Low-orbit constellation configuration maintaining method using perturbation force and adjacent position relative station deviation

Abstract

The invention provides a low-orbit constellation configuration maintenance method using perturbation force and adjacent position relative station deviation, and belongs to the technical field of low-orbit constellation configuration maintenance and control. The method comprises the following steps: acquiring orbit parameters of each satellite and adjacent satellites thereof in a low-orbit satellite constellation in a space, and calculating a relative drift distance and an allowable drift range of each satellite; on the basis of a low-orbit satellite constellation dynamic model and the relative drift distance, calculating theoretical retention time of each satellite in an allowable drift range, and further determining a constellation control sequence and an optimal control moment of each satellite; and when the satellite reaches the optimal control moment, determining the control quantity of the satellite orbit parameters and the propulsion system parameters of the satellite during orbit maneuver so as to maintain the constellation configuration. According to the method, the relative standing position relation of the adjacent satellites serves as control input, autonomous stable maintenance of the constellation relative configuration is achieved by controlling the orbit height and the inclination angle of the satellites, and unnecessary maintenance control and fuel consumption are avoided.

Description

Technical Field

[0001] This invention belongs to the field of low-Earth orbit constellation configuration maintenance and control technology, and specifically relates to a method for maintaining low-Earth orbit constellation configuration using perturbation force and relative positional deviation of adjacent stations. Background Technology

[0002] A satellite constellation is a satellite system composed of multiple satellites with stable orbital geometry and relatively fixed spatiotemporal relationships, used to accomplish specific space missions. A single satellite cannot achieve uninterrupted global or regional communication and observation, while a satellite constellation, through the interconnection and supplementation of satellites, can simultaneously cover a wider area or improve the coverage characteristics of a specific area, thus ensuring that the target area is covered by satellites at the required time intervals or coverage multiples. In recent years, the global demand for satellite broadband access has been continuously growing. Major spacefaring nations around the world have successively proposed the construction of large low-Earth orbit constellations.

[0003] Large low-Earth orbit (LEO) constellations have a large number of satellites, low orbital altitudes, are greatly affected by atmospheric drag, and exhibit highly homogeneous motion patterns, which differs significantly from the characteristics of existing medium- and high-Earth orbit (MEO) satellite constellations. Traditional MEO satellite constellations often employ orbit control techniques based on individual satellites. This involves designing the spatial orbit and phase of each satellite on the ground and maintaining it around its designed location. This method relies heavily on ground-based orbit design and does not consider inter-satellite relationships, making it unsuitable for directly maintaining the configuration of large constellations. Furthermore, a constellation relative configuration maintenance technique based on the average of location deviations has been proposed internationally. This technique treats the entire constellation as the control object, averages the location deviations of all satellites, and uses the average location as the reference location for each satellite. This method eliminates the need to design orbits for each satellite, maintaining only the stability of the overall relative constellation configuration. However, for large constellations, determining satellite locations becomes excessively complex and may lead to unnecessary maintenance control. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing constellation configuration maintenance technologies and propose a method for maintaining the configuration of a low-Earth orbit (LEO) constellation using perturbation forces and relative station position deviations of neighboring satellites. This invention uses the relative station positions of adjacent satellites as control inputs, achieving autonomous and stable maintenance of the constellation's relative configuration by controlling the satellites' orbital altitude and inclination. Utilizing the relative station positions of adjacent satellites not only effectively reduces the complexity of station determination and ensures that satellites autonomously and quickly determine their permissible spatial positions, but also avoids unnecessary maintenance control and fuel consumption, which is of great significance for the construction and operation of large LEO constellations.

[0005] This invention proposes a method for maintaining the configuration of a low-Earth orbit constellation using perturbation forces and relative station position deviations, comprising:

[0006] Obtain the orbital parameters of each satellite and its neighboring satellites in a low-Earth orbit satellite constellation;

[0007] Based on the orbital parameters, the relative drift and allowable drift range of each satellite in the constellation are calculated;

[0008] Based on the preset low-Earth orbit satellite constellation dynamics model and the relative drift amount, the theoretical holding time of each satellite within the allowable drift range is calculated;

[0009] Based on the theoretical hold time, the control sequence of the constellation and the optimal control time for each satellite are determined;

[0010] Under the control sequence, when the satellite reaches the optimal control time, the control values ​​of the satellite orbital parameters and the satellite propulsion system parameters during orbital maneuvers are determined to maintain the constellation configuration.

[0011] In one specific embodiment of the present invention, the low-Earth orbit satellite constellation dynamics model includes two parts: the orbital dynamics model of a single satellite and the satellite constellation configuration;

[0012] The orbital dynamics model of the single satellite takes into account the Earth's non-spherical J2 perturbation and atmospheric drag perturbation, and its expression is as follows:

[0013] (1)

[0014] in, For the acceleration of a single satellite, Let the satellite's radius vector be the position vector in the geocentric inertial coordinate system. This represents the satellite's radius modulus in the geocentric inertial coordinate system. The gravitational constant is the constant of gravity. For the J2 term perturbation acceleration of the Earth's non-spherical shape, This is atmospheric drag perturbation acceleration;

[0015] Earth's gravitational acceleration on satellites The gradient of the Earth's gravitational potential function U is expressed as... ,in, This represents the satellite's radius modulus in a geocentric fixed coordinate system. The coordinates of the satellite in the geocentric coordinate system are the geocentric latitudes. The longitude of the satellite in the geocentric fixed coordinate system; in the geocentric fixed coordinate system In the equation, considering the perturbation of the J2 term of the non-spherical Earth, the expression for the gravitational potential function of the Earth is as follows:

[0016] (2)

[0017] in, The radius of the Earth's equator. These are the coefficients of the Earth's gravitational potential model.

[0018] The dynamic model of atmospheric perturbation is expressed as follows:

[0019] (3)

[0020] in, This is the atmospheric drag vector. Let S be the drag coefficient, and S be the equivalent cross-sectional area with respect to atmospheric drag. V is the atmospheric density at the satellite's location in space, V is the satellite's velocity vector relative to the atmosphere, and V is the satellite's velocity magnitude relative to the atmosphere.

[0021] Given the satellite's mass m, the vector expression for the atmospheric drag perturbation acceleration experienced by the satellite is as follows:

[0022] (4)

[0023] The satellite constellation configuration adopts the Walker-Delta constellation configuration, and the constellation configuration code is ( );in, This represents the total number of satellites that make up a constellation; The number of orbital planes indicates the number of the constellation's orbital planes, with the ascending nodes of the orbital planes spaced at equal intervals. Uniform distribution; The number of satellites on each orbital plane. The phases of satellites in the same orbital plane are at equal intervals. Uniform distribution; Indicates the orbital inclination angle; Indicates the orbital altitude; Represents the phase factor, taking An integer between 1 and 2 represents the phase relationship between adjacent orbital planes and numbered satellites in the constellation; that is, the phase difference between adjacent orbital planes and numbered satellites is 1 / 2. .

[0024] In one specific embodiment of the present invention, it further includes:

[0025] Each satellite in the constellation is assigned a two-dimensional number; the orbital planes are numbered according to the initial design configuration of the constellation, in order from 0 to 360° of the ascending node's equatorial ascension, denoted as... , =1,2,…,P, where P represents the orbital plane number of the constellation; satellites in the same orbital plane are renumbered according to their in-plane phase from 0 to 360°, denoted as , =1,2,…,S, where S represents the number of satellites on each orbital plane; thus, the number of any satellite in the constellation is determined and denoted as . ;

[0026] For any satellite Determine the corresponding neighboring satellite number in the constellation for this satellite, specifically including:

[0027] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0028] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0029] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0030] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0031] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0032] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0033] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0034] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0035] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star .

[0036] In a specific embodiment of the present invention, obtaining the orbital parameters of each satellite and its adjacent satellites in a low-Earth orbit satellite constellation includes:

[0037] All satellites in a constellation obtain their absolute positions in space. and motion state Where x, y, and z are the satellite radius vectors, respectively. The projection components on the three coordinate axes of the geocentric inertial coordinate system, v x v y v z These are the satellite's motion speeds. Projected components on the three coordinate axes of the geocentric inertial coordinate system;

[0038] Satellites determine their absolute position in space and motion state Subsequently, it was transformed into orbital parameters using orbital mechanics methods, including Kepler orbital elements. and near-circular orbit elements ,in For the semi-major axis of the track, For orbital eccentricity, For track inclination, Right ascension of the ascending node, For the perigee argument, For the near point angle, and The projection components of the orbital eccentricity in the two-dimensional nodal coordinate system, It is the angle of the mean latitude.

[0039] In one specific embodiment of the present invention, before calculating the relative drift and allowable drift range of each satellite in the constellation, the method further includes:

[0040] Determine the constellation configuration maintenance requirements and calculate the positioning maintenance reference for each satellite in the constellation;

[0041] The determination of constellation configuration preservation requirements includes:

[0042] 1) Absolute orbital altitude of all satellites in the constellation It remains stable within the design range over a long period;

[0043] 2) The absolute orbital inclination difference of all satellites in the constellation and the difference in right ascension of the relative ascending node Stay within the design range;

[0044] 3) The relative phase difference between each satellite in the constellation and its neighboring satellites All remained within the design range;

[0045] The calculation of the positioning of each satellite in the constellation to maintain the reference includes:

[0046] 1) Orbital inclination and right ascension of the ascending node maintain the reference:

[0047] Orbital inclination angle based on constellation design As a baseline, the required orbital inclination angle for each satellite is... Maintain at Within the interval, i.e., the difference in absolute orbital inclination. Maintain at Within the interval, where, The maximum allowable drift threshold for the track inclination angle;

[0048] The right ascension of the ascending node of each orbital plane is based on the theoretical right ascension of the ascending node of the corresponding orbital plane after averaging the drift deviation from the actual constellation configuration. For the th The orbital plane requires the right ascension of the ascending node of each satellite on that plane. Maintained within interval c, i.e., the difference in right ascension relative to the ascending node. Maintain at Within the interval, where, This is the maximum allowable drift threshold for the right ascension of the ascending node;

[0049] The actual constellation configuration after removing the average drift bias Theoretical right ascension of the ascending node of the orbital plane The determination method is as follows:

[0050] (5)

[0051] 2) The orbital altitude and the aspect ratio of the mean latitude are maintained at the baseline:

[0052] The orbital altitude is the nominal orbital altitude in the constellation design configuration. As a baseline, the absolute orbital altitude of each satellite is required. Maintain at Within the interval, i.e., the absolute orbital altitude difference Maintain at Within the interval, where, This represents the maximum allowable drift threshold at the track height.

[0053] The mean latitude angle of each satellite is maintained by the relative orbital altitude difference. Based on all satellites with values ​​less than 0, any satellite relative orbital altitude difference family The calculation expression is as follows:

[0054] (6)

[0055] In the formula, , , , Satellites Compared to the relative orbital altitudes of its A1, A2, B1, and B2 satellites, , , , Satellites The absolute orbital altitudes of satellites A1, A2, B1, and B2;

[0056] This reference uses all adjacent satellites with orbital altitudes greater than the main satellite as reference satellites, requiring the relative phase difference between each satellite and all reference satellites. All remained at Within the interval; where, The maximum allowable drift threshold for the horizontal latitude angle; when the relative orbital altitude difference family When all values ​​in the equation are greater than 0, the main star does not need to consider the maintenance of the mean latitude argument, and at this time the main star is the reference star for all adjacent stars.

[0057] In one specific embodiment of the present invention, calculating the relative drift and permissible drift range of each satellite in the constellation includes:

[0058] 1) Calculate the relative drift of each satellite within the constellation;

[0059] For any satellite The calculation process for the relative drift is as follows:

[0060] 1-1) Calculate the relative drift of the track height;

[0061] Among them, satellite Absolute orbital altitude :

[0062] (8)

[0063] In the formula, For satellite Its own absolute orbital altitude, For satellite Its own orbital semi-major axis, The average radius of the Earth;

[0064] satellite Absolute orbital height difference :

[0065] (9)

[0066] In the formula, The nominal orbital altitude for constellation configuration design;

[0067] The absolute orbital altitude difference of the satellite As the relative drift in satellite orbital altitude, the relative drift in the satellite's orbital altitude direction must be maintained at a certain value. Within the range;

[0068] 1-2) Calculate the relative drift of the track inclination angle;

[0069] Among them, satellite Absolute orbital inclination difference :

[0070] (10)

[0071] In the formula, For satellite Its own orbital inclination, Orbital inclination angles for constellation configurations;

[0072] The absolute orbital inclination difference of the satellite As a relative drift of the satellite's orbital inclination, the relative drift of the satellite's orbital inclination must be maintained at a certain value. Within the range;

[0073] 1-3) Calculate the relative shift of the right ascension of the ascending node;

[0074] Among them, satellite Relative difference in right ascension of ascending node :

[0075] (11)

[0076] In the formula, For satellite Its own ascending node right ascension, After removing the average drift bias from the actual constellation configuration The theoretical right ascension of the ascending node of the orbital plane;

[0077] The difference in right ascension of the relative ascending node of the satellite As the relative drift of the satellite's right ascension at the ascending node, the relative drift of the satellite in the direction of the right ascension at the ascending node must be maintained at... Within the range;

[0078] 1-4) Calculate the in-plane phase relative drift;

[0079] Among them, satellite relative phase difference family :

[0080] (12)

[0081] In the formula, For satellite Its own latitudinal argument, , , , Satellites The mean latitude argument of stars A1, A2, B1, and B2;

[0082] The relative phase difference family of satellites As the relative drift of the satellite's in-plane phase, the relative drift of the satellite relative to the reference star in the in-plane phase direction must be maintained at... Within the range;

[0083] 2) Based on the results of step 1), calculate the allowable drift range for each satellite;

[0084] The allowable drift range includes three interval constraints, namely: , , ;

[0085] When none of the adjacent satellites of the main body are used as reference satellites, the in-plane phase relative drift of the main body is unconstrained; only the relative drift of orbital altitude and the relative drift of right ascension of the ascending node are maintained at [values ​​to be filled in]. , Interval.

[0086] In one specific embodiment of the present invention, calculating the theoretical holding time of each satellite within the allowable drift range includes:

[0087] 1) Calculate the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node;

[0088] set up For the current moment, when At that time, the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node. The calculation expression is as follows:

[0089] (13)

[0090] when At that time, the theoretical dwell time of the satellite within the allowable drift range of the right ascension of the ascending node. The calculation expression is as follows:

[0091] (14)

[0092] when At that time, the actual right ascension of the satellite's ascending node has no tendency to move relative to the surrounding area. ;

[0093] In the formula, , which is the first-order long-term drift rate of the right ascension of the ascending node caused by the J2 term perturbation of the Earth's non-spherical shape; The nominal orbital angular velocity, This is the semi-major diameter of the track.

[0094] 2) Calculate the theoretical holding time of the satellite in the orbital plane; the specific steps are as follows:

[0095] 2-1) Calculate the theoretical holding time of the satellite within the allowable drift range of its orbital altitude. :

[0096] (15)

[0097] In the formula, The rate of change of orbital altitude, The nominal semi-major axis of the track;

[0098] 2-2) Calculate the theoretical holding time of the satellite within the in-plane phase allowable drift range. ;

[0099] 2-2-1) Calculate the theoretical holding time of the satellite's in-plane phase relative to the coplanar reference star within the allowable drift range. :

[0100] (16)

[0101] 2-2-2) Calculate the theoretical holding time of the satellite's in-plane phase relative to the out-of-plane reference star within the allowable drift range. :

[0102] Among them, the deviation of the short-term orbital altitude change rate of the main star relative to the eccentric reference star Bi is... It has a quadratic function:

[0103] (17)

[0104] According to equation (17), we can obtain The future time interval corresponding to the given time is represented by a set. Furthermore, there is the theoretical holding time of the satellite's in-plane phase relative to any out-of-plane reference star within the allowable drift range. :

[0105] (18)

[0106] 2-2-3) Based on the results of steps 2-2-1) and 2-2-2), determine the theoretical hold-up time family of the main star relative to its four neighboring stars. The theoretical holding time of the in-plane phase within the allowable drift range ;

[0107] 2-3) Based on the results of steps 2-1) and 2-2), determine the theoretical holding time of the satellite in the orbital plane. .

[0108] In one specific embodiment of the present invention, determining the control sequence of the constellation and the optimal control time for each satellite includes:

[0109] 1) Determine the control sequence for the orbital planes of the constellation satellites;

[0110] For orbital plane control, the theoretical holding time for all satellites within the allowable drift range of right ascension at the ascending node is... Arrange in a sequence , where the set With sets To satisfy the one-to-one mapping relationship, and have Starting from the last satellite in the sequence, traverse the sequence. If the theoretical hold-up time difference between any two adjacent satellites in the sequence is less than one orbital period, then... This advances the control timing of the preceding star, making After the traversal is complete, a discrete sequence of optimal control times for each satellite is generated; when any satellite reaches the optimal control time determined in this sequence... Then, position maintenance control will begin;

[0111] 2) Determine the control sequence for satellites within the orbital plane;

[0112] For control within the orbital plane, the constellation relaxation coefficient k is set, representing the ratio of the overall constellation maintenance period to the ideal total duration of constellation control. );

[0113] when At that time, the theoretical hold time of all satellites in the orbital plane Arrange in a sequence , where the set With sets To satisfy the one-to-one mapping relationship, and have Starting from the last satellite in the sequence, traverse the sequence. If the theoretical hold-up time difference between any two adjacent satellites in the sequence is less than one orbital period, then... This advances the control timing of the preceding star, making After the traversal is complete, a discrete sequence of optimal control times for each satellite is generated; when any satellite reaches the optimal control time determined in this sequence... Then, position maintenance control will begin;

[0114] when At that time, the theoretical hold times of the main star and adjacent satellites within the orbital plane are arranged into a sequence. ,in, Starting from the last satellite in the sequence, traverse the sequence, where if the difference in the theoretical hold time between two adjacent satellites in the sequence is less than one orbital period, i.e. This advances the control timing of the preceding star, making After the traversal is complete, a discrete sequence of optimal control times for adjacent satellites is generated. When any satellite reaches the set optimal control time... Then, position maintenance control will begin.

[0115] In a specific embodiment of the present invention, the control parameters of the satellite orbit are calculated as follows:

[0116] 1) Calculate the track surface drift control parameters;

[0117] The planned maintenance period is set as follows Let the control time before be After control, the time is ;

[0118] Calculate the relative drift rate of the ideal ascending node right ascension after control. :

[0119] (19)

[0120] During track maneuvering, Heng is established;

[0121] like ,but ;like ,but ;

[0122] Expected orbital inclination offset Represented as:

[0123] (20)

[0124] In the formula, the long-term drift rate of the right ascension of the ascending node considering the perturbation of the J2 term of the Earth's non-spherical shape is given. ;

[0125] Judgment: If Then let The sign remains unchanged, and the modulus is updated to Otherwise, keep constant;

[0126] This allows us to obtain the absolute orbital inclination angle after control. and change in orbital inclination :

[0127] (twenty one)

[0128] 2) Calculate the orbital altitude and phase coupling control parameters;

[0129] For cases where the height exceeds the limit, i.e. :

[0130] (twenty two)

[0131] The control value for the track height at this time is:

[0132] (twenty three)

[0133] in, The first proportionality coefficient, with a value between between;

[0134] For the phase-leading case, i.e. :

[0135] (twenty four)

[0136] In the formula, Number the reference stars in the neighborhood; Corresponding to relative coplanar leading, Corresponding to the relative antiplane leading;

[0137] When there is relative coplanar advance, the relative deviation of the track height will hardly change, and the control amount of the track height is:

[0138] (25)

[0139] In the formula, The corresponding orbital altitude offset with a phase maintenance period greater than T days:

[0140] (26)

[0141] In the case of relative out-of-plane advance, due to the short-term deviation in the rate of change of orbital altitude between the two stars... ,in, The rate of change of the orbital altitude of the main star. Given the rate of change of orbital altitude of Bi star, the orbital altitude offset is calculated as follows:

[0142] (27)

[0143] By solving the equation system (28) simultaneously, the relative track height difference after ideal control is obtained. At this time, the control amount of track height is calculated according to equation (29).

[0144] (28)

[0145] (29)

[0146] in, This is the second proportionality coefficient, and its value ranges from... between;

[0147] In all cases, if control is in effect Exceeding The scope is determined according to As the absolute height deviation after control, the control quantity for track height is recalculated:

[0148] (30).

[0149] In one specific embodiment of the present invention, the satellite's propulsion system parameters are calculated as follows:

[0150] 1) Control of track surface drift:

[0151] Through normal velocity pulse The change in the spacecraft's orbital inclination, the increase in normal velocity and the mass of fuel consumed in a single propulsion are shown in equations (31) and (32), respectively:

[0152] (31)

[0153] (32)

[0154] 2) Control of orbital altitude and phase:

[0155] Through lateral velocity pulse The lateral velocity increment and fuel consumption for a single control operation, depending on the change in the spacecraft's orbital altitude, are shown in equations (33) and (34), respectively:

[0156] (33)

[0157] (34)

[0158] 3) Determine the satellite's orbital control position and implement control based on propulsion parameters;

[0159] Control of track surface drift:

[0160] Satellites pass through latitude azimuth or A normal impulse is generated at the point to achieve track surface adjustment; according to Argument of latitude at time Calculate the start-up time:

[0161] (36)

[0162] In the formula, This refers to the actual orbital angular velocity of the satellite.

[0163] Control of orbital altitude and phase:

[0164] Through phase difference The two lateral maneuvers changed the spacecraft's orbital altitude, offsetting the change in eccentricity;

[0165] Assume the first orbital altitude control time is The second orbital altitude control time is Then, the activation times for the two control actions under pulse thrust conditions are as follows:

[0166] (37).

[0167] Features and beneficial effects of the present invention:

[0168] This invention aims to maintain the relative stability of adjacent satellites. Using the relative orbital relationships of adjacent satellites as state input, it achieves autonomous and stable maintenance of the constellation's relative configuration by controlling the satellites' orbital altitude and inclination. This method effectively reduces the complexity of determining the constellation's satellite positions, facilitating the satellites' autonomous and rapid determination of their permissible spatial positions. Furthermore, this invention employs a flexible and variable reference base, selecting adjacent satellites with a relative orbital altitude difference greater than zero as the maintenance reference. It also uses a "super-tolerance" discrete sequence control strategy to discretize the control time. This not only reduces unnecessary fuel consumption for constellation maintenance and extends constellation lifespan but also avoids the situation of simultaneously controlling a large number of satellites in a short period, thus contributing to the stability of constellation service performance. This constellation maintenance method not only demonstrates high innovation but also possesses practical application feasibility, providing an effective technical solution for solving the problem of maintaining the relative configuration of large low-Earth orbit constellations. Attached Figure Description

[0169] Figure 1 This is an overall flowchart of a method for maintaining the configuration of a low-Earth orbit constellation using perturbation force and relative station position deviation of adjacent stations, according to an embodiment of the present invention.

[0170] Figure 2 This is a schematic diagram of the inter-satellite relationship between the main satellite and adjacent satellites in a specific embodiment of the present invention.

[0171] Figure 3 This is a schematic diagram of the permissible drift range of a single satellite in a specific embodiment of the present invention.

[0172] Figure 4 This is a diagram showing the maximum deviation of the orbital altitude of the constellation satellites within 90 days in a specific embodiment of the present invention.

[0173] Figure 5 This is a diagram showing the maximum phase deviation of constellation satellites within 90 days in a specific embodiment of the present invention.

[0174] Figure 6 This is a constellation satellite status diagram for 90 days in a specific embodiment of the present invention.

[0175] Figure 7 This is a distribution diagram of the control time intervals for constellation satellites in a specific embodiment of the present invention. Detailed Implementation

[0176] This invention proposes a method for maintaining the configuration of a low-Earth orbit constellation using perturbation forces and relative station position deviations. The invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0177] Since the relative drift rate of the orbital plane of a low-Earth orbit constellation is much smaller than the relative drift rate of the phase within the plane, the control problem of the orbital plane can still be simplified to the control problem of a traditional single satellite. The following specific embodiments will focus on the control strategy of the phase within the satellite orbital plane. The examples of the various parameters listed are only preferred embodiments of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0178] This invention proposes a method for maintaining the configuration of a low-Earth orbit constellation using perturbation forces and relative station position deviations, comprising:

[0179] Obtain the orbital parameters of each satellite and its neighboring satellites in a low-Earth orbit satellite constellation;

[0180] Based on the orbital parameters, the relative drift and allowable drift range of each satellite in the constellation are calculated;

[0181] Based on the preset low-Earth orbit satellite constellation dynamics model and the relative drift amount, the theoretical holding time of each satellite within the allowable drift range is calculated;

[0182] Based on the theoretical hold time, the control sequence of the constellation and the optimal control time for each satellite are determined;

[0183] Under the control sequence, when the satellite reaches the optimal control time, the control values ​​of the satellite orbital parameters and the satellite propulsion system parameters during orbital maneuvers are determined to maintain the constellation configuration.

[0184] In a specific embodiment of the present invention, the overall process of the method for maintaining the low-Earth orbit constellation configuration using perturbation force and adjacent relative station position deviation is as follows: Figure 1 As shown, it includes the following steps:

[0185] 1) Construct a dynamic model of a low-Earth orbit satellite constellation.

[0186] In this embodiment, the low-Earth orbit satellite constellation dynamics model comprises two parts: the orbital dynamics model of a single satellite and the satellite constellation configuration. In a specific embodiment of the invention, the orbital dynamics model of a single satellite considers the Earth's non-spherical J2 perturbation and atmospheric drag perturbation, and the satellite constellation configuration is selected as a Walker-delta configuration constellation.

[0187] Among them, the orbital dynamics model of a single satellite considering the J2 term perturbation of the Earth's non-spherical shape and the atmospheric drag perturbation is shown in expression (1):

[0188] (1)

[0189] in, For the acceleration of a single satellite, Let the satellite's radius vector be the position vector in the geocentric inertial coordinate system. This represents the satellite's radius modulus in the geocentric inertial coordinate system. The gravitational constant is the constant of gravity. For the J2 term perturbation acceleration of the Earth's non-spherical shape, This is the acceleration caused by atmospheric drag perturbation.

[0190] Earth's gravitational acceleration on satellites It can be expressed as the gradient of the Earth's gravitational potential function U. ,in, This represents the satellite's radius modulus in a geocentric fixed coordinate system. The coordinates of the satellite in the geocentric coordinate system are the geocentric latitudes. This represents the satellite's longitude in a geocentrically fixed coordinate system. In the geocentrically fixed coordinate system... In the equation (2), the gravitational potential function of the Earth considering the J2 term perturbation due to the Earth's non-spherical shape is shown:

[0191] (2)

[0192] in, The radius of the Earth's equator. These are the coefficients of the Earth's gravitational potential model. According to measurements, in this embodiment The coefficients used are from the EGM96 Earth gravity field model.

[0193] The dynamic model of atmospheric perturbation is shown in expression (3):

[0194] (3)

[0195] in, This is the atmospheric drag vector. Let S be the drag coefficient, and S be the equivalent cross-sectional area with respect to atmospheric drag. Let V be the atmospheric density at the satellite's location in space, V be the satellite's velocity vector relative to the atmosphere, and V be the velocity magnitude of the satellite relative to the atmosphere. If the satellite's mass m is known, then the atmospheric drag perturbation acceleration vector experienced by the satellite is shown in expression (4):

[0196] (4)

[0197] Atmospheric density is strictly speaking a function of time and space, that is... This embodiment uses the NRLMSISE-00 atmospheric model.

[0198] In this embodiment, the satellite constellation configuration adopts the Walker-Delta constellation configuration. The Walker-Delta constellation is described by a constellation configuration code (… ).in, This represents the total number of satellites that make up a constellation; The number of orbital planes indicates the number of the constellation's orbital planes, with the ascending nodes of the orbital planes spaced at equal intervals. Uniform distribution; assume To determine the number of satellites on each orbital plane, we have: The phases of satellites in the same orbital plane are at equal intervals. Uniform distribution; Indicates the orbital inclination angle; Indicates the orbital altitude; Represents the phase factor, taking An integer between 1 and 2 represents the phase relationship between adjacent orbital planes and numbered satellites in the constellation; that is, the phase difference between adjacent orbital planes and numbered satellites is 1 / 2. .

[0199] The Walker-delta constellation configuration is currently the most commonly used satellite constellation configuration, therefore this embodiment uses it as the object to describe the specific implementation method. The method described in this embodiment is still applicable to other isomorphic constellation configurations.

[0200] 2) Obtain the orbital parameters of all satellites in the constellation and their adjacent satellites in space; the specific steps are as follows:

[0201] 2-1) Each satellite in the constellation is assigned a two-dimensional number.

[0202] In this embodiment, based on the Walker-Delta constellation configuration theory, all satellites in the constellation can be numbered in two dimensions. The specific method is as follows:

[0203] First, based on the initial design configuration of the constellation, the orbital planes can be numbered in order from 0 to 360° according to the ascending node's equatorial longitude, denoted as... , =1,2,…,P, where P represents the orbital plane number of the constellation. Then, satellites on the same orbital plane can be renumbered according to their in-plane phase from 0 to 360°, denoted as... , =1, 2, ..., S, where S represents the number of satellites on each orbital plane. In summary, any satellite in the constellation can determine its unique number using this numbering rule. .

[0204] 2-2) Based on the results of step 2-1), determine the numbers of the adjacent satellites of each satellite in the constellation.

[0205] In this embodiment, for any satellite in the constellation This allows us to determine the numbers of adjacent satellites within the constellation for that satellite. The specific calculation logic is as follows:

[0206] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0207] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0208] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0209] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0210] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0211] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0212] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0213] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ;

[0214] when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star .

[0215] 2-3) Based on the results of step 2-2), obtain the orbital parameters of all satellites in the constellation and their neighboring satellites.

[0216] In this embodiment, all satellites in the constellation obtain their absolute position in space through their onboard space positioning payloads. and motion state Where x, y, and z are the satellite radius vectors, respectively. The projection components on the three coordinate axes of the geocentric inertial coordinate system, v x v y v z These are the satellite's motion speeds. The projection components on the three coordinate axes of the geocentric inertial coordinate system.

[0217] Satellites determine their absolute position in space and motion state Subsequently, it can be converted into orbital parameters using orbital mechanics methods, including classical Kepler orbital elements. and near-circular orbit elements ,in For the semi-major axis of the track, For orbital eccentricity, For track inclination, Right ascension of the ascending node, For the perigee argument, For the near point angle, and The projection components of the orbital eccentricity in the two-dimensional nodal coordinate system, This refers to the phase angle of the mean latitude. Since the theory is quite comprehensive, it will not be elaborated upon here.

[0218] 3) Based on the results of step 2), calculate the station maintenance reference, relative drift, and allowable drift range for each satellite in the constellation; the specific steps are as follows:

[0219] 3-1) Determine the constellation configuration preservation requirements.

[0220] In this embodiment, the constellation configuration must be maintained as follows:

[0221] 3-1-1) Absolute orbital altitude of all satellites in the constellation It remains stable within the design range over a long period.

[0222] 3-1-2) Absolute orbital inclination difference of all satellites in the constellation and the difference in right ascension of the relative ascending node Stay within the design range.

[0223] 3-1-3) Family of relative phase differences between each satellite in the constellation and its neighboring satellites All remained within the design range.

[0224] 3-2) Calculate the baseline for each satellite's position in the constellation.

[0225] In this embodiment, the station maintenance benchmark includes:

[0226] 3-2-1) The orbital inclination and the right ascension of the ascending node (orbital plane) are maintained as references:

[0227] Orbital inclination angle based on constellation design As a baseline, the required orbital inclination angle for each satellite is... Maintain at Within the interval, i.e., the difference in absolute orbital inclination. Maintain at Within the interval. Among them, This is the maximum allowable drift threshold for the track inclination angle.

[0228] The right ascension of the ascending node of each orbital plane is taken as the reference value based on the theoretical right ascension of the ascending node of the corresponding orbital plane after averaging the drift deviation of the actual constellation configuration. This requires that each satellite (assuming it is at position 1)... Right ascension of the ascending node of the orbital plane Maintain at Within the interval, i.e., the difference in right ascension relative to the ascending node. Maintain at Within the interval. Among them, This is the maximum allowable drift threshold for the right ascension of the ascending node.

[0229] The actual constellation configuration after removing the average drift bias Theoretical right ascension of the ascending node of the orbital plane The method for determining is shown in equation (5):

[0230] (5)

[0231] 3-2-2) Orbital altitude and mean latitude argument (phase) maintenance benchmark:

[0232] The orbital altitude is the nominal orbital altitude in the constellation design configuration. As a baseline, the absolute orbital altitude of each satellite is required. Maintain at Within the interval, i.e., the absolute orbital altitude difference Maintain at Within the interval. Among them, This is the maximum allowable drift threshold for the orbital height.

[0233] The average latitude argument (phase) of each satellite is maintained by the relative orbital altitude difference. The satellites corresponding to all values ​​less than 0 in the data are used as the baseline. relative orbital altitude difference family The definition is shown in equation (6):

[0234] (6)

[0235] In the formula, , , , Satellites Compared to the relative orbital altitudes of its A1, A2, B1, and B2 satellites, , , , Satellites The absolute orbital altitudes of satellites A1, A2, B1, and B2.

[0236] This reference point uses all adjacent satellites with orbital altitudes greater than the main satellite as reference satellites. The relative phase difference between each satellite and all reference satellites is required. All remained at Within the interval. Among them, This is the maximum allowable drift threshold for the latitude angle. When the relative orbital altitude difference is... When all values ​​in the equation are greater than 0, the main star does not need to consider the maintenance of the mean latitude argument (phase), that is, the main star is the reference star for all neighboring stars.

[0237] In one specific embodiment of the present invention, the inter-satellite relationship between the main satellite and its neighboring satellites is as follows: Figure 2 As shown, the satellite with the pentagram in the center is the main satellite in this embodiment. The four adjacent black satellites in space are its neighboring satellites, i.e., satellites that directly establish inter-satellite links. The remaining gray satellites are non-neighboring satellites, i.e., satellites that do not directly establish inter-satellite links. The main satellite obtains the spatial position data of the four adjacent satellites through inter-satellite links. Assume that the data in this embodiment has the following results:

[0238] (7)

[0239] If the orbital altitudes of satellites A1 and B2 are higher than those of the main satellite (black satellites marked with triangles in the diagram), and the orbital altitudes of satellites A2 and B1 are lower than those of the main satellite (black satellites without graphic markings in the diagram), then satellites A1 and B2 are taken as the reference satellites.

[0240] 3-3) Calculate the relative drift of each satellite in the constellation.

[0241] For any satellite In this embodiment, the calculation process for the relative drift is as follows:

[0242] 3-3-1) Calculate the relative drift of the track height.

[0243] Among them, satellite Absolute orbital altitude :

[0244] (8)

[0245] In the formula, For satellite Its own absolute orbital altitude, For satellite Its own orbital semi-major axis, This is the average radius of the Earth.

[0246] satellite Absolute orbital height difference :

[0247] (9)

[0248] In the formula, The nominal orbital altitude for constellation design configurations.

[0249] In this embodiment, the absolute orbital altitude difference of the satellite is used. As the relative drift in satellite orbital altitude, the relative drift in the satellite's orbital altitude direction must be maintained at a certain value. Within the interval. In a specific embodiment of the present invention, the allowable drift threshold of the track height is taken. .

[0250] 3-3-2) Calculate the relative drift of the track inclination angle.

[0251] Among them, satellite Absolute orbital inclination difference :

[0252] (10)

[0253] In the formula, For satellite Its own orbital inclination, The orbital tilt angle for designing constellations.

[0254] In this embodiment, the absolute orbital inclination difference of the satellite is... As a relative drift of the satellite's orbital inclination, the relative drift of the satellite's orbital inclination must be maintained at a certain value. Within the interval. In a specific embodiment of the present invention, the allowable drift threshold of the track inclination angle is taken. It should be noted that the main perturbations experienced by low-Earth orbit satellites do not have a long-term impact on orbital inclination, and even a small difference in absolute orbital inclination can cause significant relative precession of the orbital plane. Therefore, in practical implementations, the relative drift of orbital inclination is only used as a backup control constraint.

[0255] 3-3-3) Calculate the relative shift of the right ascension of the ascending node.

[0256] In this embodiment, the satellite Relative difference in right ascension of ascending node :

[0257] (11)

[0258] In the formula, For satellite Its own ascending node right ascension, After removing the average drift bias from the actual constellation configuration The theoretical right ascension of the ascending node on the orbital plane is calculated from the ground and then fed up to all satellites in the constellation.

[0259] In this embodiment, the difference in right ascension of the relative ascending node of the satellite is used. As the relative drift of the satellite's right ascension at the ascending node, the relative drift of the satellite in the direction of the right ascension at the ascending node must be maintained at... Within the interval. In a specific embodiment of the present invention, the allowable drift threshold of the right ascension of the ascending node is taken. .

[0260] 3-3-4) Calculate the in-plane phase relative drift.

[0261] Among them, satellite relative phase difference family :

[0262] (12)

[0263] In the formula, For satellite Its own latitude argument (phase). , , , Satellites The mean latitude argument (phase) of stars A1, A2, B1, and B2.

[0264] In this embodiment, the relative phase difference family of the satellite As the relative drift of the satellite's in-plane phase, the relative drift of the satellite relative to the reference star in the in-plane phase direction must be maintained at... Within the interval. In a specific embodiment of the present invention, the in-plane phase drift tolerance threshold is taken. .

[0265] 3-4) Based on the results of step 3-3), calculate the allowable drift range for each satellite.

[0266] In one specific embodiment of the present invention, the allowable drift range of a single satellite is as follows: Figure 3 As shown in the figure, the gray satellite represents the projection of the theoretical phase of the main star relative to a reference star onto the nominal orbit corresponding to the theoretical right ascension of the main star's ascending node after removing the average drift deviation; this is called the virtual reference star. The black satellite represents the actual spatial position of the main star. In space, with the gray satellite as the geometric center, the relative drift of the orbital altitude (corresponding to the allowable drift threshold), the relative drift of the ascending node's right ascension (corresponding to the allowable drift threshold), and the relative drift of the in-plane phase (corresponding to the allowable drift threshold) together constitute the allowable drift range of the main star. The direction corresponding to the relative drift of the orbital altitude is the geocentric direction relative to the radius vector of the main star; the direction corresponding to the relative drift of the ascending node's right ascension is the east-west direction of the theoretical ascending node's right ascension at the equator; and the direction corresponding to the relative drift of the in-plane phase is the tangent direction of the theoretical orbit of the virtual reference star. The allowable drift thresholds in these three directions correspond to three one-dimensional intervals: , , .

[0267] Furthermore, it should be noted that in special cases, when none of the adjacent satellites of the main star are used as reference stars, the in-plane phase relative drift of the main star can be considered unconstrained, with only the relative drift in orbital altitude and the relative drift in right ascension of the ascending node remaining constant. , For intervals, there is no need to consider the relative drift of the in-plane phase.

[0268] 4) Based on the results of steps 1) and 3), calculate the theoretical holding time of each satellite within the allowable drift range. The specific steps are as follows:

[0269] 4-1) Calculate the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node.

[0270] set up For the current moment, when At that time, the actual right ascension of the satellite's ascending node tends to shift eastward relative to the theoretical right ascension of the ascending node on the orbital plane after the mean drift deviation. Therefore, the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node is limited. It can be calculated from equation (13):

[0271] (13)

[0272] when At that time, the actual right ascension of the satellite's ascending node tends to shift westward relative to the theoretical right ascension of the ascending node on the orbital plane after the mean drift deviation. Therefore, the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node is limited. It can be calculated from equation (14):

[0273] (14)

[0274] when At that time, the actual right ascension of the satellite's ascending node has no tendency to move relative to the surrounding area; therefore, it is considered that... .

[0275] In equations (13) and (14), , which is the first-order long-term drift rate of the right ascension of the ascending node caused by the J2 term perturbation of the Earth's non-spherical shape. The nominal orbital angular velocity, This is the semi-major diameter of the track.

[0276] 4-2) Calculate the theoretical holding time of the satellite in the orbital plane; the specific steps are as follows:

[0277] 4-2-1) Calculate the theoretical holding time of the satellite within the allowable drift range of its orbital altitude. .

[0278] In this embodiment, the theoretical holding time of the satellite within the allowable orbital altitude drift range is... It can be obtained by calculation using equation (15):

[0279] (15)

[0280] In the formula, The rate of change of orbital altitude, The nominal semi-major axis of the track.

[0281] 4-2-2) Calculate the theoretical holding time of the satellite within the in-plane phase allowable drift range. .

[0282] In this embodiment, a theoretical hold-time family is defined for the main star relative to its four neighboring stars. Where A1 and A2 are coplanar neighboring satellites, and B1 and B2 are non-coplanar neighboring satellites. The theoretical retention time of a satellite relative to a non-reference satellite is defined as... Next, we calculate the theoretical holding time of the satellite phase relative to the reference star within the allowable drift range.

[0283] 4-2-2-1) Calculate the theoretical holding time of the satellite's in-plane phase relative to the coplanar reference star within the allowable drift range. :

[0284] (16)

[0285] In the formula, i is a formal parameter, which can be 1 or 2; when i = 1, Ai represents star A1, and the same applies to Bi in the following text.

[0286] 4-2-2-2) Calculate the theoretical holding time of the satellite's in-plane phase relative to the out-of-plane reference star within the allowable drift range. :

[0287] Define the short-term orbital altitude variation rate deviation of the main star relative to the eccentric reference star Bi. It has a quadratic function:

[0288] (17)

[0289] According to equation (17), we can obtain The future time interval corresponding to the given time is represented by a set. This leads to the theoretical holding time of the satellite's in-plane phase relative to any out-of-plane reference star within the allowable drift range. :

[0290] (18)

[0291] 4-2-2-3) The theoretical holding time of the satellite's in-plane phase relative to the coplanar reference star within the allowable drift range, based on calculations. The theoretical holding time of the in-plane phase relative to the out-of-plane reference star within the allowable drift range. The theoretical retention time family of the main star relative to its four neighboring stars can be determined. The theoretical holding time of the in-plane phase within the allowable drift range .

[0292] 4-2-3) Based on the results of steps 4-2-1) and 4-2-2), considering the coupling relationship between orbital altitude and in-plane phase maintenance control, the minimum value of the two is taken as the theoretical maintenance time of the satellite in the orbital plane. .

[0293] 5) Based on the results of step 4), each satellite in the constellation obtains the theoretical hold-up time of all other satellites to determine the control sequence of the constellation and the optimal control time for each satellite.

[0294] In this embodiment, all satellites in the constellation can determine their theoretical hold-up time and actively control themselves after reaching the theoretical hold-up time, i.e., after the satellite exceeds the allowable drift range. However, this control logic may lead to two or more satellites controlling themselves simultaneously, resulting in a degraded constellation performance. Therefore, it is necessary to plan the constellation satellite control sequence as a whole to avoid this situation. Furthermore, since the control period in the satellite orbital plane is much longer than the control period within the orbital plane, this embodiment discusses the constellation satellite orbital plane control sequence and the control sequence within the orbital plane separately, assuming that they are also uncoupled. The specific steps are as follows:

[0295] 5-1) Determine the control sequence for the orbital planes of the constellation satellites.

[0296] In this embodiment, for the control of the orbital plane (right ascension of the ascending node), there are generally: Therefore, the "over-range" discrete sequence control strategy can be directly used to sort and discretize the orbital plane control of the entire constellation in time.

[0297] The logic is to determine the theoretical holding time of all satellites within the allowable drift range of their right ascension at the ascending node. Arrange in a sequence , where the set With sets To satisfy the one-to-one mapping relationship, and have Starting with the last satellite in the sequence, if the difference in the theoretical hold-up time between any two adjacent satellites in the sequence is less than one orbital period, then... This advances the control timing of the preceding star, making This process continues until the first satellite is completed. The final sequence is arranged into a discrete sequence of optimal control times for each satellite. Specifically, when a satellite reaches its optimal control time calculated using the above method... Then, station maintenance control begins to achieve a discrete distribution of satellite control times within the constellation.

[0298] 5-2) Determine the control sequence of the satellite within the orbital plane.

[0299] In this embodiment, for the control within the orbital plane (orbital height and in-plane phase), based on the ideal sequence time... With orbital period The magnitude relationship, and set the constellation relaxation coefficient k ( This represents the ratio of the overall constellation's maintenance period to the ideal total duration of its control. Low-Earth orbit constellations can be classified and different control strategies can be employed; specifically including:

[0300] 5-2-1) When At the same time, the control within the constellation's orbital plane can also employ the "over-tolerance" discrete sequence control strategy to sort and discretize the overall orbital plane control of the constellation over time.

[0301] The logic is based on the theoretical hold time of all satellites within the orbital plane. Arrange in a sequence , where the set With sets To satisfy the one-to-one mapping relationship, and have Starting with the last satellite in the sequence, if the difference in the theoretical hold-up time between any two adjacent satellites in the sequence is less than one orbital period, then... This advances the control timing of the preceding star, making This process continues until the first satellite completes its mission. The final sequence is arranged into a discrete sequence of optimal control times for each satellite. When a satellite reaches its optimal control time calculated using the above method... Then, station maintenance control begins to achieve a discrete distribution of satellite control times within the constellation.

[0302] 5-2-2) When When it is difficult to discretize the global control time of the constellation through the "over-tolerance" discrete sequence control strategy, the control within the constellation orbital plane can be discretized by the local "over-tolerance" discrete sequence control strategy.

[0303] The logic is to arrange the theoretical dwell times of the main star and adjacent satellites within the orbital plane into a sequence. X1, X2, X3, X4, and X5 can take values ​​from the numbers of the main star, A1 star, A2 star, B1 star, and B2 star, and these values ​​are unique. Starting with the last satellite in the sequence, if the difference in the theoretical hold-up time between any two adjacent satellites in the sequence is less than one orbital period, i.e. This advances the control timing of the preceding star, making This process continues until the first satellite finishes. Ultimately, this results in a discrete sequence of optimal control times for adjacent satellites. When a satellite reaches its designated optimal control time... Then, station maintenance control begins to achieve a local discrete distribution of satellite control time in the constellation.

[0304] 6) Based on the model in step 1) and the results in steps 3) and 5), when the satellite reaches the optimal control time, determine the control quantities of the satellite orbital parameters and the satellite propulsion system parameters during orbital maneuvers. The specific steps are as follows:

[0305] 6-1) Calculate the control variables for satellite orbital parameters, specifically including:

[0306] 6-1-1) Calculate the track surface drift control parameters.

[0307] While the orbital inclination of low-Earth orbit (LEO) satellites remains almost constant, deviations in orbital inclination are the primary factor causing relative deviations in the right ascension of the ascending node. Based on this principle, indirect control of the right ascension of the ascending node can be achieved through a small offset in orbital inclination.

[0308] In this embodiment, the planned maintenance period is set as follows: In a specific embodiment of the present invention, Day. Assume the time before control is... After control, the time is .

[0309] Based on the allowable deviation range setting and The orbital state parameters of a spacecraft at any given time can be used to calculate the relative drift rate of the ideal ascending node's right ascension after control. :

[0310] (19)

[0311] During track maneuvering, Heng was established.

[0312] like ,but Conversely, if ,but .

[0313] Expected orbital inclination offset It can be represented as:

[0314] (20)

[0315] In the formula, the long-term drift rate of the right ascension of the ascending node considering the perturbation of the J2 term of the Earth's non-spherical shape is given. .like Then let The sign remains unchanged, and the modulus is updated to No action will be taken for the remaining cases.

[0316] This allows us to obtain the absolute orbital inclination angle after control. and change in orbital inclination

[0317] (twenty one)

[0318] 6-1-2) Calculate the orbital height and phase coupling control parameters.

[0319] Orbital altitude deviation is the main factor causing relative phase deviation in spacecraft, and atmospheric drag causes a continuous decrease in orbital altitude. By utilizing the approximate law of atmospheric drag perturbation, a small offset can be made to the spacecraft's orbital altitude, achieving direct control over orbital altitude and indirect control over phase.

[0320] In this embodiment, it is assumed that the control time before time is After control, the time is .

[0321] For cases where the height exceeds the limit ( ):

[0322] (twenty two)

[0323] The purpose of orbit control is to keep the spacecraft's orbital altitude within the allowable deviation range for as long as possible, without exceeding the orbital altitude limit, and to reserve a certain redundancy for the position control of adjacent satellites. The control amount for orbital altitude can be calculated using equation (23):

[0324] (twenty three)

[0325] in, The first proportionality coefficient, with a value between between.

[0326] For the case of phase lead ( ):

[0327] (twenty four)

[0328] In the formula, Number the neighboring reference stars according to The differences can be further subdivided into relative coplanar advance ( ) and relative anti-plane advance ( ).

[0329] When the relative coplanar lead is maintained, the relative deviation of the track height will hardly change, and the control amount of the track height can be calculated according to formula (25):

[0330] (25)

[0331] In the formula, The orbital altitude offset corresponding to a phase maintenance period greater than T days can be calculated using equation (26).

[0332] (26)

[0333] In the case of relative out-of-plane advance, due to the short-term deviation in the rate of change of orbital altitude between the two stars... ,in, The rate of change of the orbital altitude of the main star. Let be the rate of change of the orbital altitude of Bi star. The offset of the orbital altitude can be calculated by inversely using the phase quadratic variation trend of equation (27).

[0334] (27)

[0335] By solving the equations in the system of equations (28), the relative orbital height difference after ideal control can be obtained. At this time, the control amount of orbital height can be calculated according to equation (29).

[0336] (28)

[0337] (29)

[0338] in, This is the second proportionality coefficient, and its value ranges from... between.

[0339] Furthermore, in all the above situations, if control is implemented... Exceeding The scope is determined according to As the absolute height deviation after control, the control quantity of track height is recalculated.

[0340] (30)

[0341] In this control logic, all satellite orbit control is an orbit raising maneuver, which avoids the fuel consumption caused by satellite orbit lowering control and helps to extend the constellation's operational lifespan.

[0342] 6-2) Calculate the satellite's propulsion system parameters.

[0343] In this embodiment, the velocity pulse increment required for track surface control is relatively large, so only the pulse thrust method is considered; the velocity increment required for in-plane control is relatively small, so both the pulse thrust method and the small thrust method are considered.

[0344] Pulse thrust is a method that uses a high-thrust engine to generate an impulse instantaneously, thereby changing the spacecraft's velocity. Typically, chemical thrusters are used, with a specific impulse of [value missing]. In this embodiment, it is taken as .

[0345] 6-2-1) Control of track surface drift:

[0346] Through normal velocity pulse The change in the spacecraft's orbital inclination, the increase in normal velocity and the mass of fuel consumed in a single propulsion are shown in equations (31) and (32), respectively:

[0347] (31)

[0348] (32)

[0349] 6-2-2) Control of orbital altitude and phase:

[0350] Through lateral velocity pulse The lateral velocity increment and fuel consumption for a single control of the spacecraft's orbital altitude are shown in equations (33) and (34), respectively.

[0351] (33)

[0352] (34)

[0353] The low-thrust method generates impulse by continuously operating a low-thrust engine, thereby changing the spacecraft's velocity. This embodiment uses the Hall effect thruster employed in Starlink Gen 1 as a reference, taking the thrust... , specific impulse The operating time of the small-thrust engine and the operating duration of the electric thruster were calculated using an analytical orbit control generation method. and The relational expression is as follows:

[0354] (35)

[0355] The method for determining the lateral velocity increment and fuel mass consumed in a single control is consistent with that in equation (34).

[0356] 6-2-3) Determine the satellite's orbital control spatial position and implement control based on propulsion parameters.

[0357] Control of track surface drift:

[0358] Satellites pass through latitude azimuth or A normal impulse is generated at the point, achieving track surface adjustment. According to... Argument of latitude at time It can calculate the start-up time:

[0359] (36)

[0360] In the formula, This represents the actual orbital angular velocity of the satellite.

[0361] Control of orbital altitude and phase:

[0362] To ensure that the eccentricity of the track does not change during track height adjustments, phase difference is generally used. Two lateral maneuvers alter the spacecraft's orbital altitude to counteract the change in eccentricity. Assume the first orbital altitude control occurs at... The second orbital altitude control time is Then, the activation times for the two control actions under pulse thrust conditions are as follows:

[0363] (37)

[0364] By combining all the above methods, it is possible to determine the positioning benchmarks of large constellations, plan the control sequences, determine the control parameters, and ultimately achieve the long-term stable maintenance of the relative configuration of constellations.

[0365] Next, a specific embodiment will be used to further demonstrate the constellation configuration maintenance result obtained by the method described in this embodiment. In this embodiment, the Walker-Delta constellation configuration code is: The maximum deviation of satellite orbital altitude, maximum deviation of phase, satellite status, and distribution of control time intervals within 90 days can be obtained as follows: Figures 4 to 7 As shown.

[0366] Figure 4 This is a diagram showing the absolute orbital altitude difference of constellation satellites within 90 days in a specific embodiment of the present invention. Figure 4 middle, This is the arithmetic mean of the absolute orbital altitude differences of all satellites in the constellation. This represents the maximum value of the absolute orbital altitude differences among all satellites in the constellation. This represents the minimum absolute orbital altitude difference among all satellites in the constellation. The results show that the absolute orbital altitude difference of all satellites in the constellation remained within the allowable drift threshold for 90 days. Within the specified range, it meets the control requirements.

[0367] Figure 5 This is a schematic diagram of the maximum phase deviation of constellation satellites within 90 days in a specific embodiment of the present invention. Figure 5 middle, This is the arithmetic mean of the in-plane phase relative drift of all satellites in the constellation. This represents the maximum in-plane phase relative drift of all satellites in the constellation. This represents the minimum in-plane phase relative drift of all satellites in the constellation. The results show that the in-plane phase relative drift of all satellites in the constellation remains within the allowable drift threshold over 90 days. Within the specified range, it meets the control requirements.

[0368] Figure 6 This is a constellation satellite status diagram within 90 days in a specific embodiment of the present invention. The results show that the method successfully discretizes the actual control time of the constellation satellites within 90 days, that is, at most only one satellite is being controlled at any given time, which meets the discretization requirements.

[0369] Figure 7 This is a distribution diagram of the control time interval of constellation satellites in a specific embodiment of the present invention. The results show that the method successfully discretizes the actual control time of constellation satellites within 90 days. The two adjacent control times in the constellation are all greater than one orbital period, which meets the discretization requirements.

[0370] In summary, it can be seen that the constellation configuration drift and control timing are both within the engineering constraints, proving the feasibility of the low-Earth orbit constellation configuration maintenance method proposed in this embodiment, which utilizes perturbation forces and relative station position deviations.

Claims

1. A method for maintaining the configuration of a low-Earth orbit constellation using perturbation forces and relative station position deviations, characterized in that, include: Obtain the orbital parameters of each satellite and its neighboring satellites in a low-Earth orbit satellite constellation; Based on the orbital parameters, the relative drift and allowable drift range of each satellite in the constellation are calculated; Based on the preset low-Earth orbit satellite constellation dynamics model and the relative drift amount, the theoretical holding time of each satellite within the allowable drift range is calculated; Based on the theoretical hold time, the control sequence of the constellation and the optimal control time for each satellite are determined; Under the control sequence, when the satellite reaches the optimal control time, the control values ​​of the satellite orbital parameters and the satellite propulsion system parameters during orbital maneuvers are determined to maintain the constellation configuration.

2. The method according to claim 1, characterized in that, The low-Earth orbit satellite constellation dynamics model consists of two parts: the orbital dynamics model of a single satellite and the satellite constellation configuration. The orbital dynamics model of the single satellite takes into account the Earth's non-spherical J2 perturbation and atmospheric drag perturbation, and its expression is as follows: （1） in, For the acceleration of a single satellite, Let the satellite's radius vector be the coordinate vector in the geocentric inertial coordinate system. This represents the satellite's radius modulus in the geocentric inertial coordinate system. The gravitational constant is the constant of gravity. For the J2 term perturbation acceleration of the Earth's non-spherical shape, This is atmospheric drag perturbation acceleration; Earth's gravitational acceleration on satellites The gradient of the Earth's gravitational potential function U is expressed as... ,in, This represents the satellite's radius modulus in a geocentric fixed coordinate system. The coordinates of the satellite in the geocentric coordinate system are the geocentric latitudes. The longitude of the satellite in the geocentric fixed coordinate system; in the geocentric fixed coordinate system In the equation, considering the perturbation of the J2 term of the non-spherical Earth, the expression for the gravitational potential function of the Earth is as follows: （2） in, The radius of the Earth's equator. These are the coefficients of the Earth's gravitational potential model. The dynamic model of atmospheric perturbation is expressed as follows: （3） in, This is the atmospheric drag vector. Let S be the drag coefficient, and S be the equivalent cross-sectional area with respect to atmospheric drag. V is the atmospheric density at the satellite's location in space, V is the satellite's velocity vector relative to the atmosphere, and V is the satellite's velocity magnitude relative to the atmosphere. Given the satellite's mass m, the vector expression for the atmospheric drag perturbation acceleration experienced by the satellite is as follows: （4） The satellite constellation configuration adopts the Walker-Delta constellation configuration, and the constellation configuration code is ( );in, This represents the total number of satellites that make up a constellation; The number of orbital planes indicates the constellation's orbital planes, with the ascending nodes of the orbital planes spaced at equal intervals. Uniform distribution; The number of satellites on each orbital plane. The phases of satellites in the same orbital plane are at equal intervals. Uniform distribution; Indicates the orbital inclination angle; Indicates the orbital altitude; Represents the phase factor, taking An integer between 1 and 2 represents the phase relationship between adjacent orbital planes and numbered satellites in the constellation; that is, the phase difference between adjacent orbital planes and numbered satellites is 1 / 2. .

3. The method according to claim 2, characterized in that, Also includes: Each satellite in the constellation is assigned a two-dimensional number; specifically, based on the initial design configuration of the constellation, the orbital planes are numbered sequentially from 0 to 360° according to the ascending node's equatorial ascension. , =1,2,…,P, where P represents the orbital plane number of the constellation; satellites in the same orbital plane are renumbered according to their in-plane phase from 0 to 360°, denoted as , =1,2,…,S, where S represents the number of satellites on each orbital plane; thus, the number of any satellite in the constellation is determined and denoted as . ; For any satellite Determine the corresponding neighboring satellite number in the constellation for this satellite, specifically including: when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star ; when , At that time, satellite The adjacent satellites are A1 satellites in the same orbital plane. A2 star B1 star in the adjacent orbital plane B2 star .

4. The method according to claim 3, characterized in that, The acquisition of orbital parameters in space for each satellite and its neighboring satellites in the low-Earth orbit satellite constellation includes: All satellites in a constellation obtain their absolute positions in space. and motion state Where x, y, and z are the satellite radius vectors, respectively. The projection components on the three coordinate axes of the geocentric inertial coordinate system, v x v y v z These are the satellite's motion speeds. Projected components on the three coordinate axes of the geocentric inertial coordinate system; Satellites determine their absolute position in space and motion state Subsequently, it was transformed into orbital parameters using orbital mechanics methods, including Kepler orbital elements. and near-circular orbit elements ,in For the semi-major axis of the track, For orbital eccentricity, For track inclination, Right ascension of the ascending node For the perigee argument, For the near point angle, and The projection components of the orbital eccentricity in the two-dimensional nodal coordinate system, It is the angle of the mean latitude.

5. The method according to claim 4, characterized in that, Before calculating the relative drift and allowable drift range of each satellite in the constellation, the method further includes: Determine the constellation configuration maintenance requirements and calculate the positioning maintenance reference for each satellite in the constellation; The determination of constellation configuration preservation requirements includes: 1) Absolute orbital altitude of all satellites in the constellation It remains stable within the design range over a long period; 2) The absolute orbital inclination difference of all satellites in the constellation Difference of right ascension of relative ascending node Stay within the design range; 3) The relative phase difference between each satellite in the constellation and its neighboring satellites All remained within the design range; The calculation of the positioning of each satellite in the constellation to maintain the reference includes: 1) Orbital inclination and right ascension of the ascending node maintain the reference: Orbital inclination angle based on constellation design As a baseline, the required orbital inclination angle for each satellite is... Maintain at Within the interval, i.e., the difference in absolute orbital inclination. Maintain at Within the interval, where, The maximum allowable drift threshold for the track inclination angle; The right ascension of the ascending node of each orbital plane is based on the theoretical right ascension of the ascending node of the corresponding orbital plane after averaging the drift deviation from the actual constellation configuration. For the th The orbital plane requires the right ascension of the ascending node of each satellite on that plane. Maintained within interval c, i.e., the difference in right ascension relative to the ascending node. Maintain at Within the interval, where, This is the maximum allowable drift threshold for the right ascension of the ascending node; The actual constellation configuration after removing the average drift bias Theoretical right ascension of the ascending node of the orbital plane The determination method is as follows: （5） 2) The orbital altitude and the aspect ratio of the mean latitude are maintained at the baseline: The orbital altitude is the nominal orbital altitude in the constellation design configuration. As a baseline, the absolute orbital altitude of each satellite is required. Maintain at Within the interval, i.e., the absolute orbital altitude difference Maintain at Within the interval, where, This represents the maximum allowable drift threshold at the track height. The mean latitude angle of each satellite is maintained by the relative orbital altitude difference. Based on all satellites with values ​​less than 0, any satellite relative orbital altitude difference family The calculation expression is as follows: （6） In the formula, , , , Satellites Compared to the relative orbital altitudes of its A1, A2, B1, and B2 satellites, , , , Satellites The absolute orbital altitudes of satellites A1, A2, B1, and B2; This reference uses all adjacent satellites with orbital altitudes greater than the main satellite as reference satellites, requiring the relative phase difference between each satellite and all reference satellites. All remained at Within the interval; where, The maximum allowable drift threshold for the horizontal latitude angle; when the relative orbital altitude difference family When all values ​​in the equation are greater than 0, the main star does not need to consider the maintenance of the mean latitude argument, and at this time the main star is the reference star for all adjacent stars.

6. The method according to claim 5, characterized in that, The calculation of the relative drift and allowable drift range of each satellite in the constellation includes: 1) Calculate the relative drift of each satellite within the constellation; For any satellite The calculation process for the relative drift is as follows: 1-1) Calculate the relative drift of the track height; Among them, satellite Absolute orbital altitude : （8） In the formula, For satellite Its own absolute orbital altitude, For satellite Its own orbital semi-major axis, The average radius of the Earth; satellite Absolute orbital height difference : （9） In the formula, The nominal orbital altitude for constellation configuration design; The absolute orbital altitude difference of the satellite As the relative drift in satellite orbital altitude, the relative drift in the satellite's orbital altitude direction must be maintained at a certain value. Within the range; 1-2) Calculate the relative drift of the track inclination angle; Among them, satellite Absolute orbital inclination difference : （10） In the formula, For satellite Its own orbital inclination, Orbital inclination angles for constellation configurations; The absolute orbital inclination difference of the satellite As a relative drift of the satellite's orbital inclination, the relative drift of the satellite's orbital inclination must be maintained at a certain value. Within the range; 1-3) Calculate the relative shift of the right ascension of the ascending node; Among them, satellite Relative difference in right ascension of ascending node : （11） In the formula, For satellite Its own ascending node right ascension, After removing the average drift bias from the actual constellation configuration The theoretical right ascension of the ascending node of the orbital plane; The difference in right ascension of the relative ascending nodes of the satellites As the relative drift of the satellite's right ascension at the ascending node, the relative drift of the satellite in the direction of the right ascension at the ascending node must be maintained at... Within the range; 1-4) Calculate the in-plane phase relative drift; Among them, satellite relative phase difference family : （12） In the formula, For satellite Its own latitudinal argument, , , , Satellites The mean latitude argument of stars A1, A2, B1, and B2; The relative phase difference family of satellites As the relative drift of the satellite's in-plane phase, the relative drift of the satellite relative to the reference star in the in-plane phase direction must be maintained at... Within the range; 2) Based on the results of step 1), calculate the allowable drift range for each satellite; The allowable drift range includes three interval constraints, namely: , , ; When none of the adjacent satellites of the main body are used as reference satellites, the in-plane phase relative drift of the main body is unconstrained; only the relative drift of orbital altitude and the relative drift of right ascension of the ascending node are maintained at [values ​​to be filled in]. , Interval.

7. The method according to claim 6, characterized in that, The calculation of the theoretical holding time for each satellite within the allowable drift range includes: 1) Calculate the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node; set up For the current moment, when At that time, the theoretical holding time of the satellite within the allowable drift range of the right ascension of the ascending node. The calculation expression is as follows: （13） when At that time, the theoretical dwell time of the satellite within the allowable drift range of the right ascension of the ascending node. The calculation expression is as follows: （14） when At that time, the actual right ascension of the satellite's ascending node has no tendency to move relative to the surrounding area. ; In the formula, , which is the first-order long-term drift rate of the right ascension of the ascending node caused by the J2 term perturbation of the Earth's non-spherical shape; The nominal orbital angular velocity, This is the semi-major diameter of the track. 2) Calculate the theoretical holding time of the satellite in the orbital plane; the specific steps are as follows: 2-1) Calculate the theoretical holding time of the satellite within the allowable drift range of its orbital altitude. : （15） In the formula, The rate of change of orbital altitude, The nominal semi-major axis of the track; 2-2) Calculate the theoretical holding time of the satellite within the in-plane phase allowable drift range. ; 2-2-1) Calculate the theoretical holding time of the satellite's in-plane phase relative to the coplanar reference star within the allowable drift range. : （16） 2-2-2) Calculate the theoretical holding time of the satellite's in-plane phase relative to the out-of-plane reference star within the allowable drift range. : Among them, the deviation of the short-term orbital altitude change rate of the main star relative to the eccentric reference star Bi is... It has a quadratic function: （17） According to equation (17), we can obtain The future time interval corresponding to the given time is represented by a set. Furthermore, there is the theoretical holding time of the satellite's in-plane phase relative to any out-of-plane reference star within the allowable drift range. : （18） 2-2-3) Based on the results of steps 2-2-1) and 2-2-2), determine the theoretical hold-up time family of the main star relative to its four neighboring stars. The theoretical holding time of the in-plane phase within the allowable drift range ; 2-3) Based on the results of steps 2-1) and 2-2), determine the theoretical holding time of the satellite in the orbital plane. .

8. The method according to claim 7, characterized in that, The determination of the control sequence of the constellation and the optimal control time for each satellite includes: 1) Determine the control sequence for the orbital planes of the constellation satellites; For orbital plane control, the theoretical holding time for all satellites within the allowable drift range of right ascension at the ascending node is... Arrange in a sequence , where the set With sets To satisfy the one-to-one mapping relationship, and have Starting from the last satellite in the sequence, traverse the sequence. If the theoretical hold-up time difference between any two adjacent satellites in the sequence is less than one orbital period, then... This advances the control timing of the preceding star, making After the traversal is complete, a discrete sequence of optimal control times for each satellite is generated; when any satellite reaches the optimal control time determined in this sequence... Then, position maintenance control will begin; 2) Determine the control sequence for satellites within the orbital plane; For control within the orbital plane, the constellation relaxation coefficient k is set, representing the ratio of the overall constellation maintenance period to the ideal total duration of constellation control. ); when At that time, the theoretical hold time of all satellites in the orbital plane Arrange in a sequence , where the set With sets To satisfy the one-to-one mapping relationship, and have Starting from the last satellite in the sequence, traverse the sequence. If the theoretical hold-up time difference between any two adjacent satellites in the sequence is less than one orbital period, then... This advances the control timing of the preceding star, making After the traversal is complete, a discrete sequence of optimal control times for each satellite is generated; when any satellite reaches the optimal control time determined in this sequence... Then, position maintenance control will begin; when At that time, the theoretical hold times of the main star and adjacent satellites within the orbital plane are arranged into a sequence. ,in, Starting from the last satellite in the sequence, traverse the sequence, where if the difference in the theoretical hold time between two adjacent satellites in the sequence is less than one orbital period, i.e. This advances the control timing of the preceding star, making After the traversal is complete, a discrete sequence of optimal control times for adjacent satellites is generated. When any satellite reaches the set optimal control time... Then, position maintenance control will begin.

9. The method according to claim 8, characterized in that, The calculation method for the control quantities of the satellite orbital parameters is as follows: 1) Calculate the track surface drift control parameters; The planned maintenance period is set as follows Let the control time before be After control, the time is ; Calculate the relative drift rate of the ideal ascending node right ascension after control. : （19） During track maneuvering, Heng is established; like ,but ;like ,but ; Expected orbital inclination offset Represented as: （20） In the formula, the long-term drift rate of the right ascension of the ascending node considering the perturbation of the J2 term of the Earth's non-spherical shape is taken into account. ; Judgment: If Then let The sign remains unchanged, and the modulus is updated to Otherwise, keep constant; This allows us to obtain the absolute orbital inclination angle after control. and change in orbital inclination : （21） 2) Calculate the orbital altitude and phase coupling control parameters; For cases where the height exceeds the limit, i.e. : （22） The control value for the track height at this time is: （23） in, The first proportionality coefficient, with a value between between; For the phase-leading case, i.e. : （24） In the formula, Number the reference stars in the neighborhood; Corresponding to relative coplanar leading, Corresponding to the relative antiplane leading; When there is relative coplanar advance, the relative deviation of the track height will hardly change, and the control amount of the track height is: （25） In the formula, The corresponding orbital altitude offset with a phase maintenance period greater than T days: （26） In the case of relative out-of-plane advance, due to the short-term deviation in the rate of change of orbital altitude between the two stars... ,in, The rate of change of the orbital altitude of the main star. Given the rate of change of orbital altitude of Bi star, the orbital altitude offset is calculated as follows: （27） By solving the equation system (28) simultaneously, the relative track height difference after ideal control is obtained. At this time, the control amount of track height is calculated according to equation (29). （28） （29） in, This is the second proportionality coefficient, and its value ranges from... between; In all cases, if control is in effect Exceeding The range is determined according to As the absolute height deviation after control, the control quantity for track height is recalculated: （30）。 10. The method according to claim 9, characterized in that, The satellite's propulsion system parameters are calculated as follows: 1) Control of track surface drift: Through normal velocity pulse The change in the spacecraft's orbital inclination, the increase in normal velocity and the mass of fuel consumed in a single propulsion are shown in equations (31) and (32), respectively: （31） （32） 2) Control of orbital altitude and phase: Through lateral velocity pulse The lateral velocity increment and fuel consumption for a single control operation, depending on the change in the spacecraft's orbital altitude, are shown in equations (33) and (34), respectively: （33） （34） 3) Determine the satellite's orbital control position and implement control based on propulsion parameters; Control of track surface drift: Satellites pass through latitude azimuth or A normal impulse is generated at the point of origin, achieving track surface adjustment; according to Argument of latitude at time Calculate the start-up time: （36） In the formula, This refers to the actual orbital angular velocity of the satellite. Control of orbital altitude and phase: Through phase difference The two lateral maneuvers changed the spacecraft's orbital altitude, offsetting the change in eccentricity; Assume the first orbital altitude control time is The second orbital altitude control time is Then, the activation times for the two control actions under pulse thrust conditions are as follows: （37）。

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