## 4 Results and Discussion
### Motorway Scenario  
In evaluating the performance of the INS and the NN approaches on vehicular motion tracking, both techniques are investigated on a less challenging trajectory characterised by an approximate straight-line drive on the motorway. The results, as shown on Table 8, show that across all 9 test sequences, the INS records its best and average displacement and orientation rate CRSE of 1.63 m, 15.01 m, and 0.08 rad/s, 0.13 rad/s, respectively. However, we observe that the NN outperforms the INS significantly on the displacement and orientation estimation across all metrics, as illustrated in Figure 4. Comparatively, the best and average displacement and orientation rate CRSE of the NN approach is recorded as 0.84 m and 1.93 m, and 0.08 rad/s and 0.13 rad/s. Essentially, this shows that the NN is able to offer up to an 89% improvement on the displacement max CRSE metric after about 268 m of travel. Achieving a CAE best of 0.16 m Northwards and 0.016 m Eastwards, the results also indicate that it is possible to estimate the vehicle position with lane-level accuracy using the proposed approach. Being the lowest errors across all scenarios evaluated as shown in Figures 4-7, we can infer that this was the least challenging scenario due to minimal accelerations and directional change. Furthermore, the reliability of the NN in consistently tracking the vehicles' motion with such accuracy is highlighted by its low standard deviation of 0.84. Figure 8b shows the trajectory of the vehicle along the motorway. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Displacement Estimation** & **Orientation Estimation** \\ \hline Learning rate & 0.004 & 0.001 \\ \hline Dropout & 10\% & 10\% \\ \hline Sequence Length & See Table 3 & See Table 2 \\ \hline Hidden layers & 2 & 2 \\ \hline Hidden neurons & 32 per layer & 32 per layer \\ \hline Batch Size & 256 & 256 \\ \hline Epochs & 40 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Training parameters for the IDNN. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **IDNN (m)** & **INS DR (m)** & \
\begin{tabular}{c} **IDNN** \\ **(Rad/s)** \\ \end{tabular} &
\begin{tabular}{c} **INS DR \\ **(Rad/s)** \\ \end{tabular} \\ \hline \multirow{4}{*}{CRSE} & max & 3.23 & 30.11 & 0.05 & 0.21 \\ \cline{2-6}  & min & 0.84 & 1.63 & 0.02 & 0.08 \\ \cline{2-6}  & \(\mu\) & 1.93 & 15.01 & 0.04 & 0.13 \\ \cline{2-6}  & \(\sigma\) & 0.84 & 9.12 & 0.01 & 0.03 \\ \hline \multirow{4}{*}{CAE} & max & 2.56 & 30.11 & 0.02 & 0.13 \\ \cline{2-6}  & min & 0.19 & 0.04 & 0.00 & 0.04 \\ \cline{2-6}  & \(\mu\) & 0.96 & 13.33 & 0.01 & 0.10 \\ \cline{2-6}  & \(\sigma\) & 0.84 & 10.17 & 0.01 & 0.03 \\ \hline \multirow{4}{*}{AEPS (/s)} & max & 0.06 & 0.30 & 0.00 & 0.00 \\ \cline{2-6}  & min & 0.00 & 0.01 & 0.00 & 0.00 \\ \cline{2-6}  & \(\mu\) & 0.02 & 0.15 & 0.00 & 0.00 \\ \cline{2-6}  & \(\sigma\) & 0.02 & 0.10 & 0.00 & 0.00 \\ \hline \multirow{4}{*}{Total Distance} & max & 268.40 & & & \\ \cline{2-6}  & min & 234.47 & & & \\ \cline{2-6}  & \(\mu\) & 251.29 & & & \\ \cline{2-6}  & \(\mu\) & & & & \\ \hline Number of Sequences evaluated & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Showing the performance of the IDNN and dead reckoned Inertial Navigation Systems (INS DR) on the motorway scenario. Figure 4: Showing the evolution of the estimation error over time in the motorway scenario based on the (**a**) Displacement CRSE, (**b**) Displacement cumulative absolute error (CAE), (**c**) Orientation rate CRSE and (**d**) Orientation rate CAE. Figure 5: Showing the comparison of the CAE performance of the IDNN and INS DR across all investigated scenarios on the (**a**) displacement estimation and (**b**) orientation rate estimation. Figure 6: Showing the comparison of the average error per second (AEPS) performance of the IDNN and INS DR across all investigated scenarios on the (**a**) displacement estimation and (**b**) orientation rate estimation.