Maneuvering space target optical arc segment library association method based on orbit dynamic characteristics

Abstract

The invention discloses a maneuvering space target optical arc segment library association method based on orbit dynamic characteristics. The method comprises the following steps: 1, acquiring optical segmental arc data and constructing a constraint admissible domain; 2, calculating a flat longitude difference to obtain a flat longitude difference-time point cloud; 3, performing linear extraction and segmental arc clustering on the flat longitude difference-time point cloud; and 4, screening based on maneuvering hypothesis to obtain a unique correct cluster, and realizing association. Through the process, the maneuvering space target optical arc segment library association method based on the orbit dynamic characteristics is provided, and association is achieved from the overall distribution characteristics of multiple arc segments through the orbit flat longitude characteristics. By applying strict permissible domain conditions and adopting a position estimation only method to calculate the flat longitude, the minimum flat longitude range of the optical segmental arc can be calculated, and feature distinguishing and correlation are facilitated. The random sampling consistency algorithm can realize detection and extraction clustering of all linear features, and can further screen to obtain a correct result. The method does not need orbit determination, is high in calculation speed and is suitable for mass data scenes.

Description

Technical Field

[0001] The present invention provides a method for associating optical arc segments of maneuvering space targets based on orbital dynamic characteristics. The method involves extracting the dynamic characteristics of optical observation arc segments using a reference orbit before the space target maneuvers and an allowed domain method, and using a straight line feature extraction algorithm to determine the correlation between the arc segments and the orbit. The method belongs to the field of space situational awareness. Background Art

[0002] With the increase in human space activities, the number of space objects has increased dramatically, leading to a very congested low-Earth orbit. By April 2025, there will be approximately 14,000 space objects in orbit, of which 11,300 are still active. At the same time, the number of space debris larger than 10 cm has exceeded 40,000. This causes these active space objects to frequently perform maneuvers to avoid collisions. Furthermore, low-orbit satellites frequently maneuver to maintain their orbital altitude, while high-orbit satellites frequently perform east-west and north-south maneuvers. The rapidly increasing number of space objects and the increasingly frequent maneuvers pose significant challenges to target tracking, anomaly identification, and catalog maintenance.

[0003] Optical surveillance is an important component of the space situational awareness system. Optical observations are usually angular observations lasting several seconds, called an arc segment. An arc segment contains continuous right ascension and declination measurements from the same object. An arc segment is first associated with the orbit in the catalog library. For freely moving targets, there are many association methods, such as covariance method, control measurement method, etc. However, when a non-cooperative target maneuvers, the orbital state undergoes changes that are unknown to the observer. At this time, the prediction obtained by the reference orbit forecast does not match the actual observation, resulting in the arc segment being unable to be associated with the reference orbit of any known target. The association of these unassociated arc segments is an important prerequisite for maneuver detection and catalog library orbit updates.

[0004] Currently, there are two mainstream technical approaches to achieve arc segment association of maneuvering targets: (1) After performing arc segment association and clustering, the arc segments belonging to the same target are orbited and then intersected with the orbit before the maneuver to confirm which target the new orbit belongs to and determine the maneuver parameters. (2) Under certain maneuvering conditions, the arc segments are directly associated and intersected with the reference orbit before the maneuver. The first method requires a pairwise association of all unassociated arc segments. Related methods include the allowed domain method, the initial value method, the boundary value method, etc. Arc segment association does not rely on prior orbital information and can simultaneously achieve the identification of maneuvering targets in the catalog library and the discovery of new targets. However, the computational complexity of pairwise arc segment association increases explosively with the number of arc segments; and for the association of maneuvering targets, the pairwise arc segment technical approach is too complicated.

[0005] The second technical approach makes full use of the reference orbit information in the catalog library. Based on the premise of maneuvering behavior, the orbit is directly connected to the arc segment after the maneuver. For targets that are not associated with any new arc segments in the catalog library, it is highly suspected that the target has maneuvered. At this time, the last associated arc segment is used as the time reference 0 point, and the arc segment association program for the maneuvering target is entered. Using the target orbit in the catalog library as the reference orbit, after the association is completed, precise orbit determination and maneuver detection are performed. The difficulty in associating the arc segment of a maneuvering target is that the maneuvering information is unknown. It is difficult to give an association criterion between the arc segment and the orbit before the maneuver that can take into account the maneuver and not associate with the wrong target.

[0006] In summary, the present invention focuses on exploring the orbital parameter change characteristics brought about by the maneuvering behavior itself, and through this characteristic, realizes the association of optical arc segments with cataloged space targets that produce unknown maneuvers. A method for associating optical arc segments with a library of maneuvering space targets based on orbital dynamic characteristics is proposed. At the same time, erroneous arc segment elimination, arc segment-orbit association and maneuver detection are realized, thereby realizing the long-term tracking of maneuverable spacecraft. Summary of the Invention

[0007] (1) Purpose of the invention

[0008] This paper exploits the regular, long-term drift in orbital phase caused by spacecraft maneuvers, compares the difference in longitude and latitude between the observed arc and the reference orbit, and employs a linear feature detection method to propose a method for correlating the optical arc segments of maneuvering space targets with the cataloged reference orbit based on orbital dynamics. This method can correlate the observed arc segments of a space target after maneuvering with the cataloged reference orbit without requiring prior orbit determination, enabling rapid maneuver identification and detection.

[0009] (2) Technical solution

[0010] The present invention relates to a method for associating optical arcs of maneuverable space targets based on orbital dynamic characteristics. The method requires all optical observation arcs observed by low-orbit observation satellites or ground optical observation stations within a certain time range as input data. First, the corresponding right ascension and declination angles and angle change rates are extracted for each observation arc; then, cataloged targets that are not associated with any new arcs are selected, and strict constraints are imposed on the reference orbits in the catalog and the maneuverability, thereby generating the corresponding distance-distance change rate allowable domain for each arc, and obtaining the flat longitude range corresponding to the sampling arc in the allowable domain; then, the flat longitude of each arc is subtracted from the target's pre-maneuver distance before the target is maneuvered.

[0011] The mean longitude obtained from the reference orbit forecast is used to form a two-dimensional point cloud distribution map of mean longitude difference-time. Straight line features are extracted from it, and straight line screening is performed in combination with maneuverability to obtain the arc segment belonging to the maneuvering target and complete the association.

[0012] The optical arc segment correlation method of maneuverable space target based on orbital dynamic characteristics of the present invention is described in the attached Figure 1 , and its implementation steps are as follows:

[0013] Step 1: Obtain optical arc segment data and construct the constraint allowable domain

[0014] For a segment of optical observation arc data, extract the normalized vector of angle and angle change rate:

[0015]

[0016] Where α and β represent right ascension and declination; Represents the rate of change of the angle of right ascension and declination.

[0017] Given the position and velocity of the observer at a given reference time, r o and Then we have:

[0018] r=r o +ρu ρ (2)

[0019]

[0020] where r and Represents the inertial position and velocity of the maneuvering target, ρ and Represents the relative distance from the target to the observer and the rate of change of distance. ρ ,u α and u β Calculated by the following formula:

[0021] u ρ =[cosαcosβ sinαcosβ sinβ] T (4)

[0022] u α =[-sinαcosβ cosαcosβ 0] T (5)

[0023] u β =[-cosαsinβ -sinαsinβ cosβ] T (6)

[0024] Therefore, if the distance and the rate of change of distance are given Then the target's orbital state can be fully described. Combined with the constraints of the target's orbital state, all distances and distance change rates that meet the constraints can be screened. This also gives us the set of possible orbital states of the target.

[0025] Select a cataloged target in the catalog database that is not associated with any new arc. In the arc-orbit association scenario, since the reference orbit information before the maneuver is available, more stringent constraints can be imposed. More stringent constraints can make the set of candidate orbital state solutions as small as possible, thereby limiting the range of variation in mean longitude. When the range of variation in mean longitude is very small, the mean longitude difference point cloud formed by the arc has a more significant straight line distribution feature, which reduces the difficulty of arc association through features. Constraints are imposed on the semi-major axis, eccentricity, orbit inclination, right ascension of the ascending node, and perigee:

[0026]

[0027] where a,e,i,Ω,r p Represents the target's semi-major axis, eccentricity, orbit inclination, right ascension of the ascending node and perigee; (a min ,a max ), (e min ,e max ), (i min ,i max ), (Ω min ,Ω max ) and r p,min is its corresponding constraint boundary. The role of perigee constraint is to prevent the orbit altitude from being too low, so it is generally taken as a fixed priori value. The constraints on orbital elements need to be calculated by combining the reference orbit before maneuvering with the maneuvering capability of the spacecraft. The calculated position and velocity are instantaneous quantities, and the converted orbital elements also contain short-period oscillations. Therefore, the constraint boundaries of the orbital elements are calculated according to the following formula:

[0028]

[0029] as well as

[0030]

[0031] where a 1m ,e 1m ,i 1m ,Ω 1m is the average orbital element corresponding to the pre-maneuver reference orbit at the measurement time, including the long-term drift caused by the J2 perturbation; Δa M,max ,Δi M,max ,ΔΩ M,max It is obtained by the following formula:

[0032]

[0033] Δe M,maxrepresents the change in eccentricity caused by maneuvering, which is generally taken as 1e-3; sup|·| represents the short-period oscillation term a s ,e s ,i s ,Ω s Take an upper bound. Δa max ,Δe max ,Δi max ,ΔΩ max It can be made larger than Equation (9) to ensure that all possible orbital states after the maneuver are covered.

[0034] Step 2: Calculate the mean longitude difference of all optical arc segments to form a point cloud

[0035] Step 1 obtains the constraint allowed domain of a single arc segment. By sampling the allowed domain, the candidate orbit state can be obtained. In order to make the mean longitude not affected by the arc length, only the position in the candidate orbit state is used to estimate the mean longitude. Since the orbital planes before and after the maneuver are very close, the angle between the spacecraft position after the maneuver and the ascending node vector of the reference orbit, plus the right ascension of the ascending node before the maneuver, can be used as the estimated value of the target true longitude after the maneuver. The true longitude is then converted to mean longitude using the orbital elements before the maneuver. The mean longitude calculated using this method has an error of less than 0.005 rad, and the range of variation in mean longitude is also extremely small, generally less than 0.01 rad.

[0036] The reference time of the arc segment predicted by the reference orbit before the maneuver is measured. Subtracting the predicted reference orbit longitude from the longitude is the longitude difference. For each arc segment, after sampling the allowed domain, a point set of longitude difference can be obtained, which is recorded as By processing all arc segments within a period of time, we can obtain a point cloud distribution map on the two-dimensional plane of mean longitude difference-time, where the time reference zero point is the time of the last arc segment that can be associated with the orbit before maneuvering.

[0037] Step 3: Extract lines and cluster arcs for the mean longitude difference-time point cloud

[0038] For the point cloud obtained in step 2, a random sampling consensus algorithm is used to detect line features. The specific operation is as follows: First, two point sets are randomly selected, the mean of the point sets is calculated, and the line model parameters are obtained. Then, the distance between each point set and the model is calculated. Point sets less than the set threshold TH are regarded as inliers, and the loss function is calculated. The above process is continuously iterated to minimize the loss function and obtain the optimal model and inliers:

[0039]

[0040] The error term err(·) is:

[0041]

[0042] Where N represents the total number of arc segments, d i Represents the i-th point set The distance from the model, The upper and lower boundary points are and TH is the correlation threshold, t i is the measurement time of the i-th arc segment. The specific expression of the straight line model is l(t;c) = c1t + c2, where c = [c1, c2] is the model parameter. The interior point of the final model is the associated arc segment. TH, as the association threshold, has a clear physical meaning, representing the difference between the mean longitude difference and a true straight line. It should be neither too large nor too small and is generally set to 3e-3 rad.

[0043] After selecting multiple point sets that satisfy the model parameters, the mean can be calculated and the model parameters can be updated using least squares to ensure consistency between the model and the inliers. Because multiple straight line models may exist in a point cloud distribution with a mean-longitude difference, a maximum number of iterations is set. After finding a set of models and inliers, these inliers are removed from the point cloud, and the iteration is repeated on the remaining point cloud until all straight line models in the point cloud are found. Ultimately, all arc segment clusters and their corresponding straight line fitting parameters are obtained.

[0044] Step 4: Based on the maneuver hypothesis, the correct cluster is obtained and the association is achieved

[0045] Step 3 obtains all possible clusters, but only one set of clusters belongs to the selected target, which can be screened by the straight line parameter requirements of the maneuvering target: (1) the cluster has at least 3 arc segments; (2) the straight line model parameters meet the characteristics of the maneuvering target, and the absolute value of the slope is less than Zero distance comes from the uncertainty of maneuvering time, so its absolute value is less than Δt is the time interval between the last arc segment before the maneuver and the first arc segment of the linear model, which is generally no more than 12 hours. Therefore, the zero distance can also be given an upper bound of 0.1 rad. (3) The maneuver occurs between the last arc segment before the maneuver and the first arc segment of the cluster, so the zero point of the line must be between them. Based on the above conditions, the only correct cluster can be screened and the arc segment can be associated with the selected target in the catalog library.

[0046] In summary, the implementation steps of the present invention are as follows: Figure 1As shown. The arc-orbit correlation method proposed by the above process is derived from the perspective of orbital dynamics. It is essentially different from traditional methods and has good interpretability. The idea is to achieve correlation from the overall distribution characteristics of multiple arcs through the characteristics of orbital longitude. By imposing strict allowable domain conditions and using the position estimation method to calculate the longitude, the minimum longitude range of the optical arc can be calculated, which is convenient for feature differentiation and association. The random sampling consistency algorithm can detect all straight line features, extract clusters, and further screen to obtain correct results. This method does not require orbit determination, has a fast calculation speed, and is suitable for massive data scenarios.

[0047] (3) Advantages

[0048] The advantages of the optical arc segment library association method for maneuverable space targets based on orbital dynamics characteristics provided by the present invention are:

[0049] ① The optical arc segment library association method proposed in this invention is applicable to low-orbit space targets and maneuverable spacecraft, has a wide range of applications, and has a high accuracy rate of association results;

[0050] ② The strict constraint allowable region method proposed in this invention adopts the trajectory of the selected target before maneuvering and combines the maneuverability to strictly constrain it, which can make the allowable region extremely small, facilitating the subsequent straight line feature detection.

[0051] ③ The method proposed in this invention for calculating the longitude and latitude based only on position is to estimate the position given by the orbit before the maneuver combined with the allowed domain. The error of the longitude and latitude estimation is small and is not affected by the arc length.

[0052] ④ The straight line feature extraction method and screening method provided by the present invention fully considers the characteristics of maneuvering behavior, can extract all straight line features, and quickly screen to obtain the correct clustering with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flowchart of the implementation steps of the present invention

[0054] Figure 2 This is a diagram of the constraint allowed domain in this method, where blue represents the semi-major axis constraint, red represents the eccentricity constraint, green represents the orbital inclination constraint, and yellow represents the ascending node right ascension constraint.

[0055] Figure 3 This is the point cloud diagram of target longitude difference-time

[0056] Figure 4 This is a schematic diagram of the correlation results of the line extraction algorithm. Four groups of lines are proposed from the point cloud. DETAILED DESCRIPTION

[0057] The specific implementation process of the present invention will be further described in detail below in conjunction with the technical solution.

[0058] The present invention relates to a method for associating optical arc segments of maneuverable space targets based on orbital dynamic characteristics. The method requires all optical observation arc segments observed by a low-orbit observation satellite or a ground-based optical observation station within a certain time range as input data. First, the corresponding right ascension and declination angles and angle change rates are extracted for all observation arc segments. Then, a cataloged target that is not associated with any new arc segments is selected. Using the cataloged reference orbit and combining it with maneuverability, strict constraints are imposed to generate a corresponding range-range change rate per segment, thereby obtaining the corresponding latitude and longitude range of the sampled arc segments within the allowable domain. Next, the latitude and longitude obtained by predicting the reference orbit of the target before maneuvering is subtracted from the latitude and longitude of each arc segment to form a two-dimensional point cloud distribution map of latitude and longitude difference-time. Linear features are extracted from the map and, combined with maneuverability, linear screening is performed to obtain the arc segments belonging to the maneuverable target, completing the association.

[0059] The optical arc segment correlation method of maneuverable space target based on orbital dynamic characteristics of the present invention is described in the attached Figure 1 , and its implementation steps are as follows:

[0060] Step 1: Obtain optical arc segment data and construct the constraint allowable domain

[0061] For a segment of optical observation arc data, extract the normalized vector of angle and angle change rate:

[0062]

[0063] Where α and β represent right ascension and declination; Represents the rate of change of the angle of right ascension and declination.

[0064] Given the position and velocity of the observer at a given reference time, r o and Then we have:

[0065] r=r o +ρu ρ (15)

[0066]

[0067] where r and Represents the inertial position and velocity of the maneuvering target, ρ and Represents the relative distance from the target to the observer and the rate of change of distance. ρ ,u α and u β Calculated by the following formula:

[0068] u ρ=[cosαcosβ sinαcosβ sinβ] T (17)

[0069] u α =[-sinαcosβ cosαcosβ 0] T (18)

[0070] u β =[-cosαsinβ -sinαsinβ cosβ] T (19)

[0071] Therefore, if the distance and the rate of change of distance are given Then the target's orbital state can be fully described. Combined with the constraints of the target's orbital state, all distances and distance change rates that meet the constraints can be screened. This also gives us the set of possible orbital states of the target.

[0072] Select a cataloged target in the catalog database that is not associated with any new arc. In the arc-orbit association scenario, since the reference orbit information before the maneuver is available, more stringent constraints can be imposed. More stringent constraints can make the set of candidate orbital state solutions as small as possible, thereby limiting the range of variation in mean longitude. When the range of variation in mean longitude is very small, the mean longitude difference point cloud formed by the arc has a more significant straight line distribution feature, which reduces the difficulty of arc association through features. Constraints are imposed on the semi-major axis, eccentricity, orbit inclination, right ascension of the ascending node, and perigee:

[0073]

[0074] where a,e,i,Ω,r p Represents the target's semi-major axis, eccentricity, orbit inclination, right ascension of the ascending node and perigee; (a min ,a max ), (e min ,e max ), (i min ,i max ), (Ω min ,Ω max ) and r p,min is its corresponding constraint boundary. The role of perigee constraint is to prevent the orbit altitude from being too low, so it is generally taken as a fixed priori value. The constraints on orbital elements need to be calculated by combining the reference orbit before maneuvering with the maneuvering capability of the spacecraft. The calculated position and velocity are instantaneous quantities, and the converted orbital elements also contain short-period oscillations. Therefore, the constraint boundaries of the orbital elements are calculated according to the following formula:

[0075]

[0076] as well as

[0077]

[0078] where a 1m ,e 1m ,i 1m ,Ω 1m is the average orbital element corresponding to the pre-maneuver reference orbit at the measurement time, including the long-term drift caused by the J2 perturbation; Δa M,max ,Δi M,max ,ΔΩ M,max It is obtained by the following formula:

[0079]

[0080] Δe M,max represents the change in eccentricity caused by maneuvering, which is generally taken as 1e-3; sup|·| represents the short-period oscillation term a s ,e s ,i s ,Ω s Take an upper bound. Δa max ,Δe max ,Δi max ,ΔΩ max It can be made larger than Equation (23) to ensure that all possible orbital states after the maneuver are covered. Figure 2 As an illustration of the constraints on the allowable domain, the constraints are: minimum observation distance 30km, maximum observation distance 15000km; semi-major axis range 7470~7530km; eccentricity range 0.01~0.03; orbit inclination range 79.9°~80.1°, ascending node right ascension range 39.1°~39.3°.

[0081] Step 2: Calculate the mean longitude difference of all optical arc segments to form a point cloud

[0082] Step 1 obtains the constrained allowed domain of a single arc segment. By sampling the allowed domain, the candidate orbital state (r, r) can be obtained. In order to make the flat longitude unaffected by the arc segment length, only the position in the candidate orbital state is used to estimate the flat longitude. Since the orbital planes before and after the maneuver are very close, the angle between the spacecraft position after the maneuver and the ascending node vector of the reference orbit, plus the right ascension of the ascending node before the maneuver, can be used as the estimated value of the target true longitude after the maneuver. The true longitude is then converted to mean longitude using the orbital elements before the maneuver. The mean longitude calculated using this method has an error of less than 0.005 rad, and the range of variation in mean longitude is also extremely small, generally less than 0.01 rad.

[0083] The reference time of the arc segment predicted by the reference orbit before the maneuver is measured. Subtracting the predicted reference orbit longitude from the longitude is the longitude difference. For each arc segment, after sampling the allowed domain, a point set of longitude difference can be obtained, which is recorded as By processing all arcs within a period of time, we can obtain a point cloud distribution diagram on the two-dimensional plane of mean longitude difference and time, where the time reference zero point is the time of the last arc segment that can be associated with the orbit before the maneuver. Figure 3 Schematic diagram of a point cloud belonging to an object.

[0084] Step 3: Extract lines and cluster arcs for the mean longitude difference-time point cloud

[0085] For the point cloud obtained in step 2, a random sampling consensus algorithm is used to detect line features. The specific operation is as follows: First, two point sets are randomly selected, the mean of the point sets is calculated, and the line model parameters are obtained. Then, the distance between each point set and the model is calculated. Point sets less than the set threshold TH are regarded as inliers, and the loss function is calculated. The above process is continuously iterated to minimize the loss function and obtain the optimal model and inliers:

[0086]

[0087] The error term err(·) is:

[0088]

[0089] Where N represents the total number of arc segments, d i Represents the i-th point set The distance from the model, The upper and lower boundary points are and TH is the correlation threshold, t i is the measurement time of the i-th arc. The specific expression of the straight-line model is l(t;c) = c1t + c2, where c = [c1, c2] is the model parameter. The interior point of the final model is the associated arc. TH, as the association threshold, has a clear physical meaning, representing the difference between the mean longitude difference and a true straight line. It should be neither too large nor too small, and is generally set to 3e-3 rad. A too small value may result in too few associated arcs, making final orbit determination impossible; a too large value may easily result in too many erroneous arcs being associated.

[0090] After selecting multiple point sets that satisfy the model parameters, the mean can be calculated and the model parameters can be updated using least squares to ensure consistency between the model and the inliers. Because multiple straight line models may exist in a point cloud distribution with a mean-longitude difference, a maximum number of iterations is set. After finding a set of models and inliers, these inliers are removed from the point cloud, and the iteration is repeated on the remaining point cloud until all straight line models in the point cloud are found. Ultimately, all arc segment clusters and their corresponding straight line fitting parameters are obtained.

[0091] Step 4: Based on the maneuver hypothesis, the correct cluster is obtained and the association is achieved

[0092] Step 3 obtains all possible clusters, but only one set of clusters belongs to the selected target, which can be screened by the straight line parameter requirements of the maneuvering target: (1) the cluster has at least 3 arc segments; (2) the straight line model parameters meet the characteristics of the maneuvering target, and the absolute value of the slope is less than Zero distance comes from the uncertainty of maneuvering time, so its absolute value is less than Δt is the time interval between the last arc segment before the maneuver and the first arc segment of the linear model, which is generally no more than 12 hours. Therefore, the zero distance can also be given an upper bound of 0.1 rad. (3) The maneuver occurs between the last arc segment before the maneuver and the first arc segment of the cluster, so the zero point of the line must be between them. Based on the above conditions, the only correct cluster can be screened and the arc segment can be associated with the selected target in the catalog library.

[0093] In summary, the implementation steps of the present invention are as follows: Figure 1 As shown. The arc-orbit correlation method proposed by the above process is derived from the perspective of orbital dynamics. It is essentially different from traditional methods and has good interpretability. The idea is to achieve correlation from the overall distribution characteristics of multiple arcs through the characteristics of orbital longitude. By imposing strict allowable domain conditions and using the position estimation method to calculate the longitude, the minimum longitude range of the optical arc can be calculated, which is convenient for feature differentiation and association. The random sampling consistency algorithm can detect all straight line features, extract clusters, and further screen to obtain correct results. This method does not require orbit determination, has a fast calculation speed, and is suitable for massive data scenarios.

Claims

1. A method for associating optical arc segments of maneuverable space targets based on orbital dynamics characteristics, characterized by: The steps are as follows: Step 1: Obtain the optical arc segment and generate the constraint allowable domain. The corresponding right ascension and declination angles and angle change rates are extracted for each observation arc. Then, cataloged targets that are not associated with any new arcs are selected, and strict constraints are imposed on the reference orbits in the catalogs combined with the maneuverability to generate the corresponding range-range change rate allowable domain for each arc. Step 2: Calculate the mean longitude difference and obtain the mean longitude difference-time point cloud. Candidate orbit states can be obtained through allowed domain sampling, and only positions within the candidate orbit states are used to estimate the latitude and longitude. The reference time is measured for the arc predicted by the reference orbit before the maneuver. Subtracting the predicted reference orbit latitude and longitude yields the latitude and longitude difference. For each arc, a set of latitude and longitude difference points is obtained through allowed domain sampling. By processing all arcs within a certain period of time, a point cloud distribution diagram is obtained on the two-dimensional plane of latitude and longitude difference versus time, where the time reference zero point is the time of the last arc associated with the orbit before the maneuver. Step 3: Extract straight lines and cluster arc segments for the mean longitude difference-time point cloud. A random sampling consensus algorithm is used to detect line features, and all line models in the point cloud are found with a given maximum number of iterations. Finally, all arc segment clusters and their corresponding line fitting parameters are obtained. Step 4: Filter the correct cluster based on the maneuver hypothesis to achieve association Screening is performed based on the straight line parameter requirements of the maneuvering target. Clusters with at least three arc segments, straight line model parameters that meet the characteristics of the maneuvering target, and straight line zero point position conditions are screened to obtain the only correct cluster and realize the association of the arc segment with the selected target in the catalog library.

2. The method for associating optical arc segments of maneuverable space targets based on orbital dynamics characteristics according to claim 1 is characterized by: The specific method of obtaining the constraint allowable domain in step 1 is: using the reference orbit before the maneuver, constraints are imposed on the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node and perigee, and the constraint boundaries of the orbital elements are calculated by combining the reference orbit before the maneuver with the maneuverability of the spacecraft.

3. The method for associating optical arc segments of maneuverable space targets based on orbital dynamics characteristics according to claim 1 is characterized by: The specific method for calculating the difference in longitude and latitude in step 2 is to estimate the longitude and latitude using only the position. Since the orbital planes before and after the maneuver are very close, the angle between the spacecraft position after the maneuver and the ascending node vector of the reference orbit, plus the right ascension of the ascending node before the maneuver, can be used as the estimate of the target true longitude after the maneuver. The true longitude is then converted to latitude and longitude using the orbital elements before the maneuver. The reference time of the arc segment predicted by the reference orbit before the maneuver is measured. Subtracting the predicted reference orbit latitude and longitude to obtain the difference in longitude and latitude is the reference time.

4. The method for associating optical arc segments of maneuverable space targets based on orbital dynamics characteristics according to claim 1 is characterized by: The specific implementation method of step three to extract all arc clusters is as follows: first, randomly select two point sets, calculate the mean of the point sets, and obtain the parameters of the straight line model. Then, calculate the distance between each point set and the model, take the point set that is less than the set threshold TH as the inlier, and calculate the loss function. Continuously iterate according to the above process, minimize the loss function, and obtain the optimal model and inlier. After selecting multiple point sets that meet the model parameters, you can calculate the mean and use the least squares to update the model parameters to ensure the consistency of the model and the inlier. Since there may be multiple straight line models in the point cloud distribution of the difference in longitude and latitude, in fact, the maximum number of iterations is given. After finding a set of models and inliers, these inliers are removed from the point cloud, and the remaining point cloud is iterated again until all straight line models in the point cloud are found. Finally, all arc clusters and their corresponding straight line fitting parameters are obtained.

5. The method for associating optical arc segments of maneuverable space targets based on orbital dynamics characteristics according to claim 1 is characterized by: Step 4: The specific implementation method for obtaining the only correct cluster is: screening by the straight line parameter requirements of the maneuvering target, requiring: (1) the cluster has at least 3 arc segments; (2) the straight line model parameters meet the characteristics of the maneuvering target, and the absolute value of the slope is less than Zero distance comes from the uncertainty of maneuvering time, so its absolute value is less than Δt is the time interval between the last arc segment before the maneuver and the first arc segment of the linear model, which is generally no more than 12 hours. Therefore, the zero distance can also be given an upper bound of 0.1 rad. (3) The maneuver occurs between the last arc segment before the maneuver and the first arc segment of the cluster, so the zero point of the line must be between them. Based on the above conditions, the only correct cluster can be screened and the arc segment can be associated with the selected target in the catalog library.

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