## 4 Galileo Augmenting GPS SFSE Precise Positioning Experiment  
### Evaluation Index  
This section is for the performance evaluation of the two baselines in the different strategies: (a) single GPS, (b) GPS with baseline constraint (C-GPS), (c) GPS/Galileo, and (d) GPS/Galileo with baseline constraint (C-GPS/Galileo). Taking that the bridge vibration may cause the beating of centimeters or even decimeters at any moment into consideration, the addition of constraints at all times will inevitably lead to the correct solution under the vibration condition being affected by the baseline average, so that the result is biased towards the baseline average rather than the true value. Therefore, only if the calculated baseline length differs from the average length by more than a certain degree will the solution will be recalculated with the baseline length constraint.  
The following indicators evaluated the experimental results: number of satellites (NOS), PDOP, ADOP, bootstrapped success rate (Bstr), actual success rate (Asrt), and the baseline precision. The precision of the baseline solution (expressed by the standard deviation) is calculated through a baseline  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **elevation\({}^{\text{p}}\)** & **0** & **5** & **10** & **15** & **20** & **25** & **30** & **35** & **40** \\ \hline GPS & num & 12.0 & 10.6 & 8.9 & 7.7 & 6.7 & 5.9 & 5.1 & 4.4 & 3.6 \\  & P-num & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 95.9\% & 78.7\% & 44.8\% \\  & PDOP & 1.336 & 1.545 & 1.883 & 2.365 & 3.277 & 4.929 & 7.146 & 10.25 & 15.19 \\  & P-PDOP & 100\% & 100\% & 100\% & 99.6\% & 96.5\% & 82.2\% & 61.5\% & 39.7\% & 16.8\% \\ GPS/ & num & 17.7 & 15.9 & 13.6 & 11.6 & 10.1 & 8.8 & 7.7 & 6.6 & 5.4 \\ Galileo & P-num & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 98.9\% \\  & PDOP & 1.084 & 1.241 & 1.48 & 1.854 & 2.416 & 3.063 & 4.27 & 6.536 & 11.3 \\  & P-PDOP & 100\% & 100\% & 100\% & 100\% & 99.5\% & 98.3\% & 89.5\% & 71.7\% & 30.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: The visibility, PDOP and their pass rate of GPS and GPS/Galileo under different cutoff angles (\({}^{\circ}\)).  
Figure 4: The satellite visibility, Position Dilution of Precision (PDOP), and their pass rate curves of GPS and GPS/Galileo under different cutoff angles (\({}^{\circ}\)): (**a**) The satellite visibility; (**b**) PDOP; (**c**) Pass rate of GPS under different cutoff angles (**d**) Pass rate of GPS/Galileo under different cutoff angles.  
reference value that is solved by the software RTKLIB. ADOP is an indicator to estimate the accuracy of floating point ambiguity and it can be expressed by [33]:  
\[ADOP=\sqrt{\left|Q_{a}\right|^{\frac{1}{n}}} \tag{19}\]  
where \(Q_{a}\) is the variance-covariance matrix of the float ambiguities and the symbol \(||\) denotes the determinants. Bsrt is an indicator for evaluating the success of integer ambiguity resolution and it is expressed as [34].  
\[Bstr=\prod_{i=1}^{n}\left[2\Phi\left(\frac{1}{2\sigma_{z_{i}|t}}\right)-1\right] \tag{20}\]  
where \(\sigma_{z_{i}|t}\) is the conditional standard deviations of the estimated ambiguities. However, the residual ionosphere, troposphere, or multipath errors in float ambiguities may cause some differences between Bsrt and Asrt [35]. Therefore, Bsrt is a only a theoretical predictive value, not an actual success rate. In view of this, the Asrt will be mainly used to evaluate the correctness of ambiguity resolution and it can be defined as:  
\[Asrt=\frac{NOCE}{NOTE}*100\% \tag{21}\]  
where, \(NOCE\) is the number of correct fixed-ambiguity epochs and \(NOTE\) is the number of total epochs. It is considered as a correct fixed-ambiguity epoch if the baseline vector that is computed by the fixed integer ambiguities is approximate to the reference value.