## 5 Conclusions  
In this contribution, for the first time we provide initial assessment of tightly combined RTK with GPS, Galileo, and BDS-3 operational satellites using raw B1C-L1-E1/B2a-L5-E5a data collected with scientific geodetic iGMAS and commercial M300 Pro receivers. The carrier-to-noise density ratio, pseudorange multipath and noise, as well as double-differenced carrier phase and code residuals of B1C/B2a signals are first characterized in comparison with L1-E1/L5-E5a signals. Our experimental results indicate that the observational quality of B1C/B2a signals that transmitted by BDS-3 operational satellites is comparable to their corresponding GPS/Galileo L1-E1/L5-E5a signals. Then, we investigate the size and stability of phase and code differential ISBs between B1C/B2a and L1-E1/L5-E5a signals using short baseline data collected with both identical and different receiver types. It is verified that the BDS-3/GPS/Galileo differential ISBs are indeed close to zero with two receivers of the same type. In contrast, they are generally present but stable in the time domain if receivers of different types are involved, which allows for calibration and correction in advance. Finally, a formal as well as empirical analysis is given to evaluate performance of instantaneous tightly combined BDS-3/GPS or BDS-3/GPS/Galileo RTK with single-frequency (B1C-L1-E1) and dual-frequency (B1C-L1-E1/B2a-L5-E5a) \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Freq.**} & \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**10\({}^{\circ}\)**} & \multicolumn{3}{c}{**20\({}^{\circ}\)**} \\ \cline{3-8}  & & **E (cm)** & **N (cm)** & **U (cm)** & **E (cm)** & **N (cm)** & **U (cm)** \\ \hline \multirow{4}{*}{SF} & GB 1 CCM & 62.5/0.3 & 86.3/0.3 & 157.0/0.9 & 63.6/0.3 & 89.7/0.3 & 212.3/1.0 \\  & GB TCM & 58.2/0.3 & 82.6/0.3 & 156.0/0.9 & 60.6/0.3 & 85.6/0.4 & 199.0/1.0 \\  & GEB 2 CCM & 53.6/0.2 & 70.3/0.3 & 134.8/0.8 & 55.5/0.2 & 71.4/0.3 & 160.6/0.8 \\  & GEB TCM & 49.5/0.2 & 67.3/0.3 & 130.7/0.9 & 52.0/0.2 & 68.6/0.3 & 154.0/0.9 \\ \hline \multirow{4}{*}{DF} & GB LCM & 54.5/0.2 & 75.0/0.3 & 137.6/0.8 & 55.2/0.2 & 76.4/0.3 & 177.3/0.8 \\  & GB TCM & 48.3/0.3 & 65.9/0.3 & 130.9/1.0 & 48.9/0.3 & 66.7/0.3 & 158.9/1.0 \\ \cline{1-1}  & GEB LCM & 39.5/0.3 & 48.9/0.3 & 102.9/0.9 & 40.7/0.3 & 49.5/0.3 & 118.0/0.9 \\ \cline{1-1}  & GEB TCM & 35.6/0.2 & 45.7/0.3 & 93.4/0.8 & 36.3/0.2 & 46.3/0.3 & 105.8/0.8 \\ \hline \hline \end{tabular} \({}^{1,2}\) “GB” and “GEB” represent GPS/BDS-3 and GPS/Galileo/BDS-3, respectively.  
\end{table} 
Table 6: STDs of float/correctly-fixed single-epoch RTK errors in the North, East, and Up. Figure 13: Positioning errors with single-frequency observations under 10\({}^{\circ}\) elevation cut-off angle. The ratio threshold of 2.0 is adopted for ambiguity validation. observations. Compared with the loosely combined model, the tightly combined model can provide us with much lower ADOP and higher ratio values. Meanwhile, the empirical ambiguity resolution success rate and positioning accuracy are remarkably improved as well, especially under constrained observational conditions with limited observed satellites and only single-frequency observations. In such cases, the improvement of the empirical ambiguity resolution success rate can reach up to approximately 10%\(\sim\)60%, which further confirm the feasibility and benefits of tightly combined real-time kinematic (RTK) positioning with GPS, Galileo and BDS-3 operational satellites. In-depth investigation on the phase and code differential ISBs between BDS-3 operational satellites and GPS/Galileo for more types of receivers are still required in the future. Moreover, the ISBs between BDS-3 operational satellites with respect to QZSS, IRNSS, and SBAS will also need to be estimated so as to investigate the interoperability of BDS-3 with these systems. Conceptualization, M.W., W.L. and X.Z. ; methodology, M.W. ; software, M.W. and W.W.; validation, M.W. and W.W.; resources, W.L. and X.Z. ; writing--original draft preparation, M.W. and W.L.