Space-based optical monitoring platform space debris initial orbit determination method and system

Abstract

The application provides a space debris initial orbit determination method and system for a space-based optical monitoring platform, wherein step 1 is acquiring information of imaging of the same target by the space-based optical monitoring platform within a period of time; step 2 is setting a distance limit of the target from the space-based optical monitoring platform; step 3 is initializing a plurality of starting point and ending point possible distance combinations; step 4 is calculating an optimal objective function value, recording a current objective function value of each group, a distance of each group, an objective function minimum corresponding objective function value, distance and orbit parameter; step 5 is updating the plurality of starting point and ending point possible distance combinations and updating the optimal objective function value corresponding to each group; and step 6 is repeating step 5 until a convergence condition is met. The application can be universally applied to space debris initial orbit determination for the space-based optical monitoring platform without additional prior information of the space debris.

Description

Technical Field

[0001] This invention relates to the technical field of orbit determination methods, specifically to a method and system for determining the initial orbit of space debris from a space-based optical monitoring platform. Background Technology

[0002] With the rapid development of human spaceflight, the number of man-made objects in space has increased dramatically, the vast majority of which are space debris. The sources of space debris include defunct spacecraft, launch vehicle bodies, objects jettisoned or detached from spacecraft, rocket ejecta, and debris from spacecraft explosions or destruction. Space debris poses a serious threat to the safety of normally functioning spacecraft, and the world currently attaches great importance to it.

[0003] Currently, the equipment used for space debris monitoring is mainly ground-based. Ground-based monitoring is easily affected by atmospheric interference, while space-based monitoring has the advantages of high coverage and high timeliness. The key link in the monitoring and management of space debris by the space-based optical monitoring platform is orbit determination. Since both space debris and the monitoring platform are in motion, space debris only appears in the camera field of view of the space-based optical monitoring platform for a very short time. Orbit determination requires calculating the target's orbit information from the limited angle measurement information.

[0004] Current methods for determining the orbits of space debris fall into two categories: initial orbit calculation and precise orbit determination. Precise orbit determination is generally used for long arcs, requiring initial orbit values ​​in addition to angular measurement information. Initial orbit calculation is generally used for short arcs, without initial orbit values ​​as input. Reference 1 (Li Bin, "Research on Several Key Issues of Rapid and Precise Orbit Determination and Prediction of Space Debris," Doctoral Dissertation, Wuhan University, 2017) studies the method of orbit determination using active optical means, namely laser ranging. Reference 2 ("GJB6776.4-2009 Space Target Orbit Measurement and Cataloging Method Part 4: Orbit Determination Method") presents an improved method for orbit determination based on ground-based space target observation. For orbit information of targets that is only calculated from angular measurement information, Reference 3 (Liu Xiangchun, "Research on Space Debris Orbit Determination Method Based on Space-Based Photographic Tracking," Master's Thesis, National University of Defense Technology, 2009) presents an initial orbit determination method based on the generalized Laplace method. Reference 4 (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 5 (Du Jianli, "Research on Space-Based Monitoring System for Space Debris Cataloging," Doctoral Dissertation, Wuhan University, 2018) presents a method for determining the initial orbit of space debris based on the distance search method.

[0005] A space debris removal method and system are disclosed in patent document CN111661368A. The method includes: controlling a satellite platform equipped with a debris removal device to move to a predetermined orbit for the accumulation of small space debris; controlling the debris removal device to emit a high-energy particle beam, wherein the high-energy particles in the high-energy particle beam attach to the surface of the small space debris, increasing the charge on the surface of the small space debris, so that the small space debris lowers its orbit and falls into the Earth's atmosphere.

[0006] Therefore, a new technical solution needs to be proposed. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for determining the initial orbit of space debris on a space-based optical monitoring platform.

[0008] According to the present invention, a method for determining the initial orbit of space debris on a space-based optical monitoring platform includes the following steps:

[0009] Step S1: Obtain information on the imaging of the same target by the space-based optical monitoring platform, 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 nominal values ​​of the target's distance from the space-based optical monitoring platform, and update the upper limit of the distance between the starting point and the ending point based on the measured data;

[0011] Step S3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points;

[0012] Step S4: Calculate the optimal objective function values ​​corresponding to multiple distance combinations, and record the objective function values ​​of each group, the distances of each group, and the objective function value, distance, and orbital parameters corresponding to the minimum objective function value.

[0013] Step S5: Update the distance combinations of multiple start and end points, and calculate the optimal objective function value for each group. If the updated objective function value is less than the original objective function value of the group, then overwrite the original objective function value and distance record of the group with the updated objective function value and distance. At the same time, record the objective function value, distance, and orbital parameters corresponding to the minimum objective function value among all combinations.

[0014] Step S6: Repeat step S5 until the convergence condition is met.

[0015] Preferably, the orbital parameters of the space debris 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 them and the epoch geocentric celestial coordinate system. The parameters describing the orbital information of the space debris are position and velocity. If the orbital root number is needed, it is transformed according to the relationship.

[0016] Preferably, in step S2, 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 distance at the starting point t0 is ρ0, and the distance at the ending point t is ρ0. k The distance corresponding to time ρ k The nominal upper limit of the target's distance from the space-based optical monitoring platform is ρ. max The method for updating the upper limit of the starting distance is as follows:

[0017] Step S2.1: Initial value ρ of the upper limit of the starting distance 0,max =ρ max ;

[0018] Step S2.2: Calculate the target position of the starting point.

[0019]

[0020] Step S2.3: Calculate the geocentric distance r0 from the starting point, where r0 equals the vector The modulus;

[0021] Step S2.4: Compare r0 with the minimum perigee value. If r0 is greater than the minimum perigee value, output the current ρ. 0,max Otherwise ρ 0,max =ρ 0,max -10, repeat steps S2.2-S2.4, where the minimum perigee is set to 6400km.

[0022] Preferably, the method for initializing multiple sets of distance combinations between the start and end points in step S3 is as follows:

[0023] Step S3.1: Within the lower limit ρ of the starting point distance range min and the upper limit of distance ρ 0,max Within this range, M sets of distance values ​​are generated at equal intervals;

[0024] Step S3.2: For the starting point distance of the j-th group (j=0,1,…,M-1), at the lower limit ρ of the ending point distance... min and the upper limit of distance ρ k,maxThe endpoint distance is found by measuring the step size, and the judgment is based on the distance between the starting point ρ0 and the endpoint ρ. k The perigee of the determined orbit must be greater than the minimum perigee value. A search yields a ρ value that satisfies this criterion. k This allows us to proceed to the search of group j+1;

[0025] Step S3.3: Output all possible N (N≤M) combinations of distances between the start and end points, Pxj=(ρ 0,j ,ρ k,j (j = 0, 1, ..., M-1).

[0026] Preferably, the optimal objective function f in step S4 is:

[0027]

[0028] in, For the corresponding t i At time (i = 0, 1, ..., k), the measured pointing of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. The pointer at time ti is the estimated value calculated based on the distance between the starting point and the ending point, and · represents the vector dot product operation;

[0029] For the distance combination (ρ) in step S3 0,j ,ρ k,j (j = 0, 1, ..., N-1) Calculate the objective function sequentially to obtain the respective objective functions f. j By comparison, the objective function value f corresponding to the minimum objective function among N groups is obtained. g Distance Pg, orbital parameters.

[0030] Preferably, the optimal position Pb of the j-th group is set at the beginning. j That is, the position (ρ) obtained from initialization. 0,j ,ρ k,j The method for updating the distance combination between the start and end points of the j-th group in step S5 is as follows:

[0031] Step S5.1: Calculate N sets of optimal positions Pb j The position of the centroid B of (j=0,1,…,N-1):

[0032]

[0033] Among them, Pb j This represents the optimal position reached by the j-th distance combination during the update process, where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the optimal position Pb of the Nth distance combination. j The equivalent centroid position;

[0034] Step S5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j :

[0035]

[0036] Among them, Pb j The optimal position reached by the j-th distance combination during the update process, Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position, and Px on the left side of the equals sign. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j To update the value of the j-th distance combination, For Pb j The corresponding weighting coefficients are random numbers uniformly distributed within the range (0,1), u j The weight control number is a random number uniformly distributed in the range (0,1) during the update process. The index j takes values ​​from 0 to N-1, and N is the number of possible distance combinations obtained during initialization.

[0037] Step S5.3: Calculate the optimal objective function value f for each group of Pxj. new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value f corresponding to the minimum objective function among all current combinations. g Distance Pg, orbital parameters.

[0038] Preferably, the convergence condition in step S6 is set as follows: f g <= f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

[0039] The present invention also provides a system for determining the initial orbit of space debris on a space-based optical monitoring platform, the system comprising the following modules:

[0040] Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform, 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;

[0041] Module M2: Based on the camera's observation capabilities, set the upper and lower nominal values ​​of the target's distance from the space-based optical monitoring platform, and update the upper limit of the distance between the start and end points based on the measured data;

[0042] Module M3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points;

[0043] Module M4: Calculates the optimal objective function values ​​corresponding to multiple distance combinations, and records the objective function values, distances, and orbital parameters corresponding to the minimum objective function value for each group.

[0044] Module M5: Updates multiple sets of distance combinations between the start and end points, and calculates the optimal objective function value for each set. If the updated objective function value is less than the original objective function value of the set, the updated objective function value and distance will overwrite the original objective function value and distance record of the set. At the same time, the objective function value, distance, and orbital parameters corresponding to the minimum objective function value among all current combinations will be recorded.

[0045] Module M6: Repeat module M5 until the convergence condition is met.

[0046] Preferably, the orbital parameters of the space debris 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 them and the epoch geocentric celestial coordinate system. The parameters describing the orbital information of the space debris are position and velocity. If the orbital root number is needed, it is transformed according to the relationship.

[0047] In module M2, 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 distance at the starting point t0 is ρ0, and the distance at the ending point t is ρ0. k The distance corresponding to time ρ k The nominal upper limit of the target's distance from the space-based optical monitoring platform is ρ. max The update system for the upper limit of the starting distance is as follows:

[0048] Module M2.1: Initial value ρ of the upper limit of the starting distance 0,max =ρ max ;

[0049] Module M2.2: Calculates the target position of the starting point.

[0050]

[0051] Module M2.3: Calculates the geocentric distance r0 from the starting point, where r0 equals the vector The modulus;

[0052] Module M2.4: Compare r0 with the minimum perigee value. If r0 is greater than the minimum perigee value, output the current ρ. 0,max Otherwise ρ 0,max =ρ 0,max -10, repeat module M2.2-module M2.4, where the minimum perigee is set to 6400km.

[0053] Preferably, the module M3 initializes multiple sets of distance combination systems for the start and end points as follows:

[0054] Module M3.1: Lower limit ρ of the starting distance range min and the upper limit of distance ρ 0,max Within this range, M sets of distance values ​​are generated at equal intervals;

[0055] Module M3.2: For the starting distance of the j-th group (j=0,1,…,M-1), the lower limit ρ of the ending distance is... min and the upper limit of distance ρ k,max The endpoint distance is found by measuring the step size, and the judgment is based on the distance between the starting point ρ0 and the endpoint ρ. k The perigee of the determined orbit must be greater than the minimum perigee value. A search yields a ρ value that satisfies this criterion. k This allows us to proceed to the search of group j+1;

[0056] Module M3.3: Output all possible N (N≤M) combinations of distances between the start and end points, Pxj=(ρ 0,j ,ρ k,j (j = 0, 1, ..., M-1);

[0057] The optimal objective function f in module M4 is:

[0058]

[0059] in, For the corresponding t i At time (i = 0, 1, ..., k), the measured pointing of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. The pointer at time ti is the estimated value calculated based on the distance between the starting point and the ending point, and · represents the vector dot product operation;

[0060] For the distance combination (ρ) in module M3 0,j ,ρ k,j (j = 0, 1, ..., N-1) Calculate the objective function sequentially to obtain the respective objective functions f. jBy comparison, the objective function value f corresponding to the minimum objective function among N groups is obtained. g Distance Pg, orbital parameters;

[0061] Initially, set the optimal position Pb of group j. j That is, the position (ρ) obtained from initialization. 0,j ,ρ k,j The system in module M5 that updates the distance combination between the start and end points of the j-th group is as follows:

[0062] Module M5.1: Calculate N sets of optimal positions Pb j The position of the centroid B of (j=0,1,…,N-1):

[0063]

[0064] Among them, Pb j This represents the optimal position reached by the j-th distance combination during the update process, where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the optimal position Pb of the Nth distance combination. j The equivalent centroid position;

[0065] Module M5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j :

[0066]

[0067] Among them, Pb j The optimal position reached by the j-th distance combination during the update process, Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position, and Px on the left side of the equals sign. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j To update the value of the j-th distance combination, For Pb j The corresponding weighting coefficients are random numbers uniformly distributed within the range (0,1), u j The weight control number is a random number uniformly distributed in the range (0,1) during the update process. The index j takes values ​​from 0 to N-1, and N is the number of possible distance combinations obtained during initialization.

[0068] Module M5.3: Calculate the optimal objective function value f for each group of Pxj. new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,jDistance record Pb j Simultaneously, record the objective function value f corresponding to the minimum objective function among all current combinations. g Distance Pg, orbital parameters;

[0069] The convergence condition in module M6 is set as follows: f g <= f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] 1. This invention provides a method for determining the initial orbit of space debris on a space-based optical monitoring platform. It does not require the initial orbit value of the space debris or other additional orbit information and can be universally applied to space debris of different orbit types.

[0072] 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 a target on a space-based optical monitoring platform. Attached Figure Description

[0073] 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:

[0074] Figure 1 This is a flowchart of the present invention;

[0075] Figure 2 This is a graph showing the relationship between the objective function of this invention and the number of iterations;

[0076] Figure 3 This is an error diagram between the estimated location of space debris and its actual location obtained by this invention;

[0077] Figure 4 This is a cumulative probability density map of position errors obtained by determining the initial trajectory for 1000 different arc segments according to the present invention. Detailed Implementation

[0078] 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 protection scope of the present invention.

[0079] Example 1:

[0080] According to the present invention, a method for determining the initial orbit of space debris on a space-based optical monitoring platform includes the following steps:

[0081] Step S1: Obtain information on the imaging of the same target by the space-based optical monitoring platform, 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.

[0082] Step S2: Based on the camera's observation capabilities, set the upper and lower nominal values ​​of the target's distance from the space-based optical monitoring platform, and update the upper limit of the distance between the starting point and the ending point based on the measured data;

[0083] In step S2, 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 distance at the starting point t0 is ρ0, and the distance at the ending point t is ρ0. k The distance corresponding to time ρ k The nominal upper limit of the target's distance from the space-based optical monitoring platform is ρ. max The method for updating the upper limit of the starting distance is as follows:

[0084] Step S2.1: Initial value ρ of the upper limit of the starting distance 0,max =ρ max ;

[0085] Step S2.2: Calculate the target position of the starting point.

[0086]

[0087] Step S2.3: Calculate the geocentric distance r0 from the starting point, where r0 equals the vector The modulus;

[0088] Step S2.4: Compare r0 with the minimum perigee value. If r0 is greater than the minimum perigee value, output the current ρ. 0,max Otherwise ρ 0,max =ρ 0,max -10, repeat steps S2.2-S2.4, where the minimum perigee is set to 6400km.

[0089] Step S3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points.

[0090] The method for initializing multiple sets of starting and ending distance combinations in step S3 is as follows:

[0091] Step S3.1: Within the lower limit ρ of the starting point distance range min and the upper limit of distance ρ 0,max Within this range, M sets of distance values ​​are generated at equal intervals;

[0092] Step S3.2: For the starting point distance of the j-th group (j=0,1,…,M-1), at the lower limit ρ of the ending point distance... min and the upper limit of distance ρ k,max The endpoint distance is found by measuring the step size, and the judgment is based on the distance between the starting point ρ0 and the endpoint ρ. k The perigee of the determined orbit must be greater than the minimum perigee value. A search yields a ρ value that satisfies this criterion. k This allows us to proceed to the search of group j+1;

[0093] Step S3.3: Output all possible N (N≤M) combinations of distances between the start and end points, Pxj=(ρ 0,j ,ρ k,j (j = 0, 1, ..., M-1).

[0094] The optimal objective function f in step S4 is:

[0095]

[0096] in, For the corresponding t i At time (i = 0, 1, ..., k), the measured pointing of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. The pointer at time ti is the estimated value calculated based on the distance between the starting point and the ending point, and · represents the vector dot product operation;

[0097] For the distance combination (ρ) in step S3 0,j ,ρ k,j (j = 0, 1, ..., N-1) Calculate the objective function sequentially to obtain the respective objective functions f. j By comparison, the objective function value f corresponding to the minimum objective function among N groups is obtained. g Distance Pg, orbital parameters.

[0098] Step S4: Calculate the optimal objective function values ​​corresponding to multiple distance combinations, and record the objective function values ​​of each group, the distances of each group, and the objective function value, distance, and orbital parameters corresponding to the minimum objective function value.

[0099] Step S5: Update the distance combinations of multiple start and end points, and calculate the optimal objective function value for each group. If the updated objective function value is less than the original objective function value of the group, then overwrite the original objective function value and distance record of the group with the updated objective function value and distance. At the same time, record the objective function value, distance, and orbital parameters corresponding to the minimum objective function value among all combinations.

[0100] Initially, set the optimal position Pb of group j. j That is, the position (ρ) obtained from initialization. 0,j ,ρ k,j The method for updating the distance combination between the start and end points of the j-th group in step S5 is as follows:

[0101] Step S5.1: Calculate N sets of optimal positions Pb j The position of the centroid B of (j=0,1,…,N-1):

[0102]

[0103] Among them, Pb j This represents the optimal position reached by the j-th distance combination during the update process, where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the optimal position Pb of the Nth distance combination. j The equivalent centroid position;

[0104] Step S5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j :

[0105]

[0106] Among them, Pb j The optimal position reached by the j-th distance combination during the update process, Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position, and Px on the left side of the equals sign. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j To update the value of the j-th distance combination, For Pb j The corresponding weighting coefficients are random numbers uniformly distributed within the range (0,1), u j The weight control number is a random number uniformly distributed in the range (0,1) during the update process. The index j takes values ​​from 0 to N-1, and N is the number of possible distance combinations obtained during initialization.

[0107] Step S5.3: Calculate the optimal objective function value f for each group of Pxj. new,jIf the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value f corresponding to the minimum objective function among all current combinations. g Distance Pg, orbital parameters.

[0108] Step S6: Repeat step S5 until the convergence condition is met.

[0109] The orbital parameters of space debris 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 them and the epoch geocentric celestial coordinate system. The parameters describing the orbital information of space debris are position and velocity. If the orbital root numbers are needed, they are transformed according to the relationship.

[0110] In step S6, the convergence condition is set as follows: f g <= f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

[0111] Example 2:

[0112] Example 2 is a preferred embodiment of Example 1, and is used to illustrate the present invention in more detail.

[0113] This invention also provides a system for determining the initial orbit of space debris on a space-based optical monitoring platform, the system comprising the following modules:

[0114] Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform, 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;

[0115] Module M2: Based on the camera's observation capabilities, set the upper and lower nominal values ​​of the target's distance from the space-based optical monitoring platform, and update the upper limit of the distance between the start and end points based on the measured data;

[0116] Module M3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points.

[0117] Module M4: Calculates the optimal objective function values ​​corresponding to multiple distance combinations, and records the objective function values, distances, and orbital parameters corresponding to the minimum objective function value for each group.

[0118] Module M5: Updates multiple sets of distance combinations between the start and end points, and calculates the optimal objective function value for each set. If the updated objective function value is less than the original objective function value of the set, the updated objective function value and distance will overwrite the original objective function value and distance record of the set. At the same time, the objective function value, distance, and orbital parameters corresponding to the minimum objective function value among all current combinations will be recorded.

[0119] Module M6: Repeat module M5 until the convergence condition is met.

[0120] The orbital parameters of space debris 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 them and the epoch geocentric celestial coordinate system. The parameters describing the orbital information of space debris are position and velocity. If the orbital root numbers are needed, they are transformed according to the relationship.

[0121] In module M2, 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 distance at the starting point t0 is ρ0, and the distance at the ending point t is ρ0. k The distance corresponding to time ρ k The nominal upper limit of the target's distance from the space-based optical monitoring platform is ρ. max The update system for the upper limit of the starting distance is as follows:

[0122] Module M2.1: Initial value ρ of the upper limit of the starting distance 0,max =ρ max ;

[0123] Module M2.2: Calculates the target position of the starting point.

[0124]

[0125] Module M2.3: Calculates the geocentric distance r0 from the starting point, where r0 equals the vector The modulus;

[0126] Module M2.4: Compare r0 with the minimum perigee value. If r0 is greater than the minimum perigee value, output the current ρ. 0,max Otherwise ρ 0,max =ρ 0,max -10, repeat module M2.2-module M2.4, where the minimum perigee is set to 6400km.

[0127] The initialization system for multiple sets of distance combinations between the start and end points in module M3 is as follows:

[0128] Module M3.1: Lower limit ρ of the starting distance range min and the upper limit of distance ρ 0,max Within this range, M sets of distance values ​​are generated at equal intervals;

[0129] Module M3.2: For the starting distance of the j-th group (j=0,1,…,M-1), the lower limit ρ of the ending distance is... min and the upper limit of distance ρ k,max The endpoint distance is found by measuring the step size, and the judgment is based on the distance between the starting point ρ0 and the endpoint ρ. k The perigee of the determined orbit must be greater than the minimum perigee value. A search yields a ρ value that satisfies this criterion. k This allows us to proceed to the search of group j+1;

[0130] Module M3.3: Output all possible N (N≤M) combinations of distances between the start and end points, Pxj=(ρ 0,j ,ρ k,j (j = 0, 1, ..., M-1);

[0131] The optimal objective function f in module M4 is:

[0132]

[0133] in, For the corresponding t i At time (i = 0, 1, ..., k), the measured pointing of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. The pointer at time ti is the estimated value calculated based on the distance between the starting point and the ending point, and · represents the vector dot product operation;

[0134] For the distance combination (ρ) in module M3 0,j ,ρ k,j (j = 0, 1, ..., N-1) Calculate the objective function sequentially to obtain the respective objective functions f. j By comparison, the objective function value f corresponding to the minimum objective function among N groups is obtained. g Distance Pg, orbital parameters;

[0135] Initially, set the optimal position Pb of group j. j That is, the position (ρ) obtained from initialization. 0,j ,ρ k,j The system in module M5 that updates the distance combination between the start and end points of the j-th group is as follows:

[0136] Module M5.1: Calculate N sets of optimal positions Pb j The position of the centroid B of (j=0,1,…,N-1):

[0137]

[0138] Among them, Pb j This represents the optimal position reached by the j-th distance combination during the update process, where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the optimal position Pb of the Nth distance combination. j The equivalent centroid position;

[0139] Module M5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j :

[0140]

[0141] Among them, Pb j The optimal position reached by the j-th distance combination during the update process, Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position, and Px on the left side of the equals sign. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j To update the value of the j-th distance combination, For Pb j The corresponding weighting coefficients are random numbers uniformly distributed within the range (0,1), u j The weight control number is a random number uniformly distributed in the range (0,1) during the update process. The index j takes values ​​from 0 to N-1, and N is the number of possible distance combinations obtained during initialization.

[0142] Module M5.3: Calculate the optimal objective function value f for each group of Pxj. new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value f corresponding to the minimum objective function among all current combinations. g Distance Pg, orbital parameters;

[0143] The convergence condition in module M6 is set as follows: f g <= f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

[0144] Example 3:

[0145] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0146] For space-based optical monitoring platforms, this invention provides a universally applicable and robust method for determining the initial orbit of space debris. It requires no initial orbital values ​​of the space debris or other additional orbital information, is unaffected by the relative position of the space debris and the monitoring platform, and is universally applicable to different types of space-based optical monitoring platforms.

[0147] For determining the orbital information of space debris, there are generally six variables that need to be determined, which can be represented as position, velocity, or orbital elements at a certain moment. For space-based optical monitoring platforms, a single imaging session can only acquire angular information of the space debris relative to the platform, lacking distance information. Therefore, theoretically, in the absence of measurement errors, three imaging sessions are required to determine the orbit of the space debris. When both the angular information from the space-based optical monitoring platform and its own orbit determination information contain errors, data from a longer observation period are needed to ensure the accuracy of the calculated orbit of the space debris, including the following steps:

[0148] Step S1: The input to the space debris initial orbit determination problem is the information of the space-based optical monitoring platform 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 of the calibrated target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. The time is generally 2-5 minutes, and the pointing information is a unit vector.

[0149] The orbital parameters of space debris are defined in the epoch-based 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-based geocentric celestial coordinate system and the geocentric celestial coordinate system. The parameters describing the orbital information of space debris are position (unit: km) and velocity (unit: km / s). If the orbital root numbers are needed, they can be converted according to the relationship.

[0150] Step S2: When calculating the trajectory of space debris, without additional prior information, based on the camera's observation capabilities, upper and lower nominal values ​​for the target's distance from the space-based optical monitoring platform can be set. The upper distance limits for the start and end points are then updated based on measured data.

[0151] 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 distance at the starting point t0 is ρ0, and the distance at the ending point t is ρ0. k The distance corresponding to time ρ k ,ρ0、ρk It is an unknown.

[0152] The nominal upper limit of the distance between the target and the space-based optical monitoring platform is ρ. max The calculation method for the upper limit of the starting distance is to ensure that the distance between space debris and the Earth's center is greater than the actual possible distance.

[0153] Step S2.1: First, let the initial value of the upper limit of the starting distance be ρ. 0,max =ρ max .

[0154] Step S2.2: Then calculate the target position of the starting point.

[0155]

[0156] Step S2.3: Calculate the geocentric distance r0 from the starting point, where r0 equals the vector The modulus.

[0157] Step S2.4: Compare r0 with the minimum perigee value. If r0 is greater than the minimum perigee value, output the current ρ. 0,max Otherwise ρ 0,max =ρ 0,max -10, repeat steps S2.2-S2.4. The minimum perigee distance can be set to 6400 km. Endpoint ρ k The upper limit of the distance can be calculated similarly.

[0158] Step S3: Minimize the solution space by constraining distance limits. Within the distance limits, initialize multiple possible distance combinations between the start and end points.

[0159] Step S3.1: First, within the lower limit ρ of the starting point distance range. min and the upper limit of distance ρ 0,max Within the range, M sets of distance values ​​are generated at equal intervals.

[0160] Step S3.2: For the starting point distance of the j-th group (j=0,1,…,M-1), at the lower limit ρ of the ending point distance... m i n and the upper limit of distance ρ k,max The appropriate endpoint distance is found by following a certain step size. The judgment is based on the distance between the starting point ρ0 and the endpoint ρ. k The perigee of the determined orbit must be greater than the minimum perigee. A search yields a ρ value that satisfies this criterion. k Then you can proceed to the search of group j+1.

[0161] Step S3.3: Output all N (N≤M) possible combinations of distances Px between the start and end points. j =(ρ0,j ,ρ k,j (j = 0, 1, ..., N-1).

[0162] Step S4: Calculate the optimal objective function value corresponding to each of the multiple distance combinations, and record the objective function value of each group, the distance of each group, and the objective function value and distance corresponding to the minimum objective function.

[0163] The optimal objective function f is:

[0164]

[0165] in, For the corresponding t i At time (i = 0, 1, ..., k), the measured pointing (unit vector) of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. t is calculated based on the distance between the starting point and the ending point. i The time point points to the estimated value (unit vector), and · represents the vector dot product operation. In the ideal case with no measurement error, the objective function f = 0 corresponds to the accurate solution for the space debris orbit. When measurement error exists, the estimated space debris orbit that minimizes the objective function is considered the optimal solution.

[0166] For distance combination (ρ) 0,j ,ρ k,j (j = 0, 1, ..., N-1) Calculate the objective function sequentially to obtain the respective objective functions f. j By comparison, the objective function value f corresponding to the minimum objective function among N groups is obtained. g Distance Pg, orbital parameters.

[0167] Step S5: Update the possible distance combinations of the start and end points for multiple sets, and calculate the optimal objective function value for each set. If the updated objective function value is less than the original objective function value for that set, then overwrite the original objective function value and distance record for that set with the updated objective function value and distance. Simultaneously, record the objective function value and distance corresponding to the minimum objective function value among all current combinations.

[0168] Initially, set the optimal position Pb of group j. j That is, the position (ρ) obtained from initialization. 0,j ,ρ k,j The method for updating the possible distance combinations between the start and end points of the j-th group is as follows:

[0169] Step S5.1: Calculate N sets of optimal positions Pb j The position of the centroid B of (j=0,1,…,N-1):

[0170]

[0171] Among them, Pb j This represents the optimal position reached during the update process for the current j-th distance combination (start distance, end distance), where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the N optimal positions Pb. j (2D) Equivalent centroid location (2D).

[0172] Step S5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j :

[0173]

[0174] Among them, Pb j The optimal position reached by the current j-th distance combination (start distance, end distance) during the update process, Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position, and Px on the left side of the equals sign. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j This is the value of the j-th distance combination before the update (i.e., currently). For Pb j The corresponding weighting coefficients are random numbers uniformly distributed within the range (0,1), u j The weight control number is a random number uniformly distributed within the range (0,1) during the update process. The index j takes values ​​from 0 to N-1, and N is the number of possible distance combinations obtained during initialization.

[0175] Step S5.3: Calculate Px for each group j The corresponding optimization objective function value f new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value f corresponding to the minimum objective function among all current combinations. g Distance Pg, orbital parameters.

[0176] Step S6: Repeat the above steps until the convergence condition is met.

[0177] The convergence condition is set as: f g <= f T , where f TA threshold is set to optimize the objective function f. If the value is less than this threshold, a suitable initial trajectory is considered to have been found, i.e., the trajectory parameters corresponding to the current distance Pg. Solutions that minimize the objective function are continuously obtained through updates, while the use of random numbers prevents the algorithm from converging to a local optimum rather than the global optimum.

[0178] The present invention also provides a system for determining the initial orbit of space debris on a space-based optical monitoring platform, the system comprising the following modules:

[0179] Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform, 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; the orbital parameters of space debris are defined in the epoch geocentric celestial coordinate system. If orbital parameters in other coordinate systems are needed, they are transformed according to their transformation relationship with the epoch geocentric celestial coordinate system. The parameters describing the orbital information of space debris are position and velocity. If the orbital root number is needed, it is transformed according to the relationship.

[0180] Module M2: Based on the camera's observation capabilities, set the upper and lower nominal values ​​of the target's distance from the space-based optical monitoring platform. Update the upper distance limit between the start and end points based on measured data. 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:

[0181] (i = 0, 1, ..., k), the distance corresponding to the starting point t0 is ρ0, and the distance corresponding to the ending point t is ρ0. k The distance corresponding to time ρ k The nominal upper limit of the target's distance from the space-based optical monitoring platform is ρ. max The update system for the upper limit of the starting distance is as follows:

[0182] Module M2.1: Initial value ρ of the upper limit of the starting distance 0,max =ρ max .

[0183] Module M2.2: Calculates the target position of the starting point.

[0184]

[0185] Module M2.3: Calculates the geocentric distance r0 from the starting point, where r0 equals the vector The modulus.

[0186] Module M2.4: Compare r0 with the minimum perigee value. If r0 is greater than the minimum perigee value, output the current ρ. 0,max Otherwise ρ 0,max =ρ 0,max -10, repeat module M2.2-module M2.4, where the minimum perigee is set to 6400km.

[0187] Module M3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points; the system for initializing multiple sets of distance combinations between the start and end points is as follows:

[0188] Module M3.1: Lower limit ρ of the starting distance range min and the upper limit of distance ρ 0,max Within the range, M sets of distance values ​​are generated at equal intervals.

[0189] Module M3.2: For the starting distance of the j-th group (j=0,1,…,M-1), the lower limit ρ of the ending distance is... min and the upper limit of distance ρ k,max The endpoint distance is found by measuring the step size, and the judgment is based on the distance between the starting point ρ0 and the endpoint ρ. k The perigee of the determined orbit must be greater than the minimum perigee value. A search yields a ρ value that satisfies this criterion. k Then you can proceed to the search of group j+1.

[0190] Module M3.3: Output all possible N (N≤M) combinations of distances between the start and end points, Pxj=(ρ 0,j ,ρ k,j (j=0,1,…,M-1). Distance combination (ρ) 0,j ,ρ k,j (j = 0, 1, ..., N-1) Calculate the objective function sequentially to obtain the respective objective functions f. j By comparison, the objective function value f corresponding to the minimum objective function among N groups is obtained. g Distance Pg, orbital parameters.

[0191] Module M4: Calculates the optimal objective function values ​​corresponding to multiple distance combinations, and records the current objective function value, distance, and minimum objective function value, distance, and orbital parameters for each group; the optimal objective function f is:

[0192]

[0193] in, For the corresponding t i At time (i = 0, 1, ..., k), the measured pointing of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system. The pointer at time ti is the estimated value calculated based on the distance between the starting point and the ending point. The dot symbol represents the vector inner product operation.

[0194] Module M5: Updates multiple combinations of start and end point distances and calculates the optimal objective function value for each combination. If the updated objective function value is less than the original objective function value for that combination, the updated objective function value and distance overwrite the original objective function value and distance record for that combination. Simultaneously, it records the objective function value, distance, and trajectory parameters corresponding to the minimum objective function value among all combinations. Initially, it sets the optimal position Pb for the j-th combination. j That is, the position (ρ) obtained from initialization. 0,j ,ρ k,j The system for updating the distance combination between the start and end points of the j-th group is as follows:

[0195] Module M5.1: Calculate N sets of optimal positions Pb j The position of the centroid B of (j=0,1,…,N-1):

[0196]

[0197] Among them, Pb j This represents the optimal position reached during the update process for the current j-th distance combination (start distance, end distance), where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the N optimal positions Pb. j (2D) Equivalent centroid location (2D).

[0198] Module M5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j :

[0199]

[0200] Among them, Pb j The optimal position reached by the current j-th distance combination (start distance, end distance) during the update process, Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position, and Px on the left side of the equals sign. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j This is the value of the j-th distance combination before the update (i.e., currently). For Pb j The corresponding weighting coefficients are random numbers uniformly distributed within the range (0,1), u j The weight control number is a random number uniformly distributed within the range (0,1) during the update process. The index j takes values ​​from 0 to N-1, and N is the number of possible distance combinations obtained during initialization.

[0201] Module M5.3: Calculate the optimal objective function value f for each group of Pxj. new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value f corresponding to the minimum objective function among all current combinations. g Distance Pg, orbital parameters.

[0202] Module M6: Repeat module M5 until the convergence condition is met; the convergence condition is set as: f g <= f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

[0203] The effectiveness of the method of this invention is verified below using STK simulation. The true position of the space debris at time t0 is [3914.69278784, 2287.65126217, -5710.11075207] km, and the true velocity is [1.55265807, 6.31076405, 3.53024093] km / s. The angular measurement information of the space debris within 278s is obtained, where the angular measurement information error is 6" (arcseconds), and the position error of the space-based optical monitoring platform itself is 10m. The process of gradually reducing the target function obtained by the method of this invention is shown in the attached figure. Figure 2 As shown, attached Figure 2 The objective function f is converted into angles (milliarseconds) for display. The final estimated position of the space debris at time t0 is [3913.92130643, 2287.70079483,

[0204] -5712.06648694] km, speed [1.55231912, 6.31250605, 3.53075962] km / s, the position error over the entire 278s is shown in the attached figure. Figure 3 As shown, the average position error is 2.0758 km. Using the same method, initial orbit determination was performed on space debris with different orbits, resulting in 1000 sets of different arc segments from different space debris. The angle measurement error remained at 6" and the position error of the space-based optical monitoring platform itself was 10m. The duration of the space debris arc segments ranged from 105s to 389s. The statistical results of the position error within the corresponding time of the obtained arc segments are shown below. Figure 4 As shown, in the simulation, 70% of the initial orbital position errors were within 2.67 km, and 90% of the initial orbital position errors were within 4.54 km.

[0205] 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.

[0206] 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 initial orbit of space debris on a space-based optical monitoring platform, characterized in that, The method includes the following steps: Step S1: Obtain information on the imaging of the same target by the space-based optical monitoring platform, 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 nominal values ​​of the target's distance from the space-based optical monitoring platform, and update the upper limit of the distance between the starting point and the ending point based on the measured data; Step S3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points; Step S4: Calculate the optimal objective function values ​​corresponding to multiple combinations of starting and ending distances, and record the objective function values, distances, and minimum objective function values, distances, and orbital parameters for each group. Step S5: Update the distance combinations of multiple start and end points, and calculate the optimal objective function value for each group. If the updated objective function value is less than the original objective function value of the group, then overwrite the original objective function value and distance record of the group with the updated objective function value and distance. At the same time, record the objective function value, distance, and orbital parameters corresponding to the minimum objective function value among all combinations. Step S6: Repeat step S5 until the convergence condition is met; The method for initializing multiple sets of distance combinations between the start and end points in step S3 is as follows: Step S3.1: Lower limit of the distance range from the starting point and the maximum distance Within this range, M sets of distance values ​​are generated at equal intervals; Step S3.2: For the starting distance of the c-th group, c=0,1,…,M-1, at the lower limit of the ending distance... and the maximum distance The endpoint distance is determined by the step length, and the judgment is based on the starting distance. Distance from the finish line The perigee of the determined orbit must be greater than the minimum perigee value; a search will yield an orbit that satisfies this criterion. You can then proceed to the search for group c+1; Step S3.3: Output all possible N combinations of distances Px between the start and end points. j = j = 0, 1, ..., N-1, where N ≤ M; Initially, set the optimal position Pb of group j. j That is, the position obtained from initialization. The method for updating the distance combination between the start and end points of the j-th group in step S5 is as follows: Step S5.1: Calculate N sets of optimal positions Pb j The position of the center of mass B: Among them, Pb j This represents the optimal position reached by the j-th distance combination during the update process, where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the optimal position Pb of the Nth distance combination. j The equivalent centroid position; Step S5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j : Among them, Pb j Px represents the optimal position reached by the j-th distance combination during the update process, and Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j To update the value of the j-th distance combination, For Pb j The corresponding weighting coefficients are Random numbers uniformly distributed within a range This is the weight control number, and it is used during the update process. A random number uniformly distributed within the range, with the index j ranging from 0 to N-1, where N is the number of possible distance combinations obtained during initialization; Step S5.3: Calculate Px for each group j The corresponding optimization objective function value f new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value corresponding to the minimum objective function among all current combinations. Distance Pg, orbital parameters.

2. The method for determining the initial orbit of space debris on a space-based optical monitoring platform according to claim 1, characterized in that, In step S2, 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: i = 0, 1, ..., k, corresponding to t i The measured pointing direction of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system at a given time is: The distance corresponding to the starting point at time t0 is End point t k The distance corresponding to the time is The nominal upper limit of the target's distance from the space-based optical monitoring platform is [value missing]. The method for updating the upper limit of the starting distance is as follows: Step S2.1: Initial value of the upper limit of the starting distance = ; Step S2.2: Calculate the target position of the starting point. : Step S2.3: Calculate the geocentric distance of the starting point. , equal to vector The modulus; Step S2.4: Comparison With the minimum value of the perigee, if If the value is greater than the minimum value of the nearest point, output the current value. ,otherwise = -10, repeat steps S2.2-S2.4, where the minimum perigee is set to 6400km.

3. The method for determining the initial orbit of space debris on a space-based optical monitoring platform according to claim 1, characterized in that, The optimal objective function f in step S4 is: in, For the corresponding t i The actual pointing direction of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system at any given time. t is calculated based on the distance between the starting point and the ending point. i The timeline points to the estimated value. This represents the vector dot product operation; For the distance combination in step S3 Calculate the objective function sequentially for j=0,1,…,N-1, and obtain the respective objective function values. By comparing, we obtain the objective function value corresponding to the minimum objective function among the N groups. Distance Pg, orbital parameters.

4. The method for determining the initial orbit of space debris on a space-based optical monitoring platform according to claim 1, characterized in that, The convergence condition in step S6 is set as follows: f g <=f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

5. A system for determining the initial orbit of space debris on a space-based optical monitoring platform, characterized in that, The system includes the following modules: Module M1: Acquires information on the imaging of the same target by the space-based optical monitoring platform, 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 nominal values ​​of the target's distance from the space-based optical monitoring platform, and update the upper limit of the distance between the start and end points based on the measured data; Module M3: Within the distance limit, initialize multiple sets of distance combinations between the start and end points; Module M4: Calculates the optimal objective function values ​​corresponding to multiple combinations of start and end distances, and records the objective function values, distances, and minimum objective function values, distances, and orbital parameters for each group. Module M5: Updates multiple sets of distance combinations between the start and end points, and calculates the optimal objective function value for each set. If the updated objective function value is less than the original objective function value of the set, the updated objective function value and distance will overwrite the original objective function value and distance record of the set. At the same time, the objective function value, distance, and orbital parameters corresponding to the minimum objective function value among all current combinations will be recorded. Module M6: Repeat module M5 until the convergence condition is met; The module M3 initializes multiple sets of distance combinations between the start and end points as follows: Module M3.1: Lower limit of the starting distance range and the maximum distance Within this range, M sets of distance values ​​are generated at equal intervals; Module M3.2: For the starting distance of the c-th group, c=0,1,…,M-1, at the lower limit of the ending distance. and the maximum distance The endpoint distance is determined by the step length, and the judgment is based on the starting distance. Distance from the finish line The perigee of the determined orbit must be greater than the minimum perigee value; a search will yield an orbit that satisfies this criterion. You can then proceed to the search for group c+1; Module M3.3: Outputs all possible N combinations of distances Px between the start and end points. j = j = 0, 1, ..., N-1, where N ≤ M; Initially, set the optimal position Pb of group j. j That is, the position obtained from initialization. The system in module M5 that updates the distance combination between the start and end points of the j-th group is as follows: Module M5.1: Calculate N sets of optimal positions Pb j The position of the center of mass B: Among them, Pb j This represents the optimal position reached by the j-th distance combination during the update process, where j = 0, 1, ..., N-1, N is the number of possible distance combinations obtained during initialization, and B represents the optimal position Pb of the Nth distance combination. j The equivalent centroid position; Module M5.2: Update the possible distance combinations Px between the start and end points of the j-th group. j : Among them, Pb j Px represents the optimal position reached by the j-th distance combination during the update process, and Pg represents the distance combination that minimizes the objective function value among all N possible distance combinations during the update process, i.e., the global optimal position. j To update the value of the j-th distance combination, Px on the right side of the equals sign... j To update the value of the j-th distance combination, For Pb j The corresponding weighting coefficients are Random numbers uniformly distributed within a range This is the weight control number, and it is used during the update process. A random number uniformly distributed within the range, with the index j ranging from 0 to N-1, where N is the number of possible distance combinations obtained during initialization; Module M5.3: Calculate Px for each group j The corresponding optimization objective function value f new,j If the updated objective function value is less than the original objective function value f of the group j Then the updated objective function value and distance will overwrite the original objective function value f of that group. j =f new,j Distance record Pb j Simultaneously, record the objective function value corresponding to the minimum objective function among all current combinations. Distance Pg, orbital parameters.

6. The space debris initial orbit determination system for the space-based optical monitoring platform according to claim 5, characterized in that, In module M2, 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: i = 0, 1, ..., k, corresponding to t i The measured pointing direction of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system at a given time is: The distance corresponding to the starting point at time t0 is End point t k The distance corresponding to the time is The nominal upper limit of the target's distance from the space-based optical monitoring platform is [value missing]. The update system for the upper limit of the starting distance is as follows: Module M2.1: Initial value of the upper limit of the starting distance = ; Module M2.2: Calculates the target position of the starting point. : Module M2.3: Calculates the geocentric distance from the starting point. , equal to vector The modulus; Module M2.4: Comparison With the minimum value of the perigee, if If the value is greater than the minimum value of the nearest point, output the current value. ,otherwise = -10, repeat module M2.2-module M2.4, where the minimum perigee is set to 6400km.

7. The space debris initial trajectory determination system for the space-based optical monitoring platform according to claim 5, characterized in that, The optimal objective function f in module M4 is: in, For the corresponding t i The actual pointing direction of the target relative to the space-based optical monitoring platform in the epoch geocentric celestial coordinate system at any given time. t is calculated based on the distance between the starting point and the ending point. i The timeline points to the estimated value. This represents the vector dot product operation; For the distance combination in module M3 Calculate the objective function sequentially for j=0,1,…,N-1, and obtain the respective objective function values. By comparing, we obtain the objective function value corresponding to the minimum objective function among the N groups. Distance Pg, orbital parameters; The convergence condition in module M6 is set as follows: f g <=f T , where f T The threshold for optimizing the objective function f is defined as follows: if the value is less than this threshold, it is considered that the initial orbit has been found, which is the orbital parameter corresponding to the current distance Pg.

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