## 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 hasperformed 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\({}^{\circ}\). 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. Figure 1: Number of space objects since 1957 [11]. 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; [PERSON]. [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.