Preamble

Astronomical Techniques and Instruments, Vol. 2, September 2025, 299–309 Article Open Access Data matching and association based on the arc-segment differ- ence method Jiannan Sun , Zhe Kang , Zhenwei Li , Cunbo Fan 1 Changchun Observatory National Astronomical Observatories Chinese Academy of Sciences Changchun 130117, China *Correspondence:

INTRODUCTION

In recent years, rapid developments in commercial space activities, together with the frequent occurrence of space target collisions and explosive disintegration events, have caused a sharp increase in the number of space tar- gets in orbit. These occurrences have aggravated orbital con- gestion and are highly prone to triggering cascading colli- sions, thereby leading to the formation of the Kessler Syn- drome . As of December 24, 2024, the number of in- orbit space targets in Space-Track’s publicly released Two-Line Element (TLE) database stands at 30

010. This

represents an increase of approximately 1 487 targets com- pared with the same period in the previous year . The steadily growing number of space targets poses a consider- able challenge to the maintenance and expansion of the Space Surveillance and Tracking (SST) database. To

address this challenge, continuous observation of space tar- gets is essential to accurately determine their orbital parame- ters. Consequently, the multi-target capture observation model for sky surveying is used widely in space target cata- loging [ 3 ] . Nevertheless, an observation mode employing multi-target identification techniques cannot directly acquire the specific attribute information of a target. To fur- ther utilize the observation data, matching and associa- tion operations must be performed on the observation arc- segments.

When the data processing center receives a large vol- ume of observational data, the first step is to match the data against the orbital elements of the catalog database.

For observations that do not match successfully, initial orbit determination (IOD) is employed for correlation The North American Aerospace Defense Command (NORAD) publicly available database is the most com-

2 University of Chinese Academy of Sciences , Beijing 100049, China

3 Changchun Branch

Chinese Academy of Sciences Changchun 130022, China © 2025 Editorial Office of Astronomical Techniques and Instruments, Yunnan Observatories, Chinese Academy of Sciences. This is an open access article under the CC BY 4.0 license ( Citation: Sun, J. N., Kang, Z., Li, Z. W., et al. 2025. Data matching and association based on the arc-segment difference method.

Astronomical Techniques and Instruments (5): 299−309.

Abstract

In response to the issue of fuzzy matching and association when optical observation data are matched with the orbital elements in a catalog database, this paper proposes a matching and association strategy based on the arc- segment difference method. First, a matching error threshold is set to match the observation data with the known catalog database. Second, the matching results for the same day are sorted on the basis of target identity and observation residuals. Different matching error thresholds and arc-segment dynamic association thresholds are then applied to categorize the observation residuals of the same target across different arc-segments, yielding matching results under various thresholds. Finally, the orbital residual is computed through orbit determination (OD), and the positional error is derived by comparing the OD results with the orbit track from the catalog database. The appropriate matching error threshold is then selected on the basis of these results, leading to the final matching and association of the fuzzy correlation data. Experimental results showed that the correct matching rate for data arc-segments is 92.34% when the matching error threshold is set to 720″, with the arc-segment difference method processing the results of an average matching rate of 97.62% within 8 days. The remaining 5.28% of the fuzzy correlation data are correctly matched and associated, enabling identification of orbital maneuver targets through further processing and analysis.

This method substantially enhances the efficiency and accuracy of space target cataloging, offering robust technical support for dynamic maintenance of the space target database.

Keywords

Optical data processing; Space target identification; Fuzzy correlation; Arc-segment difference method; Orbit determination

monly used orbital cataloging repository for a wide range of aerospace workers, and TLE data for most space tar- gets are regularly updated on a daily basis through the Space-Track website. The matching rate is 83%−85% when using the TLE database . Calculation of TLE data requires the use of an appropriate Simplified Gen- eral Perturbation Version 4 (SGP4) or Simplified Deep- space Perturbation Version 4 (SDP4) orbital propagation models . Because the accuracy of SGP4/SDP4 models is not published and the TLE data do not contain the corre- sponding orbital accuracy information, fuzzy matching is possible when using this information, which might affect the accuracy of the space target catalog.

To reduce the probability of fuzzy matching, it is essen- tial to fully understand the accuracy of the propagation model and the orbital accuracy details of the various orbital altitude targets in the TLE database. These can be used as reference values for setting the matching thresh- old. In 2008, Flohrer analyzed the accuracy of TLE data for 11 286 space targets and indicated that the entire dataset could potentially have a maximum standard devia- tion of approximately 5 km . Regarding Low Earth Orbit (LEO) satellites, Reising analyzed the accuracy of 634 sets of TLE data for the Flock 1B satellite over the period of 1 month. When using the SGP4 model for 1- error propagation, the positional change was 10−30 km after 1 day of propagation, and 20−70 km after 2 days, mainly in the along-track direction . Typically, the TLE data of LEO satellites are updated every few hours. If not updated promptly, owing to the influence of atmospheric drag, the propagation error of the SGP4 model in the along-track direction will increase markedly. The along- track error can reach several hundred of kilometers in a 7-day prediction . For medium-orbit and high-orbit satel- lites, Racelis and Joerger’s research analysis showed that during 2013–2015, the TLE along-track errors for most cases ranged from −15 to 15 km, but during a later period (2015–2018), these errors were more constrained, staying between −6 and 6 km . In the case of Elliptical Orbit (EO)/High Elliptical Orbit (HEO) satellites, Wei’s research demonstrated that the larger the eccentricity, the greater the orbital prediction error: The 1-day prediction positional error was within 20 km, and the 3-day predic- tion positional error was within 100 km . Früh and Schild- knecht’s study also revealed a 0.08° deviation between the observation data and the TLE ephemeris of the clos- est observation moment . Therefore, when choosing the TLE database for target matching, the effects of both the inherent errors in the TLE data and the orbital propaga- tion errors specific to different orbit types must be consid- ered. Furthermore, the handling of orbital parameter anoma- lies within the TLE data is of vital importance . By set- ting an appropriate matching error threshold, the correct matching rate of data arc-segments can be improved, thereby reducing the probability of fuzzy correlation.

To address the issue of incorrect associations for GEO targets in dense trajectories, Song proposed a real- time GEO target association algorithm that utilizes two- dimensional judgments of radar ranging and speed. This algorithm improves the association accuracy but is lim- ited by the type of observation data available . Tao put forward a correlation method by analyzing the orbit determi- nation (OD) results of correlated data, achieving the cor- rect correlation of data from different passes of the same target. However, this approach is also constrained by the conditions of OD . Research on data association algo- rithms has matured remarkably, both in domestically and internationally. Notable methods include the nearest-neigh- bor method, joint probability data association, multi-hypoth- esis tracking, fuzzy association algorithms, the IOD method, and the admissible region algorithm . All of these algorithms focus on associations between data arc- segments rather than between data arc-segments and known target orbital parameters. Consequently, they do not extract attribute information from data arc-segments, which belong to the category of uncorrelated target process- ing. From a practical engineering perspective, accurately matching observation data with the orbital elements of the catalog database is essential for enhancing the correct matching rate and improving the ability to analyze anoma- lous matching data. This improvement is crucial for rapi- dly advancing space situational awareness and enhancing the cataloging and maintenance capabilities of space targets.

Here, we propose a data matching and association strat- egy based on the arc-segment difference method to address the fuzzy matching and association issues of obser- vation data during the matching process. Using the match- ing error threshold and the arc-segment dynamic associa- tion threshold, our approach processes the observation resid- uals of different arc-segments belonging to the same tar- get. Consequently, for every individual arc-segment, one of the following four types of matching and association results will be generated: True match & True association, True match & False association, False match & True associ- ation, and False match & False association. The accuracy of these matching correlation results is validated through OD. By processing false matching association data, we can effectively identify elliptical orbit targets, targets with sudden orbital changes (such as maneuvers, collisions, explosions, and fallout), and newly detected targets. Such data can serve as the primary resource for studying these targets, demonstrating substantial application value.

The remainder of this paper is structured as follows.

Section 2 details the data matching principle and the match- ing association strategy of the arc-segment difference method. Section 3 presents the experimental results and vali- dation under different matching error thresholds. More- over, the application of fuzzy association data is intro- duced. Section 4 analyzes the causes of fuzzy associa- tions. Finally, Section 5 concludes the paper.

PRINCIPLES AND METHODS Data Matching Principle The positional information derived from the TLE data, computed by SGP4/SDP4 models, is given within

the True Equator and Mean Equinox of date (TEME) coor- dinate system, which is denoted as . For the Opti- cal Survey Telescope (OST), the coordinate system of observation data obtained using the astronomical positioning method is the J2000 coordinate system. Addi- tionally, the station position represents a state quantity within the Earth-Centered, Earth-Fixed (ECEF) coordi- nate system, denoted as . When data matching is per- formed, both the TEME and ECEF coordinate systems need to be converted into the J2000 coordinate system.

The relevant transformation relations are expressed as fol- J2000

r J2000 = [( B 2 )( B 1 )( N )( A )] T r b , (2)

where represents the matrix for counterclock- wise rotation of angle around the -axis in the original coordinate system, where denotes the nuta- tion in longitude and represents the true obliquity of the ecliptic; is the polar motion correction matrix; is the Earth’s rotation matrix; is the nutation correc- tion matrix; is the precession correction matrix; super- script denotes the transposed transformation matrix; denotes the right ascension; and denotes the declination.

Assuming that the position vector of the space target at time , which has undergone orbit prediction and been transformed into the J2000 coordinate system, is denoted , and the position vector of the station after coordinate system transformation is Then, the position vector of the space target in the J2000 coordinate system with the station as the center, denoted , is given by the following:

The theoretical observation value of the space target at this moment is expressed as follows: 

α ct = arctan( y ct / x ct )

δ ct = arcsin ( z ct

The observation residual for the data is then calculated using Equation (5):

ε = √

After traversing all the targets in the catalog database, the root mean square (RMS) error of the observa- tion residuals is acquired for the entire data arc-segment.

The identity information of the target indicated by the mini- mum RMS error that satisfies the matching error thresh- old is taken as the initial matching result for that data arc-segment. This initial matching result is marked by a

NORAD identification number. Matching and Association Strategy Based on segment Difference Method By setting the matching error threshold, we can obtain the identity information of the observation arc-seg- ments corresponding to the known target in the catalog database. If a small matching error threshold is set, the matching result will have high accuracy. However, this will cause the matching success rate of the observation data to be low, and it will affect the data utilization rate.

Conversely, if a large matching error threshold is set, the matching success rate of the observation data will be high, but it will result in the formation of fuzzy matching.

This will reduce the matching accuracy and affect the cata- loging accuracy. Therefore, while ensuring a high data matching rate, it is essential to reprocess the initial match- ing results. This helps resolve the problem of fuzzy match- ing and guarantees that each observation arc-segment is cor- rectly matched and associated with other arc-segments.

On the basis of the accuracy of TLE data and the char- acteristics of orbital error propagation for targets at differ- ent altitudes, we adjust the data matching error threshold and the arc-segment dynamic association threshold to clas- sify more precisely the initial matching results. This pro- cess ensures correct matching of observation data to known targets and accurate association of data arc-seg- ments. The data matching error threshold determines whether the observation data are correctly matched to a known target, while the arc-segment dynamic association threshold assesses whether the data arc-segments matched to the same target are correctly associated. After apply- ing these criteria, the initial matching results are catego- rized into four types.

True match & True association means that the observa- tion data have been matched to the correct target in the database and that the arc-segments have been correctly asso- ciated with each other. Therefore, the correct matching rate can be calculated. True match & False association means that the correct matching data arc-segment of the tar- get already exists for the same day, and that according to the dynamic association threshold value, the data arc-seg- ment has a false association; namely, the data do not belong to the marked target. This data type serves as a source for newly detected targets. False match & True asso- ciation means that the observation residual exceeds the match threshold value, while the arc-segment difference meets the dynamic association threshold between arc-seg- ments. Thus, the arc-segment from the same target data can be accumulated. False match & False association means that the residuals of the data arc-segments exceed the matching association threshold both in matching and in association between arc-segments, but are lower than the set threshold for matching error. The overall proce- dure is described in the following. (1) The matching error threshold of the observation data is set to , and the dynamic association threshold

of the arc-segment is set to

∆ D = Φ i ∗ (⌊ | T i + 1 − T i | P

where is the RMS error of the observation residuals of the i -th observation arc-segment, and its unit is arc-sec- ond; indicates the downward rounding of the value therein; means the starting observation moment of the i -th observation arc-segment; represents the orbital period of the matching target, and its unit is minute; and varies with the sequential order of the observation arc-segments.

(2) The initial matching results are sorted in descend- ing order by target identity and the RMS error values of the observation residuals for each observation arc-egment of the same target. The discrepancy of the arc-segment is calculated as . The final matching and associ- ation result for each observation arc-segment is decided based on the following relationship, and as shown in

Φ ′ = Φ i + 1 − Φ i

True match & False association False match & False association Mark:

Φ′ > Δ D

Mark: True match & True association Mark: False match & True association Mark:

Φ′ ≤ Δ D

Φ i ≤ Δ T Φ i vs . Δ T Φ i > Δ T

This figure illustrates two relationships: the data match- ing relationship between observation residuals and the reset matching error threshold (horizontal coordinate), and the arc-segment association relationship between the obser- vation residual difference and the dynamic association threshold (vertical coordinate). If there is only one target- numbered observation arc-segment in the initial matching result, the matching error threshold is used to determine whether the result is a case of True match & True associa- tion or False match & False association. The flow chart of the process of data matching and association process- ing is shown in DATA AND RESULTS Evaluation of Experimental Data Accuracy A data matching and association experiment was per- formed using observation data collected from an array of photoelectric telescopes at the Changchun Observatory, National Astronomical Observatories, Chinese Academy of Sciences. The parameters of the telescopes are detailed Observation data were acquired from September 21–28, 2024. During this period, a cooperative target was Observation data NORAD catalog Set matching error threshold

Initial matching

results

Reset the matching error threshold, set dynamic arc-segment association threshold True match & False association False match & association False match & False association True match & association

Parameters Value Aperture for single/mm 150 Monitoring region/(°) 2 1 590 Elevation angle of observation/(°) 18–32 Resolution of CCD/pixel 3 056×3 056 Pixel size/μm 12 Exposure time/ms 200 Frame rate/fps 0.59 Detection ability/mag 10.5 Observation accuracy/('') Piror to 9

selected to evaluate the measurement accuracy of the tele- scope using its Consolidated Prediction Format (CPF) Ver- sion 2 ephemeris, which can be accessed via a file trans- fer protocol site . The CPF ephemeris provides posi- tional information for targets in a geocentric coordinate sys- tem, with accuracy typically within several meters for one-day prediction , which is sufficient for evaluation of the accuracy of observation data of 9''. Additionally, this assessment is intended to verify the stability of the operating conditions of the telescope, as detailed in During the observation period, the telescope demon- strated an RMS error of 2.88″ in right ascension and 2.84″ in declination, resulting in a combined RMS error

(NORAD number 41240) 2024–09–21 18:48:44.96 2024–09–22 17:14:54.97 2024–09–23 17:37:42.25 2024–09–24 18:00:50.89 2024–09–25 16:26:59.23 2024–09–27 17:12:17.93 2024–09–28 15:40:06.97 Observation date length/s RA/(″) Dec/(″) “RA” denotes right ascension, “Dec” indicates declination of 4.03″ for the Jason-3 satellite at an altitude of 1 336 km.

These values suggest that the measurement accuracy of the telescope remained relatively stable throughout the observation period.

The matching error thresholds were set to 60″, 180″, 360″, 720″, 1 080″, 1 800″, and 3 600″, and the average matching success rates of the observation data within 8 days were obtained as 40.56%, 65.43%, 79.98%, 91.77%, 94.97%, 96.75%, and 97.62%, respectively, as shown in As depicted in , the matching success rate rises with an increase in the matching error threshold. Evi- dently, setting a larger matching error threshold enables a higher matching success rate, which is beneficial for maxi- mizing the utilization of observation data. However, a larger threshold also results in fuzzy data matching and ambiguous arc-segment correlations. This will impact the cataloging accuracy and the handling of special target sce- narios, such as orbital maneuvers and the detection of Category As shown in , within the 8-day period, the num- ber of data arc-segments with True match & True associa- tion steadily increases as the data matching error thresh- old rises. Correspondingly, the association success rate also gradually improves, primarily because of the data arc-segments classified as False match & True associa- tion. When the matching error threshold exceeds 180″, the results for True match & False association remain unaf- fected by the magnitude of the threshold. Instead, they are determined by the difference between the residuals of the Matching success rate/(%) 1 080″ 1 800″ 3 600″ Modified Julian Day/day new targets.

The matching association strategy based on the arc-seg- ment difference method described in Section 2.2 effec- tively addresses the aforementioned issues. Given the accu- racy of LEO target TLE data and the error propagation characteristics, in addition to the matching results pre- sented in , the matching error thresholds for the obser- vation data were reset to 60″, 180″, 360″, 720″, 1 080″, and 1 800″.

A method involving comparison of the difference between the dynamic association threshold and the arc-seg- ment residual is used to handle the initial matching results. By processing the results, which have an average matching rate of 97.62% within an 8-day period, we obtain four types of results, among which the proportions of the data marked as True match & True association are 44.61%, 69.96%, 84.03%, 94.79%, 97.58%, and 99.15% for the matching error thresholds of 60″, 180″, 360″, 720″, 1 080″, and 1 800″, respectively, as shown in arc-segments and the dynamic association threshold, with each target typically corresponding to 1–2 passes of data.

In the case of False match & True association, a low match- ing error threshold corresponds to an average of nearly 10 passes of data per target. As the threshold increases, this average is reduced to approximately 3–4 passes per target.

For False match & False association, as the matching error threshold rises, the number of False match & False association arc-segments gradually declines, resulting in each space target generally corresponding to 1–2 passes True match & True association True match & False association False match & True association False match & False association “Pas” denotes the number of observed target arc-segments, “Num” indicates the number of targets

of data. Verification of Matching and Association Results To evaluate the rationality of the settings for the match- ing error threshold and the dynamic correlation threshold, the OD method is employed. This method is validated through the OD residual. The principle of OD is not the focus of this paper, but relevant details can be found in the book by Montenbruck et al.

Because the data of True match & False association and False match & False association cannot meet the requirements for OD, process- ing of False match & True association data is conducted to verify the appropriately chosen matching error thresh- old. Among the False match & True association data, data arc-segments with observation residual errors falling between two adjacent thresholds are selected. Moreover, arc-segments where the same target has observation data for 3 consecutive days are used for OD. The OD result is then compared to the TLE data, with consideration of the value of the OD residual. If the two values change 1080″

The 1 080″ threshold had too few data points for OD to converge; however, for the remaining targets, the OD solutions were successfully completed, and OD residuals were obtained for these targets. Positional errors are calcu-

steadily, then the data of this arc-segment belongs to the case of True match & True association; otherwise, they belong to the case of False match & True association.

On the basis of the observation residual data of False match & True association presented in , data arc- segments whose RMS errors lie within the adjacent match- ing error threshold intervals are chosen for the purpose of OD. The criterion adopted for OD is that the same target is selected to have at least 3-minute data arc-segments over three consecutive days, with each day comprising 1–2 data passes. Analysis reveals that 165 targets with RMS errors between 60″ and 180″ meet the OD criteria.

In the interval from 180″ to 360″, the number of such tar- gets is 143. For the interval from 360″ to 720″, there are 88 targets. In the range from 720″ to 1 080″, only five tar- gets satisfy the condition. There is merely a single target in the interval from 1 080″ to 1 800″. One target was ran- domly selected from each of these intervals to perform OD, and the corresponding observation data are dis- played in Number of data points RA/(″) Dec/(″) RMS/(″) lated by comparing the OD result with the TLE data at the observation times. In Figs. 4 , the number of observation data points is distributed according to the acquired observation time.

Matching threshold File name NORAD identification Altitude/km Length of arc/s FT_21233 FT_21233 FT_21233 FT_21233 FT_21233 FT_21233 FT_45535 FT_45535 FT_45535 FT_45535 FT_45535 FT_45535 FT_58377 FT_58377 FT_58377 FT_58377 FT_58377 FT_58377 FT_60264 FT_60264 FT_60264 FT_60264 FT_60264 FT_60264 FT_54794 FT_54794 FT_54794

40 A

Observation residual/(″) Observation residual/(″) As is evident from , when the observation resid- ual is less than 720″, the OD for False match & True asso- ciation data corresponding to different matching error thresholds yields the residual ranging from several arc-sec- onds to approximately a dozen arc-seconds. For example, the OD residuals for targets with NORAD numbers 21233, 45535, and 58377 are 8.96″, 13.57″, and 12.01″, respectively. Conversely, when the observation residual exceeds 720″, the OD residual surges to hundreds of arc- seconds. An illustrative example is the target with NORAD number 60264 in , which has an OD resid- ual of 228.75″.

NORAD numbers 21233, 45535, 58377, and 60264 are cal- culated to be 1.82, 1.63, 2.26, and 3.04 km, respectively.

Through the consistency of the distribution of the orbital residuals and the position comparison of the OD results with the TLE data error variation range, it is evident that the OD results of the first four targets are consistent with the accuracy of the TLE data. However, for the target with NORAD number 60264, notable disparity exists in the orbital residuals. This suggests that this specific arc-seg- ment is likely to reflect observation data pertaining to other targets. Given that the magnitude of the orbital resid- ual value of this arc-segment is similar to that of its obser- vational residual, it is highly probable that the data of this arc-segment do not belong to the target with NORAD num- Observation residual/(″) Observation residual/(″) Number of data point ber 60264.

Through OD verification, when the matching error threshold is set at 60″, 180″, and 360″, none of the False match & True association results obtained under these set- tings can thus accurately indicate that the observation data have been correctly matched and correlated. When the matching error threshold is set to 720″, a certain degree of fuzzy matching correlation exists in the observation data. Hence, it is reasonable to set 720″ as the data match- ing error threshold. Specifically, using the arc-segment dif- ference method, the data arcs with an average matching rate of 97.62% within an 8-day period were processed, and an overall data correct matching rate of approxi- mately 92.34% was achieved. Additionally, the remain- ing 5.28% of data with fuzzy correlations was classified and processed by allocating the 3 646 data arcs to differ- ent false match and association results.

Application of False Match and Association Data Combined with the matching results for the same tar- get over multiple days, if the matching residuals for a par- ticular day suddenly increase, it is likely that the target has undergone an orbital maneuver. In the case of True match & False association results, because the existing data arcs are correctly matched to the target information in the catalog database, and because data processing on the same day adopts the set of orbital elements closest to the time of observation, the matching residuals will not sud- denly increase in the adjacent orbital period. The occur- rence of the target’s orbital maneuver cannot be detected

RMS_RA = 7.14″ RMS_RA = 9.68″ RMS_Dec = 5.41″ RMS_Dec = 9.50″ RMS = 8.96″ RMS = 13.57″

Number of data point Number of data point Number of data point (A) target for 21233, (B) target for 45535, (C) target for 58377, and (D) target for 60264.

Position error/m −1 000 −2 000 −3 000 Position error/m −2 000 −4 000

RMS_ X = 1 347.84 m RMS_ Y = 1 219.24 m RMS_ Z = 1 340.27 m

−6 000 −8 000 in this scenario. Therefore, most of the True match & False association data should be data relating to the newly detected target. The results in list 57 targets with 98 passes of data. In the False match & True association By processing the historical TLE data of the target, the orbital altitude information can be derived. When this information is integrated with the measured data, it is revealed that the target with NORAD number 60339 exe- cuted an orbital maneuver on 22 September (Modified Julian Day = 60 0). Specifically, within a span of 2 days, the orbital altitude of the target increased by approx- imately 28 km, as illustrated in , the TLE data release epoch is 60 in Modified Julian Days with a corresponding orbital alti- tude of 465.520 km. The actual observation moment is 1 in Modified Julian Days. When the target Position error/m −1 000

RMS_ X = 1 010.43 m RMS_ Y = 951.28 m RMS_ Z = 861.70 m

−2 000 −3 000 Position error/m −2 000 −4 000

RMS_ X = 1 837.53 m RMS_ Y = 1 816.73 m RMS_ Z = 1 602.98 m

−6 000 −8 000 data, it is easier to find the target of an orbital maneuver.

Taking the target with NORAD number 60339 as an exam- ple, the results of matching and association for the observa- tion data are listed in makes an orbital maneuver, the altitude of the target orbit is no longer 465.520 km; instead, it should be within the range of 465.520–469.130 km. Because the TLE data evolves unstably during the orbital maneuver, a large match- ing error value is produced. However, once the target’s orbit stabilizes, the matching errors of the subsequently measured data all fall within the normal matching error threshold for LEO targets.

The same can be found for the orbital maneuver in the False match & False association case. Using the tar- get with NORAD number 60439 as an example, the match- ing associations for this target are listed in Modified Julian Day/day Modified Julian Day/day Modified Julian Day/day Modified Julian Day/day (A) target for 21233, (B) target for 45535, (C) target for 58377, and (D) target for 60264.

File name NORAD_ID Length of arc/s RMS_RA/(″) RMS_Dec/(″) RMS/(″)

TLE data Observational data (60 577.916 7, 475.099) Orbital altitude/km (60 577.583 3, 469.130) (60 577.333 3, 465.520) (60 577.444 1, 465.520) (60 575.802 0, 447.230) Modified Julian Day/day It is evident that the target started to make an orbi- tal maneuver on 18 September (Modified Julian Day = 3). The orbit altitude was increased by approxi- mately 55 km throughout the orbital change, as shown in On 22 September (Modified Julian Day = 60 TLE data Observational data (60 576.083 3, 473.496) Orbital altitude/km (60 575.890 1, 467.518) (60 575.75, 467.518) (60 572.272 3, 418.753) Modified Julian Day/day According to , when the matching error thresh- old is set at 720″, statistical analysis reveals that all the True match & False association data pertain to LEO tar- gets. Among the False match & True association targets, 98.07% consist of LEO targets, while the remaining 1.93% are composed of 11 HEO targets and 2 MEO tar- gets. In the case of False match & False association tar- gets, 89.10% are LEO targets, and the remaining 40 tar- gets include 23 HEO targets and 17 MEO targets. It is evi- dent that when handling data of LEO and HEO targets, fuzzy correlations are likely to occur owing to issues related to orbital accuracy. Given that the slant distance

a large matching error is evident when the target with NORAD number 60439 underwent an orbital change. How- ever, once the orbit stabilized, the matching error magni- tude aligned with the precision of the TLE data.

ANALYSIS AND DISCUSSION In the process of matching and associating space tar- get data with a known catalog database, multiple factors can give rise to fuzzy matching and association. These fac- tors include the orbital accuracy of the cataloged targets, orbital maneuvers executed by the targets, and the detec- tion of new targets. The data matching and association strat- egy proposed in this paper, based on the arc-segment differ- ence method, not only enables effective identification of fuzzy association data but also allows for its refinement and classification. By setting the data matching threshold and the arc-segment dynamic association threshold, this strategy showcases the specific application of such data, thereby enhancing the data utilization rate. of LEO targets from the station is assumed to be 1 000 km, the line-of-sight error corresponding to 720″ is approxi- mately 3.49 km, which is in line with the accuracy of LEO targets in the TLE database.

As shown in , the OD residual for the case of False match & True association is 228.75″. When this is combined with the positional error of 3.04 km depicted in , it indicates that the target’s OD scheme is cor- rect and that the matching result corresponds to a target within the known catalog database. However, the observa- tion data include data from other targets, which results in an excessively large OD residual. After eliminating the interfering data, the OD residual is found to be 18.57″, which is of similar magnitude to that of the OD residuals of the other three targets. From Tables 5 , through processing the matching results of the same target over mul- tiple days (as illustrated in Figs. 7 ), the false match- ing correlation data have found specific applications. On this basis, it is deemed that setting the matching thresh- old at 720″ is appropriate. However, if a satellite per- forms a continuous low-thrust maneuver and the TLE is the latest before that maneuver (i.e., the TLE prediction is relatively accurate), false matching association data might fail to detect the maneuver. To enhance the accuracy of determining target maneuvers, further research could be con- ducted, such as incorporating multi-source features (for example, the stability of the photometric curve and the mutation rate of orbital parameters). Meanwhile, experi- ments with MEO and HEO observation data should be File name NORAD_ID Length of arc/s RMS_RA/(″) RMS_Dec/(″) RMS/(″) FF_60439

increased to verify the universality of the proposed method.

CONCLUSIONS

This paper introduces a data matching and arc-seg- ment association strategy based on the arc-segment differ- ence method, designed to address challenges in fuzzy matching and arc-segment association during the process- ing of observation data. By optimizing the matching error threshold and the dynamic arc-segment association thresh- old, the proposed approach substantially enhances the accu- racy of data matching and mitigates the fuzzy association issues caused by orbital maneuvers or propagation errors.

Experimental results demonstrated that setting the match- ing error threshold to 720″ enables the arc-segment differ- ence method to effectively handle fuzzy matching correla- tion data, thereby improving data utilization while maintain- ing a high matching rate. Furthermore, by classifying and processing fuzzy associated data, the method not only ensures accurate association of data from the same target but also facilitates the identification of potential orbital maneuver targets. For new target validation, the method leverages observation arc-segments from the same target to extend the arc length and enhance the OD accuracy. In the case of maneuvering targets, the measured data pro- vide robust evidence of orbital changes, underscoring the method’s effectiveness in processing fuzzy correlation data.

The paper also validates the appropriateness of the selected matching error threshold through OD analysis, demonstrating that the recommended threshold effec- tively screens fuzzy correlation data. This approach improves the efficiency of the space target catalog and enhances the precision of target orbits in the database.

Future research could further explore the practical applica- tions and value of fuzzy associated data, building on the foundation established in this study.

ACKNOWLEDGEMENTS This research was supported by National Natural Sci- ence Foundation of China (12273080).

AI DISCLOSURE STATEMENT Deepseek was employed for language and grammar checks within the article. The authors carefully reviewed, edited, and revised the Deepseek-generated texts to their own preferences, assuming ultimate responsibility for the content of the publication.

AUTHOR CONTRIBUTIONS Jiannan Sun conceived the ideas and wrote the manuscript. Jiannan Sun and Cunbo Fan developed the methodology. Jiannan Sun, Zhe Kang, and Zhenwei Li veri- fied the research data. Zhe Kang managed and main- tained the research data and provided study resources. Zhen- wei Li provided the funding support. Cunbo Fan super- vised and revised the paper. All authors read and approved the final manuscript.

DECLARATION OF INTERESTS The authors declare no competing interests.

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