## 6 Results
### Accuracy  
For the accuracy evaluation, the dataset \"Test 2\" is used in the following, which includes static and kinematic parts. During the kinematic part, the measurement setup was carried by two persons, trying to simulate typical UAV dynamics.  
In Figure 6, the differences between the method described here and the reference attitude (Imar INS) are shown. It can be seen that the maximum difference is less than 0.5\({}^{\circ}\) for all attitudes, where the roll and the pitch angle seem to be more accurate than the yaw angle. The mean, the root mean square (rms) values and the maximum deviations (max), which were determined on the basis of the shown differences, are presented in Table 3. The rms for the roll and the pitch are about 0.03\({}^{\circ}\) in the static mode and 0.05\({}^{\circ}\) in the kinematic mode. The rms for the yaw angle is about 0.2\({}^{\circ}\) for a static and a kinematic mode, where the deviations of the yaw angle are mainly caused by the systematic errors of the GPS attitude baseline.  
In Figure 7, the Pos/IMU/Mag/Base yaw angle differences from Figure 6 are compared to the GPS baseline attitude differences and the differences of the Pos/IMU/Mag solution. The maximum deviation of the Pos/IMU/Mag solution lies in the first static part of the measurement, where the yaw angle determination has mainly been influenced by the magnetic field observations. Even if these deviations are in the order of a few degrees, the solution still serves as good prior information for the ambiguity search. From experience, this is the same for UAV flights, where the deviations between the prior information and the GPS attitudes usually have a comparable magnitude to the deviations seen here. Due to the coupling with the GPS positions (we used RTK GPS positions), in combination with horizontal accelerations, the deviations decreased during the kinematic part of the measurement.  
Although the ambiguities were held fixed for the GPS base solution (Figure 7), the cycle slip detection led to a re-initialization of the ambiguities in two epochs during this test. Furthermore, some GPS base outliers are also conspicuous (e.g., after _ca._ 4.2 min). However, the outliers do not deteriorate the attitudes from the Pos/IMU/Mag/Base integration.  
Figure 5: Ambiguity resolution (Amb. res.) success rates after a certain time, determined with a standard ambiguity resolution algorithm (standard) and our ambiguity resolution algorithm (improved) for flight test data (Flight) and test setup data (Test).  
Figure 6: Difference between the reference Euler angles (Imar INS) and the Euler angles ((**a**): roll, (**b**): pitch, (**c**): yaw), which result from the Pos/IMU/Mag/Base integration of our system. The kinematic parts are marked with a gray background.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Roll** (\({}^{\circ}\)) & **Pitch** (\({}^{\circ}\)) & **Yaw** (\({}^{\circ}\)) \\ \hline \multirow{3}{*}{static} & mean & 0.009 & \(-\)0.005 & \(-\)0.188 \\  & rms & 0.027 & 0.032 & 0.221 \\  & max & 0.105 & 0.194 & 0.440 \\ \hline \multirow{3}{*}{kinematic} & mean & \(-\)0.007 & 0.018 & \(-\)0.162 \\  & rms & 0.054 & 0.052 & 0.196 \\ \cline{1-1}  & max & 0.237 & 0.221 & 0.388 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of an experiment with the test setup.