## 1 Introduction  
Satellite-based Positioning, Navigation, and Timing (PNT) is nowadays utilizing signals from satellites at various orbital heights, such as Geostationary Orbit (GEO), Medium Earth Orbits (MEOs), Inclined Geosynchronous Orbits (IGSOs), and Low Earth Orbits (LEOs). Among them, and benefiting from the low altitudes and the fast speeds of the LEO satellites, the feasibility of LEO/GNSS-integrated PNT services has been highlighted in recent years [1, 2, 3, 4, 5, 6, 7]. LEO satellites will serve as navigation satellites and be applied to fields such as unmanned driving and artificial intelligence to achieve precise, real-time, dynamic, and global PNT services. High-precision real-time LEO satellite products are indispensable for achieving single-receiver-based cm-level accuracy in LEO-augmented PNT services. The use of GNSS observations collected onboard LEO satellites has been reliably validated and utilized in LEO satellite Precise Orbit Determination (POD) and clock determination for many years [7; 8; 9; 10]. Research has shown that LEO orbit determination using dual-frequency, multi-constellation GNSS with a batch least-squares reduced-dynamic model can achieve RMS of about 1.5 cm in post-processing mode [8] and real-time LEO satellite POD with a latency of a few minutes could also be achieved with an Orbital User Range Error (OURE) of 2-4 cm [11]. The filter-based model was also studied for the LEO satellite POD [9]. Combined with dynamic models, sub-dm to dm accuracy can be achieved. Even without any dynamic model, filter-based kinematic LEO satellite POD can also achieve accuracy at a similar level [10]. Like the real-time LEO satellite POD, GNSS observations combined with a reduced dynamics model or kinematic model can also be used to determine the LEO satellite clocks in real-time. When employing batch least-squares adjustment in the reduced-dynamic model to determine LEO satellite clocks, near-real-time clock precision of approximately 0.15 ns can be attained when using high-quality GNSS real-time orbital and clock products [12]. Nonetheless, this entails a processing duration of roughly 5 min for a 24 h processing cycle with a 30 s sampling interval, even with a modern processing unit. In such a case, a clock prediction of at least 10 min is needed to catch up with the real-time applications. This introduces prediction loss of a few sub-nanoseconds due to the complicated systematic effects contained in the LEO satellite clock estimates [12; 13; 14]. LEO satellite clocks can be determined more efficiently in a filter-based manner, yet less precise compared to the Batch Least-Squares (BLS) processing. Using triple-frequency GPS/Galileo observations from Sentinel-6A and broadcast ephemerides, a 14-day continuous evaluation of actual flight data showed that a 0.9 ns real-time clock standard deviation can be achieved [15]. [PERSON] et al. have introduced and implemented a method for real-time determination of LEO satellite clocks [16]. This approach involves near-real-time clock determination combined with ultra-short-term clock prediction. It employs Kalman-filter-based processing but allows for restarts at predefined times, thereby preventing continuous bias propagation and accumulation from earlier epochs. Using dual-frequency, real observations from Sentinel-3B and real-time GNSS products from the National Center for Space Studies (CNES) in France [17], the near-real-time GNSS clocks have a precision of about 0.2-0.3 ns, then by predicting for a short period (up to 120 s), a real-time clock precision of about 0.3 ns was achieved [16]. Integrating ground observations from a simulated regional network with onboard GNSS observations was also studied, with a precision of about 0.15 ns in the post-processing mode [18].