An improved tightly coupled model for precise point positioning ambiguity resolution with the Joint BDS-2 and BDS-3

Rapid initialization is always challenging for precise point positioning ambiguity resolution (PPP-AR), and the tightly coupled (TC) models for multi-GNSS processing are generally regarded as an effective method. However, observable-specific biases exist in the BeiDou Navigation Satellite System (BDS)-2/3 observations, including signal distortion biases in the receiver-end, wide-lane (WL) inter-system phase biases and code inter-system biases, which inhibits the fusing processing and cannot take full advantages of BDS-2 and BDS-3. We derive the relationship between these biases and form an improved TC model to enable inter-BDS-2/BDS-3 PPP-AR on this basis. Based on 15-day BDS-2/BDS-3 data sets, we analyze the characteristics of BDS-2/BDS-3 observable-specific biases and further find that the proposed model can effectively handle them. On the server side, we demonstrate that the improved TC model performs optimally by assessing the performance of phase bias estimation. The proportion of WL ambiguity residuals within ± 0.1 cycles can remain roughly 92% with improvements of 44% and 14-day WL phase bias STDs for BDS can be declined to 0.009 cycles with significant improvements of beyond 72%. Regarding PPP-AR on the user side, the improved TC model can significantly improve positioning performance relative to the loosely coupled model, especially for kinematic solutions. Convergence time in the east, north and up components decreases by 32%, 24% and 19%, and reaches around 18.1, 13.5 and 22.0 min, respectively, whereas positioning precision can have spectacular gains of 54%, 42% and 34%, and its RMS can be declined to 0.032, 0.019 and 0.047 m in kinematic solutions. All the results fully demonstrate the superiority of the improved TC model in BDS-2/BDS-3 PPP-AR. It can indeed contribute to the promotion and application of BDS in the future.