BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for the BDS-2 and BDS-3 default civil service signals (B1I/B3I) and the increase of new signals (B1C/B2a) for BDS-3, a systemically bias exists in the receiver-end when receiving and processing BDS-2 and BDS-3 signals, which leads to the inter-system bias (ISB) between BDS-2 and BDS-3 on the receiver side. To fully utilize BDS, the BDS-2 and BDS-3 combined precise time and frequency transfer are investigated considering the effect of the ISB. Four kinds of ISB stochastic models are presented, which are ignoring ISB (ISB_NO), estimating ISB as random constant (ISB_CV), random walk process (ISB_RW), and white noise process (ISB_WN). The results demonstrate that the datum of receiver clock offsets can be unified and the ISB deduced datum confusion can be avoided by estimating the ISB. The ISB_CV and ISB_RW models are superior to ISB_WN. For the BDS-2 and BDS-3 combined precise time and frequency transfer using ISB_NO, ISB_CV, ISB_RW, and ISB_WN, the stability of clock differences of old signals can be enhanced by 20.18%, 23.89%, 23.96%, and 11.46% over BDS-2-only, respectively. For new signals, the enhancements are −50.77%, 20.22%, 17.53%, and −3.69%, respectively. Moreover, ISB_CV and ISB_RW models have the better frequency transfer stability. Consequently, we recommended the optimal ISB_CV or suboptimal ISB_RW model for BDS-2 and BDS-3 combined precise time and frequency transfer when processing the old as well as the new signals.

Currently, there are more Global Navigation Satellite System (GNSS) signals available for civilians. Many types of GNSS receivers have been updated and several new receivers have been developed for new signals. To know about the performance of these signals and receivers and their stochastic model for data processing, in this study, the data quality of all GNSS signals, especially the new signals are analyzed, and two modified stochastic models with observation noise statistics (STA) and post-fit residuals (RES) are formed. The results show that for all the new signals, the corresponding carrier phase noise is at the same level as other old signals. The pseudorange noise of B2a, L5, E5a, and E5b is within 4 cm and significantly smaller than other signals for receivers without a smooth algorithm, and the multipath error of these signals is about 0.1 m which is also better than other signals. For B1C, the pseudorange multipath error is about 0.4 m, which is close to L1 and E1. Stochastic models are validated for precise orbit determination (POD). Compared with the empirical stochastic model (EMP), both modified models are helpful to reduce the mean unit weight square error and obtain high accuracy orbits with reduced iteration. The 3D orbit accuracy improvement can reach 0.27 cm (7%) for the STA model, and 0.40 cm (10%) for the RES model when compared with the final products from the international GNSS service (IGS). For BDS-3 POD by using B1C and B2a observations, the improvements in the 3D orbit consistency of two adjacent three-day solutions are 0.21 cm (3%) for the STA model and 0.29 cm (4%) for the RES model. In addition, the STA model based on the observation noise of globally distributed stations is less affected by stations with problematic observations and with reduced computation burden.