# Performance Analysis of Undifferenced NRTK Considering Time-Varying Characteristics of Atmosphere
## 4 Experimental Validation
### PSD Effect on Ambiguity Fixing Performance  
In order to verify the influence of the PSD of the atmospheric parameters on the ambiguity fixing performance, the most commonly used empirical TPSD and IPSD, 1 cm/\(\sqrt{\text{h}}\) and 1 m/\(\sqrt{\text{h}}\)[19], were selected. Empirical values cannot be adjusted according to the actual atmospheric variations, so they are relatively loose. This will not cause distortion of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Baseline** & **Length/KM** & **Location** \\ \hline SHQA-JMTY (187 KM) & 187 & (46:52N,127:28E), (46:47N,129:56E) \\ JMTY-HRFS (121 KM) & 121 & (46:47N,129:56E), (46:15N,128:33E) \\ HRFS-SHQA (107 KM) & 107 & (46:15N,128:33E), (46:52N,127:28E) \\ JMTY-MDTJ (171 KM) & 171 & (46:47N,129:56E), (45:16N,130:14E) \\ MDTJ-HRFS (170 KM) & 170 & (45:16N,130:14E), (46:15N,128:33E) \\ MDTJ-HRSZ (178 KM) & 178 & (45:16N,130:14E), (45:12N,127:58E) \\ HRSZ-HRFS (125 KM) & 125 & (45:12N,127:58E), (46:15N,128:33E) \\ HRSZ-SHQA (189 KM) & 189 & (45:12N,127:58E), (46:52N,127:28E) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information on baselines employed in the experimental validation. Figure 3: Distribution of GNSS stations. the baseline due to the tight constraints during periods of severe atmospheric variations. We divided the data from four networks into 1 h periods to statistically analyze the ambiguity fixing time and ambiguity success rate of reference stations under different scaling factors. Figure 4 shows the ambiguity fixing time of the empirical IPSD 1 m\(/\sqrt{\mathrm{h}}\) at different scaling factors. It can be seen from Figure 4 that the ambiguity fixing time at different times of IPSD was inconsistent, and the empirical IPSD was not optimal, which indicated that the empirical IPSD cannot optimize the ambiguity fixing time; optimal IPSD is at 1/4 of the empirical IPSD. At the same time, it was found that the fixing time on both sides of the optimal IPSD was not symmetrically distributed. The fixing time on the left side of the optimal IPSD (which means the IPSD is shrinking) sharply increased, because the IPSD was too small and the constraints of the ionospheric parameters were too tight. The fixing time on the right side of the optimal IPSD (indicating that the IPSD is increasing) was close to the optimal IPSD, so it is appropriate to give a loose constraint when accurate ionospheric prior information is not available. Figure 5 shows the ambiguity success rate of the empirical IPSD 1 m\(/\sqrt{\mathrm{h}}\) at different scaling factors. Figure 4: Ambiguity fixing time with different IPSDs expressed by the scale factor applied to the empirical IPSD (the value of horizontal axis represents n in the scaled multiple of 2\({}^{n}\)). Figure 5: Ambiguity success rate with different IPSDs expressed by the scale factor applied to the empirical IPSD (the value of horizontal axis represents n in the scaled multiple of 2\({}^{n}\)). Figure 5 shows that the ambiguity success rate was the same as the performance of the ambiguity fixing time. The IPSD of different times will affect the ambiguity success rate, which is not also symmetrically distributed on both sides of the optimal IPSD (1/4). On the left side of the optimal IPSD (which means the IPSD is shrinking), the success rate decreased rapidly, so the ionospheric constraints were too tight due to the too small IPSD, affecting the continuous ambiguity fixing of the reference station. Figure 6 shows the ambiguity fixing time of the empirical TPSD 1 cm\(/\sqrt{\hbar}\) at different scaling factors. It can be seen from Figure 6 that the empirical TPSD was not optimal for ambiguity fixing time, and cannot play the most effective constraint. Unlike the impact of IPSD on the ambiguity fixing time, TPSD has a relatively small impact on the fixing time. This is because tropospheric variations are relatively gentle, and the changes in TPSD do not have a significant impact on the fixing time. Figure 7 shows the ambiguity success rate of the empirical TPSD 1 cm\(/\sqrt{\hbar}\) at different scaling factors.