Improved short-term stability for real-time GNSS satellite clock estimation with clock model

As a basic service of global navigation satellite system (GNSS), the timing technique tends to be processed based on precise point positioning (PPP) with the advantages of convenience and high-precision combined. The increasing demand for real-time PPP promotes the development of real-time satellite clock estimation. In real-time satellite clock estimation, the phase white noise model is widely adopted. Nevertheless, the white noise may mask the short-term characteristic of satellite atomic clocks, thus affecting the performance of the timing service. Therefore, we developed a clock model to characterize atomic clocks for GPS, GLONASS, BDS, and Galileo satellites based on Hadamard deviation analysis of 90-week multi-GNSS final clock products generated from GeoForschungsZentrum (GFZ). The results suggest that GPS Block IIF/III, BDS-3, and Galileo clocks have relatively outstanding frequency stabilities. And for the product of these satellite clocks, the simulated real-time clock estimation indicates that the clock model can provide better stabilities than the white noise model and even GFZ final products. Moreover, the clock model can provide a short-term prediction service during the period of data interruption and accelerate the convergence of clock offsets once the data recovered in real-time applications. Finally, PPP one-way timing was performed with five MGEX stations linked with external time sources. When employing the clock products with the clock model, the average improvement rates in stabilities over intervals from 30 to 10,260 s are 59.8%, 68.2%, 74.7%, and 66.6% for GPS, GLONASS, BDS-3, and Galileo PPP one-way timing, respectively, in comparison with that of the white noise model.