# Mapping with Pleiades--End-to-End Workflow
## 5 Results
### Sensor Modeling and Parameter Optimization  
As first task, the 2D geo-location accuracy of all sensor models is evaluated following the assessment protocol defined in Section 4.1. The resulting statistics are presented in Table 3. Statistics are given in across and along track direction such as for the absolute 2D length. Here, it can be observed that most of the images have mean circular errors (represented as mean initial length) below 17 pixels, which corresponds to the 8.5 m CE90 as reported in Reference [32]. The Trento triplet holds the largest geo-location errors even above the CE90 values. As second task, all sensor models are adjusted by optimizing the constant and linear RPC terms and the resulting RMS values are also reported in Table 3. The across and along track residuals are all in the sub-pixel range (0.3 to 0.9 pixels) and show a widely homogeneous behavior. According to the nominal GSD of 0.5 m, these pixel values correspond to geo-location errors in the range of 0.15 m to 0.45 m on ground. As discussed in Section 3, the lower bound of those errors is the accuracy of the reference data. As the reference was manually measured for some test sites better results cannot be expected. Note, that the accuracies are rather high when considering the reference LiDAR data with 1 m GSD for some of the test sites. Since the discretization and manual measurement errors are assumed to be of Gaussian distribution, the least squares adjustment may find solutions which are better than the individual measurements. As third task, a specific test is performed on the image 1 of the Innsbruck stereo test data (cf. Table 1 and Figure 3). The 2D geo-location accuracy of this selected sensor model is evaluated where the parameter optimization is once based on releasing only the constant term of the RPC nominators and once by releasing the constant and linear terms. To doing so, the given 30 GCPs are divided into different sets of GCPs and ICPs. The results of this analysis, including mean and STD of checkpoint residuals, are summarized in Table 4. The table shows that utilization of the absolute minimum number of GCPs (i.e., 1 for constant and 4 for constant and linear coefficient optimization) yields systematic errors for both scenarios, as expressed by the mean residual values. Appropriate over-determination, for example, utilization of 10 GCPs in this assessment, reduces such systematic errors significantly. The numbers also show that removing the shift only might be sufficient to achieve reliable accuracy, which is also confirmed in Reference [42]. Overall, we propose to perform the constant and linear-based adjustment since smaller residuals are retrieved and potentially systematic errors can be reduced. As fourth task, another specific test is performed on all six images from the Ljubljana test site. Here, the sensor models are adjusted based on the optimization of constant and linear terms with the given GCPs. Then, those models are also evaluated on the ICPs to assess if an over-fitting occurs. Statistics are presented in Table 5. Here, the mean standard deviations after adjustment are 0.47 pixels for GCPs and 0.73 pixels for ICPs. As expected, the models adjust to the GCPs but also give decently small errors on ICPs. Overall, all models show initial displacements and thus have to be corrected before continuing with the mapping workflow. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**GCPs**} & \multirow{2}{*}{**ICPs**} & \multicolumn{2}{c}{**Mean [pxl]**} & \multicolumn{2}{c}{**STD [pxl]**} \\  & & & & **Across** & **Along** & **Across** & **Along** \\ \hline constant & 1 & 29 & 1.23 & 0.32 & 0.97 & 0.78 \\ terms & 10 & 20 & \(-\)0.14 & \(-\)0.23 & 1.04 & 0.80 \\  & 30 & 30 \({}^{\dagger}\) & 0.00 & 0.00 & 0.98 & 0.77 \\ \hline constant & 4 & 26 & \(-\)1.90 & \(-\)1.27 & 1.21 & 1.08 \\ and linear & 10 & 20 & 0.09 & \(-\)0.46 & 1.04 & 0.79 \\ terms & 30 & 30 \({}^{\dagger}\) & 0.00 & 0.00 & 0.90 & 0.59 \\ \hline \hline \end{tabular}
\end{table}