## 1 Introduction  
More than 16 countries worldwide have developed and implemented earthquake early warning (EEW) systems, with some systems already providing warnings to the public, while others are still in testing phases. Japan was a pioneer in the 1960s with the development of the UrEDAS system based on traditional seismology, which was put into operation in 1992 and performed well for small to medium-sized earthquakes. However, the system struggled with accurate magnitude estimation for large earthquakes (Mw > 7.0), as demonstrated during the Mw 9.0 earthquake in 2011, where UrEDAS's preliminary magnitude estimates were significantly lower than the actual magnitude, leading to delays in defensive measures. Recent research indicates that incorporating GPS stations can substantially enhance the accuracy and timeliness of earthquake warnings for large events. Co-seismic displacement is a crucial prerequisite for estimating earthquake magnitude. Accurate co-seismic displacement is key to determining focal depth, epicenter location, and magnitude, significantly enhancing the accuracy and timeliness of earthquake early warnings. In traditional earthquake monitoring, the observed values from strong-motion (SM) seismometers are acceleration data, which have the advantage of not being constrained by amplitude in near-field conditions. However, during large earthquakes, these instruments can be affected by ground motion, leading to tilting and rotation, which causes baseline drift [1; 2; 3]. Therefore, [PERSON] and others found that the displacement calculated by double integration of acceleration includes short-term white noise and long-term disturbances, making it difficult to ensure the reliability of the data. [4; 5]. Although many empirical baseline correction methods have been proposed to remove deviations, the processed signals still cannot accurately capture the permanent displacement of the measurement station [6]. And it is difficult to ensure timeliness. For instance, relying on SM (strong motion) measurements, the initial warning during the Mw 9.0 Great East Japan Earthquake on 11 March 2011 was issued a mere 25.8 s post-quake, citing a magnitude of 7.2. This estimate was subsequently revised to 8.1 two minutes later, and it took a further three hours for the magnitude to be refined to Mw 8.8. Compared to the final determination of Mw 9.0 by the Japan Meteorological Agency, the magnitude was significantly underestimated, which consequently led to a delayed deployment of appropriate defensive measures. In contrast, [PERSON] et al. used SM sensors and GPS for early warning. The SM sensor detected anomalies 15 s after the quake, while the GPS detected the event after the S-wave arrived, but it estimated the magnitude as Mw 8.9 just two minutes later, showing the reliability and timeliness of using GPS data for magnitude estimation in major earthquakes [7]. In some areas, GPS signals can be obstructed by physical barriers, which affects data quality. Additionally, there may be a brief delay in GPS systems following an earthquake, as it takes time for GPS satellites and receivers to process and transmit data. Global navigation satellite systems (GNSSs), by integrating multiple satellite systems, enhance global coverage and positioning accuracy. They also excel in real-time data processing, providing more timely positioning information, which is particularly important for earthquake monitoring and early warning systems [8; 9; 10; 11]. To address the above issues, high-rate GNSS technology is being employed for monitoring crustal deformation. With the refinement of GNSS-related hardware performance and GNSS observation processing methods, especially for the maturity of single-epoch instantaneous positioning technology, GNSS seismology has gradually extended from long-term continuous static displacement estimation to short-term dynamic motion monitoring [12; 13; 14].