## 5 Localization Algorithm Performance
### Position Accuracy
For epochs with quality numbers 5 and 6, it is unclear which solution is more accurate: On the one hand, the reference solution encompasses GNSS correction data from a base station as well as measurements from a navigation grade IMU. On the other hand, the algorithm under test includes odometry measurements and the poor quality number already suggests that GNSS reception is seriously impaired, reducing the usefulness of the GNSS correction data used in the reference solution. That is why the RMS errors for these quality numbers in Table 10 can only give a rough impression of the algorithm's performance under these conditions. Table 10 details the performance of the most sophisticated algorithm version (multi-frequency/multi-constellation with calibrated DCBs and odometry aiding) depending on the reference solution quality. The different characteristics of the two data sets are represented in the percentage of epochs for each quality number: While 60% of epochs in data set 1 offer high accuracy (quality number 1 or 2), 34% feature intermediate accuracy (quality number 3 or 4) and 6% exhibit poor accuracy (quality number 5 or 6), these numbers are 70%, 27% and 3% in data set 2. This confirms that data set 2 comprises better GNSS reception conditions than data set 1 on average. Looking at the epochs with a reference solution quality number of 1 or 2, the RMS error in the horizontal coordinates is between 0.7 m and 1.1 m, compared to values between 0.6 m and 0.8 m for the individual static 24 h sets. The fusion of sensor data from GNSS, IMU and odometry is therefore capable of determining antenna position and attitude under kinematic conditions well enough to provide an estimate of the vehicle's position with similar accuracy as for static measurements with very good GNSS reception. The same holds for the vertical RMS error in data set 2, which is 1.3 m/1.4 m for a reference solution quality number of 1/2, compared to values between 1.3 m and 1.7 m for the individual static 24 h sets. In data set 1, the vertical RMS error is significantly higher with 2.4 m/2.5 m for a reference solution quality number of 1/2. This stems from an interval of approximately 5 min spend uninterruptedly inside an urban canyon. During this time span, the vertical position error rises to over 7 m. Odometry cannot provide information about the vehicle's vertical velocity and is therefore unable to aid the vertical position. The horizontal position error does not exceed 3 m throughout the same interval as odometry is able to limit the horizontal velocity error. The reference solution mostly achieves quality  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Inertial Explorer** & **Perc. of Epochs,** & **RMS of \(\rho_{ent}^{n}\)** & **Perc. of Epochs,** & **RMS of of \(\beta_{ent}^{n}\)** \\
**Quality Number** & **Data Set 1 (in \%)** & **Data Set 1 (in m)** & **Data Set 2 (in \%)** & **Data Set 2 (in \%)** \\ \hline
1 & 36 & [1.0; 0.9; 2.4] & 50 & [0.7; 0.9; 1.3] \\ \hline
2 & 24 & [1.0; 1.1; 2.5] & 20 & [0.8; 0.9; 1.4] \\ \hline
3 & 23 & [0.9; 2.1; 2.4] & 2  
number of 1 or 2 while inside the urban canyon. This is not the case when GNSS observations of base and rover are processed without measurements from the navigation grade IMU, demonstrating that GNSS conditions are in fact very challenging. In both data sets, the RMS position error for the epochs with reference solution quality number 3 is roughly on the same level as it is for the quality numbers 1 and 2. The single exception is the north component in data set 1 with an RMS error of 2.1 m. The fusion of GNSS, IMU and odometry data is therefore able to extent the range of high accuracy from epochs with good GNSS reception conditions to epochs when GNSS conditions start to deteriorate. Starting with reference solution quality number 4, the RMS position error in both data sets rises significantly. The maximum 3-D position error in data set 1 is approximately 20 m, in data set 2 approximately 10 m. Both error maxima occur for a reference solution quality number of 6.