# Performance Analysis of Undifferenced NRTK Considering Time-Varying Characteristics of Atmosphere
## 4 Experimental Validation
### Real-Time Estimation Method for Atmospheric PSD  
Since the empirical PSD cannot be adjusted according to the actual observation environment, a larger empirical value is selected, which also makes the empirical PSD unable to reach the maximum constraint performance, and is not optimal for the ambiguity fixing of the reference station. Therefore, the method for real-time estimation of PSD according to the observation data was studied. The baseline SHQA-JMTY (187 KM) in Network A was taken as an example to study the IPSD and TPSD. Figure 8 shows the variation of ionospheric error and the cumulative variance \(\left(\Delta I_{\mathrm{GF,}mn}^{\mathrm{s}}(\Delta t,i)/\Delta t\right)^{2}\) under different difference intervals.  
It can be clearly seen from Figure 8 that, when the difference interval was 1 s, the accumulation of variance showed the variation of white noise, which was a curve with relatively constant slope variation. When the time difference interval increased to 15 s, because the difference interval already reflected the ionospheric variation, the curve represented the variation of the ionosphere with time. When the time difference interval reached 30 s, the variation curve was already consistent with the 60 s variation curve, and increasing the difference interval had no significant effect on the separation of the ionosphere. Therefore, in this study, the 30 s difference interval was considered as an empirical difference interval that can reflect the ionospheric variations. Figure 9 shows the variation of the troposphere and the cumulative variance \(\left(\
abla\Delta I_{\mathrm{F,}mn}^{\mathrm{s}q}(\Delta t,i)/\Delta t\right) ^{2}\) of different difference intervals of the C03 satellite.  
Figure 8: Ionospheric variation and cumulative variance under different difference intervals.  
It can also be clearly seen from Figure 9 that the tropospheric variation was relatively stable, and the variance curve at 1 s reflected the variation in white noise. Although the 10 min difference interval realized the variation in the atmosphere, it was quite different from the 20 min difference interval. Only when the difference interval reached 20 min was the variance variation in the atmosphere closer to the variance in the larger interval. Therefore, a 20 min difference interval was selected in the study as the empirical difference interval that can reflect the tropospheric variation.  
According to the previous theoretical analysis, the slope of the variance curve in Figure 8 represents the square of the PSD. Equation (44) also gives the calculation equation of IPSD. It can be seen from the analysis in Figure 8 that the influence of observation noise will not be significant when the difference interval reaches 30 s, so the variance curve of 30 s difference interval was selected when estimating the IPSD. At the same time, the updated IPSD was obtained continuously with a sliding window of 1 min. The IPSD variation curve for C03, C07, and C16 is shown in Figure 10.  
The IPSD of each satellite in Figure 10 showed a trend of continuous variation over time, and the IPSD of the C16 satellite varied slowly, which corresponded to the smooth variation of the ionospheric error of C16 satellite in Figure 8. In the analysis of Figure 9, the effect of observation noise was not significant when the difference time interval was 20 min. The tropospheric variance variation curve with the difference interval of 20 min was selected, and the updated TPSD was obtained continuously with the sliding window of 1 min. Equation (45) also gives the calculation equation of TPSD. Figure 11 shows the time series of the TPSD.  
Figure 10: Time series of the IPSD for C03, C07, and C16.  
Figure 9: Topospheric variation and cumulative variance under different difference intervals.  
From Figure 11, it can be seen that the TPSD values were significantly smaller than those for the IPSD, and the trend of variation was also relatively stable, which is caused by the slow variation in tropospheric errors.