Methods and Systems for Determining the Orbit of Space Targets in Space-Based Optical Monitoring Platforms

Abstract

This invention provides a method and system for determining the orbit of a space target on a space-based optical monitoring platform, comprising: Step S1: acquiring information on the imaging of the same target by the space-based optical monitoring platform over a period of time; Step S2: setting an upper and lower limit for the distance between the target and the space-based optical monitoring platform based on the camera's observation capabilities; Step S3: constructing an optimization objective function and solving the optimization problem using the distance between the starting point and the ending point within the imaging time as undetermined parameters, and converting the solution into orbital state variables; Step S4: constructing an optimization objective function using the orbital state variables as undetermined parameters, and performing least-squares improvement using the orbital state variables as initial values, with the optimal value of the optimization objective function obtained during the improvement process being an estimated value of the target orbital state variables. This invention eliminates the need for additional prior orbital information of the space target and can be universally applied to determining the orbit of a space target on a space-based optical monitoring platform.

Description

Technical Field

[0001] This invention relates to the field of orbit determination technology, and more specifically, to a method and system for determining the orbit of a space target on a space-based optical monitoring platform. Background Technology

[0002] With the development of space resources, outer space is gradually becoming an important area of ​​focus for all countries. The detection of space targets has significant application value, such as predicting the orbits of space targets and issuing warnings about potential collisions. Space targets include man-made objects (spacecraft, space debris) as well as some natural celestial bodies and micrometeoroids. The target characteristics of space targets include size, shape, and orbital parameters.

[0003] To meet the demands of space target detection, many countries are currently researching and deploying space-based optical monitoring systems, focusing on developing visible light and infrared imaging systems, while also researching space-based microwave radar and lidar. Space-based optical monitoring platforms can be used to identify, classify, and catalog space targets, establishing target databases. A crucial element in this process is determining the orbits of space targets.

[0004] Since both the space target and the monitoring platform are in motion, the space target generally only appears in the camera field of view of the space-based optical monitoring platform for a very short time. Orbit determination requires extrapolating the target's orbit information from the limited angle measurement data available. For orbit determination without initial values ​​for a single arc segment, references 1 (Liu Xiangchun, "Research on Space Debris Orbit Determination Method Based on Space-Based Photographic Tracking," Master's Thesis, National University of Defense Technology, 2009) and 2 (Wu Junzhong, "Target Orbit Determination and Tracking Based on Space-Based Angle Measurement Information," Master's Thesis, Harbin Institute of Technology, 2017) present initial orbit determination methods based on the generalized Laplace method. Reference 3 (Zhang Pin, "A Method for Determining the Initial Orbit of Space Targets Applicable Only to Angle Observations," Master's Thesis, Wuhan University, 2017) presents the Gauss method, the Gooding method, and numerical methods. Reference 4 (Du Jianli, "Research on Space-Based Monitoring System for Space Debris Cataloging," Doctoral Dissertation, Wuhan University, 2018) presents an initial orbit determination method for space debris based on the distance search method. Reference 5 (Li Xinran, "A Short Arc Orbit Determination Method Based on Evolutionary Computation", Doctoral Dissertation of University of Science and Technology of China, 2018) presents an orbit determination method based on genetic algorithm, particle swarm optimization and differential evolution.

[0005] Due to the ill-conditioned nature of the problem of estimating the target's orbit using only angle measurement information, existing methods may result in non-convergence or convergence to trivial solutions during the iterative process. In order to provide a high-precision and robust method for determining the orbit of a space-based optical monitoring platform, this invention constructs and solves 2D and 6D optimization objective functions respectively. It can effectively and stably calculate the orbit of the space target without prior information about the target orbit. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method and system for determining the orbit of a space target on a space-based optical monitoring platform.

[0007] According to the present invention, a method and system for determining the orbit of a space target on a space-based optical monitoring platform are provided, the scheme of which is as follows:

[0008] Firstly, a method for determining the orbit of a space target on a space-based optical monitoring platform is provided, the method comprising:

[0009] Step S1: Obtain information on the imaging of the same target by the space-based optical monitoring platform over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system.

[0010] Step S2: Based on the camera's observation capabilities, set the upper and lower limits of the target's distance from the space-based optical monitoring platform;

[0011] Step S3: Using the distance between the starting point and the ending point within the imaging time as the parameters to be determined, construct the optimization objective function and solve the optimization problem, and convert the solution into orbital state variables;

[0012] Step S4: Construct an optimization objective function with the orbital state variables as undetermined parameters, and perform least squares improvement with the orbital state variables as initial values. The optimal value of the optimization objective function during the improvement process is used as the estimated value of the target orbital state variables.

[0013] Preferably, the orbital state parameters are defined in the epoch geocentric celestial coordinate system. If orbital parameters in other coordinate systems are required, they are transformed according to the transformation relationship between the orbital parameters in other coordinate systems and the epoch geocentric celestial coordinate system.

[0014] Preferably, step S3 includes: if the imaging times are t0, t1, ..., t k The corresponding space-based optical monitoring platform is located in the epoch geocentric celestial coordinate system as follows: The calibrated target's orientation relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system is as follows:

[0015] The upper limit of the distance between the target and the space-based optical monitoring platform is ρ max The lower limit of the distance is ρ min The distance ρ between the starting point ρ0 and the ending point within the imaging time. k For parameters to be determined, the objective function is... Defined as:

[0016]

[0017] Where |||| represents taking the modulus of a vector, and <> represents calculating the inner product of two vectors. For the reason The determined orbit is at t0, t1, ..., t k The location at any given moment.

[0018] Preferably, in step S3, the objective function of the optimization problem has two-dimensional parameters and no obvious analytical form, and simulated annealing, neural networks, or genetic algorithms are used.

[0019] Preferably, the objective function of the optimization problem in step S4 uses the orbital state variables as undetermined parameters. for:

[0020]

[0021] in, For the position of the state quantity speed The determined orbit is at t0, t1, ..., t k Given the position at a given time, the optimization problem has six undetermined parameters.

[0022] Preferably, the six-dimensional state quantity is recorded in step S4. The improvement process is as follows:

[0023]

[0024] in, To improve the quantity, The initial values ​​are the orbital state variables obtained in step S3; The following system of linear equations was solved by taking the least squares solution:

[0025]

[0026] Among them, the difference in observations For the current state quantity The calculated estimated value of the angle measurement, H i It is a partial derivative matrix. H i It is a 3×6 dimensional matrix; derived from the current state variables. Calculate separately H i Thus, the solution is obtained. Later update Repeat the improvement process until the convergence condition is met.

[0027] Preferably, in step S4, the multivariate partial derivative matrix H i The numerical derivative calculation method is adopted.

[0028] Preferably, in step S4, the improved convergence condition is set to reach the upper limit of the number of iterations or the objective function. Less than the set threshold or improvement amount The modulus is less than the set threshold.

[0029] Preferably, in step S4, the objective function in each iterative step of the improvement process is recorded. The values ​​are compared to obtain the state variable corresponding to the minimum objective function value. To determine the parameter estimates for the final trajectory.

[0030] Secondly, a space-based optical monitoring platform space target orbit determination system is provided, the system comprising:

[0031] Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system.

[0032] Module M2: Based on the camera's observation capabilities, set the upper and lower limits of the target's distance from the space-based optical monitoring platform;

[0033] Module M3: Using the distance between the start and end points within the imaging duration as undetermined parameters, construct the optimization objective function and solve the optimization problem, then convert the solution into orbital state variables;

[0034] Module M4: Constructs an optimization objective function with the orbital state variables as undetermined parameters, and performs least squares improvement with the orbital state variables as initial values. The optimal value of the optimization objective function during the improvement process is used as the estimated value of the target orbital state variables.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] 1. This invention provides a method for determining the orbit of a space target on a space-based optical monitoring platform, which does not require initial orbit values ​​or other additional orbit information and can be universally applied to space targets with different orbit types;

[0037] 2. The method of the present invention is reasonable, simple to calculate, and easy to implement, and can be widely applied to the determination of the initial orbit of space targets on space-based optical monitoring platforms. Attached Figure Description

[0038] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0039] Figure 1 This is a flowchart of the present invention;

[0040] Figure 2 The relationship between the objective function and the number of iterations is given when the undetermined parameters are the starting distance and the ending distance.

[0041] Figure 3 The objective function varies with the number of improvements when the undetermined parameters are 6-dimensional orbital state variables. Detailed Implementation

[0042] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0043] This invention provides a method for determining the orbit of a space target on a space-based optical monitoring platform, referring to... Figure 1 As shown, it specifically includes:

[0044] Step S1: Obtain information on the imaging of the same target by the space-based optical monitoring platform over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information (unit vector) of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system.

[0045] Step S2: Based on the camera's observation capabilities, set the upper and lower limits of the target's distance from the space-based optical monitoring platform.

[0046] Step S3: Using the distance between the starting point and the ending point within the imaging time as the undetermined parameter, construct the optimization objective function and solve the optimization problem, and convert the solution into orbital state variables.

[0047] Step S4: Construct an optimization objective function with the orbital state variables as undetermined parameters, and perform least squares improvement with the orbital state variables as initial values. The optimal value of the optimization objective function during the improvement process (including the initial value) is the estimated value of the target orbital state variables.

[0048] The orbital state parameters are defined in the epoch-centered celestial coordinate system. If orbital parameters in other coordinate systems are needed, they are transformed according to the transformation relationship between the orbital parameters in other coordinate systems and the epoch-centered celestial coordinate system. The state parameters describing the orbital information of space debris are position (unit: km) and velocity (unit: km / s). Position and velocity can be converted into Keplerian elements or singularity-free elements.

[0049] In step S3, if the imaging times are t0, t1, ..., t k The corresponding space-based optical monitoring platform is located in the epoch geocentric celestial coordinate system as follows: The calibrated target's orientation relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system is as follows:

[0050] The upper limit of the distance between the target and the space-based optical monitoring platform is ρ max The lower limit of the distance is ρ min The distance ρ between the starting point ρ0 and the ending point within the imaging time. k For parameters to be determined, the objective function is... Defined as:

[0051]

[0052] Where |||| represents taking the modulus of a vector, and <> represents calculating the inner product of two vectors. For the reason The determined orbit is at t0, t1, ..., t k Location at any given moment. By The method for determining the orbit is the Lambert problem. The solution can be converted into orbital state variables, such as position. speed

[0053] In step S3, the objective function of the optimization problem has two undetermined parameters and no obvious analytical form. Simulated annealing, neural networks, or genetic algorithms can be used.

[0054] In step S4, the objective function of the optimization problem uses the orbital state variables as undetermined parameters. for:

[0055]

[0056] in, For the position of the state quantity speed The determined orbit is at t0, t1, ..., t k Given the position at a given time, the optimization problem has six undetermined parameters.

[0057] The 6-dimensional state quantity recording in step S4 The improvement process is as follows:

[0058]

[0059] in, To improve the quantity, The initial values ​​are the orbital state variables obtained in step S3; The following system of linear equations was solved by taking the least squares solution:

[0060]

[0061] Among them, the difference in observations For the current state quantity The calculated estimated value of the angle measurement, H i It is a partial derivative matrix. H i It is a 3×6 dimensional matrix; derived from the current state variables. Calculate separately H i Thus, the solution is obtained. Later update Repeat the improvement process until the convergence condition is met.

[0062] In step S4, the multivariate partial derivative matrix H i A numerical derivative calculation method is employed. In step S4, the improved convergence condition is set to reach the upper limit of the number of iterations or the objective function. Less than the set threshold or improvement amount The modulus is less than the set threshold.

[0063] In step S4, the objective function in each iteration of the improvement process (including the initial value) is recorded. The values ​​are compared to obtain the state variable corresponding to the minimum objective function value. To determine the parameter estimates for the final trajectory.

[0064] This invention also provides a space target orbit determination system for a space-based optical monitoring platform, specifically comprising:

[0065] Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system.

[0066] Module M2: Based on the camera's observation capabilities, set the upper and lower limits of the target's distance from the space-based optical monitoring platform.

[0067] Module M3: Using the distance between the start and end points within the imaging duration as undetermined parameters, construct the optimization objective function and solve the optimization problem, then convert the solution into orbital state variables.

[0068] Module M4: Constructs an optimization objective function with the orbital state variables as undetermined parameters, and performs least squares improvement with the orbital state variables as initial values. The optimal value of the optimization objective function during the improvement process is used as the estimated value of the target orbital state variables.

[0069] The present invention will now be described in more detail.

[0070] For a space-based optical monitoring platform, the information that can be obtained includes: information on imaging the same target over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information (unit vector) of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. Its mathematical model is based on this information to calculate the orbital state variables of the space target.

[0071] Orbital state parameters are defined in the epoch geocentric celestial coordinate system. If orbital parameters in other coordinate systems are needed, they can be transformed according to the transformation relationship between the epoch geocentric celestial coordinate system and the epoch geocentric celestial coordinate system. The state parameters describing the orbital information of space debris are position (unit: km) and velocity (unit: km / s). Position and velocity can be converted into Keplerian elements or singularity-free elements.

[0072] Generally, based on the camera's observation capabilities, upper and lower limits can be set for the distance between the target and the space-based optical monitoring platform. If the camera's observation capabilities cannot be accurately quantified, these upper and lower limits can be set as the widest possible boundaries of reasonable values.

[0073] Solving the orbital state variables of a space target is essentially an inverse operation involving 6 undetermined parameters. Directly optimizing in 6-dimensional space faces a huge computational burden. Therefore, we first consider using the distance between the starting point and the ending point within the imaging time as the undetermined parameters, constructing an optimization objective function and solving the optimization problem, and then converting the solution into orbital state variables.

[0074] If the imaging times are t0, t1, ..., t k The corresponding space-based optical monitoring platform is located in the epoch geocentric celestial coordinate system as follows: The calibrated target's orientation relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system is as follows: The upper limit of the distance between the target and the space-based optical monitoring platform is ρ max The lower limit of the distance is ρ min The distance ρ between the starting point ρ0 and the ending point within the imaging time. k For parameters to be determined, the objective function is... Defined as:

[0075]

[0076] Where |||| represents taking the modulus of a vector, and <> represents calculating the inner product of two vectors. For the reason The determined orbit is at t0, t1, ..., t k Location at any given moment. By The method for determining the orbit is the Lambert problem. The solution can be converted into orbital state variables, such as position. speed The objective function of this optimization problem has two-dimensional parameters and no obvious analytical form. It can be solved using simulated annealing, neural networks, or genetic algorithms.

[0077] The solution to the optimization problem corresponding to Equation (1) physically represents the optimal trajectory between the starting and ending points strictly within the imaging time. However, the measured values ​​of the starting and ending points also have measurement errors. Therefore, the solution to the optimization problem constructed by Equation (1) is not the trajectory closest to the measured value. Therefore, the 2D undetermined parameter space is extended to the original 6D space. The 6D trajectory state variables are used as undetermined parameters to construct the optimization objective function. The obtained trajectory state variables are used as initial values ​​for least squares improvement. The optimal value of the optimization objective function during the improvement process (including the initial value) is used as the estimated value of the target trajectory state variables.

[0078] The objective function of the optimization problem with orbital state variables as undetermined parameters for:

[0079]

[0080] in, For the position of the state quantity speed The determined orbit is at t0, t1, ..., t k The position at any given time. The optimization problem has 6 undetermined parameters. The 6-dimensional state variables are delimited. The improvement process is as follows:

[0081]

[0082] in, To improve the quantity, The initial values ​​are the orbital state variables obtained in step S3; The following system of linear equations was solved by taking the least squares solution:

[0083]

[0084] Among them, the difference in observations For the current state quantity The calculated estimated value of the angle measurement, H i It is a partial derivative matrix. H i It is a 3×6 dimensional matrix; derived from the current state variables. Calculate separately H i Thus, the solution is obtained. Later update Repeat the improvement process until the convergence condition is met.

[0085] Multivariate partial derivative matrix H i A numerical derivative calculation method is employed. The convergence condition is improved by setting it to reach the upper limit of the number of iterations or the objective function. Less than the set threshold or improvement amount The modulus is less than the set threshold.

[0086] Record the objective function in each iterative step of the improvement process (including initial values). The values ​​are compared to obtain the state variable corresponding to the minimum objective function value. To determine the parameter estimates for the final trajectory.

[0087] The effectiveness of the method of the present invention is verified by simulation. Simulation data is generated to show the imaging time, the position of the space-based optical monitoring platform, and the angle measurement data of the target relative to the space-based optical monitoring platform. The angle measurement information error is (3σ)6”, the position error of the space-based optical monitoring platform is 10m, and the target observation time is 10min. Figure 2 The figure shows the relationship between the value of the optimization objective function and the number of iterations when the starting distance and the ending distance are undetermined parameters. Figure 3 The figure shows the relationship between the value of the optimal objective function and the number of improvements when the orbital state variables are the undetermined parameters. The value of the optimal objective function before improvement is 2388.44 milliarcseconds. By comparing the minimum value of the optimal objective function (2056.21 milliarcseconds) during the improvement process, the estimated value of the orbital state variables is obtained. The actual position of the target is [-19943.42894259, -37132.50468067, 516.09877262] km, and the speed is [2.7039634, -1.45572064, -0.15142241] km / s. The estimated results are: location [-19951.33058628, -37147.67367162, 516.3470737] km, speed [2.69227267, -1.47091244, -0.15126814] km / s.

[0088] This invention provides a method and system for determining the orbit of a space target on a space-based optical monitoring platform. It constructs and solves both a 2D and a 6D optimization objective function, requiring no prior information about the target orbit, and can effectively and stably calculate the space target orbit. This method is reasonable, computationally simple, and easy to implement, and can be widely applied to determine the initial orbit of space targets on space-based optical monitoring platforms.

[0089] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0090] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for determining the orbit of a space target on a space-based optical monitoring platform, characterized in that, include: Step S1: Obtain information on the imaging of the same target by the space-based optical monitoring platform over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. Step S2: Based on the camera's observation capabilities, set the upper and lower limits of the target's distance from the space-based optical monitoring platform; Step S3: Using the distance between the starting point and the ending point within the imaging time as the parameters to be determined, construct the optimization objective function and solve the optimization problem, and convert the solution into orbital state variables; Step S4: Construct an optimization objective function with the orbital state variables as undetermined parameters, and perform least squares improvement with the orbital state variables as initial values. The optimal value of the optimization objective function during the improvement process is used as the estimated value of the target orbital state variables.

2. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 1, characterized in that, The orbital state parameters are defined in the epoch geocentric celestial coordinate system. If orbital parameters in other coordinate systems are needed, they are transformed according to the transformation relationship between the orbital parameters in other coordinate systems and the epoch geocentric celestial coordinate system.

3. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 1, characterized in that, Step S3 includes: if the imaging times are t0, t1, ..., t k The corresponding space-based optical monitoring platform is located in the epoch geocentric celestial coordinate system as follows: The calibrated target's orientation relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system is as follows: The upper limit of the distance between the target and the space-based optical monitoring platform is ρ max The lower limit of the distance is ρ min The distance ρ between the starting point ρ0 and the ending point within the imaging time. k For parameters to be determined, the objective function is... Defined as: Where || represents taking the modulus of a vector, and <> represents calculating the inner product of two vectors. For the reason The determined orbit is at t0, t1, ..., t k The location at any given moment.

4. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 1, characterized in that, In step S3, the objective function of the optimization problem has two-dimensional parameters and no obvious analytical form. Simulated annealing, neural networks, or genetic algorithms are used.

5. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 1, characterized in that, In step S4, the objective function of the optimization problem uses the orbital state variables as undetermined parameters. for: in, For the position of the state quantity speed The determined orbit is at t0, t1, ..., t k Given the position at a given time, the optimization problem has six undetermined parameters.

6. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 5, characterized in that, The six-dimensional state quantity notation in step S4 The improvement process is as follows: in, To improve the quantity, The initial values ​​are the orbital state variables obtained in step S3; The following system of linear equations was solved by taking the least squares solution: Among them, the difference in observations For the current state quantity The calculated estimated value of the angle measurement, H i It is a partial derivative matrix. H i It is a 3×6 dimensional matrix; derived from the current state variables. Calculate separately H i Thus, the solution is obtained. Later update Repeat the improvement process until the convergence condition is met.

7. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 6, characterized in that, In step S4, the multivariate partial derivative matrix H i The numerical derivative calculation method is adopted.

8. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 6, characterized in that, In step S4, the improved convergence condition is set to reach the upper limit of the number of iterations or the objective function. Less than the set threshold or improvement amount The modulus is less than the set threshold.

9. The method for determining the orbit of a space target on a space-based optical monitoring platform according to claim 6, characterized in that, In step S4, the objective function in each iterative step of the improvement process is recorded. The values ​​are compared to obtain the state variable corresponding to the minimum objective function value. To determine the parameter estimates for the final trajectory.

10. A space target orbit determination system for a space-based optical monitoring platform, characterized in that, include: Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform over a period of time, including the imaging time, the position of the space-based optical monitoring platform in the epoch geocentric celestial coordinate system, and the pointing information of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. Module M2: Based on the camera's observation capabilities, set the upper and lower limits of the target's distance from the space-based optical monitoring platform; Module M3: Using the distance between the start and end points within the imaging duration as undetermined parameters, construct the optimization objective function and solve the optimization problem, then convert the solution into orbital state variables; Module M4: Constructs an optimization objective function with the orbital state variables as undetermined parameters, and performs least squares improvement with the orbital state variables as initial values. The optimal value of the optimization objective function during the improvement process is used as the estimated value of the target orbital state variables.

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