# Performance Analysis of Undifferenced NRTK Considering Time-Varying Characteristics of Atmosphere
## 4 Experimental Validation
### Fixing Performance Analysis between Estimated PSD and Empirical PSD  
The estimated PSD can provide more reasonable constraints on the atmospheric parameters and improve the ambiguity fixing performance. Through the research in Section 4.3, the PSD can be estimated according to the actual observation data. To compare the ambiguity fixing performance of the estimated PSD with the empirical PSD, the following PSD schemes were set to solve the ambiguity.  
Scheme 1: Estimated PSD (EST).  
Scheme 2: Empirical PSD (EMP), TPSD: 1 cm/\(\sqrt{\text{h}}\); IPSD: 1 m/\(\sqrt{\text{h}}\)[19].  
Divide the data of the four networks into 1 h periods for statistical analysis of the ambiguity fixing time and ambiguity fixing success rate. Figures 12 and 13 show the statistics for the ambiguity fixing time and the ambiguity fixing success rate between estimated PSD and empirical PSD.  
Figure 11: Time series of the TPSD for C03.  
Figure 12: Ambiguity fixing time between estimated PSD and empirical PSD.  
From Figure 12, it can be seen that for the ambiguity fixing time of the reference network, EST PSD was always better than EMP PSD. Among the four networks, EST PSD improved the fixing time by 14.7%, 19.3%, 17.9%, and 21.5%. This is because the empirical EMP cannot be adjusted based on the actual observations situation, and can only choose relatively loose constraint values, with limited constraint effects. The ambiguity fixing success rate of EST PSD in Figure 13 was significantly improved, by 9.5%, 12.9%, 12.7%, and 11.9% in the four networks. Figure 14 shows the sequence of ambiguity floating solutions between estimated PSD and empirical PSD.  
From Figure 14, it can be seen that there were differences in the early stage of the convergence process of the ambiguity floating solutions, which is also the main reason for the inconsistent ambiguity fixing time. In the later stage of the convergence, the floating solutions difference between the two methods will continue to decrease. Figure 15 shows the estimated IPSD and empirical IPSD for Network \(A\) over a period of time.  
Figure 14: Ambiguity floating solutions between estimated PSD and empirical PSD.  
Figure 13: Ambiguity fixing success rate between estimated PSD and empirical PSD.  
From Figure 15, it can be seen that EMP IPSD was much larger than EST IPSD, and EMP IPSD always maintained a value that cannot be adjusted in real time based on ionospheric variation. However, EST IPSD showed constant variation and showed different trends on different satellites, which corresponded to the ionospheric variation. EST IPSD variation on each baseline was similar, which was due to the consistency of ionospheric variation in small areas. Figure 16 shows the comparison of estimated TPSD and empirical TPSD.  
It can be seen from Figure 16 that the TPSD values were much smaller than those of the IPSD. The overall variation of the troposphere is stable, and the variation of TPSD is relatively stable. The estimated TPSD is also smaller than the empirical TPSD. Estimated TPSD will impose stronger constraints on the equation, and this constraint will not cause divergence of the positioning results.  
Figure 16: A comparison plot of the estimated TPSD with the empirical TPSD.  
Figure 15: A comparison plot of the estimated IPSD with the empirical IPSD.