## 1 Introduction  
Because geosynchronous orbit (GEO) satellites have the advantages of low propellant consumption required for operation, continuous signal coverage for fixed areas, and easy alignment with ground communication antennas, many countries have frequently deployed artificial satellites in GEO in recent years. The GEO space targets have become increasingly congested, and space target collisions have occurred on occasion. The debris created by the collisions poses a hazard to the space targets' safety. To avoid satellite collisions, it is critical to identify, locate, monitor, and categorize space targets [1, 2]. In order to achieve this goal, researchers have proposed the Space-Based Space Surveillance (SBSS) plan. This system has two significant advantages: one is the dynamic perception of space targets. The purpose of monitoring space objects is achieved by identifying, locating, and cataloguing space objects. The other is early warning. When space debris or abandoned aircraft threaten to collide with aircraft in normal operation, an early warning can be given in advance, and the threat can be avoided by controlling the aircraft to change the orbit altitude. The SBSS program was originally developed by the United States [3, 4]. The Midcourse Space Experiment (MSX) satellite, launched in 1996, was the first space-based surveillance satellite deployed by the United States. The satellite is in a sun-synchronous orbit (SSO) at an altitude of 800 km, and it is equipped with a space-based visible (SBV) sensor with a \(6.4^{\circ}\times 1.6^{\circ}\) field of view (FOV), which considerably enhances the sensor's revisit rate to critical targets and the capacity to detect and monitor artificial satellites [5, 6]. Following the successful test of the MSX satellite, the US launched the SBSS project in 2002, with the goal of improving real-time perception of the space warfare environment and establishing a space surveillance network (SSN). The first SBSS satellite, Block 10, was launched into a 630 km sun-synchronous low Earth orbit (LEO) in 2010 and began operations in 2013. The satellite was primarily used to monitor targets in geostationary Earth orbit (GEO)and can meet both measurement accuracy and wide-area search capability performance requirements [7]. [PERSON] and colleagues presented a strategy for space-based surveillance of space objects, particularly GEO targets, in 2011. The aim was to launch a satellite into an SSO with an orbital altitude of 800 km, with a sensor with a field of view of \(6^{\circ}\times 6^{\circ}\). This spacecraft can cover all controlled GEO satellites in one day, but it takes 1.5 to 3 days to cover uncontrolled GEO satellites and space debris [8]. Sapphire, Canada's first military satellite, was successfully launched in 2013. The satellite operates in a dawn-dusk sun-synchronous orbit (DDSSO) at an altitude of 786 km. The satellite contains a payload with an FOV of \(1.4^{\circ}\times 1.4^{\circ}\) that is primarily used to identify medium- and high-orbit space debris from low orbit, and it will eventually join the US SSN. In 2013, Canada launched the NEOSS satellite at the same time. The optical system has an FOV of \(0.85^{\circ}\times 0.85^{\circ}\) and an aperture of 15 cm [9]. Researchers at the Lincoln Laboratory in the United States have also pushed for more research into the space-based observation method of observing GEO targets from LEO satellites [1; 10]. They originally presented a GEO belt-based pinch point (PP) area observation mode, which uses the LEO satellite's narrow FOV sensor to scan a tiny region of the GEO belt and achieves high detection effectiveness for most GEO objects [11]. Following that, [PERSON] et al. presented an observation mode of the Earth's shadow edge, which can accomplish the observation goal by controlling the sensor on the DDSSO satellite to always point to a certain area of the Earth's shadow edge [12]. The European Space Agency (ESA) proposed a \"leak-proof fence\" architecture for viewing GEO targets in 2014 [13].