## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**PLL Bandwidth** & **VT** & **Positioning** & **3\(\sigma\) Threshold** & **Direction** & **O-KF-VT** & **A-VTTCES-KF** & **U-Blox** \\  & **LR** & **Method** & **[m]** & **Direction** & **[m]** & **[m]** & **[m]** \\ \hline
5 Hz & 5 Hz & RTK (3\(\sigma\)) & 2 & E & 0.360 & 0.356 & 0.624 \\  & & & 2 & N & 0.461 & 0.365 & 0.674 \\  & & & 4 & U & 0.916 & 0.783 & 0.752 \\  & & & All & 1.087 & 0.934 & 1.187 \\  & & DGPS (3\(\sigma\)) & 2 & E & 0.999 & 1.000 & 1.044 \\  & & & 5 & N & 0.980 & 0.926 & 0.914 \\  & & & 10 & U & 1.968 & 1.701 & 1.519 \\  & & & & All & 2.415 & 2.180 & 2.057 \\ \hline
5 Hz & 10 Hz & RTK (3\(\sigma\)) & 2 & E & 0.340 & 0.321 & 0.626 \\  & & & 2 & N & 0.569 & 0.605 & 0.672 \\  & & & 4 & U & 0.875 & 0.864 & 0.751 \\  & & & All & 1.098 & 1.103 & 1.186 \\  & & DGPS (3\(\sigma\)) & 2 & E & 0.556 & 0.532 & 0.638 \\  & & & 5 & N & 1.071 & 1.009 & 0.970 \\  & & & 10 & U & 1.954 & 1.767 & 1.587 \\  & & & All & 2.297 & 2.103 & 1.966 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: RMSEs of the RTK and code-based DGPS positioning results. Regarding the case using 5-Hz-VT-LR SDR, some discussions can be stated as follow. Firstly, the A-VTTCES-KF outperforms the O-KF-VT in terms of the listed positioning results for most of the cases. Hence, the proposed algorithm can be confirmed that it is efficient on the error suppression. For example, the overall RTK positioning performance has been improved by 14.17%, while the positioning accuracy of the DGPS algorithm has a gain of 9.73%. Secondly, the A-VTTCES-KF has a more distinctive superiority towards the north and up directions, while there are few accuracy improvements in the eastern axis. Some analysis will be subsequently given to explain the phenomenas. As mentioned earlier, the time-correlated error induced by the VT technique is tightly coupled with the clock drift estimations which are highly associated with the constitution of the Doppler measurements. Paying attention to the sky plot of the satellites in the kinematic field test as illustrated in Figure 11, more SVs are distributed along the east-west direction. As we know, the position accuracy is dependent on the dilution of precision (DOP) corresponding to the expression, \(\left(\mathbf{H}^{T}\mathbf{H}\right)^{-1}\), where \(\mathbf{H}\) denotes the measurement design matrix [42]. This fact leads to the consequence that the clock drift residuals will be averaged along the east direction in the positioning estimation. Referring to Figures 11 and 12, the signal power of SV32, which is shown to be significant of guaranteeing an adequate DOP distribution along the south-north direction, is severely reduced by the environmental interference at most of the time in the field test. Such that the positioning accuracies, especially related to the carrier-based positioning algorithms, will be highly degraded in terms of the northern direction. Because the clock drift errors are intimately added to the northern positioning results. As far as we know, the positioning accuracy in terms of the up direction is always highly influenced by the clock estimation results, since there must be no satellite distributed on or under the ground. This fact will not only decrease the positioning accuracy, but also tie the performance of the clock errors tightly to the positioning solutions, in terms of the height. Again, the time-correlated error coupled in the clock drift estimations could be suppressed by the proposed A-VTTCES-KF, so, the northern and vertical carrier-based positioning results, which have a close relationship with the clock drift noise error as explained earlier, will gain more distinctive improvements, when compared with the ones in terms of the eastern positioning results. The theoretical analysis has been proved to be consistent with the experimental results as listed in Table 7.