Improved Medium Baseline RTK Positioning Performance Based on BDS/Galileo/GPS Triple-Frequency-Only Observations  
[PERSON]  
1 China Railway First Group Urban Rail Transit Engineering Co., Ltd., Wuxi 214000, China;  
[EMAIL_ADDRESS] (X.D. ); [EMAIL_ADDRESS] (X.Y. ); [EMAIL_ADDRESS] (J.W. );  
[EMAIL_ADDRESS] (Y.L.) [PERSON]  
1 China Railway First Group Urban Rail Transit Engineering Co., Ltd., Wuxi 214000, China;  
[EMAIL_ADDRESS] (X.D. ); [EMAIL_ADDRESS] (X.Y. ); [EMAIL_ADDRESS] (J.W. );  
[EMAIL_ADDRESS] (Y.L.) [PERSON]  
4 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China;  
[EMAIL_ADDRESS]  
[PERSON]  
3 School of Transportation, Southeast University, Nanjing 210096, China  
Based on double-difference (DD) carrier phase residuals of zero baselines, [PERSON] et al. [5] found that the phase observation accuracy for L1/L2/E5a/E5b is between 1.0 and 2.0 mm, while that for B1I is over 2 mm when DD is performed with two satellites from two different orbit types. [PERSON] et al. [6] showed that B2a/B2b/L5/E5a/E5b have similar signal strength by analyzing the carrier-to-noise density ratio (C/N\({}_{0}\)). They also expressed that code observation noise of B1C/B2a/B2b have no significant difference compared to those of L1/L5 and E1/E5a/E5b. In an in-depth assessment of new observation signals (i.e., B1C and B2a) from BDS-3, [PERSON] et al. [7] concluded that the phase observation accuracy of B1C/B2a is better than that of B1I/B2I/B3I and BDS-3/GPS/Galileo medium earth orbit (MEO) satellites have the same level of signal strength, code, and phase observation accuracy at the interoperable frequency. These research results are very useful for the establishment of multi-GNSS stochastic model. With code and phase observations, real-time kinematic (RTK) technology is well-known in achieving millimeter- to centimeter-level positioning. For short baselines (<10 km), DD between two observing stations and two satellites can eliminate satellite orbit errors, satellite and receiver clock offset/hardware bias, and atmospheric delay, thus ensuring the integer characteristic of ambiguity [8; 9]. [PERSON] et al. [10] first evaluated GPS/Galileo single-frequency short baseline RTK and found that, when compared to GPS-only strategy, GPS/Galileo ambiguity resolution (AR) is significantly improved. [PERSON] et al. [11] combined single-frequency short baseline observations of GPS, Galileo, BDS, and Quasi-Zenith Satellite System (QZSS) and showed a significant improvement of the time-to-correct-fix. Using dual-frequency observations of GPS and BDS, [PERSON] [12] also confirmed the benefit of combining two GNSS for short baselines. [PERSON] et al. [13] assessed GPS/BDS/Galileo dual-frequency short baseline RTK and obtained lower ambiguity dilution of precision (ADOP) and higher ratios. For medium to long baselines, the DD method finds it difficult to eliminate ionosphere and troposphere delay errors, which hinders rapid AR. [PERSON] [14] utilized ionosphere-free (IF) combination to eliminate ionosphere delay errors; however, this could not be beneficial for signal reacquisition and rapid re-convergence after signal loss. Thus, raw code and phase measurements are adopted in [15], with DD ionosphere delay being estimated as a parameter. By using triple-frequency observations, [PERSON] et al. [16] improved GPS/BDS AR for medium baselines. [PERSON] et al. [17] presented a detailed description of the AR strategy for extra-wide-lane (EWL), wide-lane (WL), and raw N1/N2 ambiguity, and analyzed contribution of QZSS to multi-GNSS long baseline RTK. In [16; 17], non-triple-frequency satellite observations were also used due to the limited availability of triple-frequency satellites.