Impact of ISB stochastic models on LEO satellite clock estimation with onboard multi-GNSS observations

High precision of real-time (RT) low Earth orbit (LEO) satellite clocks is crucial for enabling future LEO-enhanced positioning, navigation, and timing services. For filter-based RT processing, multi-GNSS observations from onboard LEO satellites can strengthen the observation model and improve the LEO precise orbit determination, but have limited improvement effect on the clock estimation. The time references for RT GNSS clocks of different constellations (even from the same analysis center) are different and vary with time. This requires estimating constellation-wise LEO satellite clocks or time-varying inter-system biases (ISBs). This contribution investigates multi-GNSS LEO satellite clock and the corresponding signal-in-space ranging errors (SISRE) using GPS/Galileo observations collected onboard Sentinel-6A satellite, and GNSS products from various analysis centers with different latencies, including the Centre National d'Etudes Spatiales real-time (RT), the GeoForschungsZentrum Multi-GNSS Experimental (MGEX) rapid, the European Space Agency MGEX final, and the Wuhan University MGEX final products. Three ISB stochastic models were implemented, i.e. the constant, the random walk, and the white noise models. Results show that the ISB estimates exhibit systematic effects of orbital periods (ca. 1.85 h) when applying the random walk or white noise models using the post-processing products. The white noise model shows the best performance when applying the RT GNSS products with large time-varying differences in the constellation-wise time references, with improvements of about 40.8% and 12.5% for clock precision, and about 38.1% and 7.9% for SISRE, respectively, compared to the constant and random walk models. When using the post-processing products with very similar time references for different constellations, the three ISB stochastic models do not deliver significant differences in clock precision and SISRE. This contribution provides a reference for ISB estimation strategy when using multi-constellation GNSS measurements to estimate RT LEO satellite clocks.