# Initial Positioning Assessment of BDS New Satellites and New Signals
## 5 RTK Performance  
In this section, we evaluate the RTK performance using the current BDS constellation. Two baselines at different lengths are selected. One is a 20 m baseline from station YARR to YAR3 (29.05\({}^{\circ}\)S, 115.35\({}^{\circ}\)E), the other is a 10 km baseline from station STR1 to TID1 (35.40\({}^{\circ}\)S, 148.98\({}^{\circ}\)E). Data on 1 January 2019 is selected for the RTK assessment of the two baselines.  
For the RTK strategy, dual-frequency data on BII and B3I are used. Conventional continuous mode without considering troposphere and ionosphere difference is applied during ambiguity resolution  
Figure 12: SPP comparison of BII (**upper**), B1c (**middle**) and B2a (**lower**) at station BSHM (BDS-3 only).  
Figure 13: OMC of BII (**upper**), B1c (**middle**) and B2a (**lower**) at station BSHM. Different color means different satellite in each subplot. OMC may contain residual error of receiver clock, but it is the same for each satellite at the same epoch.  
(AR). To reduce the impact of noise from low elevation satellites, the cut-off elevation is set as 10\({}^{\circ}\) for float solution in Kalman Filter and 20\({}^{\circ}\) in the procedure of ambiguity fixing. A threshold of 3.0 with a success rate of 0.99 is set for ratio test in LAMBDA method [34]. In the case of AR, ambiguity dilution of precision (ADOP) is an important concept indicating the success rate of AR. According to [PERSON] [35], ADOP can be defined as:  
\[ADOP=\sqrt{|Q_{d}|^{\frac{1}{n}}}\ \ \ (cycle) \tag{6}\]  
where \(Q_{d}\) is the variance-covariance matrix of float ambiguities and \(|\cdot|\) is the determinant of the matrix, n is the dimension of the ambiguity vector. As pointed out by [PERSON] and [PERSON] [36], if ADOP is smaller than 0.14 cycle, the AR success rate would better than 0.99.  
To analyze the contribution of BDS-3 in RTK, an epoch-by-epoch ADOP value is computed at the two baselines using BDS-2-only and BDS-2+BDS-3 satellites. As shown in Figure 14, the ADOP value at 20 m baseline is well below 0.14 cycle, which indicates the possibility of reliable ambiguity resolution for instantaneous RTK. While for 10 km baseline, ADOP is slightly worse than 20 m baseline due to satellite geometry. The percentage of ADOP below 0.14 cycle is 75.3% if BDS-2 is used, which could lead to wrong fixings for the ambiguity for instantaneous RTK. While for the BDS-2+BDS-3 combination, more than 99% of ADOP is below 0.14 cycle. In summary, for both baselines, ADOP performance would improve in different levels after BDS-3 satellites are added.  
RTK performance of BDS-2-only and BDS-2+BDS-3 scenarios at these two baselines are depicted in Figures 15 and 16, together with the statistical results of RMS and 95% accumulated error listed in Table 6. This illustrates that BDS-3 contributes to a more stable and precise RTK performance in the horizontal and vertical component, with a 1-2 mm improvement for 20 m baseline and 1-2 cm improvement for the 10 km baseline. Although it is not shown here, it should be pointed out that if we perform instantaneous RTK at the 10 km baseline [33], it would lead to some wrong ambiguity fixing for the BDS-2-only case.  
Figure 14: Epoch-by-epoch ADOP of BDS-2-only and BDS-2+BDS-3 at 20 m baseline (**upper**) and 10 km baseline (**lower**). The black dashed line refers to an ADOP value of 0.14 cycle.  
Figure 16: Ten km baseline RTK performance in horizontal (**upper**) and vertical (**lower**) using BDS-2-only (green) and BDS-2+BDS-3 (red). The gray circle shows the 95% confidence level of horizontal error. Ambiguity fix percentage is 100% for both cases.  
Figure 15: Twenty m baseline RTK performance in horizontal (**upper**) and vertical (**lower**) using BDS-2-only (green) and BDS-2+BDS-3 (red). The gray circle shows the 95% confidence level of horizontal error. Ambiguity fix percentage is 100% for both cases.