## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**PLL Bandwidth** & **VT LR** & **Positioning Method** & **Direction** & **O-KF-VT (\%)** & **U-Blox (\%)** \\ \hline
5 Hz & 5 Hz & RTK (3\(\sigma\)) & E & 0.83 & 42.79 \\  & & & N & 21.26 & 46.14 \\  & & & U & 14.63 & \(-\)3.99 \\  & & & All & 14.17 & 21.40 \\  & & DGPS (3\(\sigma\)) & E & \(-\)0.10 & 4.21 \\  & & & N & 5.51 & \(-\)1.31 \\  & & & U & 13.57 & \(-\)11.98 \\  & & & All & 9.73 & \(-\)5.98 \\ \hline
5 Hz & 10 Hz & RTK (3\(\sigma\)) & E & 5.59 & 48.72 \\  & & & N & \(-\)6.33 & 9.97 \\  & & & U & 1.26 & \(-\)15.05 \\  & & & All & \(-\)0.46 & 7.00 \\  & & DGPS (3\(\sigma\)) & E & 4.32 & 16.61 \\  & & & N & 5.79 & \(-\)4.02 \\  & & & U & 9.57 & \(-\)11.34 \\  & & & All & 8.45 & \(-\)6.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary on the improvements of the positioning accuracy using the A-VTTCES-KF. The term of O-KF-VT in the table corresponds to the improvements in percentage, with respect to the A-VTTCED-KF positioning accuracy, versus the counterpart of the SDR using O-KF-VT algorithm; the term of U-Blox in the table corresponds to the improvements in percentage, with respect to the A-VTTCED-KF positioning accuracy, versus the counterpart of the U-Blox receiver. The sign of minus represents that the accuracy is reduced. Thirdly, it can also be found that, the code-based DGPS positioning results, though, embrace similar improvement trends as the RTK solutions do, the increasing rates are smaller than the ones obtained from the RTK algorithm. As we know, the code-based positioning results are more likely to be relied on the clock bias estimations, and the carrier-based ones are more possibly dependent on the clock drift estimations. The clock bias can be assumed to be equivalent to the integration of the clock drift, and the integration time is identical to the update interval of the positioning estimation process. In other words, the clock drift passing through a resembling low-pass filter produced by the integration implementation gives the clock bias, and the time-correlated error will be reduced through this process. Therefore, it is reasonable that the DGPS positioning results have a slower improvement rate when compared with the RTK method. Fourthly, there are significant increases in RTK positioning accuracy along the east and north directions when compared with the solutions produced by the U-Blox receiver, while a slight decrease in vertical accuracy occurs. The bandwidth of the PLL becomes smaller on the condition that a VT loop is involved in the GNSS SDR. For example, the bandwidth of the PLL applied to the ST loop is set to 18 Hz while the bandwidth with respect to the VT loop shrink to 5 Hz for our GNSS SDR in this research. The RTK solutions are more sensitive to the performance of the PLL and the estimation accuracy of the local clock drift due to the characteristics of the receiver design [42]. The vertical positioning results are ultra-tightly coupled with clock error estimations due to the geometry of the satellite distribution in the vertical direction. There is no sign transition in terms of the cosine direction vector for the height, while the corresponding coefficient for the clock error estimation is equivalent to one. In this case, this fact leads to the consequence that the height positioning results are highly related to the clock error estimations. Other two directions' positioning results do not meet the same issue as the vertical one does. It can be inferred that the clock estimation in our presented GNSS SDR is less accurate than the results computed with the U-Blox receiver. Hence, it is totally possible that the local clock in the GNSS SDR is too coarse to enhance the positioning performance in the height. Fifthly, the code-based DGPS positioning performance is not only relying on the PLL, but also mostly determined by the DLL, multipath mitigation algorithms applied in the code discriminator, and the clock bias estimations.