## 3 Data Collection, Experimental Setup and NN Model Selection
### Dataset
#### 3.1.1 Performance Evaluation Metrics  
The performance of both the INS- and NN-based approaches are evaluated using the metrics defined below:  
Cumulative Root Squared Error (CRSE)--The CRSE measures the cumulative root squared of the prediction error every second for the total duration of the GNSS outage defined as 10 s. It ignores the contributions of the negative sign of the error estimations, enabling a better understanding of the performance of the positioning techniques. \[\text{CRSE}=\sum_{t=1}^{N_{t}}\sqrt{e_{pred}{}^{2}} \tag{20}\]  
Cumulative Absolute Error (CAE)--The CAE measures the absolute error of the prediction every second and summates the values throughout the duration of the GNSS outage, contrastingly to the CRSE, signs are not ignored. This tool is useful to better understand if the position technique is generally under or over predicting points and how prediction variance affects the overall positioning of the vehicle after the 10 s outage period. \[\text{CAE}=\sum_{t=1}^{N_{t}}e_{pred}. \tag{21}\]  
Average Error Per Second (AEPS)--The AEPS measures the average error of the prediction every second of the GNSS outage. It is useful to compare the general performance of the models and has uses in showing any significant outliers. \[\text{AEPS}=\frac{1}{N_{t}}\cdot\sum_{t=1}^{N_{t}}e_{pred}. \tag{22}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Challenging Scenarios**} & \multirow{2}{*}{**IO-VNB Data Subset**} & \multicolumn{2}{c}{**Total Time Driven, Distance**} \\  & & **Covered, Velocity** \\  & & **and Acceleration** \\ \hline \multirow{4}{*}{Roundabout} & V-Vta\(11\) & 1.0 min, 0.92 km, 26.8–97.7 km/h, \\  & & \(-\)0.45 to +0.15 g \\ \cline{2-3}  & V-Vfb02d & 1.5 min, 0.84 km, 0.0–57.3 km/h, \\  & & \(-\)0.33 to +0.31 g \\ \hline \multirow{4}{*}{Changes in acceleration} & V-Vfb02e & 1.6 min, 1.52 km, 37.4–73.9 km/h, \\  & & \(-\)0.24 to +0.19 g \\ \cline{2-3}  & V-Vta12 & 1.0 min, 1.27 km, 44.7–85.3 km/h, \\  & & 0.44 to +0.13 g \\ \hline \multirow{4}{*}{Hard Brake} & V-Vw16b & 2.0 min, 1.99 km, 1.3–86.3 km/h, \\  & & \(-\)0.75 to +0.29 g \\ \cline{2-3}  & V-Vw17 & 0.5 min, 0.54 km, 31.5–72.7 km/h, \\  & & \(-\)0.8 to +0.19 g \\ \cline{2-3}  & V-Vta9 & 0.4 min, 0.43 km, 48.9–87.7 km/h, \\  & & \(-\)0.6 to +0.14 g \\ \hline \multirow{4}{*}{Sharp Cornering and Successive left and right turns} & V-Vw6 & 2.1 min, 1.08 km, 3.3–40.7 km/h, \\  & & \(-\)0.34 to +0.26 g \\ \cline{1-1} \cline{2-3}  & V-Vw7 & 2.8 min, 1.23 km, 0.4–42.2 km/h, \\  & & \(-\)0.37 to +0.37 g \\ \cline{1-1} \cline{2-3}  & V-Vw8 & 2.7 min, 1.12 km, 0.0–46.4 km/h, \\  & & \(-\)0.37 to +0.27 g \\ \hline \hline \end{tabular}
\end{table} 
Table 3: IO-VNB data test subset used in the challenging scenarios. Mean (\(\mu\))--The mean of the CRSE, CAE and AEPS across all test sequences within each scenario is evaluated to reveal the average performance of the positioning technique in each scenario. \[\mu_{CRSE}=\ \ \frac{1}{N_{\rm s}}\sum_{i=1}^{N_{\rm s}}CRSE,\ \mu_{CAE}=\ \ \frac{1}{N_{\rm s}}\sum_{i=1}^{N_{\rm s}}CAE,\ \mu_{AEPS}=\ \ \frac{1}{N_{\rm s}}\sum_{i=1}^{N_{\rm s}}AEPS. \tag{23}\]  
Standard Deviation (\(\sigma\))--The standard deviation measures the variation of the CRSEs, CAEs and AEPSs of the sequences of each test scenario. \[\sigma_{CRSE}=\sqrt{\frac{\Sigma(CRSE_{i}-\mu)^{2}}{N_{\rm s}}}\,\ \sigma_{CAE}=\sqrt{\frac{ \Sigma(CRSE_{i}-\mu)^{2}}{N_{\rm s}}},\ \sigma_{AEPS}=\sqrt{\frac{\Sigma(CRSE_{i}-\mu)^{2}}{N_{\rm s}}}. \tag{24}\]  
where \(N_{t}\) is GNSS outage length of 10 s, \(t\) is the sampling period, \(e_{pred}\) is the prediction error and \(N_{\rm s}\) is the total number of test sequences in each scenario. Minimum (\(min\))--The minimum metric informs of the minimum CRSE, CAE and AEPS of all sequences evaluated in each test scenario. Maximum (\(max\))--The maximum CRSE, CAE and AEPS provide information of the maximum CRSE of all sequences evaluated in each test scenario. It provides information on the possible accuracy of the positioning techniques in such scenarios.