## 3 Results
Figure 12: \(C/N_{0}\) estimations of the GNSS SDR and U-Blox receiver during the time spanning of the field test. The Doppler estimation curves for all the used SVs are plot in Figure 13, where O-KF-VT denotes the estimations based on VT-based SDR using the ordinary adaptive KF algorithm regardless of compensating the time-correlated error. During the beginning dozens of seconds, there is a fixed bias Doppler error between the VT-based GNSS SDR and the U-Blox receiver in terms of all the satellites, since it takes some time for the KF to converge. When the convergence procedure is done, the Doppler measurement value of which the quality is highly dependent on the accuracy of the clock drift estimation can be gradually close to the values produced by the U-Blox receiver as far as possible. According to the zoomed-in pictures which is displayed in Figure 13, related to SV8, SV15, and SV24, the Doppler outliers are more possibly induced by the ordinary adaptive KF algorithm and the one provided by the U-Blox receiver, while the A-VTTCES-KF manages to maintain producing the Doppler measurements with the higher quality when compared with these two traditional approaches. The velocity estimations through different algorithms are plot in Figure 14, where ST stands for the scalar tracking results of the GNSS SDR, and A-VTTCES-KF denotes the proposed algorithm as mentioned earlier. The tested ground vehicle was not moving at the first sixty seconds. After that, the autonomous vehicle started to move. The maximum absolute velocities in the east and north were approximately at 13 m/s and 9 m/s, respectively. The velocity estimation fails to be produced by the ST SDR after 18,370 s. Furthermore, it can also be found that there is a large estimation slip at around 18,310 s in the implementation process of the ST SDR. Figure 13: Doppler estimations of the GNSS SDR and U-Blox receiver during the time spanning of the field test. Outliers caused by the O-KF-VT SDR and the U-Blox receiver are highlighted while such cases seldom happen to the A-VTTCES-KF SDR. The error distributions produced by the RTK positioning method in the horizontal plain of the local level frame are illustrated in Figure 15. The error estimations output by the U-Blox receiver are also provided as the comparison. As shown in the figure, the number of the outliers are reduced by the proposed A-VTTCES-KF when compared with the ordinary KF algorithm. Figure 14: Velocity estimations for the field test. The maximum absolute velocities in the east and north were approximately at 13 m/s and 9 m/s, respectively. The velocity estimation fails to be produced by the SDR using ST loop after 18,370 s.  
Figure 15: RTK positioning errors distributed in the northern and eastern directions. The curves in terms of how the number of satellites contributing to the PVT solutions changes with the spanning of the navigation epochs are displayed in Figure 16. Referring to Figure 12, apart from SV10 and SV20, the power loss of the other satellites occurred due to the blockages in the environmental place from the GPS time of 18,250 s to 18,350 s. The ST-based GNSS SDR failed to neither keep tracking most of the navigation satellites nor output the PVT solutions during and after this period. Nevertheless, the degraded numbers of satellites rise back again after some durations with severely environmental interferences in the VT GNSS SDR. On the other hand, although the SDR using the VT algorithms, i.e., O-KF-VT and A-VTTCES-KF, is not as robust as the commercial and self-contained U-Blox receiver, the tracking loops assisted with the VT technique are more than enough to tolerate the weak situation for much longer time when compared with the traditional scalar tracking architecture. Since the field test is implemented in a moving autonomous ground vehicle, the dynamic stress residuals after the VT assistance on the tracking loop could be larger than the ones produced by a static receiver user.