## 1 Introduction  
Time information plays a crucial role in many industries, such as power systems, financial systems, intelligent transportation, and military applications. There are currently various methods for time transfer, such as satellite two-way satellite time and frequency comparison technology (TWSTFT), fiber-optic time transfer technology, and GNSS technology [1, 2]. The TWSTFT method cannot be widely applied due to its expensive terminals. In addition, the application range of fiber optic time synchronization is also limited due to the high cost issue. Compared to the aforementioned methods, GNSS has its own unique advantages. The cost of time transfer using GNSS is lower, and it is more convenient to use GNSS for time transfer. More importantly, the current GNSS technology has been officially adopted by the BIPM for international UTC (Coordinated Universal Time) time comparisons [3; 4; 5]. As satellite navigation systems advance at a breakneck pace, time transfer applications based on GNSS satellites have become one of the widely used timing methods [6; 7]. The original GNSS time transfer technology used the common view (CV) time transfer technique, but because the CV time transfer technique requires simultaneous observation of the same satellite, it is limited by distance [8]. With the provision of precise satellite orbit and clock offset products by the IGS (International GNSS Service), scholars have further developed the all-in-view (AV) time transfer technology. This technology is not limited by distance and can achieve the same level of time transfer accuracy as CV [9]. Nevertheless, the aforementioned time transfer methodologies are constrained by the precision of GNSS pseudorange measurements. Given that the accuracy of GNSS carrier phase observations surpasses that of pseudorange observations by a factor of two, researchers have subsequently refined the technology for precise point positioning (PPP) time transfer [5; 6; 7; 10]. Within the recent past, the research domain of PPP time transfer has experienced substantial growth and refinement. The evolution has been notable, moving from the confines of single-system PPP time transfer to the broader capabilities of multi-system synchronization [11; 12; 13]. Additionally, it has advanced from the limitations of single-frequency measurements to the more nuanced accuracy afforded by multi-frequency PPP time transfer [14; 15; 16]. Most notably, the shift from the float solution to the fixed solution in PPP time transfer [17; 18] has marked a significant leap in precision and reliability. The research has evolved from estimating receiver clock errors using white noise estimation to parameter estimation using a clock model for receiver clock errors [6; 19; 20]. Yet, the studies on PPP time transfer previously mentioned have largely been centered around international UTC evaluations and post-processing time transfer endeavors. With the rapid development of society, users' demands for real-time performance are increasing, making the research on real-time PPP time transfer an urgent priority. Thankfully, the landscape of real-time PPP time transfer has seen significant progress since 2013, with the International GNSS Service (IGS) making real-time data streams readily available. This development has catalyzed scholarly exploration into the capabilities of real-time PPP, leading to groundbreaking achievements in accuracy. Researchers have now mastered the art of real-time PPP time transfer, attaining a level of precision that is astonishingly within the sub-nanosecond realm [21]. Subsequently, based on the real-time PPP time transfer method, scholars have calculated the real-time clock differences to UTC(k) time or GNSS time and broadcasted them to users. After receiving these real-time satellite orbit and clock difference products, users can utilize the PPP algorithm to achieve one-way precise time synchronization [22; 23]. Their results indicate that real-time one-way PPP timing can achieve timing accuracy better than 0.5 nanoseconds. [PERSON] et al.