One-step correction strategy for BDS-2/BDS-3 satellite observation code bias and multipath delay

Global navigation satellite systems and positioning, navigation, and timing services, such as the newly developed BeiDou satellite system (BDS), require high-accuracy satellite observations. Satellite-induced code bias is present in BDS-2 satellite observations while it is negligibly present in BDS-3 satellite observations. The traditional method of mitigating BDS code bias involves two steps, first addressing multipath delay and then code bias, and does not obtain optimal results. A one-step strategy is therefore proposed to model and eliminate code bias and multipath delay considering BDS-2 and BDS-3 integrated processing. A combined least-square and autoregressive strategy is selected to estimate the model coefficients of code bias and construct the multipath delay with one solution. Moreover, inter-satellite correlations of BDS-2 and BDS-3 are extracted to improve the weight matrix in the estimation of model coefficients. To verify the proposed strategy, experiments are designed for eight schemes to analyze the coefficients and residuals of modelling code bias. Experimental results indicate that a more stable and accurate code bias model is acquired by introducing inter-satellite correlation; with the one-step strategy, the model residuals are reduced and a more optimal code bias model is output. Meanwhile, the single-frequency precise point positioning (PPP) and real-time PPP of BDS-2 and BDS-3 combined estimations are tested for different stations, frequencies, and code bias models. The results of final positions reveal that accuracy in the Up (U) direction is improved compared with that in the East (E) and North (N) directions; improvements are greater for B1I than for B3I. In general, the one-step strategy enhances the precision of single-frequency (B1I/B3I) PPP, especially in the U direction. However, the effects on BDS ultra-rapid orbit determination are negligible. Equally, the double-frequency real-time PPP solution is improved, compared with adopting the traditional method, by 10.6-64.9%, 0.0-59.1%, and 12.6-67.2% for E, N, and U directions, respectively, through BDS-2/BDS-3 integrated processing. The proposed one-step strategy therefore outperforms the two-step strategy in terms of rapidly processing high-precision BDS observations.