## 4 Orbit Association Methods  
Space-based optical space situational awareness systems offer several advantages, including a short detection wavelength, a large frame information capacity, and the ability to monitor multiple space targets. Currently, this kind of system has emerged as the mainstream solution for monitoring space target and has entered the experimental and application phases. In the development of space-based space situational awareness systems, one of the crucial technologies is predicting the orbits of identified space targets based on optical imaging results. This process, often referred to as orbit determination, serves as the core and foundation of space-based space situational awareness tasks [35]. Orbit determination can be categorized into batch processing and sequential processing, depending on specific processing methods [36]. It can also be classified into real-time tracking and post-event tracking based on processing timeliness. According to the orbit model used in the orbit determination process, orbit determination tasks can be classified into dynamic orbit determination, kinematic orbit determination, and reduced-dynamic orbit determination. In terms of processing steps, the orbit determination process involves orbit association, initial orbit determination (IOD), and orbit refinement (or precise orbit determination) [37]. In scenarios where optical observations are the sole source of information, obtaining direct measurements of the distance and velocity of space targets in relation to the observing platform is unattainable. Only information about the relative angles and angular velocities of the target's motion can be gathered. Before commencing the initial orbit determination, it is crucial to confirm, through orbit association, whether multiple observation results pertain to the same target [43]. The admissible region method is a classical approach for correlating diverse observation outcomes [44]. This method utilizes the mechanical principles governing the motion of space targets as constraint conditions, restricting the feasible range of distances and its change rate (equivalent to the orbital elements) from observation platforms to the target during angle-only measurement process. Subsequently, the orbital element of the target will be determined within the feasible range. Expanding upon the admissible region method, as shown in Table 2, [PERSON] et al. introduced an approach that integrates the gravity as a constraint on the the motion of the targets. Simultaneously they utilized the orbital altitudes of the targets as a constraint to construct the feasible domain of their motion. This method, grounded in the admissible region framework, successfully achieves the association of the observed short arcs of the space targets [45]. Following the principles laid out by [PERSON] et al., [PERSON] et al. proposed a recursive intersection method to address the problem of orbit association. This approach employs orbital mechanical energy, distance from Earth, and permissible ranges for perigee and apogee as constraints for feasible target orbital solutions. It calculates intersections of different orbital segments corresponding to multiple observations, and associates different observed orbit segments according to the existence of intersections associated with various observation results [46]. The recursive intersection method simplifies the orbital association process but requires manual screening and processing of results during implementation, making it unsuitable for associating large-scale orbital observation data. [PERSON] et al. mapped the feasible domain where the targets might exist to a 6D Poincare space, which is divided into multiple hypercubes. In the Poincare space, the density of virtual particles, representing the probability of the existence of the observed target in space, is distributed among different hypercubes. Bayesian theorem is then employed to achieve the association between different observation segments [47; 48; 49].