A constellation configuration maintenance method and device based on a subsatellite point trajectory drift

Abstract

This invention relates to the field of satellite orbit control technology, and discloses a method and apparatus for maintaining constellation configuration based on sub-satellite point trajectory drift. The method includes: acquiring constellation orbit data and an upper limit for orbital drift; calculating the upper limit of the semi-major axis of the operating orbit based on the orbit data, the upper limit for orbital drift, a preset orbital drift formula, and a preset ascending node longitude formula, thereby calculating the maneuvering time and the maneuvering drift of each satellite; performing cluster analysis on each satellite based on its maneuvering drift to obtain the average maneuvering drift corresponding to the satellite group; calculating the velocity increment of each satellite at the maneuvering time based on the constellation orbit data and the average maneuvering drift corresponding to each satellite group; and adjusting the operating state of each satellite based on its velocity increment when the operating time of each satellite reaches the maneuvering time. This invention can maintain constellation configuration and performance, improving the accuracy of constellation maintenance control.

Description

Technical Field

[0001] This invention relates to the field of satellite orbit control technology, and in particular to a constellation configuration maintenance method and apparatus based on sub-satellite point trajectory drift. Background Technology

[0002] Existing strategies for maintaining constellation configurations include configuration biasing and limit cycle methods. Configuration biasing primarily involves setting a basic bias value for the initial configuration, compensating for long-term drift and mitigating the effects of other perturbations. Limit cycle methods mainly control the semi-major axis. After considering solar radiation pressure, three-body gravity, and atmospheric drag, the semi-major axis gradually decays. When it decays to a certain value, the original configuration is considered disrupted, and the semi-major axis is restored to its original altitude. The goal of these methods is to maintain the geometric stability of the constellation; the majority of the optimized variables are the orbital semi-major axis, with orbital inclination considered to a lesser extent.

[0003] Most current constellation configuration maintenance aims to achieve a stable constellation spatial geometry rather than stable constellation performance. Configuration offset methods are only suitable for homogeneous constellations (i.e., constellations composed of satellites with identical orbital altitudes and inclinations). Due to the characteristics of homogeneous constellations, the perturbation forces acting on the satellites within the constellation are uniform, and the offset required for configuration offset methods is not excessive. However, if the target constellation is heterogeneous, the offset required for configuration offset methods varies significantly, directly disrupting the initial constellation configuration. Limit cycle methods primarily consider controlling each individual satellite within the constellation, neglecting the relative relationships between satellites; this is an absolute configuration control method, which is highly resource-intensive and detrimental to fuel conservation and cost reduction. Summary of the Invention

[0004] This invention provides a constellation configuration maintenance method and apparatus based on sub-satellite point trajectory drift, which can maintain constellation configuration and constellation performance, and improve the accuracy of constellation maintenance control.

[0005] To address the aforementioned technical problems, this invention provides a constellation configuration maintenance method based on sub-satellite point trajectory drift, comprising:

[0006] Obtain orbital data for the first constellation; wherein, the orbital data includes operational orbital data and reference orbital data for several satellites in the first constellation;

[0007] Obtain the maximum orbital drift of the first constellation;

[0008] Based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula, the upper limit of the semi-major axis of the running track is calculated.

[0009] Based on the preset ascending node longitude formula, the orbit data, and the upper limit of the semi-major axis of the operating orbit, the maneuvering time and the maneuvering drift of each satellite corresponding to the upper limit of the semi-major axis of the operating orbit are calculated respectively.

[0010] Based on the maneuvering drift of each satellite, cluster analysis is performed on each satellite to obtain several satellite groups, and the average maneuvering drift of each satellite group is calculated.

[0011] Based on the orbital data of the first constellation and the average maneuver drift of each of the satellite groups, the first velocity increment of each of the satellites at the maneuver time is calculated respectively;

[0012] When the operating time of each of the satellites reaches the maneuvering time, the operating state of each satellite is adjusted based on the first velocity increment corresponding to each satellite, so that each satellite enters the phasing orbit from the current operating orbit and maintains the constellation configuration of the first constellation.

[0013] As a preferred embodiment, the step of calculating the upper limit of the semi-major axis of the operating track based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula includes:

[0014] Based on the preset formulas for track drift and ascending node longitude, the first correlation between track drift and the semi-major axis of the running track is derived.

[0015] Based on the first correlation, the upper limit of the orbital drift, and the orbital data, the upper limit of the semi-major axis of the operating orbit is calculated;

[0016] The formula for the preset track drift amount is as follows:

[0017]

[0018] In the formula, This represents the amount of orbital drift. The radius of the Earth; The inclination difference between the reference track and the operating track; The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; The inclination angle of the reference orbit;

[0019] The formula for the longitude of the preset ascending node is:

[0020]

[0021] In the formula, The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; For the semi-major axis of the running track; Use the semi-major axis of the reference track; This is the atmospheric drag coefficient; This refers to the satellite's frontal area; This is the Earth's rotational angular velocity; Atmospheric density; For satellite quality; The gravitational constant of Earth; Let be the latitude argument at time t; The initial latitude argument; This represents the longitude error of the initial ascending node.

[0022] As a preferred embodiment, the step of calculating the maneuvering time and the maneuvering drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit based on the preset ascending node longitude formula, the orbit data, and the upper limit of the semi-major axis of the orbit includes:

[0023] Based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude argument is calculated;

[0024] Based on the preset latitude argument formula, the maneuver latitude argument, and the orbit data, the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit is calculated.

[0025] Based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data, the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit is calculated.

[0026] As a preferred embodiment, the calculation of the maneuver latitude argument based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data includes:

[0027] Based on the preset formula for the longitude of the ascending node, a second correlation relationship between the latitude argument and the semi-major axis of the orbit is derived.

[0028] Based on the second correlation, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude angle is calculated.

[0029] As a preferred embodiment, the step of calculating the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit based on the preset latitude argument formula, the maneuver latitude argument, and the orbit data includes:

[0030] Based on the preset latitude argument formula, a third correlation relationship between latitude argument and maneuver time is obtained;

[0031] The maneuver time is calculated based on the third correlation, the maneuver latitude argument, and the orbital data;

[0032] The preset latitude argument formula is as follows:

[0033]

[0034] In the formula, Let be the latitude argument at time t; The initial latitude argument; This is the initial time. The gravitational constant of Earth; For the semi-major axis of the running track; It is the derivative of the semi-major axis of the orbit with respect to time.

[0035] As a preferred embodiment, the step of calculating the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data includes:

[0036] The windward area and mass of several satellites are obtained from the basic satellite data in the orbital data.

[0037] The maneuver drift of each satellite is calculated by substituting the maneuver latitude angle, the windward area and mass of each satellite, the orbital data and the reference orbital data into the preset ascending node longitude formula.

[0038] As a preferred embodiment, the calculation of the first velocity increment of each satellite at the maneuvering moment, based on the orbital data of the first constellation and the average maneuvering drift corresponding to each of the satellite groups, includes:

[0039] The drift difference between each satellite is calculated based on the maneuver drift of each satellite and the average drift of each satellite group.

[0040] The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the drift difference of each satellite, and the orbital data.

[0041] Based on the semi-major axis of the phasing orbit and the semi-major axis of the reference orbit of each satellite, the phasing orbit velocity and the reference orbit velocity of each satellite at the maneuver time are calculated.

[0042] Based on the phasing orbit velocity and reference orbit velocity of each satellite at the maneuvering moment, the first velocity increment of each satellite at the maneuvering moment is calculated.

[0043] As a preferred embodiment, the step of calculating the phasing orbit semi-major axis of each satellite based on the preset orbit semi-major axis formula, the drift difference of each satellite, and the orbit data includes:

[0044] Based on the drift difference of each satellite, the orbital period of the reference satellite, and the Earth's rotation angular velocity, the phase adjustment period of each satellite is calculated.

[0045] The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the phasing period of each satellite, and the orbital data.

[0046] The formula for the semi-major axis of the preset track is:

[0047]

[0048] In the formula, For the semi-major axis of the track; For orbital period; is the Earth's gravitational constant.

[0049] As a preferred embodiment, after each of the aforementioned satellites enters the phasing orbit from its current operating orbit, the system further includes:

[0050] The upper limit of the semi-major axis of the operating orbit is determined to be the semi-major axis of the control orbit of each of the aforementioned satellites;

[0051] Calculate the second velocity increment and the third velocity increment of each satellite based on the semi-major axis of the phasing orbit and the semi-major axis of the control orbit, respectively.

[0052] The Hohmann orbit change method is used to adjust the operating speed of each satellite based on the second and third velocity increments, so that each satellite can enter the control orbit from the phasing orbit.

[0053] Accordingly, the present invention provides a constellation configuration maintenance device based on sub-satellite point trajectory drift, comprising: a first acquisition module, a second acquisition module, an upper limit calculation module, a drift amount calculation module, a cluster analysis module, a velocity increment calculation module, and a control module;

[0054] The first acquisition module is used to acquire orbital data of the first constellation; wherein, the orbital data includes the operational orbital data and reference orbital data of several satellites in the first constellation;

[0055] The second acquisition module is used to obtain the upper limit of the orbital drift of the first constellation;

[0056] The upper limit calculation module is used to calculate the upper limit of the semi-major axis of the running track based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula.

[0057] The drift calculation module is used to calculate the maneuver time and the maneuver drift of each satellite based on the preset ascending node longitude formula, the orbit data and the upper limit of the semi-major axis of the operating orbit, respectively.

[0058] The clustering analysis module is used to perform clustering analysis on each satellite based on the maneuvering drift of each satellite, to obtain several satellite groups, and to calculate the average maneuvering drift of each satellite group.

[0059] The velocity increment calculation module is used to calculate the first velocity increment of each satellite at the maneuvering moment based on the orbital data of the first constellation and the average maneuvering drift corresponding to each of the satellite groups.

[0060] The control module is used to adjust the operating state of each satellite based on the first velocity increment corresponding to each satellite when the operating time of each satellite reaches the maneuvering time, so that each satellite enters the phasing orbit from the current operating orbit and maintains the constellation configuration of the first constellation.

[0061] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0062] This invention provides a constellation configuration maintenance method based on sub-satellite point trajectory drift. When the operating time of each satellite reaches the maneuvering time, it is considered that the orbital drift of the first constellation to which each satellite belongs has reached the upper limit of the orbital drift of the first constellation. At this time, by calculating the first velocity increment of each satellite at the maneuvering time, and adjusting the operating state of each satellite based on the first velocity increment, the satellite can enter the phasing orbit from its current operating orbit, thereby reducing the orbital drift of the first constellation and maintaining the initial constellation configuration. The first velocity increment of each satellite at the maneuvering time is calculated based on the cluster analysis of the maneuvering drift of each satellite at the maneuvering time. The relative relationship between the satellites is considered when calculating the first velocity increment, which can maintain the constellation configuration while maintaining constellation performance, thereby improving the accuracy of constellation maintenance control. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating an embodiment of the constellation configuration maintenance method based on sub-satellite point trajectory drift provided by the present invention.

[0064] Figure 2 A schematic diagram of track drift provided by the present invention;

[0065] Figure 3 This invention provides a schematic diagram of the change in orbital drift.

[0066] Figure 4This is a flowchart illustrating a satellite clustering method provided by the present invention;

[0067] Figure 5 A schematic diagram of satellite clustering provided by the present invention;

[0068] Figure 6 A schematic flowchart of another embodiment of the constellation configuration maintenance method based on sub-satellite point trajectory drift provided by the present invention;

[0069] Figure 7 This is a schematic diagram of an embodiment of the constellation configuration maintenance device based on sub-satellite point trajectory drift provided by the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content and operations / steps, nor does it necessarily have to be performed in the order described. For example, some operations / steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0072] The following detailed description of some embodiments of the present invention is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0073] Example 1

[0074] like Figure 1 The diagram shown is a flowchart of an embodiment of the constellation configuration maintenance method based on sub-satellite point trajectory drift provided by the present invention. The method includes steps 101 to 107, each of which is detailed below:

[0075] Step 101: Obtain the orbital data of the first constellation; wherein, the orbital data includes the operational orbital data and reference orbital data of several satellites in the first constellation.

[0076] In this embodiment of the invention, the first constellation is a homogeneous or heterogeneous constellation composed of multiple satellites. The orbital data of the first constellation includes the operational orbit data and reference orbit data corresponding to each satellite in the first constellation. The operational orbit data corresponds to the actual orbits of each satellite, including basic satellite data and basic orbital data. The basic satellite data includes the satellite's latitude argument, satellite mass, and windward area, etc. The basic orbital data includes the semi-major axis of the operational orbit, the operational orbit inclination, and the longitude of the ascending node, etc. The reference orbit data is the pre-planned operational orbit for each satellite, including basic satellite data and basic orbital data. The basic satellite data includes the satellite's latitude argument, satellite mass, and windward area, etc. The basic orbital data includes the pre-set semi-major axis of the reference orbit, the reference orbit inclination, and the longitude of the ascending node, etc.

[0077] Step 102: Obtain the maximum orbital drift of the first constellation.

[0078] In this embodiment of the invention, to maintain the constellation configuration, the satellites in the first constellation are controlled to operate according to a reference orbit. However, over time, the nadir trajectory of each satellite's actual operating orbit will gradually deviate from the nadir trajectory of the reference orbit. During actual satellite operation, the orbital inclination determines the amount of drift between the actual operating orbit and the reference orbit. Therefore, to control the orbital drift of each satellite, it is necessary to control the orbital inclination. Since atmospheric drag has a negligible effect on the orbital inclination, it can be controlled by controlling the orbital semi-major axis. Because each satellite generates a drift relative to the reference orbit at every moment of its operation, it is necessary to determine the time to control the orbital semi-major axis of each satellite. In this embodiment, the moment when the satellite's orbital drift reaches its upper limit is determined as the time to control the orbital semi-major axis.

[0079] In this embodiment of the invention, the upper limit of the orbital drift of the first constellation can be determined according to the mission requirements, and this upper limit of orbital drift is used as the basic control benchmark thereafter. As an example of this embodiment of the invention, assuming the mission requirement is: the distance difference between the sensor's projection on the ground and the target point does not exceed 5km, then 5km can be used as the upper limit of the orbital drift of the first constellation.

[0080] Step 103: Calculate the upper limit of the semi-major axis of the running track based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula.

[0081] As a preferred embodiment, the upper limit of the semi-major axis of the running track is calculated based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula, including:

[0082] Based on the preset formulas for track drift and ascending node longitude, the first correlation between track drift and the semi-major axis of the running track is derived.

[0083] Based on the first correlation, the upper limit of the orbital drift, and the orbital data, the upper limit of the semi-major axis of the operating orbit is calculated;

[0084] The formula for the preset track drift amount is as follows:

[0085]

[0086] In the formula, This represents the amount of orbital drift. The radius of the Earth; The inclination difference between the reference track and the operating track; The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; The inclination angle of the reference orbit;

[0087] The formula for the longitude of the preset ascending node is:

[0088]

[0089] In the formula, The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; For the semi-major axis of the running track; Use the semi-major axis of the reference track; This is the atmospheric drag coefficient; This refers to the satellite's frontal area; This is the Earth's rotational angular velocity; Atmospheric density; For satellite quality; The gravitational constant of Earth; Let be the latitude argument at time t; The initial latitude argument; This represents the longitude error of the initial ascending node.

[0090] In an embodiment of the present invention, see Figure 2 This is a schematic diagram of track drift provided by the present invention. The track drift is defined as follows: ,in, For the Earth's radius, Let be the angle between the reference orbital plane and the operating orbital plane. The expression can be obtained by approximation and simplification using a spherical triangle and Taylor expansion. ,in, It is the difference in inclination between the reference track and the running track. It is the inclination angle of the reference orbit. This represents the difference in longitude between the ascending nodes of the reference orbit and the operating orbit. Therefore, the formula for the preset orbital drift can be derived. According to the pre-defined formula for orbital drift, the orbital drift is determined by the difference in inclination angle, the difference in longitude of the ascending node, and the orbital inclination angle of the reference plane. In practice, the effect of atmospheric drag on the inclination angle is negligible. and If both are constants, then the orbital drift is determined by... Decide.

[0091] In this embodiment of the invention, under the influence of atmospheric drag, the semi-major axis of the satellite's orbit will continuously decay, and the decay varies over time as follows:

[0092]

[0093] in, Indicates the atmospheric drag coefficient; It is the satellite's windward area; It is the angular velocity of the satellite's orbit; It is the semi-major axis of the track; It is atmospheric density; It refers to satellite quality.

[0094] Because the semi-major axis of a satellite's orbit decays over time, the satellite's orbital period changes as follows:

[0095]

[0096] in, Indicates the argument of latitude. Indicates the angle of depression at perigee. Indicates the angle of approach. It is the Earth's gravitational constant.

[0097] In this embodiment of the invention, the change in the longitude of the ascending node is defined as follows:

[0098]

[0099] Substituting the changes in the semi-major axis of the orbit and the orbital period into the above formula and simplifying, we obtain the formula for the longitude of the preset ascending node:

[0100]

[0101] According to the preset formula for the longitude of the ascending node, it can be known that... It is Since it is a quadratic function, combining it with the preset orbital drift formula, the orbital drift amount can be obtained. and the semi-major axis of the running track The first correlation between them. Substituting the obtained upper limit of orbital drift into the first correlation, the upper limit of the semi-major axis of the running orbit can be calculated.

[0102] Step 104: Based on the preset ascending node longitude formula, the orbit data, and the upper limit of the semi-major axis of the operating orbit, calculate the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit and the maneuver drift of each satellite.

[0103] As a preferred embodiment, based on the preset ascending node longitude formula, the orbital data, and the upper limit of the semi-major axis of the orbit, the maneuvering time and the maneuvering drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit are calculated, including:

[0104] Based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude argument is calculated;

[0105] Based on the preset latitude argument formula, the maneuver latitude argument, and the orbit data, the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit is calculated.

[0106] Based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data, the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit is calculated.

[0107] As a preferred embodiment, the maneuver latitude argument is calculated based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data, including:

[0108] Based on the preset formula for the longitude of the ascending node, a second correlation relationship between the latitude argument and the semi-major axis of the orbit is derived.

[0109] Based on the second correlation, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude angle is calculated.

[0110] In this embodiment of the invention, since it can be known from the preset formula for the longitude of the ascending node, It is It is a quadratic function, so the argument of latitude can be derived. and the semi-major axis of the running track The second correlation between them. Substituting the upper limit of the semi-major axis of the orbit calculated above into the second correlation, the maneuver latitude argument can be calculated.

[0111] As a preferred embodiment, based on the preset latitude argument formula, the maneuvering latitude argument, and the orbital data, the maneuvering time corresponding to the upper limit of the semi-major axis of the operating orbit is calculated, including:

[0112] Based on the preset latitude argument formula, a third correlation relationship between latitude argument and maneuver time is obtained;

[0113] The maneuver time is calculated based on the third correlation, the maneuver latitude argument, and the orbital data;

[0114] The preset latitude argument formula is as follows:

[0115]

[0116] In the formula, Let be the latitude argument at time t; The initial latitude argument; This is the initial time. The gravitational constant of Earth; For the semi-major axis of the running track; It is the derivative of the semi-major axis of the orbit with respect to time.

[0117] In this embodiment of the invention, when the satellite's orbital drift reaches its upper limit, the moment for controlling the semi-major axis of the orbit is determined, which is the maneuver moment. The latitude argument corresponding to this moment is the maneuver latitude argument. The latitude argument can be obtained from the preset latitude argument formula. The third correlation between the maneuver time t and the calculated maneuver latitude argument can be used to calculate the maneuver time. The maneuver time is the last time the satellite's orbital drift reaches its upper limit. The time.

[0118] In an embodiment of the present invention, see Figure 3 This is a schematic diagram of orbital drift variation provided by the present invention. The horizontal axis represents the satellite's orbital time t in days, and the vertical axis represents the orbital drift. The unit is kilometers. The waveform represents the change in orbital drift over time. The orbital drift reaches its upper limit at two specific moments. The first to reach the upper limit of orbital drift After that point, the orbital drift will not continue to exceed the orbital drift limit. Instead, it decreases over time; it reaches its upper limit of orbital drift in the second instance. After that point, the orbital drift will continue to exceed the orbital drift limit over time. Controlling the system at this point reduces the frequency of control and lowers costs. Therefore, the second system will reach the upper limit of orbital drift. The time is determined as the maneuver time.

[0119] As a preferred embodiment, the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit is calculated based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data, including:

[0120] The windward area and mass of several satellites are obtained from the basic satellite data in the orbital data.

[0121] The maneuver drift of each satellite is calculated by substituting the maneuver latitude angle, the windward area and mass of each satellite, the orbital data and the reference orbital data into the preset ascending node longitude formula.

[0122] In this embodiment of the invention, basic data of each satellite in the first constellation are obtained, including the satellite's windward area and satellite mass. The data of each satellite and the upper limit of the semi-major axis of the orbit and the maneuver latitude angle calculated above are substituted into the preset ascending node longitude formula to calculate the maneuver drift of each satellite at the maneuver time.

[0123] Step 105: Based on the maneuvering drift of each satellite, perform cluster analysis on each satellite to obtain several satellite groups, and calculate the average maneuvering drift corresponding to each satellite group.

[0124] In this embodiment of the invention, controlling each satellite of the first constellation during maneuvers requires calculating the first velocity increment for each satellite. If all satellites were individually adjusted based on their drift, the required velocity increment would be significantly increased. To maintain constellation configuration and performance, the relative positions of the satellites' nadir trajectories need not change excessively. Therefore, the multiple satellites of the first constellation can be divided into several groups, and controlled separately for each group. However, grouping all satellites according to a uniform standard might lead to satellites that don't require control participating in the control process, increasing fuel consumption. Therefore, cluster analysis can be used to reasonably classify the satellites.

[0125] In an embodiment of the present invention, see Figure 4 This is a flowchart illustrating a satellite clustering method provided by the present invention. This embodiment uses the K-Means algorithm for cluster analysis. First, the number of satellite groups K is set according to the user's needs. K center points are initialized based on the number of groups K, and then the distances between all satellites and each center point are calculated. , Let be the distance from the i-th satellite to the j-th center point. The distance can be calculated using the Euclidean distance formula. Then, the satellites are grouped according to the distance between each satellite and its center point. After grouping, K center points are recalculated. It is determined whether the center points have changed before and after the recalculation. If there is no change, the grouping information is output, resulting in K satellite groups. Once the multiple satellites of the first constellation are divided into multiple satellite groups, for each satellite group, the average maneuver drift of each satellite within that group is calculated to obtain the average maneuver drift of each satellite group. See [link to documentation]. Figure 5 This is a satellite clustering diagram provided by the present invention. Assuming that there are 3 groups of satellites, the center point of the first group, the center point of the second group, and the center point of the third group are set respectively, and the data points near the center point of each group are classified as satellites of the same satellite group.

[0126] Step 106: Based on the orbital data of the first constellation and the average maneuver drift of each of the satellite groups, calculate the first velocity increment of each of the satellites at the maneuver time.

[0127] As a preferred embodiment, based on the orbital data of the first constellation and the average maneuver drift corresponding to each of the satellite groups, the first velocity increment of each satellite at the maneuver moment is calculated, including:

[0128] The drift difference between each satellite is calculated based on the maneuver drift of each satellite and the average drift of each satellite group.

[0129] The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the drift difference of each satellite, and the orbital data.

[0130] Based on the semi-major axis of the phasing orbit and the semi-major axis of the reference orbit of each satellite, the phasing orbit velocity and the reference orbit velocity of each satellite at the maneuver time are calculated.

[0131] Based on the phasing orbit velocity and reference orbit velocity of each satellite at the maneuvering moment, the first velocity increment of each satellite at the maneuvering moment is calculated.

[0132] As a preferred embodiment, the phasing orbit semi-major axis of each satellite is calculated based on a preset orbit semi-major axis formula, the drift difference of each satellite, and the orbit data, including:

[0133] Based on the drift difference of each satellite, the orbital period of the reference satellite, and the Earth's rotation angular velocity, the phase adjustment period of each satellite is calculated.

[0134] The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the phasing period of each satellite, and the orbital data.

[0135] The formula for the semi-major axis of the preset track is:

[0136]

[0137] In the formula, For the semi-major axis of the track; For orbital period; is the Earth's gravitational constant.

[0138] In this embodiment of the invention, when the satellite's operating time reaches the maneuvering time, a phasing maneuver strategy can be used to control each satellite and guide it into a phasing orbit. At this time, it is necessary to calculate the semi-major axis of the phasing orbit, which can be done using the following preset formula:

[0139]

[0140] in, The semi-major axis of the phase-adjusting track; The orbital period for phasing orbits is determined based on the phase adjustment required for the satellite, and the phase can be determined based on the difference between each satellite and the mean of its constellation.

[0141]

[0142] in, Indicates the first The first in the group Satellite drift; Indicates the first The average maneuver drift of the group.

[0143] In the calculation Then, the required phase shift size for the corresponding phase shift track can be calculated:

[0144]

[0145] Where n represents the angular velocity of the reference orbit, according to The numerical values ​​can determine the control drift direction of the nadir point trajectory. Then the trajectory of the sub-satellite point needs to be shifted further eastward to compensate for the missing drift. Therefore, the trajectory of the sub-satellite point needs to be shifted westward to reduce the amount of drift. This is based on the control time required. The corresponding phase-shifting track period can be calculated as follows:

[0146]

[0147] in, The period of the reference orbit.

[0148] In this embodiment of the invention, after calculating the semi-major axis of the phase-adjusting track based on the above analysis, the first velocity increment is determined based on the semi-major axis of the track:

[0149]

[0150] in, and These are the unit relative angular momentum of the reference orbit and the phasing orbit, respectively; It is the semi-major axis of the reference orbit.

[0151] Step 107: When the operating time of each of the satellites reaches the maneuvering time, the operating state of each of the satellites is adjusted based on the first velocity increment corresponding to each of the satellites, so that each of the satellites enters the phasing orbit from the current operating orbit and maintains the constellation configuration of the first constellation.

[0152] In this embodiment of the invention, after calculating the first velocity increment corresponding to each satellite, when the operating time of each satellite reaches the maneuvering time, the first velocity increment is increased for each satellite, so that each satellite enters the phasing orbit from the current operating orbit, thereby reducing the orbital drift of the first constellation and maintaining the initial constellation configuration of the first constellation.

[0153] As a preferred embodiment, after each satellite enters the phasing orbit from its current orbit, the following further includes:

[0154] The upper limit of the semi-major axis of the operating orbit is determined to be the semi-major axis of the control orbit of each of the aforementioned satellites;

[0155] Calculate the second velocity increment and the third velocity increment of each satellite based on the semi-major axis of the phasing orbit and the semi-major axis of the control orbit, respectively.

[0156] The Hohmann orbit change method is used to adjust the operating speed of each satellite based on the second and third velocity increments, so that each satellite can enter the control orbit from the phasing orbit.

[0157] In this embodiment of the invention, after each satellite in the first constellation enters a phasing orbit from its current operating orbit through control, a Hohmann maneuver is used to move the satellite from the phasing orbit to the control orbit to ensure a reduction in the frequency of constellation configuration maintenance control. The Hohmann maneuver comprises two stages: one stage restores the semi-major axis of the orbit to its initial length to control the relative drift of its nadir trajectory; the other stage raises the semi-major axis to reduce the impact of the drift. The Hohmann maneuver can be controlled using the following formula:

[0158]

[0159] in, It is the first velocity increment corresponding to the first velocity pulse; It is the second velocity increment corresponding to the second velocity pulse; and These are the semi-major axis of the orbit and the velocity at the moment before the first velocity pulse. and These are the semi-major axis and velocity one moment after the second velocity pulse; It is the difference in the semi-major axis before and after the track change.

[0160] In this embodiment, each satellite is moved from the phasing orbit to the control orbit; therefore... and This corresponds to the semi-major axis and speed of the phase-adjusting track; and This corresponds to the semi-major axis of the control orbit and its velocity. The upper limit of the semi-major axis of the operating orbit calculated above is used to determine the semi-major axis of the control orbit. This embodiment, by adjusting the semi-major axis of the satellite's actual operating orbit, can reduce the control frequency, allowing the orbital drift of each satellite to return to normal. Figure 3 The initial state on the far left, when the orbital drift of each satellite reaches [a certain value] again. Figure 3 When the rightmost intersection point is reached, automatic control is adjusted again.

[0161] See Figure 6 This is a schematic flowchart of another embodiment of the constellation configuration maintenance method based on sub-satellite point trajectory drift provided by the present invention. The control flow of this embodiment is as follows: the upper limit of the sub-satellite point trajectory drift is determined according to the task requirements. (This drift amount takes into account the overall drift of the sub-satellite point trajectory, including the equator and high-latitude regions), according to Confirm the upper limit of the semi-major axis of the track. Then, the timing of the maneuver is determined using the semi-major axis attenuation formula and the ascending node longitude drift formula. At the same time, confirm the amount of maneuvering drift at the equator at that moment. The maneuvering drift of different satellites The K-Means algorithm is used for clustering to redetermine the drift of each satellite by taking into account the relative relationships between them, and then the velocity increment required for control is calculated.

[0162] Implementing the above embodiments has the following effects:

[0163] This invention provides a constellation configuration maintenance method based on sub-satellite point trajectory drift. When the operating time of each satellite reaches the maneuvering time, it is considered that the orbital drift of the first constellation to which each satellite belongs has reached the upper limit of the orbital drift of the first constellation. At this time, by calculating the first velocity increment of each satellite at the maneuvering time, and adjusting the operating state of each satellite based on the first velocity increment, the satellite can enter the phasing orbit from its current operating orbit, thereby reducing the orbital drift of the first constellation and maintaining the initial constellation configuration. The first velocity increment of each satellite at the maneuvering time is calculated based on the cluster analysis of the maneuvering drift of each satellite at the maneuvering time. The relative relationship between the satellites is considered when calculating the first velocity increment, which can maintain the constellation configuration while maintaining constellation performance, thereby improving the accuracy of constellation maintenance control.

[0164] Example 2

[0165] See Figure 7 This is a schematic diagram of an embodiment of the constellation configuration maintenance device based on sub-satellite point trajectory drift provided by the present invention. The device includes a first acquisition module 201, a second acquisition module 202, an upper limit calculation module 203, a drift amount calculation module 204, a cluster analysis module 205, a velocity increment calculation module 206, and a control module 207.

[0166] The first acquisition module 201 is used to acquire orbital data of the first constellation; wherein, the orbital data includes the operational orbital data and reference orbital data of several satellites in the first constellation;

[0167] The second acquisition module 202 is used to acquire the upper limit of the orbital drift of the first constellation;

[0168] The upper limit calculation module 203 is used to calculate the upper limit of the semi-major axis of the running track based on the track data, the upper limit of track drift, the preset track drift formula and the preset ascending node longitude formula;

[0169] The drift calculation module 204 is used to calculate the maneuver time and the maneuver drift of each satellite based on the preset ascending node longitude formula, the orbit data and the upper limit of the semi-major axis of the operating orbit, respectively.

[0170] The clustering analysis module 205 is used to perform clustering analysis on each of the satellites based on the maneuvering drift of each satellite, to obtain several satellite groups, and to calculate the average maneuvering drift of each satellite group.

[0171] The velocity increment calculation module 206 is used to calculate the first velocity increment of each satellite at the maneuvering moment based on the orbital data of the first constellation and the average maneuvering drift corresponding to each of the satellite groups;

[0172] The control module 207 is used to adjust the operating state of each satellite based on the first velocity increment corresponding to each satellite when the operating time of each satellite reaches the maneuvering time, so that each satellite enters the phasing orbit from the current operating orbit and maintains the constellation configuration of the first constellation.

[0173] As a preferred embodiment, the upper limit of the semi-major axis of the running track is calculated based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula, including:

[0174] Based on the preset formulas for track drift and ascending node longitude, the first correlation between track drift and the semi-major axis of the running track is derived.

[0175] Based on the first correlation, the upper limit of the orbital drift, and the orbital data, the upper limit of the semi-major axis of the operating orbit is calculated;

[0176] The formula for the preset track drift amount is as follows:

[0177]

[0178] In the formula, This represents the amount of orbital drift. The radius of the Earth; The inclination difference between the reference track and the operating track; The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; The inclination angle of the reference orbit;

[0179] The formula for the longitude of the preset ascending node is:

[0180]

[0181] In the formula, The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; For the semi-major axis of the running track; Use the semi-major axis of the reference track; This is the atmospheric drag coefficient; This refers to the satellite's frontal area; This is the Earth's rotational angular velocity; Atmospheric density; For satellite quality; The gravitational constant of Earth; Let be the latitude argument at time t; The initial latitude argument; This represents the longitude error of the initial ascending node.

[0182] As a preferred embodiment, based on the preset ascending node longitude formula, the orbital data, and the upper limit of the semi-major axis of the orbit, the maneuvering time and the maneuvering drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit are calculated, including:

[0183] Based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude argument is calculated;

[0184] Based on the preset latitude argument formula, the maneuver latitude argument, and the orbit data, the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit is calculated.

[0185] Based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data, the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit is calculated.

[0186] As a preferred embodiment, the maneuver latitude argument is calculated based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data, including:

[0187] Based on the preset formula for the longitude of the ascending node, a second correlation relationship between the latitude argument and the semi-major axis of the orbit is derived.

[0188] Based on the second correlation, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude angle is calculated.

[0189] As a preferred embodiment, based on the preset latitude argument formula, the maneuvering latitude argument, and the orbital data, the maneuvering time corresponding to the upper limit of the semi-major axis of the operating orbit is calculated, including:

[0190] Based on the preset latitude argument formula, a third correlation relationship between latitude argument and maneuver time is obtained;

[0191] The maneuver time is calculated based on the third correlation, the maneuver latitude argument, and the orbital data;

[0192] The preset latitude argument formula is as follows:

[0193]

[0194] In the formula, Let be the latitude argument at time t; The initial latitude argument; This is the initial time. The gravitational constant of Earth; For the semi-major axis of the running track; It is the derivative of the semi-major axis of the orbit with respect to time.

[0195] As a preferred embodiment, the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit is calculated based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data, including:

[0196] The windward area and mass of several satellites are obtained from the basic satellite data in the orbital data.

[0197] The maneuver drift of each satellite is calculated by substituting the maneuver latitude angle, the windward area and mass of each satellite, the orbital data and the reference orbital data into the preset ascending node longitude formula.

[0198] As a preferred embodiment, based on the orbital data of the first constellation and the average maneuver drift corresponding to each of the satellite groups, the first velocity increment of each satellite at the maneuver moment is calculated, including:

[0199] The drift difference between each satellite is calculated based on the maneuver drift of each satellite and the average drift of each satellite group.

[0200] The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the drift difference of each satellite, and the orbital data.

[0201] Based on the semi-major axis of the phasing orbit and the semi-major axis of the reference orbit of each satellite, the phasing orbit velocity and the reference orbit velocity of each satellite at the maneuver time are calculated.

[0202] Based on the phasing orbit velocity and reference orbit velocity of each satellite at the maneuvering moment, the first velocity increment of each satellite at the maneuvering moment is calculated.

[0203] As a preferred embodiment, the phasing orbit semi-major axis of each satellite is calculated based on a preset orbit semi-major axis formula, the drift difference of each satellite, and the orbit data, including:

[0204] Based on the drift difference of each satellite, the orbital period of the reference satellite, and the Earth's rotation angular velocity, the phase adjustment period of each satellite is calculated.

[0205] The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the phasing period of each satellite, and the orbital data.

[0206] The formula for the semi-major axis of the preset track is:

[0207]

[0208] In the formula, For the semi-major axis of the track; For orbital period; is the Earth's gravitational constant.

[0209] As a preferred embodiment, after each satellite enters the phasing orbit from its current orbit, the following further includes:

[0210] The upper limit of the semi-major axis of the operating orbit is determined to be the semi-major axis of the control orbit of each of the aforementioned satellites;

[0211] Calculate the second velocity increment and the third velocity increment of each satellite based on the semi-major axis of the phasing orbit and the semi-major axis of the control orbit, respectively.

[0212] The Hohmann orbit change method is used to adjust the operating speed of each satellite based on the second and third velocity increments, so that each satellite can enter the control orbit from the phasing orbit.

[0213] Implementing the above embodiments has the following effects:

[0214] This invention provides a constellation configuration maintenance method based on sub-satellite point trajectory drift. When the operating time of each satellite reaches the maneuvering time, it is considered that the orbital drift of the first constellation to which each satellite belongs has reached the upper limit of the orbital drift of the first constellation. At this time, by calculating the first velocity increment of each satellite at the maneuvering time, and adjusting the operating state of each satellite based on the first velocity increment, the satellite can enter the phasing orbit from its current operating orbit, thereby reducing the orbital drift of the first constellation and maintaining the initial constellation configuration. The first velocity increment of each satellite at the maneuvering time is calculated based on the cluster analysis of the maneuvering drift of each satellite at the maneuvering time. The relative relationship between the satellites is considered when calculating the first velocity increment, which can maintain the constellation configuration while maintaining constellation performance, thereby improving the accuracy of constellation maintenance control.

[0215] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A constellation configuration maintenance method based on sub-satellite point trajectory drift, characterized in that, include: Obtain orbital data for the first constellation; wherein, the orbital data includes operational orbital data and reference orbital data for several satellites in the first constellation; Obtain the maximum orbital drift of the first constellation; Based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula, the upper limit of the semi-major axis of the running track is calculated. Based on the preset ascending node longitude formula, the orbit data, and the upper limit of the semi-major axis of the operating orbit, the maneuvering time and the maneuvering drift of each satellite corresponding to the upper limit of the semi-major axis of the operating orbit are calculated respectively. Based on the maneuvering drift of each satellite, cluster analysis is performed on each satellite to obtain several satellite groups, and the average maneuvering drift of each satellite group is calculated. Based on the orbital data of the first constellation and the average maneuver drift of each of the satellite groups, the first velocity increment of each of the satellites at the maneuver time is calculated respectively; When the operating time of each of the satellites reaches the maneuvering time, the operating state of each satellite is adjusted based on the first velocity increment corresponding to each satellite, so that each satellite enters the phasing orbit from the current operating orbit and maintains the constellation configuration of the first constellation.

2. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 1, characterized in that, The step of calculating the upper limit of the semi-major axis of the running track based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula includes: Based on the preset formulas for track drift and ascending node longitude, the first correlation between track drift and the semi-major axis of the running track is derived. Based on the first correlation, the upper limit of the orbital drift, and the orbital data, the upper limit of the semi-major axis of the operating orbit is calculated; The formula for the preset track drift amount is as follows: In the formula, This represents the amount of orbital drift. The radius of the Earth; The inclination difference between the reference track and the operating track; The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; The inclination angle of the reference orbit; The formula for the longitude of the preset ascending node is: In the formula, The difference in longitude between the ascending nodes of the reference orbit and the operating orbit; For the semi-major axis of the running track; Use the semi-major axis of the reference track; This is the atmospheric drag coefficient; This refers to the satellite's frontal area; This is the Earth's rotational angular velocity; Atmospheric density; For satellite quality; The gravitational constant of Earth; Let be the latitude argument at time t; The initial latitude argument; This represents the longitude error of the initial ascending node.

3. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 2, characterized in that, The calculation of the maneuver time and maneuver drift of each satellite, based on the preset ascending node longitude formula, the orbit data, and the upper limit of the semi-major axis of the orbit, respectively, includes: Based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude argument is calculated; Based on the preset latitude argument formula, the maneuver latitude argument, and the orbit data, the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit is calculated. Based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data, the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit is calculated.

4. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 3, characterized in that, The calculation of the maneuver latitude argument based on the preset ascending node longitude formula, the upper limit of the semi-major axis of the operating track, and the track data includes: Based on the preset formula for the longitude of the ascending node, a second correlation relationship between the latitude argument and the semi-major axis of the orbit is derived. Based on the second correlation, the upper limit of the semi-major axis of the operating track, and the track data, the maneuver latitude angle is calculated.

5. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 4, characterized in that, The calculation of the maneuver time corresponding to the upper limit of the semi-major axis of the operating orbit, based on the preset latitude argument formula, the maneuver latitude argument, and the orbit data, includes: Based on the preset latitude argument formula, a third correlation relationship between latitude argument and maneuver time is obtained; The maneuver time is calculated based on the third correlation, the maneuver latitude argument, and the orbital data; The preset latitude argument formula is as follows: In the formula, Let be the latitude argument at time t; The initial latitude argument; This is the initial time. The gravitational constant of Earth; For the semi-major axis of the running track; It is the derivative of the semi-major axis of the orbit with respect to time.

6. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 5, characterized in that, The step of calculating the maneuver drift of each satellite corresponding to the upper limit of the semi-major axis of the orbit based on the maneuver latitude argument, the preset ascending node longitude formula, and the orbital data includes: The windward area and mass of several satellites are obtained from the basic satellite data in the orbital data. The maneuver drift of each satellite is calculated by substituting the maneuver latitude angle, the windward area and mass of each satellite, the orbital data and the reference orbital data into the preset ascending node longitude formula.

7. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 6, characterized in that, The calculation of the first velocity increment of each satellite at the maneuvering moment, based on the orbital data of the first constellation and the average maneuvering drift corresponding to each of the satellite groups, includes: The drift difference between each satellite is calculated based on the maneuver drift of each satellite and the average drift of each satellite group. The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the drift difference of each satellite, and the orbital data. Based on the semi-major axis of the phasing orbit and the semi-major axis of the reference orbit of each satellite, the phasing orbit velocity and the reference orbit velocity of each satellite at the maneuver time are calculated. Based on the phasing orbit velocity and reference orbit velocity of each satellite at the maneuvering moment, the first velocity increment of each satellite at the maneuvering moment is calculated.

8. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 7, characterized in that, The step of calculating the phasing orbit semi-major axis of each satellite based on the preset orbit semi-major axis formula, the drift difference of each satellite, and the orbit data includes: Based on the drift difference of each satellite, the orbital period of the reference satellite, and the Earth's rotation angular velocity, the phase adjustment period of each satellite is calculated. The semi-major axis of the phasing orbit of each satellite is calculated based on the preset orbital semi-major axis formula, the phasing period of each satellite, and the orbital data. The formula for the semi-major axis of the preset track is: In the formula, For the semi-major axis of the track; For orbital period; is the Earth's gravitational constant.

9. The constellation configuration maintenance method based on sub-satellite point trajectory drift according to claim 8, characterized in that, After each of the aforementioned satellites enters a phasing orbit from its current orbit, the following steps are also included: The upper limit of the semi-major axis of the operating orbit is determined to be the semi-major axis of the control orbit of each of the aforementioned satellites; Calculate the second velocity increment and the third velocity increment of each satellite based on the semi-major axis of the phasing orbit and the semi-major axis of the control orbit, respectively. The Hohmann orbit change method is used to adjust the operating speed of each satellite based on the second and third velocity increments, so that each satellite can enter the control orbit from the phasing orbit.

10. A constellation configuration maintenance device based on sub-satellite point trajectory drift, characterized in that, include: The system comprises a first acquisition module, a second acquisition module, an upper limit calculation module, a drift calculation module, a cluster analysis module, a velocity increment calculation module, and a control module. The first acquisition module is used to acquire orbital data of the first constellation; wherein, the orbital data includes the operational orbital data and reference orbital data of several satellites in the first constellation; The second acquisition module is used to obtain the upper limit of the orbital drift of the first constellation; The upper limit calculation module is used to calculate the upper limit of the semi-major axis of the running track based on the track data, the upper limit of track drift, the preset track drift formula, and the preset ascending node longitude formula. The drift calculation module is used to calculate the maneuver time and the maneuver drift of each satellite based on the preset ascending node longitude formula, the orbit data and the upper limit of the semi-major axis of the operating orbit, respectively. The clustering analysis module is used to perform clustering analysis on each satellite based on the maneuvering drift of each satellite, to obtain several satellite groups, and to calculate the average maneuvering drift of each satellite group. The velocity increment calculation module is used to calculate the first velocity increment of each satellite at the maneuvering moment based on the orbital data of the first constellation and the average maneuvering drift corresponding to each of the satellite groups. The control module is used to adjust the operating state of each satellite based on the first velocity increment corresponding to each satellite when the operating time of each satellite reaches the maneuvering time, so that each satellite enters the phasing orbit from the current operating orbit and maintains the constellation configuration of the first constellation.

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