## 1 Introduction  
Laser Time Transfer (LTT) is a technique based on [PERSON]'s clock synchronization approach that synchronizes time between two distant clocks using laser pulses in space. This technique allows for high-precision time transfer with an accuracy of tens of picoseconds [1], significantly enhancing the fields of deep space exploration, astronomy, space geodesy, and timing systems [2]. LTT has been shown to be reliable and precise when compared to previous radio technology-based time transfer methods such as GNSS co-visibility observation, microwave technology, and two-way satellite time-frequency transmission [3]. Since the 1970s and 1980s, significant advancements in laser ranging and time-frequency measurement technologies have spurred numerous international experiments for long-distance clock time comparison and prompted research on laser time comparison. In 1988, the Laser Synchronization from Stationary Orbit (LASSO) program conducted the pioneering international experiment for star-earth time transfer [4]. In 2007, China's Bei-Dou navigation satellite system executed star-ground laser time difference comparison experiments at the Changchun station, involving a test star orbiting at approximately 21,000 km altitude. Subsequently, in 2013, the system successfully performed the initial laser time comparison test for 36,000 km inclined orbit synchronous navigation satellites [5]. The implementation of time transmission via laser connection, exemplified by the T2L2 payload developed collaboratively by the CNES and OCA of France, commenced with the successful launch aboard the Jason-2 satellite in 2008 [6]. T2L2, a subsequent mission to LASSO [5] and part of the experimental equipment onboard the Jason-2 mission [7; 8; 9], conducted 1155 time transfer experiments during the satellite's flight at 1336 km, including 650 common-view comparison laps [10]. The current state-of-the-art for ground-to-space laser time-transfer is the Time-Transfer by Laser Link (T2L2) [11]. Extensive data processing confirmed the T2L2 approach's accuracy of 100 picoseconds and stability of more than 1 picosecond over 1000 s [12]. Moreover, an increasing number of NEO (Near-Earth Orbit) satellites will integrate onboard clocks [13], while the establishment of LEO-MEO (Low Earth Orbit--Medium Earth Orbit) constellations will facilitate bidirectional laser connections [14]. Groundspace time transfer is a crucial process for synchronizing clocks between distant ground and satellite locations using laser time transfer links. This involves exchanging timing information between space instruments and ground-based laser stations. Each ground station utilizes multiple ground-to-space links to compare time synchronization between two laser stations. The ground-to-space transmission involves emitting laser pulses from the laser station towards the satellite, with a series of mirrors on the satellite reflecting a portion of these light pulses back to the ground station. Ground-to-ground time transmission occurs in two modes: non-common-view and common-view. The visibility of the satellite greatly impacts the success of laser time transmission [10]. In the common-view mode, ground laser stations observe satellites simultaneously. However, in non-common-view scenarios, the observation methods are different. Operating in the common-view mode involves stimulating the space oscillator solely during the laser pulse, which typically lasts a few seconds. This longer time interval under common-view mode helps to synchronize noise patterns between observatories, reducing discrepancies and eliminating errors caused by satellite clock inaccuracies and atmospheric delays, resulting in high precision and accuracy [15]. However, when a satellite is not visible, accounting for noise from the space oscillator becomes essential. In the non-common-view mode, this noise can cause significant interference.