Electric propulsion GEO satellite thrust reduction point transfer reconfiguration guidance method

Abstract

The application discloses a kind of electric propulsion GEO satellite thrust reduction fixed-point transfer reconstruction guidance method, it includes S1 using volume Kalman filter method CKF to the orbit transfer dynamics model of electric thrust GEO satellite is updated, obtains the real-time estimated thrust of electric thrust GEO satellite;S2 according to real-time estimated thrust, whether electric thrust GEO satellite occurs electric thrust reduction failure using fault state function is judged, if yes, then enter step S3, otherwise, enter step S5;S3 is determined whether need reconstruction guidance using reconstruction guidance determination function constructed based on thrust reduction degree, fault occurrence stage, thrust anomaly and stable duration, if yes, enter step S4, otherwise enter step S5;S4 uses the fixed-point transfer reconstruction guidance method based on Lyapunov stability theory, and the orbit of electric propulsion GEO satellite under thrust failure is adaptively adjusted, then enter step S5;S5 judges whether electric propulsion GEO satellite reaches target point, if yes, then terminate algorithm, otherwise return to step S1.

Description

Technical Field

[0001] This invention belongs to the field of satellite orbital dynamics technology, specifically relating to a method for thrust descent and fixed-point transfer reconfiguration guidance of an electrically propelled GEO satellite. Background Technology

[0002] Thrust descent repositioning guidance for electrically propelled GEO satellites refers to the process where, during the transfer of an electrically propelled GEO satellite from low Earth orbit to GEO (geostationary orbit) and to its designated orbital position, a thrust descent fault occurs due to an anomaly in the electric thruster. This fault is identified using state estimation and judgment algorithms, and the original orbital transfer guidance strategy is replanned and adjusted based on the estimation results to ensure the successful completion of the planned GEO repositioning mission. Thrust descent fault detection is a prerequisite for guidance repositioning; only by accurately identifying the degree and timing of the thrust descent can effective guidance strategy repositioning be performed. Guidance repositioning is crucial to ensuring that the electrically propelled satellite can still complete its planned repositioning mission even under fault conditions.

[0003] In the area of ​​thrust reduction fault detection for electric propulsion satellites, existing research mainly estimates the thrust magnitude based on orbital parameters and sets fault criteria according to the thrust magnitude characteristics of the electric thruster system to achieve thrust reduction fault detection. However, this research primarily focuses on the nominal thrust estimation during satellite maneuvers in the orbital plane, making it difficult to directly apply to the dynamic thrust estimation during the stationary transfer process of electric propulsion satellites. Regarding reconfiguration guidance for electric propulsion satellites, existing research mainly optimizes position maintenance under thrust faults after electric propulsion GEO satellites enter orbit. However, for thrust reduction faults during the orbit transfer phase, optimizing the electric thrust direction and the switching sequence of the electric thrusters for orbit change guidance reconfiguration involves high computational complexity and low robustness.

[0004] To ensure the successful completion of autonomous geostationary transfer missions for electrically propelled GEO satellites and avoid excessively prolonged geostationary transfer time or additional fuel consumption due to thrust reduction faults, it is urgent to propose a fault detection and reconfiguration guidance method for thrust reduction faults during geostationary transfer of electrically propelled GEO satellites. Summary of the Invention

[0005] To address the aforementioned shortcomings in the existing technology, the electric propulsion GEO satellite thrust descent stationary transfer reconfiguration guidance method provided by this invention solves the problems of excessively prolonged stationary transfer time or additional fuel consumption under thrust descent failure.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A method for thrust descent stationary transfer reconfiguration guidance of an electrically propelled GEO satellite is provided, comprising the following steps:

[0008] S1. The orbital transfer dynamics model of the electric thrust GEO satellite is updated using the capacitive Kalman filter (CKF) method to obtain the real-time estimated thrust of the electric thrust GEO satellite.

[0009] S2. Based on the real-time estimated thrust, use the fault state function to determine whether the electric thrust GEO satellite has experienced a thrust reduction fault. If so, proceed to step S3; otherwise, proceed to step S5.

[0010] S3. Use a reconfiguration guidance determination function based on the thrust reduction degree, the fault occurrence stage, and the duration of thrust abnormality and stability to determine whether reconfiguration guidance is needed. If yes, proceed to step S4; otherwise, proceed to step S5.

[0011] S4. Using a fixed-point transfer reconfiguration guidance method based on Lyapunov stability theory, the orbit of the electrically propelled GEO satellite under thrust failure is adaptively adjusted, and then proceed to step S5.

[0012] S5. Determine whether the electrically propelled GEO satellite has reached the target point. If yes, terminate the algorithm; otherwise, return to step S1.

[0013] Furthermore, the expression for the fault state function is:

[0014]

[0015] , , ,

[0016] in, This is a fault status function, with a value of 1 indicating the presence of a fault and a value of 0 indicating the absence of a fault. The deviation of the electric thrust at time t; This is the threshold value for thrust magnitude; Duration of thrust anomaly; This is the threshold for the duration of the abnormality. The real-time estimated thrust at time t; This is the nominal thrust; The first trigger of the thrust magnitude threshold is the deviation in electric thrust magnitude. The point in time; To continuously exceed the thrust magnitude threshold The end time; and All are constants greater than 0; The sampling period.

[0017] Furthermore, the expression for the reconfiguration guidance decision function is:

[0018]

[0019] , , ,

[0020]

[0021] in, The guidance reconstruction decision function has a value of 1 indicating that guidance reconstruction is required and a value of 0 indicating that guidance reconstruction is not required. For fault state functions; This refers to the degree of thrust reduction; This is the threshold for the degree of thrust reduction; The relative progress at the moment of failure; This represents the task progress threshold. This refers to the period of relative stability after the thrust decreases. The time threshold for initiating reconfiguration guidance; The deviation of the electric thrust at time t; This is the nominal thrust; The time when the electric thruster begins to experience a thrust reduction fault; The total scheduled duration for the geostationary transfer mission of the electric propulsion satellite; A constant greater than 0; The sampling period; This is the moment when the stability condition is met for the first time; This is the moment for determining a thrust reduction fault; To estimate the average thrust magnitude within the sliding window; for The average thrust magnitude estimated in the previous window; for and The absolute deviation; To estimate the thrust standard deviation; The standard deviation threshold; Duration; It is a constant, and its value is 50 in this simulation.

[0022] Furthermore, the fault model for the electric thrust reduction fault is as follows:

[0023]

[0024] in, This refers to the operating state of the electric thruster. The time when the electric thruster begins to experience a thrust reduction fault; This represents the minimum operating state of the electric thruster during a thrust failure. The time it takes for the electric thruster's thrust to decrease to its minimum value; t represents the end time of the work; t represents the current working time.

[0025] Furthermore, the orbital transfer dynamics model The expression is:

[0026]

[0027] Where r is the position of the electrically propelled GEO satellite; v is the velocity vector; m is the weight of the electrically propelled GEO satellite; and T is the thrust of the electrically propelled GEO satellite. This is the transpose of the matrix;

[0028] Orbital transfer dynamics model State equations Represented as:

[0029]

[0030] in, , , and These are the derivatives of the satellite's position, velocity, mass, and thrust, respectively. The vector of gravitational acceleration; The J2 term perturbation acceleration vector of the Earth; The solar gravitational acceleration vector; This is the lunar gravitational acceleration vector; This is the atmospheric drag acceleration vector; The solar radiation pressure perturbation acceleration vector; This is the acceleration vector generated by the estimated electric thrust in the satellite orbit coordinate system; The average gravitational acceleration at sea level on Earth; For the specific impulse of the electric thruster of an electric propulsion satellite; This is the transformation matrix from the orbital coordinate system to the J2000 ECI coordinate system.

[0031] The beneficial effects of the above technical solution are as follows: This solution adopts an orbital transfer dynamics model state equation that includes thrust as a state variable, which can more comprehensively and accurately describe the dynamic characteristics of electrically propelled GEO satellites during orbital transfer. This state equation incorporates satellite thrust into the state variable estimation, enabling real-time capture of dynamic thrust changes. Especially in scenarios involving electric thrust descent failures, it can accurately reflect the impact of thrust anomalies on the satellite orbit. By introducing thrust as a state variable, the model not only considers external factors such as Earth's gravity and perturbation acceleration, but also achieves real-time tracking of thrust as a key control variable, providing a precise dynamic basis for subsequent fault state function judgment, reconfiguration guidance determination, and adaptive orbit adjustment based on Lyapunov stability theory.

[0032] Furthermore, the transformation matrix from the orbital coordinate system to the J2000 ECI coordinate system. The expression is:

[0033]

[0034] in, The instantaneous angular momentum vector of an electrically propelled GEO satellite; , and All are unit vectors; For the module length;

[0035] Earth's gravitational acceleration vector The expression is:

[0036]

[0037] in, It is the Earth's gravitational constant;

[0038] Solar gravitational acceleration The expression is:

[0039]

[0040] in, It is the gravitational constant of the Sun; This is the position vector of the sun in the J2000 ECI coordinate system;

[0041] Lunar gravitational acceleration The expression is:

[0042]

[0043] in, It is the gravitational constant of the moon; This represents the position vector of the moon in the J2000 ECI coordinate system.

[0044] The expression for the J2 perturbation acceleration is:

[0045]

[0046] in, , and For the vector components of the J2 perturbation acceleration; For harmonic coefficients, x, y, and z are the components of the position vector; The average radius of the Earth;

[0047] Atmospheric drag acceleration vector The expression is:

[0048]

[0049] in, The ratio of the effective area S to the mass m of the electrically propelled GEO satellite; This is the atmospheric drag coefficient; The relationship between atmospheric density and the altitude of an electrically propelled GEO satellite is expressed as follows: , , For the altitude of an electrically propelled GEO satellite, For reference height; Atmospheric elevation; Let be the velocity vector of an electrically propelled GEO satellite relative to the atmosphere, and its expression is: , This is the vector of Earth's rotational angular velocity; This is Earth's angular velocity;

[0050] Solar radiation pressure perturbation acceleration vector The expression is:

[0051]

[0052] in, This is the shadow coefficient, which is the value when the satellite is located in the umbra. When the satellite is in the penumbra, When the satellite is located outside the umbra and penumbra, ; The SRP reference value is taken from the Sun. The reflection coefficient;

[0053] The expression for estimating the acceleration vector generated by electric thrust is:

[0054]

[0055]

[0056] in, , and These are the radial, along-track, and normal acceleration components, respectively. , The optimal control thrust angle for electric thrust in the orbital coordinate system.

[0057] Furthermore, step S1 further includes:

[0058] S11. The estimated position and velocity values ​​of the electric thrust GEO satellite in the J2000 ECI coordinate system are used as the measured values ​​of the real-time on-orbit thrust estimation method for electric thrusters based on CKF. The measurement equations are... Represented as:

[0059]

[0060] in, These are the estimated position and velocity vectors of the satellite in the J2000 ECI coordinate system. The true position vector and velocity vector of the satellite in the J2000 ECI coordinate system; To estimate accuracy;

[0061] S12. Discretize the state-space model of the orbital transfer dynamics model:

[0062]

[0063] in, and These are the discretized state variables at time k and time k+1, respectively. These are the estimated values ​​of the satellite's position and velocity vectors in the J2000 ECI coordinate system at time k+1; Let be the state transition function, representing the prediction of the satellite state at time k+1 from the state of the electrically propelled GEO satellite at time k; For observation functions; These represent the system noise at time k and the measurement noise at time k+1, respectively.

[0064] S13, Given the initial state variables of the filter Initial covariance matrix Process noise covariance matrix Measure the noise covariance matrix ;

[0065] S14. Calculate the predicted values ​​of the state variables based on the initial state variables and the initial covariance matrix:

[0066]

[0067] ,

[0068] in, The predicted value of the state variable at time k+1; and They are respectively the k+1 time-th There are 1 volume points; n is the dimension of the state variable. The estimated value of the state variables at time k; The Cholesky decomposition of the covariance matrix of the state variables at time k; A matrix composed of unit vectors;

[0069] S15. Predict values ​​based on state variables and volume point Calculate the state prediction covariance matrix at time k+1. :

[0070]

[0071] S16. Based on volume point Calculate the predicted measurement value at time k+1. :

[0072] ,

[0073] in, The measurement prediction value is obtained by weighted summation after propagating the observation function through the volume points;

[0074] S17. Predict values ​​based on state variables Volume point and measurement prediction values Update the measurement covariance matrix and cross covariance matrix:

[0075] ,

[0076] in, and These are the measurement covariance matrix and the cross covariance matrix at time k+1, respectively.

[0077] S18. Based on the measurement covariance matrix and cross covariance matrix Calculate the Kalman gain:

[0078]

[0079] in, The Kalman gain at time k+1;

[0080] S19, according to , , and The estimated value of the state variable at time k+1 and state covariance matrix Update:

[0081] , ;

[0082] State variable estimate at time k+1 The thrust estimate of an electrically propelled GEO satellite is the real-time estimated thrust of an electrically thrust GEO satellite.

[0083] The beneficial effects of the above technical solution are as follows: Combining the state equation of the orbital transfer dynamics model with the commensurate Kalman filter (CKF) method fully leverages the advantages of CKF in accurately handling state estimation in nonlinear systems. Through discretization of the state equation and recursive iterative calculation, real-time high-precision estimation of the thrust of electrically propelled GEO satellites is achieved. This method constructs commensurate points through Cholesky decomposition and performs state propagation, effectively capturing the nonlinear characteristics in satellite orbital dynamics while exhibiting strong robustness to system noise and measurement noise. Incorporating thrust as a state variable into the state equation, combined with the recursive update mechanism of CKF, enables real-time tracking of dynamic changes in thrust under complex perturbation environments. This provides a reliable data foundation for the accurate detection of electric thrust descent faults, thereby ensuring the accuracy and timeliness of subsequent fault state judgment, reconfiguration guidance determination, and adaptive orbit adjustment. This significantly improves the orbit estimation accuracy and mission execution reliability of satellites under abnormal thrust conditions.

[0084] Furthermore, the matrix composed of unit vectors The expression is:

[0085] .

[0086] Furthermore, step S4 further includes:

[0087] S41. Determine the guidance mode as either the shortest time guidance law or the limited time fuel-saving guidance law based on the current mission requirements, and proceed to steps S42 and S43 respectively.

[0088] S42. Construct initial state constraints and optimal performance indicators. The weight parameters of the RQ-Law function are optimized using initial state constraints and optimal performance indicators to obtain optimized weight coefficients. Then, the process proceeds to step S44, where the optimal performance indicators are determined. The expression is:

[0089]

[0090] in, Maximum flight time for stationary transfer of electrically propelled GEO satellites; This refers to the flight time during the orbital insertion phase. This refers to the maximum permissible deviation at the end of the stationary transfer phase of an electrically propelled satellite. and All are constants. Take 0.97, Take 0.01;

[0091] S43. Construct initial state constraints and optimal performance indicators. The weight parameters of the RQ-Law function are optimized using initial state constraints and optimal performance indicators to obtain optimized weight coefficients. Then, the process proceeds to step S44, where the optimal performance indicators are determined. The expression is:

[0092] ;

[0093] S44. Based on the current state variables of the electric propulsion satellite, the current orbital information of the target point, and the optimized weighting coefficients, output the optimal control thrust angle under thrust reduction fault conditions. :

[0094] ,

[0095]

[0096]

[0097]

[0098] Where D1, D2, and D3 are auxiliary variables; Q is the RQ-Law function; For electrically propelled GEO satellites; The maximum rate of change of the eccentricity component f with respect to the thrust direction; The maximum rate of change of the eccentricity component g with respect to the thrust direction; To represent the maximum rate of change of the five orbital elements of an electrically propelled satellite with respect to the thrust direction and true longitude; The acceleration vector in the orbital coordinate system; True longitude for GEO satellites; Auxiliary variables; a is the right ascension of the ascending node; f and g are the eccentricity vector components; , Here are the vector components of the orbital inclination angle; L is the true longitude. It is the Earth's gravitational constant;

[0099] S45. Optimal control thrust angle under thrust reduction fault conditions. Adaptive adjustments are made to the orbit of electrically propelled GEO satellites.

[0100] The beneficial effects of the above technical solution are as follows: By constructing a flexible guidance mode selection mechanism and optimization strategy, efficient adaptive guidance for the orbit of an electrically propelled GEO satellite under thrust descent failure is achieved. This solution switches between the "shortest time" and "limited-time fuel-saving" guidance laws according to mission requirements. It optimizes the weight parameters of the RQ-Law function by constructing optimal performance indicators that include constraints such as orbital insertion deviation, enabling the system to balance time efficiency and fuel consumption under different operating conditions. It calculates the optimal control thrust angle in real time by combining the satellite's current state and target orbit information, fully considering dynamic parameters such as the rate of change of orbital elements and acceleration vectors to ensure the accuracy of thrust direction control. Finally, through an adaptive adjustment mechanism, the orbit is dynamically corrected during thrust descent failure, effectively avoiding the problems of excessively prolonged stationary transfer time or additional fuel consumption in traditional methods. This significantly improves the satellite's mission adaptability and guidance accuracy under failure conditions, achieving multi-objective optimization of time, fuel, and orbital control accuracy.

[0101] Furthermore, the initial state constraints include:

[0102] Initial state constraints:

[0103]

[0104] Where t0 is the initial time, a C (t0) is the semi-major axis of the orbit at the initial moment, f C (t0) is the vector of orbital eccentricity at the initial moment, g C (t0) represents the component of the orbital eccentricity at the initial moment, h C (t0) is the vector of the orbital inclination at the initial moment, k C (t0) represents the component of the orbital inclination at the initial moment, L C (t0) represents the true longitude at the initial time, and a0, f0, g0, h0, k0, and L0 are the orbital elements of the initial orbit.

[0105] End constraints:

[0106]

[0107] Among them, t f For transfer time; , , and These are the semi-major axis, eccentricity, orbital inclination, and true longitude of the GEO satellite; , , and These are the semi-major axis, eccentricity, orbital inclination, and true longitude of the target point, respectively.

[0108] Motion equation constraints:

[0109]

[0110] in, , , , , , , These are the semi-major axis, eccentricity components f and g, orbital inclination components h and k, true longitude, and rate of mass change, respectively. p is the right ascension of the ascending node; p is the semi-major diameter. This refers to the specific impulse of the electric thruster in an electric propulsion satellite.

[0111] Furthermore, the expression for optimizing the weight coefficients is as follows:

[0112]

[0113] in, and All are related weights of the penalty function; The weights are respectively the semi-major axis, the eccentricity components f and g, and the orbital inclination components h and k; and For phase parameters; , and All are associated scaling weights;

[0114] The expression for the Lypunov function Q is:

[0115]

[0116] in, Both are penalty functions. The smaller the value, the shorter the time required to complete the orbital transfer and station positioning; For scaling functions; To adjust the weighting of the orbital elements at the vernal equinox; For electrically propelled GEO satellites; For the augmented set of the target orbital elements; This represents the maximum rate of change of each orbital element of an electrically propelled GEO satellite relative to the thrust direction and true longitude.

[0117] The beneficial effects of this invention are as follows: To avoid excessively prolonged stationary transfer time and additional fuel consumption caused by thrust reduction faults in electrically propelled GEO satellites, the stationary transfer reconfiguration guidance method designed in this scheme covers three stages: thrust magnitude estimation, fault descent fault discrimination, and guidance reconfiguration. This method uses the CKF filtering algorithm to estimate the thrust magnitude online and formulates a two-factor discrimination strategy, that is, by analyzing the dynamic deviation characteristics and continuous deviation duration of the thrust estimate from the nominal thrust, the thrust reduction fault is discriminated, thereby improving the reliability of fault identification by accurately identifying the thrust reduction fault; at the same time, the guidance determination is reconfigured to avoid unnecessary calculations and guidance law adjustments.

[0118] This approach avoids excessive delays in geostationary transfer time or additional fuel consumption by performing real-time thrust estimation, fault diagnosis, and reconfiguration guidance, thus ensuring the successful completion of autonomous geostationary transfer missions for electrically propelled GEO satellites. This method can accurately estimate the actual electric thrust, providing a basis for thrust descent fault diagnosis. Considering the impact of engineering constraints such as orbit determination accuracy, attitude control accuracy, and thrust fluctuations, this method can significantly suppress the increase in flight time and fuel consumption caused by thrust descent faults and enhance the robustness of the geostationary transfer process. Attached Figure Description

[0119] Figure 1 A flowchart of a thrust descent stationary transfer and reconfiguration guidance method for electrically propelled GEO satellites.

[0120] Figure 2 The diagram shows a thrust reduction fault model for an electric thruster; (a) is a schematic diagram of thrust reduction fault mode one, (b) is a schematic diagram of thrust reduction fault mode two, (c) is a schematic diagram of thrust reduction fault mode three, and (d) is a schematic diagram of thrust reduction fault mode four.

[0121] Figure 3 This is a schematic diagram illustrating the estimation error of the electric thrust magnitude.

[0122] Figure 4 This is a schematic diagram of the thrust reduction fault determination results.

[0123] Figure 5 This is a schematic diagram showing the degree of decrease in electric thrust.

[0124] Figure 6 This is a schematic diagram of the reconstructed guidance determination result.

[0125] Figure 7This is a partial schematic diagram of the geostationary transfer result of an electric propulsion satellite under thrust reduction failure; (a) a three-dimensional trajectory diagram without reconfiguration guidance, (b) a three-dimensional trajectory diagram with reconfiguration guidance, (c) a schematic diagram of the semi-major axis change, (d) a schematic diagram of the eccentricity change, (e) a schematic diagram of the orbital inclination change, and (f) a schematic diagram of the total mass change of the satellite.

[0126] Figure 8 Another schematic diagram of the geostationary transfer result of an electric propulsion satellite under thrust reduction fault; wherein, (g) schematic diagram of in-plane control thrust angle α without reconfiguration; (h) schematic diagram of out-of-plane control thrust angle β without reconfiguration; (i) schematic diagram of in-plane control thrust angle α after reconfiguration; (j) schematic diagram of out-of-plane control thrust angle β after reconfiguration. Detailed Implementation

[0127] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0128] refer to Figure 1 , Figure 1 A flowchart illustrating the thrust descent stationary transfer reconfiguration guidance method for electrically propelled GEO satellites is shown; Figure 1 As shown, the method S includes steps S1 to S4.

[0129] In step S1, the capacitive Kalman filter (CKF) method is used to update the orbital transfer dynamics model of the electric thrust GEO satellite to obtain the real-time estimated thrust of the electric thrust GEO satellite.

[0130] In one embodiment of the present invention, this solution utilizes the thrust generated by the electric thruster. As state variables, they are modeled into the orbital dynamics model; therefore, the state variables are the orbital transition dynamics model. The expression is:

[0131]

[0132] Where r is the position of the electrically propelled GEO satellite; v is the velocity vector; m is the weight of the electrically propelled GEO satellite; and T is the thrust of the electrically propelled GEO satellite. This is the transpose of the matrix;

[0133] Orbital transfer dynamics model State equations Represented as:

[0134]

[0135] in, , , and These are the derivatives of the satellite's position, velocity, mass, and thrust, respectively. The vector of gravitational acceleration; The J2 term perturbation acceleration vector of the Earth; The solar gravitational acceleration vector; This is the lunar gravitational acceleration vector; This is the atmospheric drag acceleration vector; The solar radiation pressure perturbation acceleration vector; This is the acceleration vector generated by the estimated electric thrust in the satellite orbit coordinate system; The average gravitational acceleration at sea level on Earth; For the specific impulse of the electric thruster of an electric propulsion satellite; This is the transformation matrix from the orbital coordinate system to the J2000 ECI coordinate system.

[0136] The state equation of this scheme The expressions for each parameter are as follows:

[0137] Transformation matrix from orbital coordinate system to J2000 ECI coordinate system The expression is:

[0138]

[0139] in, The instantaneous angular momentum vector of an electrically propelled GEO satellite; , and All are unit vectors; For the module length;

[0140] Earth's gravitational acceleration vector The expression is:

[0141]

[0142] in, It is the Earth's gravitational constant;

[0143] Solar gravitational acceleration The expression is:

[0144]

[0145] in, It is the gravitational constant of the Sun; This is the position vector of the sun in the J2000 ECI coordinate system;

[0146] Lunar gravitational acceleration The expression is:

[0147]

[0148] in, It is the gravitational constant of the moon; This represents the position vector of the moon in the J2000 ECI coordinate system.

[0149] The expression for the J2 perturbation acceleration is:

[0150]

[0151] in, , and For the vector components of the J2 perturbation acceleration; For harmonic coefficients, x, y, and z are the components of the position vector; The average radius of the Earth;

[0152] Atmospheric drag acceleration vector The expression is:

[0153]

[0154] in, The ratio of the effective area S to the mass m of the electrically propelled GEO satellite; This is the atmospheric drag coefficient; The relationship between atmospheric density and the altitude of an electrically propelled GEO satellite is expressed as follows: , , For the altitude of an electrically propelled GEO satellite, For reference height; Atmospheric elevation; Let be the velocity vector of an electrically propelled GEO satellite relative to the atmosphere, and its expression is: , This is the vector of Earth's rotational angular velocity; This is Earth's angular velocity;

[0155] Solar radiation pressure perturbation acceleration vector The expression is:

[0156]

[0157] in, This is the shadow coefficient, which is the value when the satellite is located in the umbra. When the satellite is in the penumbra, When the satellite is located outside the umbra and penumbra, ; The SRP reference value is taken from the Sun. The reflection coefficient;

[0158] The expression for estimating the acceleration vector generated by electric thrust is:

[0159]

[0160]

[0161] in, , and These are the radial, along-track, and normal acceleration components, respectively. , The optimal control thrust angle for electric thrust in the orbital coordinate system.

[0162] In one embodiment of the present invention, step S1 further includes:

[0163] S11. The estimated position and velocity values ​​of the electric thrust GEO satellite in the J2000 ECI coordinate system are used as the measured values ​​of the real-time on-orbit thrust estimation method for electric thrusters based on CKF. The measurement equations are... Represented as:

[0164]

[0165] in, These are the estimated position and velocity vectors of the satellite in the J2000 ECI coordinate system. The true position vector and velocity vector of the satellite in the J2000 ECI coordinate system; To estimate accuracy;

[0166] S12. Discretize the state-space model of the orbital transfer dynamics model:

[0167]

[0168] in, and These are the discretized state variables at time k and time k+1, respectively. These are the estimated values ​​of the satellite's position and velocity vectors in the J2000 ECI coordinate system at time k+1; Let be the state transition function, representing the prediction of the satellite state at time k+1 from the state of the electrically propelled GEO satellite at time k; For observation functions; These represent the system noise at time k and the measurement noise at time k+1, respectively.

[0169] S13, Given the initial state variables of the filter Initial covariance matrix Process noise covariance matrix Measure the noise covariance matrix ;

[0170] S14. Calculate the predicted values ​​of the state variables based on the initial state variables and the initial covariance matrix:

[0171]

[0172] ,

[0173] in, The predicted value of the state variable at time k+1; and They are respectively the k+1 time-th There are 1 volume points; n is the dimension of the state variable. The estimated value of the state variables at time k; Cholesky decomposition of the covariance matrix of the state variables at time k; matrix composed of unit vectors The expression is:

[0174] .

[0175] S15. Predict values ​​based on state variables and volume point Calculate the state prediction covariance matrix at time k+1. :

[0176]

[0177] S16. Based on volume point Calculate the predicted measurement value at time k+1. :

[0178] ,

[0179] in, The measurement prediction value is obtained by weighted summation after propagating the observation function through the volume points;

[0180] S17. Predict values ​​based on state variables Volume point and measurement prediction values Update the measurement covariance matrix and cross covariance matrix:

[0181] ,

[0182] in, and These are the measurement covariance matrix and the cross covariance matrix at time k+1, respectively.

[0183] S18. Based on the measurement covariance matrix and cross covariance matrix Calculate the Kalman gain:

[0184]

[0185] in, The Kalman gain at time k+1;

[0186] S19, according to , , and The estimated value of the state variable at time k+1 and state covariance matrix Update:

[0187] , ;

[0188] State variable estimate at time k+1 The thrust estimate of an electrically propelled GEO satellite is the real-time estimated thrust of an electrically thrust GEO satellite.

[0189] According to existing research, the thrust reduction fault in electric thrusters mainly presents the following four fault modes, as illustrated in the diagram below. Figure 2 As shown, these four fault modes are as follows:

[0190] Thrust reduction failure mode 1 Figure 2 (a): When the operating state of the electric thruster abruptly changes from 100% to 0, its fault model can be represented as follows:

[0191] .

[0192] See Thrust Reduction Failure Mode 2 Figure 2 (b) The operating state of the electric thruster gradually decreases from 100% to 0, and its fault model can be represented as follows:

[0193] .

[0194] See Thrust Reduction Failure Mode 3 Figure 2(c): In this mode, the thruster's operating state decreases from full capacity to a certain value, and then recovers to 100%. The fault model can be represented as follows:

[0195]

[0196] in, This represents the minimum operating state of the electric thruster during a thrust failure. The time it takes for the electric thruster's thrust to decrease to its minimum value; This refers to the recovery time of the electric thruster's thrust magnitude.

[0197] See Thrust Reduction Failure Mode 4 Figure 2 In the middle (d) mode, the thruster's operating state decreases from full capacity to a certain value and remains unchanged. Its fault model can be represented as follows:

[0198] .

[0199] In this scheme, the thrust descent fixed-point transfer reconfiguration guidance method for electric propulsion GEO satellites is mainly applicable to thrust descent fault mode four.

[0200] In step S2, based on the real-time estimated thrust, the fault state function is used to determine whether the electric thrust GEO satellite has experienced a thrust reduction fault. If so, proceed to step S3; otherwise, proceed to step S5.

[0201] In implementation, the preferred expression for the fault state function in this scheme is:

[0202]

[0203] , , ,

[0204] in, This is a fault status function, with a value of 1 indicating the presence of a fault and a value of 0 indicating the absence of a fault. The deviation of the electric thrust at time t; This is the threshold value for thrust magnitude; Duration of thrust anomaly; This is the threshold for the duration of the abnormality. The real-time estimated thrust at time t; This is the nominal thrust; The first trigger of the thrust magnitude threshold is the deviation in electric thrust magnitude. The point in time; To continuously exceed the thrust magnitude threshold The end time; and All are constants greater than 0; The sampling period.

[0205] In step S3, a reconfiguration guidance decision function based on the thrust reduction degree, the fault occurrence stage, and the duration of thrust abnormality and stability is used to determine whether reconfiguration guidance is needed. If yes, proceed to step S4; otherwise, proceed to step S5.

[0206] In one embodiment of the present invention, the expression of the reconstructed guidance decision function is:

[0207]

[0208] , , ,

[0209]

[0210] in, The guidance reconstruction decision function has a value of 1 indicating that guidance reconstruction is required and a value of 0 indicating that guidance reconstruction is not required. For fault state functions; This refers to the degree of thrust reduction; This is the threshold for the degree of thrust reduction; The value represents the relative progress at the time of failure. The closer it is to 1, the more likely the failure occurred in the early stage of the task; the closer it is to 0, the more likely the failure occurred in the later stage of the task. This represents the task progress threshold. This refers to the period of relative stability after the thrust decreases. The time threshold for initiating reconfiguration guidance; The deviation of the electric thrust at time t; This is the nominal thrust; The time when the electric thruster begins to experience a thrust reduction fault; The total scheduled duration for the geostationary transfer mission of the electric propulsion satellite; A constant greater than 0; The sampling period; This is the moment when the stability condition is met for the first time; This is the moment for determining a thrust reduction fault; To estimate the average thrust magnitude within the sliding window; for The average thrust magnitude estimated in the previous window; for and The absolute deviation; To estimate the thrust standard deviation; The standard deviation threshold; Duration; It is a constant, and its value is 50 in this simulation.

[0211] After accurately identifying thrust descent faults through real-time estimation of electric thrust, reconfiguration guidance becomes crucial for ensuring the successful completion of the predetermined orbit transfer and positioning mission by an electric propulsion satellite. The occurrence of thrust descent faults outside the orbit transfer and positioning phase, and the varying degrees of thrust descent, have different impacts on the positioning mission. When the impact of a thrust descent fault on the positioning mission is minor, reconfiguration guidance can be omitted to avoid unnecessary calculations and guidance law adjustments, thereby reducing the system load. Conversely, when the impact of a thrust descent fault is significant, reconfiguration guidance must be initiated to adjust the orbit control strategy and ensure the successful completion of the positioning mission. Therefore, a reasonable judgment criterion needs to be established, combining the degree of thrust descent and the stage at which the thrust descent fault occurs, to determine whether to initiate reconfiguration guidance.

[0212] Since only in fault mode one does the electric thrust suddenly drop to zero, while in other fault modes the electric thrust gradually decreases, and since reconfiguration guidance requires input of the electric thrust magnitude, thus necessitating the introduction of the relatively stable duration after the thrust decrease, it is necessary to incorporate this data. As a basis for judgment.

[0213] In step S4, a fixed-point transfer reconfiguration guidance method based on Lyapunov stability theory is used to adaptively adjust the orbit of the electric propulsion GEO satellite under thrust failure, and then proceed to step S5.

[0214] In one embodiment of the present invention, step S4 further includes:

[0215] S41. Determine the guidance mode as either the shortest time guidance law or the limited time fuel-saving guidance law based on the current mission requirements, and proceed to steps S42 and S43 respectively.

[0216] S42. Construct initial state constraints and optimal performance indicators. The weight parameters of the RQ-Law function are optimized using initial state constraints and optimal performance indicators to obtain optimized weight coefficients. Then, the process proceeds to step S44, where the optimal performance indicators are determined. The expression is:

[0217]

[0218] in, Maximum flight time for stationary transfer of electrically propelled GEO satellites; This refers to the flight time during the orbital insertion phase. This refers to the maximum permissible deviation at the end of the stationary transfer phase of an electrically propelled satellite. and All are constants. Take 0.97, Take 0.01;

[0219] S43. Construct initial state constraints and optimal performance indicators. The weight parameters of the RQ-Law function are optimized using initial state constraints and optimal performance indicators to obtain optimized weight coefficients. Then, the process proceeds to step S44, where the optimal performance indicators are determined. The expression is:

[0220] ;

[0221] S44. Based on the current state variables of the electric propulsion satellite, the current orbital information of the target point, and the optimized weighting coefficients, output the optimal control thrust angle under thrust reduction fault conditions. :

[0222] ,

[0223]

[0224]

[0225]

[0226] Where D1, D2, and D3 are auxiliary variables; Q is the RQ-Law function; For electrically propelled GEO satellites; The maximum rate of change of the eccentricity component f with respect to the thrust direction; The maximum rate of change of the eccentricity component g with respect to the thrust direction; To represent the maximum rate of change of the five orbital elements of an electrically propelled satellite with respect to the thrust direction and true longitude; The acceleration vector in the orbital coordinate system; True longitude for GEO satellites; Auxiliary variables; a is the right ascension of the ascending node; f and g are the eccentricity vector components; , Here are the vector components of the orbital inclination angle; L is the true longitude. It is the Earth's gravitational constant;

[0227] S45. Optimal control thrust angle under thrust reduction fault conditions. Adaptive adjustments are made to the orbit of electrically propelled GEO satellites.

[0228] In this scheme, the initial state constraints include three constraints, namely:

[0229] Initial state constraints:

[0230]

[0231] Where t0 is the initial time, a C (t0) is the semi-major axis of the orbit at the initial moment, f C (t0) is the vector of orbital eccentricity at the initial moment, g C (t0) represents the component of the orbital eccentricity at the initial moment, h C (t0) is the vector of the orbital inclination at the initial moment, k C (t0) represents the component of the orbital inclination at the initial moment, L C (t0) represents the true longitude at the initial time, and a0, f0, g0, h0, k0, and L0 are the orbital elements of the initial orbit.

[0232] End constraints:

[0233]

[0234] Among them, t f For transfer time; , , and These are the semi-major axis, eccentricity, orbital inclination, and true longitude of the GEO satellite; , , and These are the semi-major axis, eccentricity, orbital inclination, and true longitude of the target point, respectively.

[0235] Motion equation constraints:

[0236]

[0237] in, , , , , , , These are the semi-major axis, eccentricity components f and g, orbital inclination components h and k, true longitude, and rate of mass change, respectively. p is the right ascension of the ascending node; p is the semi-major diameter. This refers to the specific impulse of the electric thruster in an electric propulsion satellite.

[0238] In steps S42 and S43, the expression for the optimization weight coefficients of this scheme is as follows:

[0239]

[0240] in, and All are related weights of the penalty function; The weights are respectively the semi-major axis, the eccentricity components f and g, and the orbital inclination components h and k; and For phase parameters; , and All are associated scaling weights;

[0241] The expression for the Lypunov function Q is:

[0242]

[0243] in, Both are penalty functions. The smaller the value, the shorter the time required to complete the orbital transfer and station positioning; For scaling functions; To adjust the weighting of the orbital elements at the vernal equinox; For electrically propelled GEO satellites; For the augmented set of the target orbital elements; This represents the maximum rate of change of each orbital element of an electrically propelled GEO satellite relative to the thrust direction and true longitude.

[0244] In step S5, it is determined whether the electrically propelled GEO satellite has reached the target point. If so, the algorithm terminates; otherwise, it returns to step S1.

[0245] To verify the effectiveness of the proposed point-to-point transfer and reconfiguration guidance method for electrically propelled GEO satellites under thrust reduction fault conditions, numerical simulation experiments were conducted using Python 3.8 on a desktop computer equipped with an Intel(R) Core(TM) i7-10700F CPU@2.90GHz and 16GB of memory. The physical parameters of the electrically propelled satellite are shown in Tables 1 and 2.

[0246] Table 1 Initial state parameters and initial errors of electric propulsion satellites

[0247]

[0248] Table 2 Physical parameters of electric propulsion satellites

[0249]

[0250] For the failure scenario of reduced thrust of electric thruster, based on the analysis of different failure modes, a simulation analysis is conducted using failure mode four, which has the most significant impact on the fixed-point transfer mission and whose cumulative effect cannot be ignored.

[0251] Simulation results can be found in the figure. Figures 3-8 , Figure 3 The error curve for estimating the magnitude of electric thrust; Figure 4 The result diagram shows the fault diagnosis of thrust reduction. Figure 5 and Figure 6 The diagram shows the decrease in electric thrust of the GEO satellite and the results of guidance reconfiguration. When the guidance reconfiguration decision function is 1, guidance reconfiguration is required. Figure 7 and Figure 8 The simulation results show that the integrated method for reconfiguring guidance for GEO satellites, considering the changes in satellite eccentricity, orbital inclination, and thrust angle, is compared with the segmented approach. The simulation results also show that after a thrust reduction failure in the electric thruster, the thrust acceleration provided by the electrically propelled GEO satellite decreases, leading to a longer time required to complete the designated geostationary transfer mission. Without reconfiguration guidance, the time required for an electrically propelled GEO satellite to complete the geostationary transfer mission is 270.06 days, an increase of 81.69 days compared to the time without the thrust reduction failure.

[0252] After reconfiguration guidance, the time required for the electrically propelled GEO satellite to complete its geostationary transfer was reduced to 254.01 days, a decrease of 16.05 days compared to the unreconfigured case. Considering time as a key performance indicator, the electrically propelled satellite operated continuously throughout the transfer process, except for the Earth's shadow area limitations, thereby minimizing fuel consumption while ensuring the shortest possible time.

[0253] pass Figures 3-8 Simulation results show that after reconfiguration guidance is applied to the stationary transfer of electric propulsion satellites, not only is the stationary transfer time shortened, but also 22.99 kg of fuel is saved, which can be further used for subsequent position holding and other tasks, thus improving the overall execution efficiency and reliability of the mission.

Claims

1. An electric propulsion GEO satellite thrust decay rendezvous reconfiguration guidance method, characterized in that, The method comprises the steps of: S1, updating an orbit transfer dynamics model of an electric propulsion GEO satellite by using a cubature Kalman filter method CKF to obtain a real-time estimated thrust of the electric propulsion GEO satellite; S2, judging whether the electric propulsion GEO satellite has an electric thrust decline fault according to the real-time estimated thrust by using a fault state function, if yes, entering step S3, otherwise, entering step S5; S3, determining whether the guidance needs to be reconstructed by using a reconstruction guidance decision function constructed based on a thrust decline degree, a fault occurrence stage and a duration of thrust anomaly and stability, if yes, entering step S4, otherwise, entering step S5; S4, performing self-adaptive adjustment on the orbit of the electric propulsion GEO satellite under the thrust fault by using a fixed-point transfer reconstruction guidance method based on Lyapunov stability theory, and then entering step S5; S5, judging whether the electric propulsion GEO satellite reaches a target point, if yes, terminating the algorithm, otherwise, returning to step S1; An expression of the reconstruction guidance decision function is as follows: ， ， ， wherein, is a reconstruction guidance decision function, taking value 1 indicating that reconstruction guidance is needed, and taking value 0 indicating that reconstruction guidance is not needed; is a failure state function; is a thrust degradation degree; is a thrust degradation degree threshold value; is a relative progress at failure time; is a mission progress threshold value; is a relative stable duration after thrust degradation; is a time threshold value for starting reconstruction guidance; is an electric thrust size deviation amount at time t; is a nominal thrust; is a time when electric thruster starts to have thrust degradation failure; is a predetermined total duration of electric propulsion satellite fixed-point transfer mission; is a constant greater than 0; is a sampling period; is a time when stability condition is first satisfied; is a thrust degradation failure decision time; is an estimated thrust size mean value in a sliding window; is is an estimated thrust size mean value in a previous window; is is an absolute deviation of and is an estimated thrust standard deviation; is a standard deviation threshold value; is a duration; is a constant, taking value 50;​ The step S4 further comprises: S41, determining a guidance mode as a time shortest guidance law or a finite time fuel consumption most saving guidance law according to a current task requirement, and entering step S42 and step S43 respectively; S42, constructing initial state constraint and optimal performance index , and using the initial state constraint and the optimal performance index to optimize the weight parameter of the RQ-Law function to obtain an optimized weight coefficient, and then entering step S44, the expression of the optimal performance index is: wherein is the maximum flight time for a spot transfer of an electric propulsion GEO satellite; is the flight time for an orbit insertion phase; is the maximum allowed deviation at the end of a spot transfer of an electric propulsion satellite; and are constants, takes the value 0.97, takes the value 0.01; S43, constructing initial state constraint and optimal performance index , and using the initial state constraint and the optimal performance index to optimize the weight parameter of the RQ-Law function to obtain an optimized weight coefficient, and then entering step S44, the expression of the optimal performance index is: Wherein, m is the weight of the electric propulsion GEO satellite; S44, output the optimal control thrust angle under the thrust drop-out failure according to the current state variable of the electric propulsion satellite, the current orbit information of the target point, and the optimized weight coefficient : ， where D1, D2 and D3 are auxiliary variables; Q is the RQ-Law function; is the orbit element of the electric propulsion GEO satellite; is the maximum rate of change of the eccentricity component f with respect to the thrust direction; is the maximum rate of change of the eccentricity component g with respect to the thrust direction; is the maximum rate of change of the 5 orbit elements of the electric propulsion satellite with respect to the thrust direction and the true longitude; is the acceleration vector in the orbit coordinate system; is the true longitude of the GEO satellite; is the auxiliary variable; a is the ascending node right ascension; f, g are the eccentricity vector components; , is the orbit inclination vector component; L is the true longitude; is the Earth gravitational constant; S45, optimal control thrust angle under thrust down fault Adaptive orbit adjustment for electric propulsion GEO satellites.

2. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method of claim 1, wherein, An expression of the fault state function is as follows: ， ， ， wherein, is a fault status function, taking value 1 if there is a fault and value 0 if there is no fault; is the electric thrust magnitude deviation at time t; is the thrust magnitude threshold value; is the thrust abnormality duration; is the abnormality duration threshold value; is the real-time estimated thrust at time t; is the nominal thrust; is the time point when the electric thrust magnitude deviation first triggers the thrust magnitude threshold value ; is the end time when the deviation lasts beyond the thrust magnitude threshold value ; and are both positive constants; is the sampling period.

3. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method according to claim 1 or 2, characterized in that, A fault model of the electric thrust decline fault is as follows: wherein, is the operational state of the electric thruster; is the time at which the electric thruster starts to exhibit a thrust degradation fault; is the minimum operational state of the electric thruster during the thrust fault; is the time at which the electric thruster thrust has degraded to a minimum value; is the end of operation time; t is the current operation time.

4. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method according to claim 1 or 2, characterized by, The orbital transfer dynamics model The expression is: where r is the position of the electric propulsion GEO satellite; v is the velocity vector; m is the weight of the electric propulsion GEO satellite; T is the thrust of the electric propulsion GEO satellite; is the transpose of the matrix Orbital transfer dynamics model Equation of state is expressed as: where, , , and are the derivatives of satellite position, velocity, mass and thrust, respectively; is the Earth-centered gravitational acceleration vector; is the Earth J2 perturbation acceleration vector; is the Sun gravitational acceleration vector; is the Moon gravitational acceleration vector; is the atmospheric drag acceleration vector; is the solar pressure perturbation acceleration vector; is the estimated acceleration vector due to electric thruster in the satellite orbital coordinate system; is the average gravity acceleration of the Earth sea level; is the specific impulse of the electric thruster of the electric propulsion satellite; is the transformation matrix from the orbital coordinate system to the J2000 ECI coordinate system.

5. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method of claim 4, wherein, The conversion matrix from the orbital coordinate system to the J2000 ECI coordinate system The expression is: wherein is the instantaneous angular momentum vector of an electrically propelled GEO satellite; , and are unit vectors; is the module length; vector of the acceleration of the earth's gravity is expressed by wherein G is the earth's gravitational constant; Solar gravitational acceleration The expression for the solar gravitational acceleration is wherein, is the solar gravitational constant; is the position vector of the sun in the J2000 ECI frame. The expression of the lunar gravitational acceleration is given by wherein, is the lunar gravitational constant; is the position vector of the moon in the J2000 ECI coordinate system; An expression of a J2 perturbation acceleration is as follows: wherein , and are the vector components of the J2 perturbation acceleration; is the harmonic term coefficient, ; x, y and z are the components of the position vector; is the mean radius of the Earth; Atmospheric drag acceleration vector The expression for the atmospheric drag acceleration vector is wherein, is the ratio of the effective area S to the mass m of the electric propulsion GEO satellite; is the atmospheric drag coefficient; is a function of the atmospheric density and the altitude of the electric propulsion GEO satellite, which is expressed as , , is the altitude of the electric propulsion GEO satellite, is the reference altitude; is the atmospheric altitude; is the velocity vector of the electric propulsion GEO satellite relative to the atmosphere, which is expressed as , is the Earth rotation angular velocity vector; is the Earth angular velocity; Solar pressure perturbation acceleration vector The expression for this is: wherein is the shadow coefficient when the satellite is in the umbra, is the penumbra coefficient when the satellite is in the penumbra, is the out-of-shadow coefficient when the satellite is outside the umbra and the penumbra, ; is the SRP reference value when the sun is at the origin; is the reflection coefficient; An expression of an acceleration vector generated by the estimated electric thrust is as follows: wherein, , and are the radial, along-track, normal acceleration components, respectively; , is the optimal control thrust angle in the orbital coordinate system.

6. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method of claim 4, wherein, The step S1 further comprises: S11, the position and velocity estimates of the electric propulsion GEO satellite in the J2000 ECI coordinate system are taken as the measurements of the CKF-based real-time on-orbit thrust estimation method for electric thrusters, and the measurement equation is is expressed as: wherein, is the position vector, velocity vector estimate of the satellite in the J2000 ECI coordinate system; is the true position vector, velocity vector of the satellite in the J2000 ECI coordinate system; is the estimation accuracy; S12, discretizing a state space model of the orbit transfer dynamics model: wherein, and are the discretized state quantities at time instant k and k+1, respectively; are the position vector and velocity vector estimates of the satellite in J2000 ECI frame at time instant k+1; is the state transition function, which represents the prediction of the satellite state at time instant k+1 from the state at time instant k of an electric propulsion GEO satellite; is the observation function; are the system noise at time instant k and the measurement noise at time instant k+1, respectively; S13, given filter initial state variable , initial covariance matrix , process noise covariance matrix , measurement noise covariance matrix ; S14, calculating a state variable prediction value according to an initial state variable and an initial covariance matrix: ， in, The predicted value of the state variable at time k+1; and They are the k+1th time. There are 1 volume points; n is the dimension of the state variable. The estimated value of the state variables at time k; The Cholesky decomposition of the covariance matrix of the state variables at time k; A matrix composed of unit vectors; S15, state variable prediction value and volume points , calculate the state prediction covariance matrix at time k+1 : S16、According to the volume point , calculate the measurement prediction value at k+1 time : ， wherein, is the measurement prediction value obtained by propagating the observation function to the volume points and then weighted summing. S17, update the measurement covariance matrix and cross covariance matrix based on the state variable prediction value , volume points and measurement prediction value , update the measurement covariance matrix and cross covariance matrix ， wherein, and Rkand Qkare the measurement covariance matrix and the cross covariance matrix at time instant k, respectively. S18. Calculate the Kalman gain from the measurement covariance matrix and the cross covariance matrix S19. Update the state estimate with the Kalman gain wherein, is the Kalman gain at time k + 1. S19. The method of any one of S1-S18, wherein the state variable estimate is updated according to , , and the state variable estimate at time k+1 is updated according to and the state covariance matrix is updated according to ， ； the state variable estimation value at the k+1 moment The thrust estimation value of the electric propulsion GEO satellite in the k+1 moment is the real-time estimation thrust of the electric propulsion GEO satellite.

7. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method of claim 1, wherein, The initial state constraint comprises: The initial state constraint: where t0 is the initial time, a C (t0) is the vector of the orbit eccentricity at the initial time, g C (t0) is the vector of the orbit eccentricity at the initial time, g C (t0) is the component of the orbit eccentricity at the initial time, h C (t0) is the vector of the orbit inclination at the initial time, k C (t0) is the component of the orbit inclination at the initial time, L C (t0) is the true longitude at the initial time, a0, f0, g0, h0, k0, L0 are all the orbital elements of the initial orbit. The terminal constraint: wherein t f is the transfer time; , , and are the semi-major axis, eccentricity, orbital inclination and true longitude of the GEO satellite, respectively; , , and are the semi-major axis, eccentricity, orbital inclination and true longitude of the target point, respectively. The motion equation constraint: wherein, , , , , , , are the semi-major axis, the eccentricity components f and g, the inclination components h and k, the true longitude, the mass variation rate, respectively; is the right ascension of the ascending node; p is the semi-latus rectum; is the specific impulse of the electric thruster of the electric propulsion satellite.

8. The electrically propelled GEO satellite thrust-down spot transfer reconfiguration guidance method of claim 7, wherein, An expression of an optimization weight coefficient is as follows: wherein and are associated weights of the penalty functions; are weights of the semi-major axis, eccentricity components f, g, inclination of the orbit components h, k, respectively; and are phase parameters; , and are associated scaling weights; An expression of a Lyapunov function Q is as follows: wherein, are penalty functions, The smaller, the shorter the time to complete the orbit transfer and station keeping; is a scaling function; is the weight corresponding to the improved equinox orbit element; is the orbit element of the electric propulsion GEO satellite; is the augmented set of target orbit elements; is the maximum rate of change of each orbit element of the electric propulsion GEO satellite with respect to the thrust direction and the true longitude.

Images