## 3 Results and Discussion
### Impacts of Filtering
#### 3.1.3 Distance  
Distance was the only recorded metric which was not used as a basis for filtering. Average inter-vehicle distance values, shown in Table 3, suggest that truck 3 drove closer to its preceding truck than what truck 2 did. This was visually confirmed from video footage. After curation, average values were 38.6 and 36.1 m, for trucks 2 and 3, respectively. Still, distributions of distances appear to differ somewhat, with spikes at 0-10 m for truck 2, and 10-20 m for truck 3. Unfiltered maximum distance values for trucks 2 and 3 were 74.4 and 71.5 m, respectively, and were virtually unaffected by filtering. Only filter 5 (downsampling) reduced maximum distances, and only by 0.1 m in both cases. This resulted in curated maximum distances of 74.3 and 71.4 m. While distance ranges were never systematically tested, maximum distance values may be used as a proxy. While driving on straight road segments, inter-vehicle distances oscillated. The trucks would occasionally drive closely together before becoming dispersed, travelling with spacing between the trucks so large that each preceding truck was eventually located beyond sensor range. Thus, for each truck, measure \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Truck Number**} \\ \cline{2-7}
**Filtering** & \multicolumn{3}{c}{**2**} & \multicolumn{3}{c}{**3**} \\ \cline{2-7}
**Step** & **Average** & **Maximum** & **Standard** & **Average** & **Maximum** & **Standard** \\ \hline Raw & 26.5 & 74.4 & 17.6 & 25.2 & 71.5 & 15.9 \\
1 & 33.5 & 74.4 & 14.8 & 29.3 & 71.5 & 14.5 \\
2 & 35.5 & 74.4 & 14.3 & 34.4 & 71.5 & 12.3 \\
3 & 37.4 & 74.4 & 13.0 & 35.5 & 71.5 & 11.5 \\
4 & 37.2 & 74.4 & 12.9 & 35.3 & 71.5 & 11.5 \\
5 & 38.2 & 74.3 & 13.0 & 36.1 & 71.4 & 11.5 \\
6 & 38.6 & 74.3 & 12.9 & 36.1 & 71.4 & 11.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distance metrics (in meters) after each filtering step. ments should exist at the radar range boundary. As stated, filter 6 (_LWRR_) did not further reduce maximum distance values than what filter 5 did. Figure 7 shows that filter 6 did not further reduce maximum distance values since it had little effect beyond approximately 50-55 m. Since _LWRR_ video coding was carried out visually, somewhat imprecisely, the farthest radar measurements still tend to appear in _LWRR_-filtered data. Had it been more precise, maximum distance values following filter 5 would best represent _actual_ upper sensor ranges. The aforementioned maximum distance values for trucks 2 and 3 fall short of the theoretical ranges 75.0 and 73.1 m by 0.9% and 2.4%, respectively. Hence, both sensors appear to underperform slightly versus expected ranges, but still fall within the estimate provided by the supplier. The deviation is smallest for truck 2. Since the datasets from both trucks are otherwise comparable, the chosen parameter values \(N_{s}\) and \(f_{0}\) for the radar sensor in truck 2 appears to be preferable. Future testing could explore this. For the curated radar data, average relative velocity and average SNR were inspected as a function of inter-vehicle distances. For both trucks 2 and 3, these metrics were calculated within successive 10-m distance bins. The lower bin was 0-10 m, and the upper bin was 70 m and above. For all bins, average relative velocities fell within the error margin of the sensors. On the other hand, average SNR values are more interesting. For all bins, average SNR very seldomly fell below 30 dB, and remained high even at long distances, indicating that the radar cross-sections of the preceding trucks are sufficiently large to allow for longer detection ranges, cf. Tables A8 and A9 in Appendix A.4. Thus, parameters could likely have been chosen to achieve a maximum range approaching, and perhaps even exceeding, 100 m. The radar user manual illustrates that cars can be detected at 75 m, while buildings can be detected at 100 m. Due to the size of the truck rear walls, they may provide 'building-like' detection ranges.