Satellite orbit thrust segment inversion method based on pattern search

Abstract

The application discloses a satellite orbit thrust segment inversion method based on a mode search, solves the problem of how to accurately invert the parameters of an unknown thrust segment in the middle by using two extremely short radar observation arc segments, and belongs to the field of satellite orbit thrust segment inversion. The application comprises the following steps: finding the epoch time of the two observation arc segments; obtaining initial orbit elements by using a Laplace-LM algorithm and substituting the initial orbit elements into POD to obtain precise orbit elements; constructing a satellite orbit dynamics model based on initial dynamic parameters, performing orbit propagation on the first precise orbit elements of the first observation arc segment from the first epoch time to the second epoch time of the second observation arc segment to obtain second propagated precise orbit elements; constructing an objective function according to the position difference between the second propagated precise orbit elements and the second precise orbit determination result; and introducing a mode search algorithm to obtain target dynamic parameters corresponding to the minimum value of the objective function.

Description

Technical Field

[0001] This invention belongs to the field of satellite orbit thrust segment inversion technology, and relates to a satellite orbit thrust segment inversion method based on pattern search. Background Technology

[0002] Space target detection systems are facing increasingly severe challenges. In recent years, the number of space targets, such as electric propulsion satellites with continuous low-thrust capabilities and some on-orbit servicing spacecraft, has increased significantly. These spacecraft are capable of continuous, subtle orbital maneuvers, which, while enhancing their mission flexibility, also poses a significant challenge to traditional space target cataloging and trajectory prediction capabilities.

[0003] Although the cumulative effect of continuous small thrusts is not as significant as that of pulsed maneuvers, it can substantially change the orbital elements of a satellite within hours or days, causing its actual trajectory to gradually deviate from the prediction model based on the natural gravitational field.

[0004] The surge in the number of space targets has led to a reduction in the resources available for existing target detection methods, typically resulting in only sparse and brief observational arcs. Timely and accurate deduction from limited observational data of whether a satellite performed thrust maneuvers during periods of invisibility, and the specific parameters of those thrusts (magnitude, duration, and start time), has a significant impact on improving subsequent space target detection capabilities.

[0005] Most existing studies average the thrust effect between two arc segments rather than accurately inverting the thrust segment. For example, Zhang Dapeng and Shen Hongxin. Study on Starlink orbital characteristics based on precise ephemeris. Mechanics and Practice, 2022, 44(6): 1268-1278. doi: 10.6052 / 1000-0879-22-355.

[0006] For example, publication number CN120180603A, invention title: Unmarked Batch Processing Orbit Determination Method and System for Continuously Low-Thrust Maneuvering Satellites; the radar observation vector acquisition module in this scheme is used to obtain the radar observation vector based on the radar measured data and radar site coordinates when radar measured data and radar site coordinates are available, and to obtain the pseudo radar observation vector based on satellite ephemeris data when measured data is unavailable. Although this scheme can significantly improve orbit determination accuracy and reduce the impact of single-point observation errors, it cannot calculate the true propulsion strategy of continuously low-thrust spacecraft because it cannot accurately invert the thrust segment.

[0007] For example, publication number CN114462256A, invention title: "Method, Apparatus, Equipment, and Medium for Determining the Trajectory of a Non-cooperative Low-Thrust Maneuvering Target," derives the calculation equation for the extended state quantity transfer matrix containing acceleration components under a high-precision perturbation orbit model. It then improves the trajectory of a non-cooperative low-thrust maneuvering target using radar observation data and the least squares method, and finally predicts the trajectory using the determined extended state quantities. While this method can determine the trajectory of a non-cooperative target performing continuous low-thrust maneuvers, it estimates the average thrust effect between observation arcs, rather than accurately inverting the thrust segment, and therefore cannot calculate the true propulsion strategy of a continuous low-thrust spacecraft. This invention, however, can accurately invert the thrust segment and summarize the true propulsion strategy of a continuous low-thrust spacecraft. Summary of the Invention

[0008] Developing continuous low-thrust inversion technology based on extremely short arc-segment observations has become an urgent need to improve space target detection capabilities. This invention aims to solve this core problem: how to accurately invert the parameters of the unknown thrust segment in the middle using two extremely short radar observation arcs. This invention discloses a satellite orbit thrust segment inversion method based on pattern search. This invention can achieve accurate thrust segment inversion and summarize the true propulsion strategy of continuous low-thrust spacecraft. This technological breakthrough will enable rapid re-cataloging and accurate orbit determination of maneuvering satellites, effectively supporting orbit prediction and space target collision avoidance, and has significant theoretical and practical value.

[0009] The objective of this invention is specifically achieved through the following technical solutions:

[0010] This invention discloses a satellite orbit thrust segment inversion method based on pattern search, the method comprising:

[0011] Step 1: After performing preprocessing to remove outliers from the radar observation data of any two observation arcs, find the first epoch time of the first observation arc and the second epoch time of the second observation arc respectively.

[0012] Step 2: Use the Laplace-LM algorithm to determine the initial orbits for the two observed arc segments respectively, and obtain the initial orbital elements corresponding to the epoch times in the two initial orbits;

[0013] Step 3: Using the two initial orbital elements as initial values, substitute them into the weighted least squares precise orbit determination algorithm POD to obtain the first precise orbital element corresponding to the first epoch and the second precise orbital element corresponding to the second epoch.

[0014] Step 4: Set the thrust start time, thrust duration, and thrust acceleration as initial dynamic parameters, and construct a satellite orbital dynamics model that includes the thrust segment based on the initial dynamic parameters; propagate the first precise orbital elements of the first observation arc from the first epoch according to the satellite orbital dynamics model, and propagate the orbit to the second epoch of the second observation arc to obtain the second propagated precise orbital elements;

[0015] Step 5: Based on the positional difference between the second propagation precise orbital elements and the second precise orbital elements, construct an objective function to measure the accuracy of the initial dynamic parameters;

[0016] Step six: Introduce the Pattern Search algorithm, adjust the initial dynamic parameters, and obtain the target dynamic parameters that describe the thrust segment information between the two observation arc segments when the objective function is minimized; based on the target dynamic parameters, obtain the actual propulsion strategy of the satellite orbit thrust segment.

[0017] In step one, the preprocessed first and second observation arc segments are as follows:

[0018] ;

[0019] In the formula, This is the first observation arc segment. This represents the first epoch of the first observation arc segment. Subscripts are sequentially assigned from 1 to m, with m being the largest index. This is the first azimuth angle observation value of the first observation arc segment, with subscripts ranging from 1 to m and so on. This is the first elevation angle observation value of the first observation arc segment, with subscripts ranging from 1 to m and so on. This represents the first distance observation value for the first observation arc segment, with subscripts ranging from 1 to m and so on. This is the second observation arc segment; This refers to the second epoch of the second observation arc, with subscripts ranging from 1 to m. This refers to the second azimuth angle observation value of the second observation arc segment, with subscripts ranging from 1 to m and so on. This is the second elevation angle observation value for the second observation arc segment, with subscripts ranging from 1 to m; This represents the second distance observation value for the second observation arc segment, with subscripts ranging from 1 to m.

[0020] In step two, the initial orbital elements corresponding to the epochs in the two initial orbits are:

[0021] ;

[0022] In the formula, This represents the first initial orbital element corresponding to the first epoch in the first initial orbit. It is the initial position of the first initial orbital element corresponding to the first epoch. It is the initial velocity corresponding to the first initial orbital element at the first epoch; This represents the second initial orbit element corresponding to the second epoch in the second initial orbit. It is the initial position of the second initial orbital element corresponding to the second epoch. It is the initial velocity of the second initial orbital element corresponding to the second epoch; This is the Laplace-LM algorithm.

[0023] In step three, the first precise orbital elements corresponding to the first epoch and the second precise orbital elements corresponding to the second epoch are:

[0024] ;

[0025] In the formula, This represents the first precise orbital element corresponding to the first epoch. It is the initial position of the first precise orbital element corresponding to the first epoch. It is the initial velocity corresponding to the first precise orbital element at the first epoch; This represents the second precise orbital element corresponding to the second epoch. It is the initial position of the second precise orbital elements corresponding to the second epoch. It is the initial velocity of the second precise orbital element corresponding to the second epoch; This is a weighted least squares precise orbit determination algorithm.

[0026] In step four, the constructed satellite orbital dynamics model is as follows:

[0027] ;

[0028] In the formula, It's the satellite position. It is a time variable; It is the satellite's speed; It is the Earth's gravitational constant; Indicates the modulus; It is the natural perturbation force experienced by the satellite; It is the continuous small thrust that the satellite experiences. It is the transformation matrix from the RTN coordinate system to the ECI coordinate system.

[0029] In step four, the satellite experiences continuous small thrusts as follows:

[0030] ;

[0031] In the formula, It is the thrust acceleration during the thrust phase. It is the beginning of the thrust phase. It refers to the duration of the thrust phase.

[0032] In step four, the transformation matrix from the RTN coordinate system to the ECI coordinate system is:

[0033] .

[0034] In step five, the objective function is:

[0035] ;

[0036] In the formula, Let be the objective function. The positional difference between the second propagation precision orbital elements and the second precision orbital elements. Indicates to Perform the modulo operation.

[0037] The beneficial effects of this invention are:

[0038] 1. A new approach of "parameterized and precise inversion of thrust segment" is proposed: Unlike the approximate treatment of averaging thrust effect in existing technologies, this invention parameterizes the unknown thrust segment between two arc segments into three specific physical dynamic parameters (thrust start time, thrust duration, and thrust acceleration), achieving a fundamental breakthrough from "effect estimation" to "precise parameter inversion".

[0039] 2. An integrated solution framework of "observation-orbit determination-thrust inversion" was constructed: the radar observation preprocessing, initial orbit determination of Laplace-LM, precise orbit determination of POD and thrust parameter optimization were organically combined to form a complete and automated thrust segment inversion technology chain, which ensured the accuracy of input information and the reliability of results.

[0040] 3. A pattern search optimization algorithm suitable for "black box" models is introduced: In view of the highly nonlinear and nondifferentiable characteristics of the orbital dynamics model, the zero-order optimizer of pattern search is creatively adopted, which avoids the failure risk of traditional gradient-based algorithms when solving such complex problems, and provides a stable and robust solution path for the core inversion problem.

[0041] 4. An objective function based on "track propagation residual" was designed: the difference between the position of the precise track propagation from the first arc segment to the second arc segment and the precise track determination result of the second arc segment was used as the objective function. The physical meaning is clear and it directly and effectively measures the accuracy of the thrust parameter setting.

[0042] 5. The invention enables the search of thrust parameters within a physical constraint space: The optimization process of this invention is inherently compatible with the physical constraints of thrust parameters (such as non-negative thrust duration and the start time being between two arc segments), ensuring that the search process is always carried out within a reasonable parameter space and guaranteeing the physical authenticity of the inversion results.

[0043] 6. It provides the ability to reverse analyze from sparse observations to complete propulsion strategies: This invention can reverse analyze the complete propulsion strategy of a satellite during the invisible period (when to start propulsion, how long to propulsion, and how much thrust) using only two extremely short observation arcs, which greatly improves the information acquisition dimension of space situational awareness.

[0044] 7. Significantly improves the precision and accuracy of orbital maneuver detection: Overcomes the information loss defects of existing averaging methods, can accurately deduce the three-dimensional parameters of the thrust phase, and elevates orbital maneuver analysis from macro-trend judgment to the level of micro-parameter quantification, providing unprecedented precision data support for interpreting the behavior and intentions of space targets.

[0045] 8. Effectively solves the applicability problem of thrust inversion algorithm under complex models: By adopting a pattern search method that does not rely on derivatives, the problem of optimization algorithm failure caused by the complexity, nonlinearity and nondifferentiability of the orbital dynamics model is successfully solved, ensuring the stable convergence of the thrust inversion process under the high-fidelity model.

[0046] 9. Significantly enhanced space target tracking capability based on sparse observation data: Even with extremely limited observation data (only two short observation arcs), it can still achieve high-precision thrust segment inversion, solving the problem of "losing tracking" or "mistracking" maneuvering targets due to data interruption, and greatly improving the effectiveness of the space surveillance network under resource constraints.

[0047] 10. Directly serving precise decision-making for space safety and collision avoidance: By accurately reconstructing thrust history, the medium- and long-term accuracy of orbit prediction can be significantly improved, providing a more credible basis for decision-making on collision warning and avoidance maneuvers for high-value spacecraft, and effectively reducing the risk of on-orbit collisions.

[0048] 11. It has achieved effective detection and identification of continuous low-thrust satellite stealth maneuvers: It can keenly capture and quantify continuous low-thrust maneuvers that are difficult to detect by traditional methods, tearing off the "stealth cloak" of such satellites, which has significant strategic value for maintaining space security and identifying potential threats.

[0049] 12. Improved the accuracy and timeliness of the space target cataloging database: It can quickly re-catalog and update the status of maneuvering satellites, ensuring the accuracy and timeliness of the cataloging database, and laying a solid data foundation for all subsequent space situational awareness activities. Attached Figure Description

[0050] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0051] Figure 1 This is a schematic diagram of the experimental results provided in an embodiment of the present invention. Detailed Implementation

[0052] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0053] This invention provides a method for inverting satellite orbit thrust segments based on pattern search, the method comprising:

[0054] Step 1: After preprocessing the radar observation data of any two observation arc segments by removing outliers, find the first observation arc segment after preprocessing. The First Era and the second observation arc The Second Era ;

[0055] The radar observation data for the two observation arcs were preprocessed to remove outliers, resulting in two segments of high-quality observation data. and .

[0056] Step 2: Use the Laplace-LM algorithm to analyze the two observed arc segments respectively. and Initial orbit determination is performed to obtain the initial orbital elements corresponding to the epoch times in the two initial orbits. and ;

[0057] The Laplace-LM algorithm is a publicly available initial orbit determination algorithm that can calculate the initial orbit value relatively accurately. For the Laplace-LM algorithm, please refer to Tao Xuefeng, Zhao Shuailong, and Li Zhi. A method for joint initial orbit determination and uncertainty estimation by multiple stations [J]. Shanghai Aerospace (Chinese and English), 2024, 41(6): 23-30.

[0058] Step 3, convert the two initial orbital elements. and As initial values, substituting them into the weighted least squares precise orbit determination algorithm (POD), we obtain the first precise orbital elements corresponding to the first epoch. and the second precise orbital elements corresponding to the second epoch. ;

[0059] POD is a mature and accurate precision orbit determination algorithm that can calculate precise orbit values ​​relatively accurately. (Reference: Liao Ying, Pan Wanghua, Wen Yuanlan, et al. Precise Satellite Orbit Determination Method Based on Compensated Least Squares Estimation [J]. Systems Engineering & Electronics, 2012, (7): 1430-1434.)

[0060] Step 4: Set the thrust start time Thrust duration and thrust acceleration As initial dynamic parameters A satellite orbital dynamics model including the thrust phase is constructed based on the initial dynamic parameters; the first precise orbital elements for the first observation arc segment are calculated according to the satellite orbital dynamics model. Orbit propagation begins from the first epoch and continues to the second epoch of the second observation arc, yielding the second propagation precise orbital elements. ;

[0061] The dynamic parameters are the parameters of the unknown thrust segment that need to be accurately inverted.

[0062] Step 5, based on the second propagation precise orbital elements With the second precision orbital elements position difference Construct an objective function to measure the accuracy of the initial dynamic parameters. ;

[0063] Step six: Introduce the Pattern Search algorithm, adjust the initial dynamic parameters, and obtain the target dynamic parameters that describe the thrust segment information between the two observation arc segments when the objective function is minimized; based on the target dynamic parameters, obtain the actual propulsion strategy of the satellite orbit thrust segment.

[0064] Among them, the Pattern Search algorithm, as a direct search optimization technique that does not rely on the gradient of the objective function, iterates and optimizes by comparing the function values ​​of adjacent sampling points. Pattern Search is particularly suitable for the thrust segment inversion problem of continuous low-thrust satellites, because the objective function of this problem is essentially a "black box" system containing a complex orbital dynamics model and thrust switching logic, whose relationship cannot be expressed analytically and is not differentiable at some points. Pattern Search completely bypasses the requirement for derivatives and can directly handle such non-analytical complex optimization problems. At the same time, its search mechanism is easy to incorporate the physical constraints of thrust parameters, ensuring that the search process is always carried out within a reasonable parameter space, providing a stable and reliable solution for this high-complexity inversion problem. The Pattern Search algorithm is a public algorithm, which can be found in (Hooke, R., & Jeeves, TA (1961). "Direct search" solution of numerical and statistical problems. Journal of the ACM, *8*(2), 212–229.).

[0065] In step one, the preprocessed first and second observation arc segments are as follows:

[0066] ;

[0067] In the formula, This is the first observation arc segment. This represents the first epoch of the first observation arc segment. Subscripts are sequentially assigned from 1 to m, with m being the largest index. This is the first azimuth angle observation value of the first observation arc segment, with subscripts ranging from 1 to m and so on. This is the first elevation angle observation value of the first observation arc segment, with subscripts ranging from 1 to m and so on. This represents the first distance observation value for the first observation arc segment, with subscripts ranging from 1 to m and so on. This is the second observation arc segment; This refers to the second epoch of the second observation arc, with subscripts ranging from 1 to m. This refers to the second azimuth angle observation value of the second observation arc segment, with subscripts ranging from 1 to m and so on. This is the second elevation angle observation value for the second observation arc segment, with subscripts ranging from 1 to m; This represents the second distance observation value for the second observation arc segment, with subscripts ranging from 1 to m.

[0068] In step two, the initial orbital elements corresponding to the epochs in the two initial orbits are:

[0069] ;

[0070] In the formula, This represents the first initial orbital element corresponding to the first epoch in the first initial orbit. It is the initial position of the first initial orbital element corresponding to the first epoch. It is the initial velocity corresponding to the first initial orbital element at the first epoch; This represents the second initial orbit element corresponding to the second epoch in the second initial orbit. It is the initial position of the second initial orbital element corresponding to the second epoch. It is the initial velocity of the second initial orbital element corresponding to the second epoch; This is the Laplace-LM algorithm.

[0071] In step three, the first precise orbital elements corresponding to the first epoch and the second precise orbital elements corresponding to the second epoch are:

[0072] ;

[0073] In the formula, This represents the first precise orbital element corresponding to the first epoch. It is the initial position of the first precise orbital element corresponding to the first epoch. It is the initial velocity corresponding to the first precise orbital element at the first epoch; This represents the second precise orbital element corresponding to the second epoch. It is the initial position of the second precise orbital elements corresponding to the second epoch. It is the initial velocity of the second precise orbital element corresponding to the second epoch; This is a weighted least squares precise orbit determination algorithm.

[0074] In step four, the constructed satellite orbital dynamics model is as follows:

[0075] ;

[0076] In the formula, It's the satellite position. It is a time variable; It is the satellite's speed; It is the Earth's gravitational constant; Indicates the modulus; It is the natural perturbation force experienced by the satellite; It is the continuous small thrust that the satellite experiences. It is the transformation matrix from the RTN coordinate system to the ECI coordinate system.

[0077] In step four, the satellite experiences continuous small thrusts as follows:

[0078] ;

[0079] In the formula, It is the thrust acceleration during the thrust phase. It is the beginning of the thrust phase. It refers to the duration of the thrust phase.

[0080] In step four, the transformation matrix from the RTN coordinate system to the ECI coordinate system is:

[0081] .

[0082] In step five, the objective function is:

[0083] ;

[0084] In the formula, Let be the objective function. The position difference between the second propagation precision orbital elements and the second precision orbit determination result. Indicates to Perform the modulo operation.

[0085] Verification experiment:

[0086] The proposed method was validated through a verification experiment. The relevant parameter settings are shown in Table 1.

[0087] Table 1

[0088]

[0089] The thrust parameters were set with reference to the Starlink V2.0 mini satellite launched by SpaceX, which has a mass of 750 kg and a Hall thruster with a thrust of 170 mN, producing a thrust acceleration of 2.27 × 10⁻⁴ m / s². Observations were made on the satellite based on the established station locations, obtaining radar observation data for two observation arcs, as shown in Table 2.

[0090] Table 2

[0091]

[0092] First, the Laplace-LM algorithm was used to determine the initial orbits for the two observed arc segments, obtaining the initial orbital elements corresponding to the epoch times in the two initial orbits; the results are shown in Table 3.

[0093] Table 3

[0094]

[0095] Using the two initial orbital elements as initial values, the weighted least squares precise orbit determination algorithm (POD) is substituted to obtain the first precise orbital element at the first epoch and the second precise orbital element at the second epoch, respectively. The results are shown in Table 4.

[0096] Table 4

[0097]

[0098] It can be seen that the results of the initial orbit determination algorithm of this invention are quite close to the results of the precise orbit determination, indicating that the selected initial orbit determination algorithm has high accuracy. Next, the precise orbit determination results of the first observation arc are substituted into the established satellite orbit dynamics model to perform orbit propagation, thereby constructing the corresponding objective function.

[0099] The objective function was minimized using the Pattern Search algorithm to obtain the target dynamic parameters for the corresponding thrust phase. The results are shown in Table 5.

[0100] Table 5

[0101]

[0102] Simulation results are as follows Figure 1 As shown, Figure 1 In the calculation, the error at the moment of thrust initiation is on the order of minutes, and the error in calculating the magnitude of thrust acceleration is on the order of 10. -5 m / s 2 The error in calculating the thrust duration is also on the order of minutes. This indicates that the method proposed in this invention can effectively derive the target dynamic parameters of the thrust segment between two observation arcs.

[0103] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A pattern search based satellite orbit thrust segment inversion method, characterized in that, The method includes: Step 1: After performing preprocessing to remove outliers from the radar observation data of any two observation arcs, find the first epoch time of the first observation arc and the second epoch time of the second observation arc respectively. Step 2: Use the Laplace-LM algorithm to determine the initial orbits for the two observed arc segments respectively, and obtain the initial orbital elements corresponding to the epoch times in the two initial orbits; Step 3: Using the two initial orbital elements as initial values, substitute them into the weighted least squares precise orbit determination algorithm POD to obtain the first precise orbital element corresponding to the first epoch and the second precise orbital element corresponding to the second epoch. Step four: Set the thrust start time, thrust duration, and thrust acceleration as initial dynamic parameters, and construct a satellite orbital dynamics model including the thrust phase based on these initial dynamic parameters; propagate the first precise orbital elements of the first observation arc from the first epoch according to the satellite orbital dynamics model, and propagate the orbit to the second epoch of the second observation arc to obtain the second propagated precise orbital elements; wherein, the constructed satellite orbital dynamics model is as follows: ； In the formula, It's the satellite position. It is a time variable; It's the satellite's speed; It is the Earth's gravitational constant; Indicates the modulus; It is the natural perturbation force experienced by the satellite; It is the continuous small thrust that the satellite experiences. It is the transformation matrix from the RTN coordinate system to the ECI coordinate system; Step 5: Based on the positional difference between the second propagation precise orbital elements and the second precise orbital elements, construct an objective function to measure the accuracy of the initial dynamic parameters; where the objective function is: ； In the formula, Let be the objective function. The positional difference between the second propagation precision orbital elements and the second precision orbital elements. Indicates to Perform modulo operation; Step six: Introduce the Pattern Search algorithm, adjust the initial dynamic parameters, and obtain the target dynamic parameters that describe the thrust segment information between the two observation arc segments when the objective function is minimized; based on the target dynamic parameters, obtain the actual propulsion strategy of the satellite orbit thrust segment.

2. The satellite orbit thrust segment inversion method based on pattern search as described in claim 1, characterized in that, In step one, the preprocessed first and second observation arc segments are as follows: ； In the formula, This is the first observation arc segment. This represents the first epoch of the first observation arc segment. Subscripts are sequentially assigned from 1 to m, with m being the largest index. This is the first azimuth angle observation value of the first observation arc segment, with subscripts ranging from 1 to m and so on. This is the first elevation angle observation value of the first observation arc segment, with subscripts ranging from 1 to m and so on. This represents the first distance observation value for the first observation arc segment, with subscripts ranging from 1 to m and so on. This is the second observation arc segment; This refers to the second epoch of the second observation arc, with subscripts ranging from 1 to m. This refers to the second azimuth angle observation value of the second observation arc segment, with subscripts ranging from 1 to m and so on. This is the second elevation angle observation value for the second observation arc segment, with subscripts ranging from 1 to m; This represents the second distance observation value for the second observation arc segment, with subscripts ranging from 1 to m.

3. The satellite orbit thrust segment inversion method based on pattern search as described in claim 2, characterized in that, In step two, the initial orbital elements corresponding to the epochs in the two initial orbits are: ； In the formula, This represents the first initial orbital element corresponding to the first epoch in the first initial orbit. It is the initial position of the first initial orbital element corresponding to the first epoch. It is the initial velocity corresponding to the first initial orbital element at the first epoch; This represents the second initial orbital element corresponding to the second epoch in the second initial orbit. It is the initial position of the second initial orbital element corresponding to the second epoch. It is the initial velocity of the second initial orbital element corresponding to the second epoch; This is the Laplace-LM algorithm.

4. The satellite orbit thrust segment inversion method based on pattern search as described in claim 3, characterized in that, In step three, the first precise orbital elements corresponding to the first epoch and the second precise orbital elements corresponding to the second epoch are: ； In the formula, This represents the first precise orbital element corresponding to the first epoch. It is the initial position of the first precise orbital element corresponding to the first epoch. It is the initial velocity corresponding to the first precise orbital element at the first epoch; This represents the second precise orbital element corresponding to the second epoch. It is the initial position of the second precise orbital elements corresponding to the second epoch. It is the initial velocity of the second precise orbital element corresponding to the second epoch; This is a weighted least squares precise orbit determination algorithm.

5. The satellite orbit thrust segment inversion method based on pattern search as described in claim 4, characterized in that, In step four, the satellite experiences continuous small thrusts as follows: ； In the formula, It is the thrust acceleration during the thrust phase. It is the beginning of the thrust phase. It refers to the duration of the thrust phase.

6. The satellite orbit thrust segment inversion method based on pattern search as described in claim 5, characterized in that, In step four, the transformation matrix from the RTN coordinate system to the ECI coordinate system is: 。

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