A method of electric propulsion thrust calibration

Abstract

The application relates to a method for calibrating electric propulsion thrust, and relates to the technical field of satellite thrust calculation. The method comprises the following steps: taking a virtual satellite before orbit control as a primary satellite, taking a real satellite after orbit control as a secondary satellite, and calculating the relative position deviation between the primary and secondary satellites in an inertial system; calculating the relative position deviation of the primary and secondary satellites in a formation coordinate system; calculating initial configuration parameters according to the orbit plane roots of the primary and secondary satellites at a preset moment before orbit control, and obtaining a solution of the initial configuration parameters; and obtaining an estimated value of the orbit control thrust according to the solution of the initial configuration parameters. In the application, the orbit before orbit control is taken as a virtual primary satellite orbit, and the orbit after orbit control is obtained as a real secondary satellite orbit by orbit determination using observation data, so that the initial configuration parameters are calculated, the parameter solution is obtained, and finally the estimated value of the thrust is obtained according to the parameter solution. The calculation precision is high, and more reliable data support is provided for satellite thrust control.

Description

TECHNICAL FIELD

[0001] The embodiment of the present application relates to satellite thrust calculation technical field, in particular to an electric propulsion thrust calibration method. BACKGROUND

[0002] In the propulsion process of a spacecraft, commonly used propulsion systems include: dual-component propulsion system and electric propulsion system. The working principle of electric propulsion is to convert external electric energy into propellant jet kinetic energy. For modern spacecraft, the application of electric propulsion can reduce cost, improve cost performance, and prolong service life, etc. Electric propulsion technology covers the ranges of ion and Hall types, small power and medium power, medium specific impulse, single mode and double mode, etc. The thrust level of the satellite propulsion system is very small, and the rated vacuum thrust of the thruster is generally several newtons to several hundred newtons. The thruster with small thrust is difficult to manufacture, and the test and measurement of the small thrust are also difficult. However, the measurement and calibration of the thrust is one of the key technologies of the satellite propulsion system. In the related technology, there are few calibration methods for electric propulsion thrust, and the precision is low.

[0003] Therefore, it is necessary to improve one or more problems in the above-mentioned related technical solutions.

[0004] It should be noted that this section aims to provide background or context to the technical solutions of the present application stated in the claims. The description herein is not admitted to be prior art merely because it is included in this section. SUMMARY

[0005] The purpose of the embodiment of the present application is to provide an electric propulsion thrust calibration method, and to at least overcome one or more problems caused by the limitations and defects of the related technology.

[0006] The present application provides an electric propulsion thrust calibration method, comprising:

[0007] Calculating the relative position deviation between the main satellite and the deputy satellite in the inertial system before orbit control;

[0008] Calculating the relative position deviation of the main satellite and the deputy satellite in the formation coordinate system;

[0009] Calculating the initial configuration parameters according to the orbit plane roots of the main satellite and the deputy satellite at the preset time before orbit control, and obtaining the solution of the initial configuration parameters;

[0010] Obtaining the estimated value of the orbit control thrust according to the solution of the initial configuration parameters.

[0011] Preferably, the inertial system trajectory of the predicted virtual satellite is obtained by extrapolating the satellite orbit before orbit control, and the inertial system trajectory of the real satellite is determined by tracking data of the real satellite after orbit control.

[0012] Preferably, the relative position deviation between the primary and secondary satellites in the inertial system is:

[0013] (t i ,dx,dy,dz),t c <t i <t f

[0014] wherein dx=x d -x c ; dy=y d -y c ; dz=z d -z c (1)

[0015] t i is the ballistic sampling time, t c is the end time of electric propulsion control, t f is the end time of ballistic data after orbit control, x d , y d , z d are the real satellite position coordinate values in the inertial system after orbit control, x c , y c , z c are the virtual satellite position coordinate values in the inertial system before orbit control.

[0016] Preferably, let t i be the inertial coordinate of the primary satellite before orbit control (x c , y c , z c ), and the geocentric vector be let the inertial coordinate of the secondary satellite after orbit control be (x d , y d , z d ), and the geocentric vector be then the relative coordinate of the primary and secondary satellites in the inertial system is first converted to the primary satellite orbit coordinate system RTN to obtain:

[0017] wherein,

[0018] are the position vector and velocity vector of the primary satellite in the inertial system, respectively;

[0019] the coordinates of the projection point P of the secondary satellite in the primary satellite orbit coordinate system RTN are the geocentric distance of the projection point P is r p , The distance from the projection point P to the primary star is r m ;

[0020] The angle a between the geocentric vector of the projection point P and the geocentric vector of the primary star satisfies the following formula:

[0021]

[0022] The relative motion coordinate value after curvature correction is:

[0023]

[0024] Wherein, Δx o , Δy o , Δz o are the relative position deviations of the primary and secondary stars in the x-axis, y-axis and z-axis of the formation coordinate system, respectively.

[0025] Preferably, the process of calculating the initial configuration parameters according to the orbital plane roots of the primary and secondary stars at t1 is as follows:

[0026] The instantaneous orbital roots of the primary and secondary stars at t1 are calculated from the J2000. inertial system trajectory of the primary and secondary stars at t1, and then converted into plane roots through the instantaneous plane conversion program. According to the definition of the formation configuration parameters, the initial configuration parameters (p0, θ0, s0, Ψ0, Δa0, Δl0) can be calculated, wherein p0 is the short semi-axis of the flying ellipse in the plane, θ0 is the initial phase angle, s0 and Ψ0 are the amplitude and phase angle of the harmonic motion out of the plane, respectively, Δa0 is the difference between the semi-major axes of the secondary and primary stars, and Δl0 is the distance from the primary star to the center of the flying ellipse.

[0027] Preferably, the difference between the observed value and the theoretical value at t i is calculated:

[0028] The initial configuration parameters are substituted into the relative motion equation to calculate the relative position (Δx, Δy, Δz) of the formation coordinate system at t i , and then the difference between the observed value and the theoretical value is calculated:

[0029]

[0030] Wherein, (Δx, Δy, Δz) is the theoretical value, and (Δx0, Δy0, Δz0) is the observed value.

[0031] Preferably, the partial derivative of (Δx, Δy, Δz) at t i to the initial configuration parameters (p0, θ0, s0, Ψ0, Δa0, Δl0) is calculated according to the relative motion equation:

[0032]

[0033] In the formula, t idenotes the data time, t0 denotes the initial time, u c denotes the virtual primary star at t i denotes the latitude amplitude at t c denotes the satellite's plane angular velocity, and according to the partial derivative definition, the following equation is obtained:

[0034] [δx H δy H δz H ] T = H [δp δθ δs δΨ δΔa δΔl] T (7).

[0035] Preferably, the least square solution of the linearized observation equation is solved by using least square iteration:

[0036] [δp δθ δs δΨ δΔa δΔl] T = (H Τ H) -1 H[δx H δy H δz H ] T (8)

[0037] Further, the iterative solution is obtained as:

[0038]

[0039] The converged configuration parameter solution (p0, θ0, s0, Ψ0, Δa0, Δl0) is obtained.

[0040] Preferably, the in-plane tangential thrust is solved by using the configuration parameters, and the process is as follows:

[0041] Supposing that the primary and secondary star semi-major axis difference in the configuration parameters is Δa0, according to the orbit control equation

[0042]

[0043] wherein da is the semi-major axis increment, e is the satellite eccentricity, M is the satellite plane mean anomaly, n is the satellite plane angular velocity, dv T is the velocity increment in the trace direction, and the satellite mass loss in the control process is ignored, and the following equation is obtained:

[0044]

[0045] wherein F T is the satellite small thrust value in the trace direction, m s is the satellite mass,

[0046] Substituting equation (11) into equation (10), and integrating in the small thrust action period can obtain

[0047]

[0048] Assuming that the tangential thrust is constant in the control process, the tangential thrust F T is:

[0049]

[0050] Where (t1, t2) is the time period of the small thrust.

[0051] Preferably, the out-of-plane normal thrust is solved by using the configuration parameters, and the process is as follows:

[0052] Let the configuration parameter out-of-plane harmonic motion amplitude s=aδi, and according to the relative inclination vector definition

[0053]

[0054] In the formula, δi is the module of the relative inclination vector, Δi is the difference between the main satellite orbit inclination and the deputy satellite orbit inclination, ΔΩ is the difference between the main satellite orbit ascending node right ascension and the deputy satellite orbit ascending node right ascension, i is the main satellite orbit inclination,

[0055] And the orbit control equation

[0056]

[0057]

[0058] Substituting formula (15) and (16) into formula (14) can obtain:

[0059]

[0060] Further, the estimated normal thrust F N is:

[0061]

[0062] Where a is the semi-major axis of the satellite, and Δt=t2-t1 is the time period of the small thrust.

[0063] The technical scheme provided by the present application can include the following beneficial effects:

[0064] The present application takes the orbit before orbit control as a virtual main satellite orbit, and then uses observation data to determine the orbit after orbit control as a real deputy satellite orbit, so as to calculate the initial configuration parameters and obtain the parameter solution, and finally obtain the estimated value of the thrust according to the parameter solution. The calculation accuracy is high, and more reliable data support is provided for satellite thrust control. BRIEF DESCRIPTION OF DRAWINGS

[0065] The accompanying drawings, which are incorporated herein and constitute part of the specification, illustrate embodiments consistent with the present application and, together with the description, further serve to explain the principles of the application. It is to be understood that the drawings are only illustrations of some embodiments of the application and that, to one of ordinary skill in the art, other embodiments can be clearly inferred from the drawings.

[0066] Figure 1 A flow chart of the method for calibrating the electric propulsion thrust in an exemplary embodiment of the present application is shown.

[0067] Figure 2 A schematic diagram of the curvature correction of the relative motion at a long distance in the present application is shown. DETAILED DESCRIPTION

[0068] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the implementations set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the example implementations to those skilled in the art. The described features, structures, or characteristics can be combined in one or more implementations.

[0069] In addition, the drawings are to be regarded as being schematic only and therefore are not intended to portray the relative actual size or proportions of the various components depicted therein. Like reference numerals are intended to represent like or similar components throughout the specification. Some of the blocks in the drawings are function blocks that represent functions implemented by a physical or logical device, and thus the function blocks can not necessarily correspond to physical or logical entities.

[0070] In the present example implementation, a method for calibrating the electric propulsion thrust is first provided, please refer to Figure 1 may include steps S101-S104. Specifically as follows:

[0071] Step S101, the relative position deviation between the primary satellite and the secondary satellite in the inertial system is calculated, with the virtual satellite before orbit control as the primary satellite and the real satellite after orbit control as the secondary satellite.

[0072] Step S102, the relative position deviation of the primary satellite and the secondary satellite in the formation coordinate system is calculated. For example, the predicted inertial trajectory of the virtual satellite can be obtained by extrapolating the satellite orbit before orbit control, and the inertial trajectory of the real satellite can be determined by tracking data of the real satellite after orbit control.

[0073] Step S103, the initial configuration parameters are calculated according to the orbital plane roots of the primary satellite and the secondary satellite at a preset time, and the solution of the initial configuration parameters is calculated.

[0074] Step S104: Obtain the estimated value of the orbital control thrust based on the solution of the initial configuration parameters.

[0075] In this embodiment, the orbit before orbit control is used as the virtual primary satellite orbit, and the orbit after orbit control is obtained using observation data as the real secondary satellite orbit. This allows for the calculation of initial configuration parameters and the acquisition of parameter solutions. Finally, the estimated thrust value is obtained based on the parameter solutions. This method offers high calculation accuracy and provides more reliable data support for satellite thrust control.

[0076] The specific calculation process is as follows.

[0077] 1. The predicted trajectory of the virtual satellite J2000 in inertial frame (t) is obtained by extrapolating the satellite's pre-controlled orbit. i ,x c ,y c ,z c ),t c <t i <t f , where t c To control the ending time, Δt = t f -t c The relative position data arc length is used in subsequent estimation procedures. The inertial frame trajectory (t) of satellite J2000 is determined using satellite tracking data after orbit control. i ,x d ,y d ,z d ),t c <t i <t f Using a virtual satellite as the primary satellite and a real satellite as the secondary satellite, calculate the relative position deviation (t) between the primary and secondary satellites in the J2000 inertial frame. i ,dx,dy,dz),t c <t i <t f ,in:

[0078] dx=x d -x c ;dy = y d -y c ;dz=z d -z c (1)

[0079] 2. Calculate the relative position deviation between the primary and secondary stars in the formation coordinate system.

[0080] like Figure 2 As shown, let t i The coordinates of the primary star (pre-orbiting orbit) in the inertial frame at that moment are (x... c ,y c ,z c The geocentric vector is denoted as The position coordinates of the deputy satellite (in the post-control orbit) in the inertial system are (x d ,y d ,z d ), and the geocentric vector is denoted as First, the relative coordinates of the main and deputy satellites in the inertial system are converted into the RTN coordinate system of the main satellite

[0081] wherein

[0082] The coordinates of the projection point P of the deputy satellite in the orbital plane of the main satellite (in the RTN coordinate system of the main satellite) are The geocentric distance of the projection point P is r p , The distance of the projection point P to the main satellite is r m .

[0083] The angle α between the geocentric vector of the projection point P and the geocentric vector of the main satellite satisfies the following formula

[0084]

[0085] Then, the relative motion coordinate value after the curvature correction is:

[0086]

[0087] 3. Calculate the initial configuration parameters according to the orbital plane of the main and deputy satellites at t1

[0088] According to the J2000. inertial trajectory of the main and deputy satellites at t1, the instantaneous orbital elements of the main and deputy satellites at t1 can be calculated, and then converted into the flat elements through the instantaneous-to-flat conversion program. According to the definition of the formation configuration parameters, the initial configuration parameters (p0, θ0, s0, Ψ0, Δa0, Δl0) can be calculated.

[0089] 4. Calculate the difference between the observation value and the theoretical value at t i

[0090] Substitute the initial values of the configuration parameters into the relative motion equation to calculate the relative position (Δx, Δy, Δz) of the formation coordinate system at t i , and then calculate the difference between the observation value and the theoretical value

[0091]

[0092] 5. Calculate the partial derivative of (Δx, Δy, Δz) with respect to the initial configuration parameters (p0, θ0, s0, Ψ0, Δa0, Δl0) at t i

[0093] ​​​

[0094] where t i denotes the data time, t0 denotes the initial time, u c is the virtual primary star latitude amplitude at t i is the virtual primary star latitude amplitude at t c is the satellite's latitude angular velocity, which is defined by the partial derivative as follows:

[0095] [δx H δy H δz H ] T = H [δp δθ δs δΨ δΔa δΔl] T (7).

[0096] 6. Least square iteration solution

[0097] The linearized observation equation has a least square solution

[0098] [δp δθ δs δΨ δΔa δΔl] T = (H Τ H) -1 H [δx H δy H δz H ] T (8)

[0099] Further, the iterative solution is

[0100]

[0101] Repeating the above steps (4) - (6), the converged configuration parameter solution (p0, θ0, s0, Ψ0, Δa0, Δl0) can be obtained.

[0102] 7. Thrust estimation according to the configuration parameter estimation

[0103] According to the configuration parameter obtained by the iterative solution, the estimated value of the thrust can be obtained.

[0104] 1) In-plane tangential control

[0105] Let the estimated configuration parameter of the primary and secondary star semi-major axis difference be Δa0, and according to the orbit control equation

[0106]

[0107] where e is the satellite eccentricity, M is the satellite mean anomaly, and n is the satellite's angular velocity.

[0108] Neglecting the satellite mass loss during the control process, we have

[0109]

[0110] where F T is the value of the small thrust in the along-track direction, m s is the mass of the satellite.

[0111] Substituting the above equation and integrating over the time period of the small thrust gives

[0112]

[0113] Assuming the tangential thrust is constant during the control process, we have

[0114]

[0115] where (t1, t2) is the time period of the small thrust.

[0116] 2) Out-of-plane normal control

[0117] Let the estimated out-of-plane harmonic motion amplitude of the configuration parameter be s = aδi, and the relative inclination vector be defined as

[0118]

[0119] According to the orbit control equation

[0120]

[0121]

[0122] Substituting equations (15) and (16) into equation (14) gives

[0123]

[0124] Further, the estimated normal thrust is

[0125]

[0126] where F N is the value of the small thrust in the normal direction, and Δt = t2-t1 is the time period of the small thrust.

[0127] To analyze the accuracy and applicability of this calibration method, five geostationary orbit tests were designed as follows.

[0128] Test 1:

[0129] The main purpose of Test 1 is to test the influence of the thrust action time on the calibration accuracy under the same total impulse (the product of the thrust and the action time). The small thrust action start time is 2021 / 11 / 22 16:00:00 (BJT), and the simulation initial values are shown in Table 1.

[0130] Table 1 Simulation initial values

[0131]

[0132] First, the ephemeris of the virtual primary star is obtained by numerical orbit extrapolation based on the initial orbit. Then, the ephemeris of the actual satellite (secondary star) after control is obtained by numerical integration based on the same initial orbit, in which the perturbation of the satellite orbit is superimposed with the perturbation of the small thrust in the thrust action period. Then, the thrust estimation value is obtained based on the calibration method of the present application. In the simulation process, the thrust value is reduced from 0.05 N to 0.0015625 N, and the corresponding ignition time length is increased from 1 hour to 32 hours. The simulation results are shown in Table 2 below.

[0133] Table 2 calibration accuracy analysis results of different thrust action time lengths

[0134] Ignition duration Thrust actual value (N) Thrust estimated value (N) Estimation error Length of use data 1 1 hour 0.05 0.050037 99.925％ 2.0 days 2 2 hours 0.025 0.025026 99.894％ 2.0 days 3 4 hours 0.0125 0.01251 99.923％ 2.0 days 4 8 hours 0.00625 0.006256 99.906％ 2.0 days 5 16 hours 0.003125 0.003129 99.878％ 2.0 days 6 32 hours 0.0015625 0.001564 99.911％ 2.0 days

[0135] As can be seen from Table 2, the calibration method of the present application is not sensitive to the ignition time length, and the accuracy is better than 99.8%.

[0136] Test two:

[0137] The main purpose of Test two is to test the influence of different orbit altitudes on the thrust calibration accuracy. The satellite simulation initial orbit altitude is increased from 700 km to 42164 km, the ignition time length is 8 hours, the thrust is 0.0065 N, and the other parameters and methods are the same as those in Test one. The simulation results are shown in Table 3 below.

[0138] Table 3 calibration accuracy analysis results of different orbit altitudes

[0139]

[0140] As can be seen from Table 3, the calibration method of the present application is suitable for low-orbit satellites and medium-high-orbit satellites.

[0141] Test three:

[0142] The main purpose of Test three is to test the influence of different orbit altitudes on the thrust calibration accuracy. The satellite simulation initial orbit altitude is 20000 km, the eccentricity is increased from 0.001 to 0.3, and the other parameters and methods are the same as those in Test two. The simulation results are shown in Table 4 below.

[0143] Table 4 calibration accuracy analysis results of different eccentricities

[0144] Ignition duration Eccentricity Thrust actual value (N) Thrust estimated value (N) Estimation error Length of use data 1 8 hours 0.001 0.00625 0.006252 99.963％ 2.0 days 2 8 hours 0.01 0.00625 0.006258 99.868％ 2.0 days 3 8 hours 0.05 0.00625 0.006308 99.071％ 2.0 days 4 8 hours 0.1 0.00625 0.006424 97.220％ 2.0 days 5 8 hours 0.2 0.00625 0.006851 90.381％ 2.0 days 6 8 hours 0.3 0.00625 0.007601 78.386％ 2.0 days

[0145] As can be seen from Table 4, the calibration method of the present application is suitable for small eccentricity satellites, and the calibration efficiency is better than 99% for satellites with an eccentricity less than 0.05. The method is not suitable for satellites with an eccentricity greater than 0.1.

[0146] Test four:

[0147] The main purpose of test four is to test the influence of different data length on the calibration precision. The ignition time is 8 hours, the thrust is 0.0065N, the data length is increased from 0.25 day to 2.5 day, and other parameters and methods are the same as those in test one. The simulation results are shown in Table 5.

[0148] Table 5: Calibration precision analysis results of different data length

[0149] Ignition duration Thrust actual value (N) Thrust estimated value (N) Estimation error Length of use data 1 8 hours 0.00625 0.006257 99.885％ 0.25 days 2 8 hours 0.00625 0.006256 99.906％ 0.5 days 3 8 hours 0.00625 0.006256 99.897％ 1.0 day 4 8 hours 0.00625 0.006256 99.899％ 1.5 days 5 8 hours 0.00625 0.006256 99.906％ 2.0 days 6 8 hours 0.00625 0.006256 99.90673 2.5 days

[0150] As shown in Table 5, the calibration method of the present application has a calibration precision of more than 99.8% for data length of 0.25 day to 2.5 day.

[0151] Test five:

[0152] The main purpose of test five is to test the influence of different control amount on the calibration precision. The ignition time is 8 hours, the thrust is increased from 0.00625N to 0.2N, and other parameters and methods are the same as those in test one. The simulation results are shown in Table 6.

[0153] Table 6: Calibration precision analysis results of different control amount

[0154] Ignition duration Thrust actual value (N) Thrust estimated value (N) Estimation error Length of use data 1 8 hours 0.00625 0.006256 99.906％ 2.0 days 2 8 hours 0.0125 0.012509 99.924％ 2.0 days 3 8 hours 0.025 0.024961 99.844％ 2.0 days 4 8 hours 0.05 0.050049 99.902％ 2.0 days 5 8 hours 0.1 0.100121 99.879％ 2.0 days 6 8 hours 0.2 0.200338 99.831％ 2.0 days

[0155] As shown in Table 6, the calibration method of the present application can achieve ideal results for different small thrusts, and the calibration precision is still more than 99.8% for a large control amount (0.2N thruster acting for 8 hours) with a semi-major axis raised by 13km.

[0156] It should be noted that, in the embodiments of the present application, unless otherwise explicitly specified and limited, the "on" or "under" of the first feature to the second feature can include that the first and second features are in direct contact, or can include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, the "on", "above" and "above" of the first feature to the second feature include that the first feature is directly above and obliquely above the second feature, or only indicates that the horizontal height of the first feature is higher than that of the second feature. The "under", "below" and "below" of the first feature to the second feature include that the first feature is directly below and obliquely below the second feature, or only indicates that the horizontal height of the first feature is less than that of the second feature.

[0157] In the description of the application, reference can be made to terms such as "one embodiment", "some embodiments", "an example", "a specific example" or "some examples" etc. It is to be understood that such terms are merely used to describe a particular feature, structure, material or characteristic under discussion. Therefore, in no way these terms restrict the scope of the application. Further, when used in the description, the terms "a" or "an" are used in the sense that they mean "one or more" unless the context clearly dictates otherwise. In addition, the term "based on" is used to describe one or more feature, structure, material or characteristic that is / are used for an action or a step which is / are performed one or more times. Also, the term "based on" is used to describe one or more feature, structure, material or characteristic that is / are used for performing an action or a step which is / are performed one or more times.

[0158] Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the specification and examples be considered as exemplary only, with the true scope and spirit of the application being indicated by the following claims.

Claims

1. A method for calibrating electric propulsion thrust, characterized in that, include: The relative positional deviation between the primary and secondary satellites in the inertial frame is calculated using a virtual satellite before orbit control as the primary satellite and a real satellite after orbit control as the secondary satellite. Calculate the relative positional deviation between the primary and secondary satellites in the formation coordinate system; wherein, the predicted inertial trajectory of the virtual satellite is obtained by extrapolating the satellite orbit before orbit control, and the inertial trajectory of the real satellite is determined by using the real satellite tracking data after orbit control; The relative positional deviation between the primary and secondary stars in the inertial frame is: in, (1) For the ballistic sampling time, The end time of electric propulsion control This is the end time of ballistic data after trajectory control. , , These are the spatial position coordinates of the actual satellite in the inertial frame after orbit control. , , These are the spatial position coordinates of the virtual satellite in the inertial frame before orbit control; set up The coordinates of the primary star's inertial frame before orbit control are as follows: The geocentric vector is denoted as The position coordinates of the secondary satellite's inertial frame after orbit control are: The geocentric vector is denoted as First, the relative coordinates of the primary and secondary star inertial frames are determined. Transforming to the primary star's orbital coordinate system (RTN) yields: ,in (2) , These are the position vector and velocity vector of the primary star's inertial frame, respectively. The coordinates of the projection point P of the secondary star in the primary star's orbital plane in the primary star's orbital coordinate system RTN are: The distance from the center of projection point P to the Earth's center is... , The distance from the projection point P to the primary star is ; The angle between the geocentric vector of projection point P and the geocentric vector of the primary star. Satisfy the following formula: (3) The relative motion coordinates after curvature correction are: (4)； in, , , These represent the relative positional deviations of the primary and secondary stars along the x, y, and z axes in the formation coordinate system, respectively. The initial configuration parameters are calculated based on the root orbits of the primary and secondary stars at a preset time before orbit control, and the solution for the initial configuration parameters is obtained. The estimated value of the orbital control thrust is obtained from the solution of the initial configuration parameters.

2. The electric propulsion thrust calibration method according to claim 1, characterized in that, according to The process of calculating the initial configuration parameters at the time of the primary and secondary satellite orbits is as follows: Depend on Calculation of the J2000 inertial frame trajectory of the primary and secondary satellites at any given time. The instantaneous orbital elements of the primary and secondary stars are converted to mean roots using an instantaneous-to-mean conversion process. Based on the definition of the formation configuration parameters, the initial configuration parameters can then be calculated. ,in It is the semi-minor axis of the flying ellipse in the plane. The initial phase angle, , These represent the amplitude and phase angle of the out-of-plane harmonic motion, respectively. The difference between the semi-major axis of the secondary star and the primary star. The distance between the main star and the center of the orbital ellipse.

3. The electric propulsion thrust calibration method according to claim 2, characterized in that, calculate The difference between the observed value and the theoretical value at time: Substitute the initial values ​​of the configuration parameters into the equations of relative motion to calculate. Relative position in formation coordinate system Then, the difference between the observed value and the theoretical value is calculated: (5) in, This is the theoretical value. These are the observed values.

4. The electric propulsion thrust calibration method according to claim 3, characterized in that, Calculated based on the equation of relative motion time For initial configuration parameters partial derivatives (6) In the formula, Indicates the data time. Indicates the initial time. For the virtual primary star Time, latitude, and angle Let the satellite's horizontal angular velocity be the value of the partial derivative. Based on the definition of the partial derivative, we have the following equation: (7)。 5. The electric propulsion thrust calibration method according to claim 4, characterized in that, Solving the linearized observation equations using least squares iteration: (8) The iterative solution is then obtained as follows: (9) Obtain the convergent configuration parameter solution .

6. The electric propulsion thrust calibration method according to claim 5, characterized in that, The in-plane tangential thrust is solved using the aforementioned configuration parameters, as follows: Let the difference in the semi-major axis between the primary and secondary stars in the configuration parameters be... According to the orbital control equations (10) in For the semi-major axis increment, For satellite eccentricity, To determine the satellite's near-apex angle, The satellite's horizontal angular velocity, Assuming the velocity increment along the track direction, and neglecting satellite mass loss during control, we can obtain... (11) in This represents the value of the small thrust along the satellite's path. For satellite quality; Substituting equation (11) into equation (10) and integrating during the period of low thrust, we can obtain the following: (12) Assuming the tangential thrust is constant during the control process, then the tangential thrust... FT for: (13) in, This refers to the period during which a small thrust is applied.

7. The electric propulsion thrust calibration method according to claim 5, characterized in that, The out-of-plane normal thrust is solved using the aforementioned configuration parameters, as follows: Let the configuration parameters be the out-of-plane harmonic amplitude. According to the definition of relative tilt vector (14) In the formula, The magnitude of the relative tilt angle vector, The difference in orbital inclination between the primary and secondary stars The difference in right ascension of the ascending node of the primary and secondary stars' orbits. The orbital inclination of the primary star; and orbital control equations (15) (16) In the formula, The satellite's horizontal angular velocity, For satellite quality; Substituting equations (15) and (16) into equation (14), we get: (17) This leads to the estimated normal thrust. for: (18) in, For the satellite's semi-major axis, This refers to the period during which a small thrust is applied.

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