An Improved Range-Searching Initial Orbit-Determination Method and Correlation of Optical Observations for Space Debris

Abstract

The Changchun Observatory of the National Astronomical Observatories, Chinese Academy of Sciences, and the Shanghai Astronomical Observatory are used to generate very short arc (VSA) angle observations of objects in low Earth orbit (LEO) and geostationary orbit (GEO) with their ground-based electrical–optical telescope arrays (EA), the Changchun EA and SAO FocusGEO, respectively. These observations are used in this paper. The range-searching (RS) algorithm for initial orbit determination (IOD) is improved through the multiple combinations of observations and the dynamic range-searching step length. Two different computation modes (the normal mode and the refining mode) of the IOD computation process are proposed. The geometrical method for the association is used. The IOD and association methods are extended to the real optical observations for both LEO and GEO objects. The results show that the IOD success rate of arcs from the LEO objects is about 91%, the error of the semimajor axis (SMA) of the initial orbital elements is less than 50 km, and the correlation accuracy rate is about 89%. The IOD success rate of arcs from the GEO objects is higher than 88%, and the correlation accuracy rate is greater than 87%. The recent COSMOS 1408 antisatellite test (ASAT) generated a large amount of debris. The algorithm of this paper and the observations of Changchun EA are used to initially identify new debris, possibly from the ASAT through initial orbit determination and track association. Finally, 64 suspected new pieces of debris can be found. The results show the effectiveness of the IOD and the correlation algorithm, as well as the potential application of the optical–electrical array in studying space events.

1. Introduction

Space debris is defined as man-made objects in space that have lost their function, including parts of failed satellites and spacecraft. Space debris, also known as “space junk”, remains above the Earth’s atmosphere for many years until it decays, deorbits, disintegrates, or collides with other objects to create new objects [1,2,3].

Weather forecasting, communications, GPS, and other important space-based everyday life applications are threatened by the increasing volume of orbital debris, all of which depend on a stable space environment [4]. In fact, space debris is already having a real impact on the space environment. As an example, the (International Space Station) ISS has performed 27 collision-avoidance missions since 1999, and, as of July 2021, five of them were to avoid debris from the Cosmos-2251 and Iridium 33 collisions and one to avoid debris from Fengyun-1 [5].

On 15 November 2021, Russia conducted an ASAT test that successfully destroyed a LEO satellite, COSMOS 1408, NORAD ID 13552, weighing about 2.2 tons, with an orbital altitude of 800 km and an inclination of 82.5°. It is estimated that the ASAT event will produce more than 1400 pieces of debris larger than 10 cm in size and more than 70,000 pieces of debris larger than 1 cm in size (from WeChat: Voice of the Chinese Academy of Sciences). As of 10 December 2021, the U.S. has cataloged over 330 pieces of debris from this event in the publicly available TLE catalog, and the number is still growing. It is foreseeable that this ASAT test will aggravate the severe LEO space environment.

There are three methods for observing debris, namely radar, optical observation, and laser ranging. Among these, laser-ranging observation has the highest accuracy [6,7] and is one to two orders of magnitude more precise than microwave radar and optical telescope observations [8]. Optical observation is an important method, and there are a growing number of core key technologies for optical detection being developed and moving from theory to engineering applications, such as super-resolution imaging, polarization spectral detection, and the integration of measurement and detection passes. These advancements provide more efficient and accurate means for detecting space debris [9,10]. Small-sized and medium-high orbit space objects are mainly detected by optical systems, and increasing the telescope aperture can improve the capability to detect faint and weak space objects [8]. The number of space objects since 1957 is shown in Figure 1.

Ground-based optical telescopes are important space surveillance equipment, and reference [12] simulated the capability of multioptical equipment to observe space debris and found that a 15 cm aperture telescope is more valuable for maintaining the space debris catalog. For observations of unknown objects, if these data are used to try to catalog a new object and expand the catalog library, it is common practice to perform IOD and then orbit correlation to achieve the correlated orbit of multiple arcs and finally catalog a new space object. The key techniques include IOD and correlation, and a suitable IOD algorithm can provide the orbit parameters needed for correlation. For the VSA observations, IOD and their correlation are the key techniques for cataloging space debris.

IOD is the rapid calculation of the initial orbit of a space object—a “rough” orbit—using a relatively simple dynamical model (usually a two-body model), without any initial information, using observations of the short-arc segment. There are various methods for IOD, including traditional algorithms such as the Gauss, Laplace, and Gooding methods, as well as modern algorithms such as genetic algorithms. The existing literature on IOD uses a long arc, generally, a few minutes to several minutes; Ref. [13] found that, when the arc length is longer than 400 s, the IOD results are better. With the increase of the arc length, the IOD element errors decrease. But when a certain degree is reached, the error increases and eventually stabilizes. However, the arc length of objects in LEO in real scenarios is often less than 60 s, or even only a dozen seconds, so there are still technical bottlenecks in the IOD with the VSA observations.

There are several algorithms for the initial orbit-correlation problem, and [14] introduced a geometric algorithm for initial orbit correlation for LEO object angle observation data, which were tested using real data, and the results showed that the correct rate of initial orbit correlation for the same object was higher than 80%. Ref. [15] proposed a new method to locate space objects using noncoherent covisual observation techniques, which were validated using optical data from the Changchun, Delingha, and Xuyi stations in the Space Object and Debris Observation Network of the Chinese Academy of Sciences and debris laser-ranging (DLR) data from Changchun station. The results showed that the SMA error of the fixing accuracy was about 1 km. Ref. [16] proposed a new algorithm that does not require initialization and finds a set of observations with minimum residuals using the method of the edge value problem, which can provide complete state and covariance information. Ref. [17] analyzed the influence of the observation geometry on the short-arc angles only IOD and concluded that the optical sensor has the worst surveillance capability for space debris in the same orbital plane. Ref. [18] analyzed the application of algebraic geometry in IOD problems and tested its performance with various scenarios of observations.

The detection of space debris clouds from space events is very significant. With the construction of optical telescopes, more and more optical telescopes are coming into use. This provides a good opportunity to detect events with ground-based telescopes. It is a good idea, but it is difficult to realize and there are few related public studies now. The difficulty lies in obtaining the exact orbit of space debris. To get the exact orbit elements of space debris, the IOD with one short arc and the correlation between the IOD elements are the basis for the detection of space debris.

In this paper, the very short arc IOD and the orbit-correlation study are carried out based on the ground-based optical array of Changchun LEO EA and SAO FoucusGEO. The paper is organized as follows. The first part introduces the background of the paper research. The second part introduces the observation equipment, data, and methods. The third part presents the data-processing results. Finally, the conclusion and outlook are presented.

2. Observations and Methods

2.1. Angle Observations

Usually, an observing device can only track a single object at the same time, and this mode of operation limits the ability to catalog space objects. So, a large field-of-view (FOV) multiobject optical telescope array observation mode was created. The equipment used in this paper is described below (shown in Figure 2 and

Table 1. Parameters of telescopes.

Name	Changchun GEO Telescopes	Changchun LEO Telescopes	FocusGEO
Number of telescopes	4	8	3
Telescope diameter	280 mm	150 mm	180 mm
Focus length	324 mm	150 mm	220 mm
CCD	4096 × 4096	3056 × 3056	1528 pixel × 1528 pixel
FOV	6.5° × 6.5°	14.1° × 14.1°	9.5° × 9.5°
Pixel scale of CCD	5.7″/pixel	16.6″/pixel	22.4″/pixel
Angle observation noise	2.4″	5.9″	3″
Detectability	16.5 mag	10.5 mag	15 mag

).

The Changchun Observatory set up an electrical–optical array (EA) telescope for observing LEO objects and GEO objects at the astronomical observation base in Jilin Province in 2017. The “mini” EA for observing LEO objects consists of eight small telescopes, each with an aperture of 15 cm and a focal length of 15 cm. The system also includes 8 cameras with 3 × 3 K resolution, 8 image processing computers, 1 GPS clock, an electronic control system, an image acquisition and processing system, etc. The monitored sky area is up to 1590 square degrees, mainly observing space debris with elevation angles from 18 to 32 degrees in the sky area with diameters ranging from 0.5 to 1 m.

The optical telescopes used for observing space debris in GEO orbit are part of an all-sky rotatable array, which is designed for observing space debris. The array consists of four 280 mm optical telescopes and two T-frame structure equatorial instruments, with an average error of 0.9” in the right ascension direction and 1” in the declination direction in terms of tracking measurement accuracy. With the same design parameters, the four telescopes can significantly expand the sky area, covering 160 square degrees, and detect objects with brightnesses between 16 and 20 magnitude.

At the end of 2017, SAO developed the FocusGEO, an EA with a large FOV dedicated to detecting GEO objects, which consists of three 0.18/0.22 m refracting optical cylinders, forming a large rectangular FOV of 9.5° × 28.5°, and can scan the GEO belt of about 3200 square degrees above the observatory in 15 min. The angle observations by the FocusGEO telescope at the Lijiang Observatory of the Yunnan Astronomical Observatory show that the telescope can observe nearly 380 GEO space objects over the station during non-full-moon clear nights. The observational capabilities of FocusGEO surpass 90% for the objects in GEO orbit that are cataloged in the NORAD catalog. With an exposure of 5 s, the telescope can detect GEO objects of 15 magnitude with a precision of about 3″ in azimuth and pitch.

2.2. The Improvement of the RS IOD Method and the Association Method

2.2.1. The Improvement of the RS IOD Method

The IOD orbit is determined using the range-searching (RS) method, and the basic process of the range-searching method is as follows [14]. Suppose that the angular observations of a space object are obtained at moments $t_1,t_2$,⋯, $t_n,$ right ascension ${RA}_1,{RA}_2,\dots ,{RA}_n$ and decimal declination ${Dec}_1$,${Dec}_2$,⋯,${Dec}_n$, respectively. The unit vector $L_i$ (i = 1, 2,⋯, n) of the direction from the station to the space object (i.e., the telescope line of sight direction) can be obtained by the following equation,

$$\left\{\begin{array}{l}{Lx}_i=\cos \left(De{c}_i\right)\cos \left(R{A}_i\right)\\ {Ly}_i=\cos \left(De{c}_i\right)\sin \left(R{A}_i\right)\\ {Lz}_i=\sin \left(De{c}_i\right)\end{array}\right.$$

(1)

${Lx}_i,{Ly}_i,{Lz}_i$ are three components of the coordinates of three directions.

With ${\rho }_1 \mathrm{a}\mathrm{n}\mathrm{d} { \rho }_n$, denoting the observed distances at moments $r_1 \mathrm{a}\mathrm{n}\mathrm{d} { r}_n$, respectively, and $R_i$ representing the position vector of the observing station, if we know ${\rho }_{1 } \mathrm{a}\mathrm{n}\mathrm{d} {\rho }_n$, we can get two position vectors $r_1 \mathrm{a}\mathrm{n}\mathrm{d} r_n$ based on $r_i=R_i+{\rho }_i{L}_i$ (i = 1, n), so that the purely angular IOD problem is converted into an orbit-determination problem based on two position vectors, which is the so-called IOD Lambert problem (the orbital parameters are calculated using the position vectors of the two moments). The Lambert problem is well known in dynamical astronomy, celestial mechanics, and astrodynamics communities for objects governed by Keplerian dynamics [19]. The classical methods can be used to solve the standard Lambert problem given two positions, such as the Gibbs method or the Herrick–Gibbs method [20,21]. If the values of ${\rho }_1 \mathrm{a}\mathrm{n}\mathrm{d} {\rho }_n$ are set to a fixed step-size sequence within a specified range, each combination of observations can be used to compute a set of orbital parameters. Subsequently, the calculated angular observations at other moments are compared with the actual observations and judged based on the residuals. This helps to eliminate the erroneous track determination results and narrows down the options to the most likely ones. Finally, the optimal solution is selected based on constraints, such as the semimajor axis (SMA) and eccentricity, within the bounds set by the limitations of the space environment. The original specific implementation process can be referred to in [22].

To improve the success rate and accuracy of IOD, the RS method is modified through the following steps.

Firstly, as many combinations of observations as possible are made over the longest possible epoch range. Since observation errors vary across different epochs, the observations at different epochs can lead to different combinations and result in different potential orbit elements. The greater the number of combinations, the higher the success rate. The iteration steps are outlined in the following pseudocode (Algorithm 1):

Algorithm 1: The iteration steps of IOD computation.

For i = 1, 2, 3, n/2, i = i + step (default 1), n is the epoch number.         For j = 2/n,n, j = j + step (default 1)                 Determine the used observations $\left({{RA}_i,Dec}_i\right)$ and $\left({{RA}_j,Dec}_j\right)$. Observations at the other epochs of the current arc are used as a discriminator.                 Solving the Lambert problem to get a set of orbit elements. If the residuals are less than the threshold preset, that means a possible solution. Then, a set of elements is added to the result sum.         End End

Secondly, to improve the accuracy of the IOD elements, the key is the accuracy of the distance. The distance is estimated and used to compute the elements again; then, a new set of orbital elements is achieved. As a possible result, it may eventually replace the previous one. A simulation test is implemented to show the influence of the observed distance on the accuracy of IOD solution elements. So, if the distance is error free or with very limited errors, the IOD elements’ accuracy is limited.

The previous method was stable, but the step length had an impact on the orbit solutions. To enhance the accuracy, the new method features a dynamic step-length adjustment based on the varying thresholds of the observation residuals and the corresponding step length. This ensures that the solution is optimized, and the accuracy is improved. The computation process is divided into two modes, the normal mode and the refining mode. There are two sets of thresholds for the two modes, respectively.

The used threshold values ${thres}_{used}$ of observation residual ${res}_i$ are set as follows,

$${thres}_{used}=\left\{\begin{array}{l}\mathrm{n}\mathrm{e}\mathrm{x}\mathrm{t}\hspace{0.25em}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left( \mathrm{if} re{s}_i>{thres}_{normal}\right)\\ {thres}_{normal}, \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left( \mathrm{if} re{s}_i<{thres}_{normal} \mathrm{and} re{s}_i>{thres}_{refine}\right)\\ {thres}_{refine},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left( \mathrm{if} re{s}_i<{thres}_{refine}\right)\end{array}\right.$$

(2)

${thres}_{normal}$ is the residual threshold at the normal mode, and ${thres}_{refine}$ is the residual threshold at the refining mode. The ${thres}_{refine}$ is set to be $thre{s}_{refine}=coefficient\times {thres}_{normal}$; the coefficient is a fraction less than one and is usually set to 0.5.

The used step length $ste{p}_{used}$ are set as follows,

$${step}_{used}=\left\{\begin{array}{l}ste{p}_{normal},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left( \mathrm{if} re{s}_i>ob{s}_{normal}\right)\\ ste{p}_{normal},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left( \mathrm{if} re{s}_i<ob{s}_{normal} \mathrm{and} re{s}_i>ob{s}_{refine}\right)\\ {step}_{refine},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left( \mathrm{if} re{s}_i<ob{s}_{refine}\right)\end{array}\right.$$

(3)

$ste{p}_{normal}$ is the step length at normal mode and $ste{p}_{refine}$, means the step length at refining mode.

We can determine the values of the used threshold and step by following the steps. First, set the value of two normal thresholds based on experience, and set ${thres}_{used}={thres}_{normal}$ and ${obs}_{used}={obs}_{nomral}$. Second, for the $i^{th}$ combination of observations, compute orbit element sets, and the observed residuals $re{s}_i$ are calculated by orbital propagation. Third, the step length and the threshold used at ${\left(i+1\right)}^{th}$ depend on the ${res}_i$ and are computed according to the above two Equations (2) and (3).

The aforementioned thresholds and steps in both the normal and refining modes are critical to the search success rate, IOD precision, and effectiveness. However, these values are not usually fixed and must be determined through extensive experiments for different scenarios. For example, they can be obtained from ground-based and space-based surveillance simulations and data-processing experiences.

2.2.2. The Association Method

The geometrical method is used for the correlation of the initial orbital elements, the core step of this correlation algorithm, and the specific implementation process can be referred to [14]. The association technique is founded on the fact that the error of SMA accumulates to produce an along-track bias at the midpoint between two propagated positions, which are estimated from two IOD solutions. By iteratively modifying the SMAs of these solutions until the errors in the SMAs are of equal magnitude but opposite signs, the along-track bias at the midpoint approaches zero if the two orbit-determination solutions pertain to the same object.

The core ideas of the initial track-association method used in this paper are as follows.

(1)

Determine the two sets of initial orbit elements for conducting the association;

(2)

The two tracks are propagated to the intermediate moments of the two by using the analytical method of orbit propagation. This allows for the correlation of the two tracks;

(3)

After propagation, the differences between the two initial tracks are calculated in the along-track, cross-track, and radial directions (ACR). The semimajor axis (SMA) of the two initial tracks is then adjusted based on the differences in the along-track direction. The tracks are repropagated, and the differences in the ACR directions of the two initial tracks are recalculated;

(4)

The final ACR difference is judged after applying multiple corrections in succession, and, if it is less than the preset threshold, the two tracks are considered to be from the same object. Otherwise, they are from different objects.

3. Results

3.1. IOD of Arcs from LEO Objects

First, the ground-based optical–electrical array observations from Changchun Observatory were used for TLE matching to identify the known objects. TLE data are public. The results are shown in

Table 2. Number of the identified space objects and the arcs.

Date	Number of the Arcs	Number of Arcs from Known Objects	Rate	Number of Known Objects
24 August 2017	4100	3458	84.34%	1299
25 August 2017	1626	1396	85.85%	594
26 August 2017	4894	4163	85.06%	1587

, where about 85% of the arc segments were from known objects. The average arc length of the observed data is about 39 s.

The errors are estimated from the TLE of the known debris. TLE can be regarded as a reference or true orbit for the IOD elements, and it is more precise than IOD elements. So, the IOD errors can be calculated by comparing the TLE orbit and the IOD elements at a common epoch for space debris. Then, the IOD elements are estimated, and the initial orbit results of the LEO objects are shown in

Table 3. IOD results of space debris in LEO.

Errors of SMA	Number	Rate
<100 km	6752	90.17%
<50 km	6099	81.45%
<30 km	5150	68.78%
<20 km	4088	54.59%
<10 km	2294	30.64%
<5 km	1143	15.26%

, which contains the initial orbit-determination success rate and the SMA errors. A set of 7488 orbits was used, and the success rate of initial orbit determination was about 95.6%, higher than the previous success rate in [14]. Finally, the initial orbit correlation was performed, and the correct rate of initial orbit correlation was about 89%.

3.2. IOD of Arcs from GEO Objects

3.2.1. Changchun GEO EA

In this paper, the test is carried out using observation data from 6–10 February 2021. The arc length distribution of the observation data is shown in Figure 3. The arcs are matched with the TLE to identify the cataloged objects. The TLE data were downloaded from www.space-track.org, (accessed on 7 February 2023). The matching results are shown in

Table 4. The matching result between the arc observation and TLE.

Date	Number of Arcs	Number of Matched Arcs	Rate (%)
6 February 2021	25,714	17,369	67.50
7 February 2021	15,513	11,302	72.86
8 February 2021	14,250	10,960	76.91
9 February 2021	11,976	9355	78.11
10 February 2021	16,709	12,734	76.20
Mean	16,832	12,344	74.32

, with approximately 74.3% of the arc segments being known objects. Based on the data and the results of the TLE matching, the number of observed arcs for each object can be analyzed, and the statistical results are shown in Figure 3, where it can be found that the number of observed arcs for most objects is no more than 100.

Some of the known observation arcs were selected for IOD, and the relationship between the IOD success rate and arc length was initially analyzed. The arc length of GEO object data was longer than 30 s, and the average arc length was about 77.4 s, with a total number of 1602 successful IODs and a success rate of 87.84%. For the observations in which the TLE was matched successfully, the TLE was used to evaluate the initial orbit parameter errors, using the SMA and inclination as examples, and the results are shown in

Table 5. The statistics for the IOD SMA errors of space objects in GEO.

Errors of SMA	Count	Rate
<100 km	962	70.58%
<50 km	743	54.51%
<30 km	546	40.06%
<10 km	232	17.02%

and

Table 6. The statistics for the IOD inclination errors of space objects in GEO.

Error (Deg)	Count	Rate
<1	523	97.03%
<0.5	515	95.55%
<0.2	488	90.54%
<0.1	444	82.37%

. According to Table 5, it can be found that 40% of the total SMA errors are less than 30 km, and about 71% of them are less than 100 km. According to Table 6, it can be found that 82% of the inclination errors are less than 0.1 (the total number of IODs is 539).

When the time interval is less than 36 h, the correlation rate of arcs of the same object is about 89%. During the data processing, some problems were found. Further preprocessing was needed, such as the duplication of data between observation files or failure to correlate consecutively observed arc segments of the same object, splitting into two or more files. The statistics revealed that many of the observation arcs for a given object had small intervals between them or even overlapped.

3.2.2. FocusGEO

The data were observed on 20, 22, and 23 October 2019, and 5002, 5093, and 4086 arcs were obtained from each day. Then the arcs are tried to match with the TLE data and the IOD elements are computed. The results are shown in

Table 7. The statistical errors of IOD SMA, eccentricity, and inclination of observations observed by FocusGEO.

SMA Error (km)	Rate (%)	Eccentricity Errors	Rate (%)	Inclination Errors (Deg)	Rate (%)
<5	4.12	<0.0001	21.70	<0.01	11.26
<10	8.24	<0.0005	47.80	<0.03	31.32
<30	21.15	<0.001	53.02	<0.05	40.66
<50	33.24	<0.005	82.42	<0.1	64.29
<100	55.49	<0.01	97.53	<0.2	83.79

and Figure 4.

Selected for calculation were 881 arcs containing 9 or 10 data points from the observation file of 20 October 2019, and the arc lengths were all about 53 s. There were 868 arcs with successful orbit computations, and the success rate was 98.52%. The TLE data were used to evaluate the initial orbit errors, and the results are shown in Table 7. The corresponding error distributions of SMA, eccentricity, and inclination errors are shown in Figure 4. It can be found that over 55% of the IOD SMA errors are less than 100 km for GEO objects and about 53% of all the IOD eccentricity errors are smaller than 0.001.

As to the IOD success rate, the rate of Changchun GEO is higher than that of FocusGEO. The reason should be that the average arc length is different. The average length of the former is about 77 s but the average length of the latter is about only 53 s. This is also the reason for the worse result of the IOD elements solution.

3.3. IOD of Observations of Space Debris Related to the COSMOS 1408 Satellite

3.3.1. Background

Space events are happening with increasing frequency, such as the breakup events of the YunHai 1-02(2019-063A, NORADID 44547), the NOAA 17(2002-032A, NORAID 27453), the ASAT 1408 in 2021, and the American GEO satellite Galaxy 11 (1999-071A, NORADID 26038) in 2022 (from ISON). The antisatellite incident had the biggest impact. On 15 November 2021, at 10:47 p.m. Beijing time, Russia conducted an antisatellite test (ASAT) that destroyed the COSMOS 1408 satellite. The satellite, a former Soviet satellite, was launched in 1982 with NORAD ID 13552. The orbit of Cosmos 1408 prior to the ASAT test had an altitude of 490 × 465 km. It is estimated that more than 1500 trackable pieces of space debris, as well as countless smaller pieces, were generated from the ASAT event. This posed a threat to the security of space assets of countries around the world. The debris number evolution and the occurred operations are shown in Figure 5.

As of 26 May 2022, 900 pieces of debris from this antisatellite event, with a cataloged target of 1740, have fallen, and 818 will fall in the next 3 years (SATEVO). The estimated in-orbit times of debris of different sizes generated by antisatellite events in NASA’s Space Debris Quarterly Report are shown in Figure 6. Based on the TLE from http://celestrak.org, (accessed on 7 February 2023), the number of pieces of space debris created in this ASAT event is 260 on 12 February 2023.

3.3.2. IOD of Unmatched Arcs of Space Objects

First, the observation data is tried to match with TLE to judge whether the observation arc is from a new object or a cataloged object. The SMA, eccentricity, and inclination of the COSMOS 1408 satellite orbit are 6,862,203.9 m, 0.00285, and 82.57°, respectively.

For the part of the observation data of the past two days that cannot be successfully matched with the TLE, the IOD is carried out. Due to the approaching full moon, object imaging was affected to a certain extent, and the amount of data on 16 November was relatively small. Due to the weather, there were no observations on 17 November. In the initial orbit results, the orbit parameters whose SMA is between 6800–6950 km and the inclination angles between 75°–90° are screened out. Counting the results of three days, respectively, it was found that only the COSMOS 1408 satellites were in this interval on 14 November, and 64 and 9 initial orbits were in this interval on 15 November and 16 November, respectively. The orbit parameter distribution is shown in Figure 7.

The number of objects observed near the orbital altitude and inclination of the COSMOS 1408 satellite is analyzed. The observation arcs that have been successfully matched with the TLE object are excluded. According to Figure 7, before the event, there was no object in the related sky area on the night of 14 November. Following the incident, 64 objects appeared in the airspace on the night of 15 November, and 9 objects appeared on the night of 16 November. Therefore, the observations on the 15th–16th are likely to be debris generated by the COSMOS 1408 event. The 64 initial orbits were correlated. One pair was successfully correlated, and the orbit-determination results of the two arc segments showed that the inclination angle was about 82.33°.

Further analysis of the initial orbit results on 16 November shows that there are a large number of objects with an inclination angle of 53° and an SMA between 6880 km and 6950 km (Figure 8). It is noted that 53 Star-link satellites were launched by SpaceX at 12:40 (UTC) on 12 November 2021 before the ASAT event. But, the TLE of these satellites was not public at that time, so they failed to match with TLEs.

4. Discussion

Optical telescopes are important devices for monitoring space objects. Two key techniques for cataloging new objects using angle observation data are IOD and IOD correlation. In response to these two problems, this paper uses the improved range-searching (RS) algorithm and geometrical method to determine the initial orbital elements and conduct track correlation. The RS method is improved through the new computation modes with different threshold constraints proposed in this paper. They are so-called the “normal mode” and “refining mode”. Accordingly, to improve the accuracy of the method, the corresponding step length for range searching is designed also. Then, the RS method and the geometrical method are extended to the real observations at multistations for both LEO and GEO objects. The observations used in this study were obtained from the ground-based optical–electrical array (EA) of the Changchun Observatory of the Chinese Academy of Sciences and the Shanghai Astronomical Observatory. Observations of both LEO and GEO objects observed by these ground-based VSAs were utilized. The results show that the success rate of the IOD of the LEO object is about 91%, 81% of the initial orbit SMA errors are less than 50 km, and the correlation accuracy rate is about 89%; the success rate of the GEO object IOD is higher than 88%, 54% of the errors of the SMA of the initial orbit is less than 50 km, and the correlation accuracy rate is greater than 87%. The measured data-processing results show that the IOD and correlation algorithm in this paper is suitable for high and low-orbit space-object observation data.

Further, this paper briefly introduces Russia’s ASAT event that occurred on 15 November 2021, and analyzes the resulting debris orbit information. The preliminary results of identifying the new debris generated by COSMOS 1408 based on ground-based observation data in Changchun show that the correlation orbit-determination algorithm in this paper can be used to quickly discover new objects. For space objects in LEO, optical data can be used as a useful supplement to radar data, and the experimental results further demonstrate the potential of EA. Limited by certain conditions, this paper only conducts a preliminary analysis of COSMOS 1408-related fragments and more observation data will be used for further research in the future.