas for calculating the radial pulse size (velocity increment size) and the latitudinal argument (control phase) at which control is applied are as follows:

[0148] (16)

[0149] in, Indicates the radial pulse size. Indicates the application of control phase, This represents the angular velocity of the primary star's orbit. This represents the semi-major axis of the primary star's orbit.

[0150] Step 4.3: When adjusting the long-term relative motion of the orbital trajectory, two tangential pulses are used to correct the average relative semi-major axis deviation in order to adjust the long-term relative motion of the orbital trajectory of the slave star relative to the master star.

[0151] When controlling the long-term relative motion of the trajectory, it is necessary to adjust the average relative semi-major axis deviation separately without changing the average relative eccentricity vector. This is achieved by correcting the average relative semi-major axis deviation using two tangential pulses. The phases of the jet propulsion during the two tangential pulse corrections are as follows: and The jet volume and direction are the same for both tangential pulse corrections. The velocity increment (tangential pulse magnitude) corresponding to a single jet is:

[0152] (17).

[0153] The satellite formation configuration control method of the present invention is mainly divided into three parts: ranging and angle measurement information calculation, average relative orbital elements calculation, and correction control pulse calculation.

[0154] 1) Calculation of distance and angle measurement information

[0155] By measuring the distance and orientation of the slave star at a fixed frequency from the primary star, the distance L and orientation information of the slave star in the LVLH coordinate system of the primary star are obtained. The position vector information of the secondary star relative to the primary star can be directly calculated based on geometric relationships.

[0156] 2) Calculation of the average relative orbital elements

[0157] Based on the position vector information obtained from geometric calculations, the relative motion characteristics along the x, y, and z axes are obtained through data fitting. Combining this with the relative motion equations of the secondary star relative to the primary star, the average relative orbital elements are analytically solved.

[0158] 3) Correction of control pulse calculation

[0159] The relative orbital element deviation is calculated based on the average relative orbital elements and the target average relative orbital elements. The average relative inclination vector deviation is corrected by applying a normal velocity increment at a specific latitude argument, thereby controlling the out-of-plane (z-axis) amplitude; the average relative eccentricity vector deviation is corrected by applying a radial velocity increment at a specific latitude argument, thereby controlling the in-plane (x, y-axis) amplitude; and the average relative semi-major axis deviation is adjusted independently without changing the relative eccentricity vector by applying two tangential pulses of the same magnitude but with a phase interval of half an orbital period.

[0160] Figure 2 A graph showing the relative semi-major axis actual value and average value over time is shown according to an embodiment of the present invention. Figure 3 The diagram shows the actual value and average value of the relative eccentricity vector over time, according to an embodiment of the present invention. Figure 4 The actual value and average value-time variation of the relative tilt vector magnitude are shown according to an embodiment of the present invention. Figure 5 A graph showing the x-direction movement distance as a function of time during formation configuration initialization 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 during formation configuration initialization according to an embodiment of the present invention is shown. Figure 7 The diagram shows the variation of the z-direction motion distance over time during formation initialization according to an embodiment of the present invention. Figure 8A graph showing the relative half-major axis-time variation of formation configuration initialization according to an embodiment of the present invention is shown. Figure 9 A graph showing the relative eccentricity-time variation during formation configuration initialization according to an embodiment of the present invention is shown. Figure 10 A graph showing the relative tilt angle-time variation during formation configuration initialization according to an embodiment of the present invention is shown. Figure 11 A graph showing the relative ascending node right ascension-time variation for formation configuration initialization according to an embodiment of the present invention is shown. Figure 12 A perigee argument-time variation diagram is shown for formation configuration initialization according to an embodiment of the present invention. Figure 13 A graph showing the relative latitude angle versus time variation during formation configuration initialization according to an embodiment of the present invention is shown. Figure 14 The diagram shows the variation of the x-direction movement distance maintained by the formation configuration according to an embodiment of the present invention over time. Figure 15 A graph showing the change over time in the y-direction movement distance maintained by a formation configuration according to an embodiment of the present invention is shown. Figure 16 The diagram shows the z-direction movement distance maintained by the formation configuration according to an embodiment of the present invention as a function of time.

[0161] The method of this invention can achieve configuration maintenance and reconfiguration control of satellite formations based on inter-satellite ranging and angular measurement information.

[0162] Taking the initialization and maintenance of a linear formation configuration at an altitude of 600km from Earth as an example, the mission requires that after the formation configuration is initialized, the slave star be kept about 10km behind the master star.

[0163] The initial orbital six-element parameters for the primary and secondary stars are as follows:

[0164] Main Star: , , , , , ;

[0165] From the stars: , , , , , .

[0166] Considering an inter-satellite ranging error of 3m (3σ) and an angle measurement error of 5 arcseconds (3σ), inter-satellite ranging and angle measurement are performed every 5 seconds in the primary star's LVLH coordinate system, and the data from the first two control orbits are accumulated. The time-position data (TX, Y, Z) of the satellite relative to the primary star are directly calculated based on geometric relationships. The relative motions in the x, y, and z directions are fitted, and the average relative orbital elements are analytically obtained from the fitting results. Figures 2-4 As shown. From Figures 2-4 As can be seen from the results, the accuracy of analytically solving the average relative orbital elements based on the fitting results of the multi-point solution information of relative motion is relatively high.

[0167] The formation configuration initialization result is obtained based on the average relative orbital elements obtained from the solution, as follows: Figures 5-7 As shown. From Figures 5-7 As can be seen, the initialization results accurately control the inter-satellite distance to around 10km and suppress the oscillations in the x, y, and z directions of relative motion.

[0168] The changes in the relative orbital elements during the corresponding initialization process are as follows: Figures 8-13 As shown. From Figures 8-13 As can be seen from the process, the relative orbital elements were controlled to be near the target value through the initialization process.

[0169] After the formation configuration was initialized, the configuration was maintained with the primary star in front and the secondary stars behind, spaced 10 km apart. The result is as follows. Figures 14-16 As shown. From Figures 14-16 As can be seen from the results, the control results can maintain the inter-satellite distance at around 10km.

[0170] 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 inter-satellite measurement information, characterized by, The method comprises the following steps: The distance and direction information of the slave stars relative to the master star are measured, and the distance and direction information of each slave star in the local coordinate system of the master star is obtained, and the position vector information of the slave star relative to the master star is directly calculated according to the geometric relationship; through multiple measurements, a series of position information of the slave star relative to the master star is obtained, and the position information is stored as a position data matrix , the x-direction motion data matrix , the y-direction motion data matrix , the z-direction motion data matrix The time corresponding to the measurement data is recorded as a time record matrix T, ; determining the motion equation of the satellite relative to the main satellite, comprising: defining the non-singular orbital elements as: ， wherein and are respectively two components of the eccentricity vector, u is the argument of the latitude, , , , , and denote respectively the semi-major axis of the satellite's orbit, the eccentricity, the inclination, the right ascension of the ascending node, the argument of the perigee and the mean anomaly. Definitions denotes the relative orbital elements of the satellite with respect to the primary satellite, defined in terms of non-singular orbital elements, denotes the form ， wherein the subscript c denotes the primary star, and the subscript d denotes the secondary star, denotes the mean relative semi-major axis, denotes the relative equatorial radius, denotes the x-axis, y-axis components of the mean relative eccentricity vector , denotes the x-axis, y-axis components of the mean relative inclination vector . expressing the motion equation of the satellite relative to the main satellite in the form of relative orbital elements: ， wherein n is the orbital angular velocity of the primary star, is the initial azimuth of the primary star's equator, t is time, x, y, z are the position coordinates of the secondary star in the primary star's local coordinate system, ， wherein, a denotes the semi-major axis of the orbit of the primary star, b denotes the amplitude of the x-wise relative motion of the secondary star in the local coordinate system of the primary star, c denotes the constant offset of the x-wise relative motion of the secondary star in the local coordinate system of the primary star, d denotes the amplitude of the y-wise relative motion of the secondary star in the local coordinate system of the primary star, e denotes the constant offset of the y-wise relative motion of the secondary star in the local coordinate system of the primary star, f denotes the long-term relative motion coefficient of the orbital trace of the secondary star in the local coordinate system of the primary star, g denotes the amplitude of the z-wise relative motion of the secondary star in the local coordinate system of the primary star, h denotes the phase of the x-wise relative motion of the secondary star in the local coordinate system of the primary star, i denotes the phase of the z-wise relative motion of the secondary star in the local coordinate system of the primary star; The position vector information of the satellite relative to the main satellite is subjected to data fitting processing, and the average relative orbit root number is calculated in combination with the relative motion equation of the satellite relative to the main satellite; the average relative orbit root number includes 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; the z-direction motion data matrix Z and the time record matrix T of the satellite relative to the main satellite are subjected to least square fitting in the function form, and the average relative inclination vector is calculated in combination with the z-direction motion expression in the motion equation of the satellite relative to the main satellite; the x-direction motion data matrix X and the time record matrix T of the satellite relative to the main satellite are subjected to least square fitting in the function form, and the x-axis and y-axis components of the average relative eccentricity vector are calculated in combination with the x-direction motion expression in the motion equation of the satellite relative to the main satellite; the y-direction motion data matrix Y and the time record matrix T of the satellite relative to the main satellite are subjected to least square fitting in the function form, and the average relative semi-major axis is calculated in combination with the y-direction motion expression in the motion equation of the satellite relative to the main satellite. The z-direction motion data matrix Z and the time record matrix T of the satellite relative to the main satellite are subjected to least square fitting in the function form, and the average relative inclination vector is calculated in combination with the z-direction motion expression in the motion equation of the satellite relative to the main satellite. The x-direction motion data matrix X and the time record matrix T of the satellite relative to the main satellite are subjected to least square fitting in the function form, and the x-axis and y-axis components of the average relative eccentricity vector are calculated in combination with the x-direction motion expression in the motion equation of the satellite relative to the main satellite. The y-direction motion data matrix Y and the time record matrix T of the satellite relative to the main satellite are subjected to least square fitting in the function form, and the average relative semi-major axis is calculated in combination with the y-direction motion expression in the motion equation of the satellite relative to the main satellite. determining the target average relative orbital elements according to the target satellite formation configuration, determining the average relative orbital element deviation based on the average relative orbital elements and the target average relative orbital elements; the average relative orbital element deviation comprises 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; and correcting the average relative orbital element deviation, so as to control the long-term relative motion of the relative motion amplitude and the orbital direction of the satellite relative to the main satellite, and perform the formation maintaining and reconstruction control of the satellite.

2. The satellite formation configuration control method based on inter-satellite measurement information according to claim 1, characterized by, When the distance between the slave star and the master star is measured in the master star LVLH coordinate system L and the direction information the position vector of the slave star relative to the master star is directly calculated according to the geometric relationship, as shown in the following formula: 。 3. The satellite formation configuration control method based on inter-satellite measurement information according to claim 2, characterized by, performing least square fitting on the z-direction motion data matrix Z of the satellite relative to the main satellite and the time record matrix T, and calculating the average relative inclination vector by combining the z-direction motion expression in the motion equation of the satellite relative to the main satellite, comprising: The function form is used to perform least square fitting on the z-direction motion data matrix Z of the satellite relative to the main satellite and the time record matrix T. The function form is used to perform least square fitting on the z-direction motion data matrix Z of the satellite relative to the main satellite and the time record matrix T. According to the z-direction movement expression from the movement equation of the satellite star relative to the main star The following correspondence is obtained: ， According to When the amplitude of the z-direction relative motion is known, the average relative inclination vector modulus is solved performing least square fitting on the x-direction motion data matrix X of the satellite relative to the main satellite and the time record matrix T, and calculating the x-axis and y-axis components of the average relative eccentricity vector by combining the x-direction motion expression in the motion equation of the satellite relative to the main satellite, comprising: use The least-squares fit is performed on the x-axis motion data matrix X and the time record matrix T of the secondary star relative to the primary star in functional form, resulting in the x-axis motion expression. The corresponding relationships are as follows: ， According to , The expression is obtained: ， When , , the semi-major axis of the primary's orbit and the initial argument of latitude of the primary are known, the x and y components of the mean relative eccentricity vector are found , : 。 4. The satellite formation configuration control method based on inter-satellite measurement information according to claim 2, characterized by, performing least square fitting on the y-direction motion data matrix Y of the satellite relative to the main satellite and the time record matrix T, and calculating the average relative semi-major axis by combining the y-direction motion expression in the motion equation of the satellite relative to the main satellite, comprising: Adopting The function form is least square fitted to the y direction movement data matrix Y of the satellite relative to the main satellite and the time record matrix T. According to the relative motion expression in the y direction The following correspondence is obtained: ， calculating the y-direction distance at the interval k orbit same latitude radial angle according to the y-direction relative motion relationship: ， where P is a primary star orbit period, , k is a calculated interval orbit order at time t, n is a primary star orbit angular velocity, denotes an initial time of y-direction fitting, denotes an average motion value in y-direction at time t, y denotes an average motion value in x-direction at time t, denotes y an average motion value in x-direction at time t; According to , The average motion change in the y direction is calculated: ； The average relative semi-major axis is obtained from the above formula : ； According to the correspondence, the average relative semi-major axis deviation is obtained : 。 5. The satellite formation configuration control method based on inter-satellite measurement information according to claim 2, characterized by, the target average relative orbital elements comprise the target average relative inclination vector, the x-axis component and the y-axis component of the target average relative eccentricity vector, and the target average relative semi-major axis.

6. The satellite formation configuration control method based on inter-satellite measurement information according to claim 5, characterized by, correcting the average relative inclination vector deviation in the average relative orbital element deviation by using the four-pulse method, so as to control the relative motion amplitude of the satellite relative to the main satellite out of the orbital plane, comprising: When regulating the amplitude of the relative motion out of the orbital plane of the primary, the x and y components of the average relative inclination vector deviation are modified by a normal impulse to regulate the amplitude of the relative motion out of the orbital plane of the primary, where the normal impulse size and the application control phase are calculated as follows:​ ， wherein, represents the phase pulse size, represents the applied control phase, represents the primary star orbital angular velocity, represents the z-direction relative motion amplitude, represents the phase of the z-direction relative motion of the secondary star in the primary star local coordinate system.

7. The satellite formation configuration control method based on inter-satellite measurement information according to claim 5, characterized by, correcting the average relative eccentricity vector deviation in the average relative orbital element deviation by using the four-pulse method, so as to control the relative motion amplitude of the satellite relative to the main satellite in the orbital plane, comprising: When regulating the amplitude of the relative motion of the satellite from the orbital plane of the primary, the radial impulses are used to correct the x-axis component of the relative eccentricity vector deviation and the y-axis component The formula for calculating the radial impulse size and the application control phase is as follows: ， wherein, represents a radial pulse size, represents an applied control phase, represents a primary star orbital angular velocity, represents a primary star semi-major axis.

8. The satellite formation configuration control method based on inter-satellite measurement information according to claim 5, characterized by, correcting the average relative semi-major axis deviation in the average relative orbital element deviation by using the four-pulse method, so as to control the long-term relative motion of the orbital direction of the satellite relative to the main satellite, comprising: When the long-term relative motion of the orbit track is regulated, the average relative long semi-axis deviation is adjusted alone without changing the average relative eccentricity vector, the average relative long semi-axis deviation is corrected by two tangential pulse corrections, the phases of the two pulse corrections are and The jet amounts of the two tangential pulse corrections are the same, the jet directions are the same, and the calculation formula of the tangential pulse size corresponding to a single jet is: 。

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