# Systematic Error Correction for Geo-Location of Airborne Optoelectronic Platforms
## 3 Results
### Flight Experiments and Results
#### 3.2.2 Systematic Error Solving  
Figure 10a shows the plane flies on the left side of the target (route L1) and Figure 10b shows the plane filed along the target (route L2). Table 5 shows the Samples of flight routes and relevant target points. A total of 260 sets of measurement data were obtained. Using the method mentioned in Section 2.3, the 260 sets of data are used to solve the best estimator of the systematic error and the computation result was shown in Figure 11.  
From Figure 10, it is not difficult to see that after 200 imaging measurements on the control points, the five installation errors are calculated as follows: the integrated navigation system heading direction is \(0.206^{\circ}\), the pitch direction is \(-0.198^{\circ}\), the roll direction is \(-0.098^{\circ}\). The azimuth angle of the imaging coordinate frame is \(0.061^{\circ}\), and the pitch angle is \(0.097^{\circ}\). Figure 11: The iteration curve of the installing errors for flight data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample ID** & **Route ID** & **Target ID** & **Usage** & **Number of Samples** \\ \hline S0 & L1, L2, L3 & P3 & For errors solving & 260 \\ S1 & L5 & P1 & For validation & 100 \\ S2 & L5 & P2 & For validation & 100 \\ S3 & L4 & P3 & For validation & 50 \\ S4 & L4 & P4 & For validation & 100 \\ S5 & L5 & P1 & For validation & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Samples of flight routes and relevant target points. Figure 10: Target positioning flight experiment: (**a**) The plane filed on the left side of the target; (**b**) The plane flew on the right side of the target. The geo-location error before and after systematic error correction of sample 0 is shown in Figure 12, where Figure 12a-c are the box plot of latitude, longitude and altitude, respectively. After correction, the root mean square error of latitude, longitude and altitude is reduced, and the mean value of the geo-location error is closer to zero. Table 6 is more intuitive. The root mean square error of target positioning is reduced from 45.65 to 12.62, and the target positioning accuracy is also reduced from 16.60 m to 1.24 m. The error correction effectively improves the geo-location accuracy of the system. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Conditions** & **Items** & \begin{tabular}{c} **Longitude** \\ **(deg)** \\ \end{tabular} & \begin{tabular}{c} **Latitude** \\ **(deg)** \\ \end{tabular} & \
\begin{tabular}{c} **Altitude (m)** \\ \end{tabular} &
\begin{tabular}{c} **Error (m)** \\ \end{tabular} \\ \hline before & sigma & 0.0003453 & 0.0002506 & 25.22 & 45.65 \\ correction & mean & 0.0001412 & 0.0001395 & \(-\)5.95 & 16.60 \\ \hline after & sigma & 0.0001021 & 0.0000745 & 7.17 & 12.62 \\ correction & mean & 0.0000044 & 0.0000010 & 0.55 & 1.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The comparison of geo-location between before and after correction. Figure 12: The computation results of the installing errors: (**a**) Box plot of latitude error of geo-location before and after correction; (**b**) Box plot of longitude error of geo-location before and after correction; (**c**) Box plot of altitude error of geo-location before and after correction; (**d**) Error of geo-location before and after correction. reduce the root-mean-square value of the geo-location error, but also make the mean error closer to 0, making preliminary preparations for future filtering:  
(1) Selection of sample points  
In order to avoid the singularity of the matrix \(\left(X^{T}X\right)\) in Equation (22), samples in a variety of states should be selected, such as the aircraft at different flying heights, positions, and different attitudes. The installation error can be solved more stably. Since different platforms have different laser rangefinder, it difficult to give a suitable flight path for the calibration.