## 3 Experiment
### Performance Analysis of TDCP-Aided GNSS with Method A  
Under an open-sky condition (e.g., PDOP value was less than four, such as Figure 11 (scenario D)), the results of TDCP-aided GNSS with/without method A were acceptable. It indicates that phase-smoothing is a critical factor in obtaining a reliable result. However, in constrained environments, due to enhanced positional connection between the adjacent epochs, TDCP-aided GNSS plus method A exhibited a more reliable outcome (blue and black lines) compared with the others without method A. For instance, in Figure 9 (scenario B, time 815 s), when the phase-smoothing approach was unavailable, the use of method A was able to improve the position state estimation, reducing the E-direction error by around 3.60 m when comparing with TDCP-based GNSS. Moreover, for the situation of deteriorated results due to the degraded cycle-slip detection (during time 872-875 s and at time 975 s), in these signal-degraded environments, the positioning errors produced with method A mitigated from 7.82 to 3.58 m (at time 873 s) and 5.53 to 2.38 m (at time 975 s) in the horizontal direction, being able to reach the SPP-nominal level. A similar case could be found in Figure 10 (scenario C, during time 963-969 s). Figure 10: (**a**) Evaluated trajectory and (**b**) error analysis for scenario C.  
Figure 11: (**a**) Evaluated trajectory and (**b**) error analysis for scenario D.  
With the help of using method A, the benefit of the proposed zero-velocity constraint with position-fix design in (24)-(26) was significantly presented when the vehicle was stationary. Due to continuously faulty signal reception, the major contribution of method A could include the precise detection for vehicle speed, assuring the timing of stoppage, the duration time, and preventing the estimated position from presenting a deteriorated change. As shown in Figures 8-11 (scenarios A-D, during time 550-610 s, 835-863 s, 907-954 s, and 1636-1663 s, indicated by yellow circles), the solution with method A yielded a more accurate outcome. The aid of method A maintains the position output  
Figure 12: (a) Evaluated trajectory and (b) error analysis for scenario E.  
that is the same as the position state before transiting to the static, averting the use of unhealthy measurements. Table 3 shows the related analysis for the stationary condition in the experiment. The position accuracy in this situation improved because of method A, and the position accuracy in 3D attained 4.87 m with an improvement of 41.7%, demonstrating that the zero-velocity constraint with position-fix design successfully enhanced the performance in the challenging circumstance. For method A, the odometer provides only a relative constraint in positional displacement, and this study uses the constraint design in (16)-(22) in the velocity domain to improve this constraint, as mentioned earlier. However, this constraint is along the forward direction of the vehicle, meaning that its aid is less influential in the lateral direction, especially for the case where the estimated heading is degraded. Table 4 shows that method A improves the positional accuracy in the forward (RMSE 1.87 m), but has limited effectiveness in the lateral (RMSE 2.10 m, similar to the TDCP-based solution without method A). A representative situation was found in Figure 8 (scenario A, during time 519-547 s), where the solution with method A still presented a deteriorated trajectory misled to the oncoming road (indicated by the white dotted line). In addition, there is still a potential risk on the position-fix design for method A. In Figure 8 (scenario A, during time 550-610 s), the height error based on the scheme with method A presented an error of 12.12 m during the static motion. In this representative case, because the result of position estimation had insufficient time to revert to the stable state before transiting to the stationary, this degraded result was selected to be the position-fix output.