## 4 Results and Discussion
### Tests Carried Out against Beacons Arranged in a Triangle  
These tests simulated a single pass and 100 SV passes along a straight stretch of the road against three beacons arranged in a triangle. They resulted in two sets of analysed data, i.e., a set of five series of 300 positions and a set of five hundred series of 300 positions. Based on these, Table 2 and Figures 15-23 were prepared for the analysis of the second group of test results. Figure 15 shows an overview of the location of the beacons in the triangle and the estimated positions relative to them during single and 100 SV crossings. Comparing Figures 6 and 15 with each other, it can be seen that the estimated positions are scattered around the reference positions in similar manners. There is an increase in the scatter of positions estimated by the GLSA method, before and after the SV passes the extreme beacons (although it should be noted here that it is much smaller). The positions estimated by the EKF and GRA methods have the most considerable clustering in relation to the reference positions. Table 2 shows the values of selected parameters of the statistical scatter of the distance to the reference position from the estimated position. Analysing the values of the arithmetic mean and standard deviation in Table 2, it is possible to identify the GRA and EKF methods as clearly the best, the GLSA method as worse, and the DR method as clearly the worst. On the other hand, by comparing Table 1 and Table 2 with each other, it should be noted that the values of the statistical parameters relating to the GLSA and GRA methods have changed most significantly in favour (they are \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**Maximum Distance to**} & \multicolumn{2}{c}{**Arithmetic Mean of**} & \multicolumn{2}{c}{**Standard Deviation**} \\
**Positioning** & \multicolumn{2}{c}{**the Reference Position**} & \multicolumn{2}{c}{**the Distance to**} & \multicolumn{2}{c}{**Distance to Reference Position**} \\
**Method** & \multicolumn{2}{c}{**(m)**} & \multicolumn{2}{c}{**the Reference Position**} & \multicolumn{2}{c}{**Position**} \\  & & & & **(m)** & & **(m)** \\ \hline  & Single & 100 & Single & 100 & Single & 100 \\  & passage & crossings & crossing & crossings & crossing & crossings \\ \hline GLSA & 78.52 & 88.89 & 3.53 & 3.39 & 9.90 & 8.95 \\ \hline EKF & 11.87 & 12.42 & 2.21 & 2.11 & 2.29 & 2.20 \\ \hline GRA & 6.22 & 6.53 & 1.32 & 1.40 & 1.08 & 1.14 \\ \hline DR & 31.48 & 30.61 & 15.22 & 16.06 & 8.32 & 8.39 \\ \hline \end{tabular}
\end{table} 
Table 2: Statistical parameters of the scatter of the distance to the reference position from the positions estimated by the GLSA, EKF, GRA, and DR methods. Figure 15: Triangle alignment of beacons and SV positions estimated relative to them during: (**a**) a single crossing, (**b**) 100 crossings. approximately twice as small). This is undoubtedly an effect of the non-co-linear alignment of the beacons with respect to each other (thus obtaining a better so-called 'geometric coefficient' calculated from the trace of the matrix \(\mathbf{C_{X}}\)). Figures 16 and 17 show plots of distance and arithmetic mean distance to the reference position from the estimated position during single and 100 SV crossings as a function of time. Comparing the graphs in Figures 7 and 8 with the graphs in Figures 17 and 18, there is an apparent reduction in the distance to the reference position from the GLSA-estimated position from about 100 m to about 40 m in the initial and final phases of the test. The curves of the other graphs are similar to each other. Figures 18 and 19 plot the moving mean distance to the reference position from the estimated position during a single and 100 SV crossings as a function of time. The graphs plotted against each other in Figures 18 and 19 clearly show that the GRA method estimates the position with the smallest moving mean distance to the reference position; this occurs almost throughout the entire test.