# Evaluation of BDS/GPS Multi-Frequency RTK Positioning Performance under Different Baseline Lengths
## 4 Multi-Frequency RTK Positioning Accuracy Analysis
### Positioning Accuracy  
Single-frequency low-cost receivers have the advantages of low price and small size and are widely used in vehicle navigation, precision agriculture, and other industries. Therefore, it is necessary to evaluate the positioning performance of BDS-3 single-frequency RTK. According to the experimental parameter settings in Tables 2 and 3, for the five groups of stations with different baseline lengths, we use the data from DOY215 (3 August 2020) to DOY221 (9 August 2020) for a total of seven days. The RMS in the three directions of East (E), North (N), and Up (U) were calculated, and the RMS in the three directions as well as the ambiguity fixing rates were averaged over the seven days of data. To analyze the BDS-3 (BIC) single-frequency RTK positioning performance, the continuous [18] ambiguity fixing strategy was chosen based on the baseline BORJ-TGBF (6 km) in the positioning mode of short baseline RTK (If not specifically stated, the continuous ambiguity fixing strategy is the default in this research). The RMS comparisons for the five frequencies of BDS-3 (BIC), BDS-3 (B2a), BDS-2+BDS-3 (B1I), BDS-2+BDS-3 (B3I), and GPS (L1) are shown in Figure 3, and the seven days of RMS and ambiguity fixing rates are averaged in Table 4. Due to the fewer visible satellites and poorer geometry distribution of BDS-3, the ambiguity fixing rate of B1C and B2a is lower than that of L1, B1I, and B3I. The positioning accuracies of single-frequency bands BIC, BII, L1, and B3I were about the same, while the accuracy was lower for band B2a. The short baseline configuration enables the single-differencing between the receivers to eliminate the errors related to satellites and the atmosphere. Therefore, we attributed the poor positioning performance for the single-frequency band B2a to its poor signal quality [4; 6; 20]. In DOY221, the fact that BDS-3 has only four satellites in multiple epochs results in poor positioning accuracy for BIC and B2a in that period. Figure 2: Number of available satellites and PDOP value. The single epoch RTK ambiguity fixing rate is one of the important indicators to evaluate the RTK performance. In short baseline RTK positioning mode, the instantaneous [18] and continuous ambiguity fixing strategies were chosen on baseline METG-MET3 (3 km) for BDS-3 (B1C/B2a), BDS-2+BDS-3 (B1I/B3I), GPS (L1L2), BDS-3 (B1C/B2a/B3I), and BDS-3 (B1I/B3I). Results for the five frequencies are shown in Figure 4; the means of RMS and ambiguity fixing rates for the seven days are shown  
It is observed from Figure 4 that the instantaneous RTK performance for BIC/B2a on DOY 218 shows a large error. To investigate the detailed reason, the valid satellite number and the corresponding PDOP is plotted in Figure 5. We can see that only four BDS-3 satellites can be observed in multiple epochs, resulting in the use of instantaneous mode during this time period, the positioning error of BICB2a is very large, and the ambiguity of the BI1B3I (BDS-3) degree cannot be fixed (the ambiguity fixing rate for the day is only 51.6%). Therefore, the positioning results of BICB2a and BI1B3I (BDS-3) of DOY218 were removed when the mean RMS and ambiguity fixing rates were calculated. From Figure 4 and Table 5, we can see that in the instantaneous positioning mode, the ambiguity fixing rates of BDS-2+BDS-3 (B1I/B3I) and GPS (L1L2) were 100% and 99.60%, which are slightly higher than those of BDS-3 (B1I/B3I), BDS-3 (B1C/B2a), and BDS-3 (B1C/B2a/B3I). In terms of positioning accuracy, BDS-2+BDS-3 (B1I/B3I) has the highest number of satellites and the smallest PDOP value, and the triple-frequency BDS-3 (B1C/B2a/B3I) observation has more observation numbers due to the additional frequency, which leads to the highest positioning accuracy. In the continuous positioning mode, the positioning accuracy is significantly improved compared with the Instantaneous mode.