## 5 Localization Algorithm Performance
### Position Accuracy
An example for the improvement in position accuracy provided by the odometry is the reduction of the 95% quantile for data set 1 from \(6.2\,\mathrm{m}\) without odometry aiding to \(4.2\,\mathrm{m}\) with odometry aiding for the multi-frequency/multi-constellation algorithm. For the multi-frequency GPS algorithm, the improvement is even larger, reducing the 95% quantile for data set 1 from \(8.2\,\mathrm{m}\) to \(4.4\,\mathrm{m}\). These findings correspond to the hypothesis that odometry aiding is most beneficial to positioning accuracy when GNSS measurement quality is poor, which is the case for a significant amount of time in data set 1 (see Table 10 for a more detailed analysis of GNSS measurement quality in both data sets). A distinction between an error in the output of the localization algorithm under test \(\hat{p}\) and an error in the reference value \(p_{ref}\) is generally impossible. Consequently, the evaluation of the estimation error \(\hat{p}_{en}^{n}\) is not as meaningful when the reference solution's quality is poor as it is when this quality is high. That is why the data sets need to be dissected into multiple parts to facilitate a more detailed analysis of the algorithm's positioning performance. Dissecting is done based on the quality of the reference solution. Table 9 lists Inertial Explorer's six different _quality numbers_ as well as their description and the corresponding 3-D accuracy. Based on the 3-D accuracy estimated by the processing software, Inertial Explorer assigns one of these quality numbers to each epoch of the reference solution. On the basis of the RMS error obtained from the static 24 h data sets (see Table 6), a 3-D accuracy in the order of 1-2 m is expected from the multi-frequency/multi-constellation algorithm under good conditions. Therefore, only epochs with quality numbers 1 and 2 (max. estimated 3-D error 0.4 m) are able to provide a reference solution that is significantly more accurate than the algorithm under test. Epochs with quality numbers 3 and 4 yield a maximum estimated 3-D error of 2 m, putting them on par with the RMS error obtained from the static 24 h sets. Epochs with quality numbers 5 and 6 may produce 3-D errors up to 10 m, rendering them unfeasible as reliable reference. Because both the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Inertial Explorer** & \multirow{2}{*}{**Description**} & \multicolumn{2}{c}{**3-D Accuracy of**} \\
**Quality Number** & & **Ref. Solution (in m)** \\ \hline
1 & Fixed integer & 0.00–0.15 \\ \hline
2 & Converged float or noisy fixed integer & 0.05–0.40 \\ \hline
3 & Converging float & 0.20–1.00 \\ \hline
4 & Converging float & 0.50–2.00 \\ \hline
5 & DGNSS & 1.00–5.00 \\ \hline
6 & DGNSS & 2.00–10.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Quality Number Description and Associated 3-D Accuracy for Novatel’s Waypoint-Inertial Explorer [21]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Quantity** & \multicolumn{3}{c}{**Data Set 1,**} & \multicolumn{3}{c}{**Data Set 1,**} & \multicolumn{3}{c}{**Data Set 2,**} & \multicolumn{3}{c}{**Data Set 2,**} \\  & **Odometry Off** & **Odometry On** & **Odometry Off** & **Odometry On** \\ \hline Arithmetic & \([-0.7;\ 0.5;\ 0.9]\) & \([-0.8;\ 1.2;\ 0.2]\) & \([-0.3;-0.4;-1.8]\) & \([-0.4;-0.6;-2.1]\) \\ mean of \(\hat{p}_{en}^{n}\) & \([\ 0.6;\ 0.1;\ 1.2]\) & \([\ 0.6;\ 0.6;\ 0.  
reference and the algorithm under test suffer from the same limitations in GNSS signal reception and thus GNSS measurement quality, the algorithm under test is likely to produce worse results during these epochs than it produces under the very good conditions prevalent in the static data. Hence, the reference is expected to be more accurate than the algorithm under test during epochs with quality numbers 3 and 4 as well. However, as the magnitude of the estimation error is comparatively more uncertain, the RMS errors for these quality numbers given in Table 10 could be significantly higher or lower.