# Evaluation of BDS/GPS Multi-Frequency RTK Positioning Performance under Different Baseline Lengths
###### Abstract  
The BeiDou Navigation Satellite System (BDS) is fully operational and provides positioning, navigation, and timing services to users worldwide. To comprehensively evaluate the BeiDou-3 Navigation Satellite System (BDS-3) global real-time kinematic (RTK) positioning performance, five sets of IGS/MEGX stations with different baseline lengths are selected in this research, and the visibility of current BDS-3, BDS-2+BDS-3, and Global Positioning System (GPS) system satellites are analyzed. The single frequency, dual-frequency, and triple-frequency positioning accuracy as well as ambiguity fixing rate under short baseline and long baseline are also analyzed. The experimental results show that the positioning accuracies of B1C, BII, L1, and B3I single-frequency bands were about the same, while for band B2a it was lower. For the short baseline dual-frequency RTK positioning mode, the accuracy of BDS-3 (BIC/B2a), BDS-3 (BII/B3I), triple-frequency BDS-3 (B1C/B2a/B3I), and GPS (L1L2) is comparable and slightly better than that of BDS-3 (BII/B3I). With the increase in baseline length, the advantages of dual-frequency BDS-3 (BIC/B2a) and triple frequency BDS (BIC/B2a/B3I) are more obvious, with triple-frequency BDS-3 (BIC/B2a/B3I) having the best positioning accuracy. In terms of ambiguity fixing performance, dual-frequency BDS-2+BDS-3 (B1I/B3I) and dual-frequency GPS (L1L2) have the highest ambiguity fixing rate. The ambiguity fixing rate of dual-frequency BDS-3 (BIC/B2a) and triple-frequency BDS-3 (B1C/B2a/B3I) can be higher than 90% within 100 km. In the case of positioning using only the BDS-3 system, the triple-frequency BDS-3 (B1C/B2a/B3I) is superior to both the dual-frequency BDS-3 (B1I/B3I) and dual-frequency BDS-3 (B1C/B2a) in terms of both positioning accuracy and ambiguity fixing rate. The BDS-2+BDS-3 (B1I/B3I) dual-frequency RTK, which has reached a level comparable to GPS, can provide global users with real-time centimeter-level differential positioning services. BDS-3; RTK; multi-frequency; Kalman filter; integer ambiguity resolution +
Footnote †: journal: remote sensing  
keeping the frequency unchanged, and changes it to the B2b frequency. Compared with the BDS-2 satellite's signal, BIC/B2a has better signal strength, and the Carrier-to-Noise density ratio (C/N\({}_{0}\)) of the B2a signal is about 3 dB higher than other signals. The code observation accuracy of BIC/B2a is about 0.05 m higher than that of the traditional B1/B2/B3 signal; especially, that of B2a is better than 0.15 m. The double-differenced (DD) results of the zero-baseline show that the observation accuracy of B1C/L1/E1/L1 (QZSS) is between 1.2 and 1.4 mm and that of B2a/L5/E5A/L5 is slightly worse, between 1.3 and 1.6 mm, which is consistent with the results of the zero-baseline solution [4]. With the continuous improvement and development of the BDS-3 global navigation satellite system, many researchers have carried out relevant research on RTK positioning of new BDS-3 frequencies. At the short baseline RTK positioning level, [PERSON] et al. [5] mainly studied the stochastic modeling and positioning performance of BDS-2 and BDS-3. Based on the established stochastic model, the performance of BDS-2 and BDS-3 RTK positioning was analyzed. The results show that for BDS-3 dual-frequency positioning, the positioning errors are several centimeters both on an ultra-short baseline and a short baseline, which is analogous to the BDS-2 dual-frequency positioning. [PERSON] et al. [6] analyzed the BDS-3-only RTK positioning using the data collected in zero and short baselines, they found that the positioning accuracies of B1C, B1I, and B3I single-frequencies were about the same, while that for frequency B2a was lower. In addition, the positioning results for dual-frequency combinations are not always better than those for single-frequency because of the absence of a good stochastic model.