## 6 Results
### Ambiguity Resolution  
Concerning the evaluation of the ambiguity resolution, there are two questions we would like to answer. To make this possible, data of three flight tests (Flights 1-3) and three measurements with the previously-presented test setup (Tests 1-3) are used. All of these measurements were performed on different days and at different locations.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Specifications**} & \multicolumn{2}{c}{**Adis16488**} & \multicolumn{2}{c}{**Imar-INS** (aNA-FJ1-SURV)} \\ \cline{2-4}  & **Gyros** & **Accelerometer** & **Fibre Optic Gyros** \\ \hline Full Scale & \(\pm\)450\({}^{\circ}\)/s & \(\pm\)18 g & \(\pm\)150\({}^{\circ}\)/s \\ Bias Stability & 6\({}^{\circ}\)/h & 0.1 mg & \(<\)0.003–0.01\({}^{\circ}\)/h \\ Random Walk & 0.3\({}^{\circ}\)/\(\sqrt{h}\) & 0.029 m/s/\(\sqrt{h}\) & 0.001\({}^{\circ}\)/\(\sqrt{h}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the IMUs.  
Figure 4: The measurement setup for the accuracy evaluation tests. This setup replicates the direct georeferencing of the UAV platform and includes a reference system for the attitude accuracy evaluations.  
1. How often does the ambiguity resolution algorithm succeed in fixing the ambiguities in the first epoch (instantaneously) after a loss of lock?  
Table 2 shows single-epoch ambiguity resolution success rates. For calculating these values, the complete integer ambiguity estimation process was re-initialized in every single epoch of the datasets. In the presentation of these values, a distinction is made between the three steps (Steps i-iii) of our ambiguity resolution algorithm (Section 2.3), on the one hand, and a standard ambiguity resolution algorithm, on the other hand. This standard ambiguity resolution algorithm includes a float solution without any prior information, an integer ambiguity estimation with the MLAMBDA method and a ratio test with a threshold of three.  
It can be seen that our algorithm leads to instantaneous ambiguity resolutions in more than 90% of the epochs. Compared to the standard approach, this is a significant improvement, especially during the UAV flights, where the GPS measurement conditions have been more challenging, due to buildings and vegetation in the surrounding areas.  
Within the different steps of our algorithm, a significant increase of the success rate can be seen between Step (i) and Step (ii), whereas the difference between Step (ii) and Step (iii) is smaller for the single-epoch ambiguity resolutions. In Flight 1, the success rate after Step (iii) even is smaller than after Step (ii). The reason for this is that some fixed solutions from Step (i) or (ii) have been rejected in the validation of Step (iii).  
2. What is the average time to fix the ambiguities?  
To answer the second question, the integer ambiguity estimation process was restarted in every epoch again, but now, the algorithm always proceeded for as many epochs as needed to resolve the ambiguities. In this way, each time to first fix could be measured. Figure 5 presents the percentage of cases in which the ambiguities could be resolved after a certain time. Here, also, a comparison is made between the standard and our improved ambiguity resolution algorithm. Accordingly, with our algorithm, the ambiguities could at least after 5 s be resolved in more than 99% of the cases during UAV flights. In contrast, with the standard algorithm, the ambiguities could after 5 s only be resolved in 20% of the cases during the UAV flights.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Standard (\%)** & **Step (i) (\%)** & **Step (ii) (\%)** & **Step (iii) (\%)** \\ \hline Flight 1 & 9.85 & 83.25 & 97.79 & 96.47 \\ Flight 2 & 7.28 & 98.06 & 98.66 & 99.11 \\ Flight 3 & 4.19 & 78.87 & 92.61 & 93.48 \\ \hline Test 1 & 24.92 & 95.95 & 98.75 & 99.53 \\ Test 2 & 34.84 & 84.70 & 91.21 & 91.78 \\ Test 3 & 32.65 & 84.69 & 96.17 & 96.17 \\ \hline