## 3 Results and Discussion
### GNSS Localization  
The results from the static tests are shown in Table 1. The columns represent the time that the user stayed in the same location and each row presents the data for a receiver. The values in the table are  
Figure 5: Straight-line path for the autonomous vehicle. pairs of standard deviations calculated for the easting and northing coordinates. Because the coordinates are in the UTM format, all values are expressed in meters. The data in Table 1 show the positioning accuracy obtained using the two GNSS modules. The UPD produced an accuracy of 8 cm easting, and 9 cm northing when the external DGNSS module was used for 1 min. The accuracy increased as more time was spent at a particular; e.g., the accuracy was 3 cm easting and 4 cm northing after 5 min. The best accuracy achieved with the internal GNSS receiver was 5 cm easting and 30 cm northing after 5 min. The DGNSS receiver was twice as accurate in the easting coordinate and approximately five times more accurate in the northing coordinate than the internal GNSS receiver. Figure 6a and b present the number of occurrences within each position range measured using the internal GNSS receiver over a 5 min interval (300 samples) for the easting and northing coordinates. All sampled easting locations fall within a range of 60 cm, and approximately 60% of the measurements are within a 20 cm range (40-60 cm, see Figure 6a). All but one recorded that northing locations fall within a range of 200 cm, and approximately 75% of the measurements are within a 120 cm range (40-160 cm, see Figure 6b). Figure 7a and b present the number of occurrences within each position range measured using the external DGNSS receiver over a 5 min interval (300 samples) for the easting and northing coordinates. All sampled easting locations fall within a range of 40 cm, and approximately 65% of the measurements are within a 20 cm range (20-40 cm, see Figure 7a). All the sampled values are within the first two intervals (compared to Figure 6a). The recorded northing locations fall within a range of 80 cm, and approximately 90% of the measurements are within 40 cm (300-340 cm, see Figure 7b). \begin{table}
\begin{tabular}{c c c c} \hline  & **1 min** & **2 min** & **5 min** \\ \hline
**GNSS \(\Delta\) [E,N] [m]** & [0.13, 0.33] & [0.10, 0.30] & [0.05, 0.30] \\
**DGNSS \(\Delta\) [E,N] [m]** & [0.08, 0.09] & [0.04, 0.05] & [0.03, 0.04] \\ \hline \end{tabular}
\end{table} 
Table 1: Static positioning accuracy. Figure 6: GNSS easting (**a**) and northing (**b**) distribution. According to the results presented in Table 1 and Figures 6 and 7, both receivers had better easting than northing accuracy. This effect was greater when the internal GNSS receiver was used; the difference between the standard deviations of the easting and northing coordinates was greater than when the external DGNSS receiver was used. However, both receivers provided sub-meter accuracy in all tests. Additionally, there was no dependency between the positioning accuracy and the time spent at one location, or at least no dependency could be found using standard statistical measures, such as the standard deviation. Figure 8 present the results from the second set of tests, in which the deviation between the straight line path and actual path was measured. The actual paths for both the internal GNSS and external DGNSS receivers are plotted. There are 22 locations in total, so it took 22 s to cover the 20 m distance between points A and B. The traverse began at the bottom left point and ended at the top right point (_i.e._, from southeast to northwest). The red line in Figure 8 represent the straight line path. The other two lines correspond to data from the selected receivers. The blue line, representing the external DGNSS receiver, does not greatly  
Figure 8: Deviation between the straight line path and the actual path obtained using the GNSS and DGNSS receivers. Figure 7: DGNSS easting (**a**) and northing (**b**) distribution.