# Positioning Performance Limits of GNSS Meta-Signals and HO-BOC Signals
## 6 GNSS Meta-Signal RTK Performance Results
### Non-Nominal Conditions: Constrained Satellite Visibility (Bad GDOP) Scenario  
The RTK performance results for the constrained satellite visibility scenario are summarized in Figure 12. In this case, we can point out the following:  
* First, notice the performance degradation on the achievable RTK performance, that is between the nominal \(\text{CRB}_{real/integer}\) (good GDOP scenario) and the corresponding one for the current bad GDOP case. At \(\text{SNR}_{\text{out}}=25\) dB. the former was \(\text{CRB}_{real/integer}=2\) mm (nominal) and the latter \(\text{CRB}_{real/integer}=1.5\) cm (non-nominal). * With respect to the nominal case where the best performance was obtained with Galileo E5, in the bad GDOP scenario and for the range of SNR considered, using this signal barely improved the float solution for \(\text{SNR}_{\text{out}}>24\) dB. Therefore, in this case, the geometry matrix had a strong impact on the ILS compared to the WLS results in Figure 9. This result came from a drastic drop of the fix success rate, as shown in Figure 11. A wrong fix could completely spoil the solution, and a 100%  
Figure 10: Nominal good GDOP scenario RTK RMSE (m) and the corresponding CRBs (m) for the different GNSS meta-signals: (**a**) GPS L2C + L5Q, (**b**) Galileo E5B + E6B, (**c**) BeiDou B2 AQ + B3Q, (**d**) Galileo E5A + E6B, (**e**) BeiDou B2 + B3Q and (**f**) Galileo E5 + E6B. fix was needed for RMSE\({}_{mixed}\) to be on CRB\({}_{real/integer}\). However, notice that compared to L2 + L5, E5B + E6, E5A + E6, or B2A + B3, where the threshold effect was more severe, considering E5 was still useful in the range SNR\({}_{\text{out}}\) =[16; 17; 18; 19; 20] dB. However, there was no need to try to exploit the phase and fix the ambiguities; therefore, the user could directly keep a code-based RTK solution. * For high SNR regimes (i.e., SNR\({}_{\text{out}}>\) 22 dB), we could see the impact of the time-delay precision, which allowed RMSE\({}_{mixed}\) < RMSE\({}_{real}\). This was clear looking at the E5A + E6 and B2A + B3 signals, which provided the lowest CRBs (see Figure 8a). However, in any case, the performance improvement was not worth the estimator behavior at lower SNRs. * Again, only the full-bandwidth combinations E5 + E6 and B2 + B3 provided a consistent performance, improving the Galileo E5, together with the highest success ratio, as shown in Figure 11. Considering that we had an ambiguity fixing measure, these signals provided the best trade-off, when the performance was fixed, on CRB\({}_{real/integer}\) as given by the RMSE\({}_{correct\ amb}\), and when not fixed, the performance was equal to or better than the float solution (i.e., RMSE\({}_{mixed}\) \(\leq\) RMSE\({}_{real}\)). * It is also worth pointing out that the behavior of RMSE\({}_{correct\ amb}\) for all the meta-signals except E5 + E6 and B2 + B3 was due to the very low fix success ratio (i.e., the worst one being E5A + E6), which implied that very few realizations from the \(10^{4}\) Monte Carlo runs were averaged. That was the reason why the RMSE with a correct ambiguity fix was not always on CRB\({}_{real/integer}\). As a conclusion, even if in the previous good GDOP scenario, the best choice was Galileo E5, it was clear that regardless of the satellite geometry, the best performance and robustness tradeoff was provided by the full-bandwidth Galileo E5 + E6 and BeiDou B2 + B3 combinations, the latter being slightly better. In addition, for these two signals, the fixing success rate was maximized. Figure 11: Nominal (**a**) and non-nominal (**b**)—good and bad GDOP, respectively—scenario RTK fixing success rate. To conclude the meta-signal-based RTK positioning performance analysis, it was interesting to assess which was the convergence point of the different meta-signals in a bad GDOP scenario; in other words, when \(\text{RMSE}_{mixed}\) = \(\text{CRB}_{real/integer}\) and, thus, the method correctly exploited the phase information.