Stochastic Models of Very High-Rate (50 Hz) GPS/BeiDou Code and Phase Observations

In recent years, very high-rate (10–50 Hz) Global Navigation Satellite System (GNSS) has gained a rapid development and has been widely applied in seismology, natural hazard early warning system and structural monitoring. However, existing studies on stochastic models of GNSS observations are limited to sampling rates not higher than 1 Hz. To support very high-rate GNSS applications, we assess the precisions, cross correlations and time correlations of very high-rate (50 Hz) Global Positioning System (GPS)/BeiDou code and phase observations. The method of least-squares variance component estimation is applied with the geometry-based functional model using the GNSS single-differenced observations. The real-data experimental results show that the precisions are elevation-dependent at satellite elevation angles below 40◦ and nearly constant at satellite elevation angles above 40◦. The precisions of undifferenced observations are presented, exhibiting different patterns for different observation types and satellites, especially for BeiDou because different types of satellites are involved. GPS and BeiDou have comparable precisions at high satellite elevation angles, reaching 0.91–1.26 mm and 0.13–0.17 m for phase and code, respectively, while, at low satellite elevation angles, GPS precisions are generally lower than BeiDou ones. The cross correlation between dual-frequency phase is very significant, with the coefficients of 0.773 and 0.927 for GPS and BeiDou, respectively. The cross correlation between dual-frequency code is much less significant, and no correlation can be found between phase and code. Time correlations exist for GPS/BeiDou phase and code at time lags within 1 s. At very small time lags of 0.02–0.12 s, time correlations of 0.041–0.293 and 0.858–0.945 can be observed for phase and code observations, respectively, indicating that the correlations in time should be taken into account in very high-rate applications.