# Real-Time Phase Bias Estimation for BeiDou Satellites Based on Consideration of Orbit Errors
###### Abstract
It was shown in [15; 16; 17] that the convergence time of float PPP can be reduced by combining the observations from the BeiDou satellites. [PERSON] et al. [18] showed that the fixing percentage for GPS-only kinematic precise point positioning integer ambiguity resolution (PPP-IAR) was 17.6% within a 10-min period, and this percentage improved to 42.8% following the addition of the IGSO and MEO satellites of the BDS. However, the fixing percentage degraded severely to 23.2% if the GEO satellites were included because of their low orbit accuracy. Researchers have performed large numbers of studies on precise orbit determination and precise positioning of the BDS [19; 20; 21; 22; 23; 24]. However, because of the lack of sufficient numbers of tracking stations and a suitably precise solar radiation pressure model, the precision of the BDS orbit is low when compared with that of the GPS satellites, particularly for the GEO satellites, which have orbit errors of the order of 2-4 m. The Centre National d'Etudes Spatiales (CNES) has been providing real-time orbit and clock corrections for all global navigation satellite systems (GNSSs) since 2016. [PERSON] et al. [25] analyzed the quality of the CNES's real-time orbit by comparing it with that of the final product from the Center for Orbit Determination in Europe (CODE) [26]. The results showed that GPS has the highest orbit precision of 2.3, 3.2, and 2.8 cm for its radial, along-track and cross-track components, respectively. For the BDS, the precision results for the three corresponding components were 12.1, 21.2, and 26.2 cm for the IGSO satellites and 4.8, 13.1, and 10.8 cm for the MEO satellites, respectively. To improve the precision of ultra-rapid orbits, [PERSON] et al. [27] used two days' worth of data to perform multi-GNSS ultra-rapid orbit determination, and updated the orbit results every hour. The results showed that when compared with the traditional strategy, the overlap accuracies of the BDS GEO, IGSO, and MEO satellites can be improved by more than 50, 18, and 44% in the radial, cross-track, and along-track directions, respectively, and the root mean square (RMS) values are summarized in detail in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline  & **GEO** & **IGSO** & **MEO** & **GPS** \\ \hline Along & 0.690 & 0.160 & 0.150 & 0.032 \\ Cross & 0.170 & 0.085 & 0.042 & 0.019 \\ Radial & 0.101 & 0.065 & 0.035 & 0.010 \\ \hline \end{tabular}
\end{table} 
Table 1: Overlap root mean square (RMS; units: m) values for ultra-rapid orbit. GEO: geostationary Earth orbit; IGSO: inclined geosynchronous satellite orbit; MEO: medium Earth orbit; GPS: global positioning system. As shown in Table 1, the accuracy of the BDS ultra-rapid orbit is very low and thus cannot satisfy the FCB estimation requirements. In this paper, we propose a new strategy for BDS FCB estimation in real time. We begin by addressing the fundamentals of simulated real-time PPP data processing. We then demonstrate how the satellite orbit will affect narrow-lane FCB estimation and provide a new narrow-lane FCB estimation strategy that takes satellite orbit errors into consideration. We use a network of 60 tracking stations to validate the proposed method. Finally, discussion and concluding remarks are presented based on our findings.