Stochastic modeling of BDS2/3 observations with application to RTD/RTK positioning

The Chinese BeiDou navigation satellite system (BDS) is gradually transitioning from a regional system (BDS2) to a global system (BDS3) to provide its positioning, navigation and timing (PNT) services to users worldwide. Real-time differencing (RTD) and real-time kinematic (RTK) positioning play important roles in the applications of BDS, and the optimal performance of these two techniques relies upon the proper choice of stochastic model. In this paper, the least-squares variance component estimation (LS-VCE) method is adopted to establish a realistic stochastic model considering the elevation-dependent precision, cross-correlation and time correlation for BDS2/3 observations collected in zero and short baselines. The factors affecting the stochastic model, including the receiver multipath mitigation technique and antenna type, are investigated. The results show that BDS3 B1C and B2a observations possess relatively high precision among all observations collected in the zero baseline, which may be attributed to the advanced signal structure and modulation technique, whereas this superior performance is absent in the short baseline due to the presence of multipath effects. A positive correlation of approximately 0.8 is found between BDS3 B1I and B3I phase observations, and similar correlations exist between BDS2 phase observations. The time correlations are weakened when applying the multipath mitigation technique, and the stochastic characteristics of observations are specific to the type of antenna. The BDS3-only RTD/RTK positioning precision with our established stochastic model is comparable to the BDS2-only positioning precision, and the BDS2 + BDS3 RTD/RTK positioning precision is improved by 40% to 65% with respect to the BDS2-only case.