Modeling and Prediction of Inter-System Bias for GPS/BDS-2/BDS-3 Combined Precision Point Positioning

The combination of Precision Point Positioning (PPP) with Multi-Global Navigation Satellite System (Multi-GNSS), called MGPPP, can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System (BDS). However, the Inter-System Bias (ISB) measurement of Multi-GNSS, including the time system offset, the coordinate system difference, and the inter-system hardware delay bias, must be considered for Multi-GNSS data fusion processing. The detected ISB can be well modeled and predicted by using a quadratic model (QM), an autoregressive integrated moving average model (ARIMA), as well as the sliding window strategy (SW). In this study, the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used. However, an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used. Meanwhile, the precision of the Predicted ISB (PISB) on the next day of all stations is about 0.1-0.6 ns. Besides, to effectively utilize the PISB, a new strategy for predicting the PISB for MGPPP is proposed. In the proposed strategy, the PISB is used by adding two virtual observation equations, and an adaptive factor is adopted to balance the contribution of the Observed ISB (OISB) and the PISB to the final estimations of ISB. To validate the effectiveness of the proposed method, some experimental schemes are designed and tested under different satellite availability conditions. The results indicate that in open sky environment, the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB, but the convergence time of MGPPP is reduced by 7.1% at most in the north (N), east (E), and up (U) components. In the blocked sky environment, the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment. Compared with the direct utilization of the PISB, the selective utilization of the PISB improves the positioning precision and convergence time by 6.7% and 12.7% at most in the N, E, and U components, respectively.