## 4 Discussion
Assuming that the positioning errors follow the Gaussian white noise distribution, the 3\(\sigma\) thresholds, which 99.7% of the absolute positioning errors should be no more than, can accordingly be approximately judged through the plot error curves from Figure 17 to Figure 20. The values in terms of the positioning RMSE are summarized and listed in Table 6, where E, N, U, and All represent the positioning errors along the east, north, up or vertical directions, and the resultant values through these three directions, respectively. Some states can be announced through the listed information which be subsequently discussed. Firstly, the results on the condition that the VT LR is equal to 5 Hz will be discussed. As to the RTK positioning results, although positioning accuracies through both the O-KF-VT and the proposed A-VTTCES-KF in the vertical direction are faced with slight reductions, they have large improvements in the east and north directions compared with the solutions of the U-Blox receiver, as well as the resultant positioning results of these two algorithms are superior to the counterparts of the commercial receiver. In addition, the positioning performances produced by the A-VTTCES-KF exceeds the results obtained from the O-KF-VT in all directions. On the other hand, the O-KF-VT and A-VTTCES-KF positioning accuracies using the code-based DGPS algorithm are very close to each other in the east direction, while the latter performs better than the former in the east and up directions. In addition, the eastern DGPS positioning results produced by the VT-based SDR perform slightly better than the solutions estimated from the U-Blox receiver, while the positioning estimations along the other two directions using the SDR have a slightly worse performance. Secondly, the positioning solutions using 10-Hz VT LR will be subsequently analyzed, and they will also be made comparisons with the ones produced by the VT-based SDR with the LR value of 5 Hz. The general results with respect to the RTK positioning using the A-VTTCES-KF show small reductions of the performance in the northern direction when compared with the O-KF-VT, but positioning accuracies are still gained in other two directions. Besides, the eastern and northern solutions produced by the U-Blox receiver are obtained in a weaker quality than the VT GNSS SDR, while the up-direction results are inversely addressed better than the solutions computed with the algorithms based on such VT mode. With regard to the DGPS estimations, the positioning results using the A-VTTCES-KF SDR outperform the solutions offered by the O-KF-VT system towards all the axes in the local level frame. Furthermore, a similarity in terms of the DGPS positioning results between the 10-Hz-VT-LR SDR and the U-Blox receiver can be found, when compared with the previous discussions on the comparisons related to the 5-Hz-VT-LR SDR and the U-Blox one. A summary for the improved performances using the A-VTTCES-KF technique is listed in Table 7, where O-KF-VT in this table corresponds to the improvement percentages when the proposed algorithm is in comparison with the O-KF-VT algorithm; U-Blox denotes the counterparts with respect to the algorithm implemented by the U-Blox receiver. Some conclusions can be drawn through the results in this table.