# Scan Matching by Cross-Correlation and Differential Evolution
## 6 Results  
In this section, the results of the computational experiments are detailed and the proposed evolutionary scan matching strategy based on cross-correlation (denoted CORR) is compared with a recent approach based on root mean square error (denoted RMSE) [44] and with the standard ICP algorithm [52]. Table 2 provides the results of the comparison between the ICP, RMSE and CORR scan matching strategies. The table is divided into 8 sections. Each of the first 7 sections summarizes the relative and absolute translation and rotation errors of all scan matching cases for scans taken after the robot traveled 75, 150, 300, 450, 750, 1500 and 3000 mm, respectively. The 8 th section provides a summary of the errors for all scan matching experiments. The absolute translation error is the euclidean distance between the true (\(l_{\text{true}}\)) and the estimated (\(l_{\text{est}}\)) location of the robot. The relative translation error (in percent) is defined as  
\[\delta_{l}=\frac{|l_{\text{true}}-l_{\text{est}}|}{l_{\text{true}}}\cdot 100. \tag{13}\]  
The absolute rotation error is calculated as the difference between the true (\(\Phi_{\text{true}}\)) and the estimated (\(\Phi_{\text{est}}\)) rotation of the robot and its relative form (in percent) is defined as  
\[\delta_{\Phi}=\frac{|\Phi_{\text{true}}-\Phi_{\text{calc}}|}{\Phi_{\text{ true}}}\cdot 100. \tag{14}\]  
The _percentile values_ corresponding to the 25 th, 50 th and the 75 th percentile (i.e., the lower quartile, median and the upper quartile) of the errors for each algorithm are shown in the individual sections of Table 2. The lower the percentile value, the better the results and thus the algorithm performance. Figure 5: Simulation framework: an example of a map, robot trajectory (**yellow**) and two simulated laser scans (**red**, **blue**). Figure 6 illustrates the distribution of the absolute and the relative translation errors of all scan matching experiments performed with the ICP, RMS and CORR algorithms. Results shown in Figure 6b indicate that the difference between the medians of the relative translation errors of the standard ICP and the proposed CORR algorithm is not significant (5.1% ICP, 5.3% CORR). This can be attributed to the uniformly distributed noise generated by the simulation framework used for the experiments [45]. Furthermore, the CORR method has significantly lower translation error values at the lower and upper quartiles than the other tested methods. This shows that the proposed algorithm achieves for the majority of the considered test cases a robust and accurate scan matching functionality. In general, the RMSE method obtains scan matching with a higher error than the other two methods. \begin{table}
\begin{tabular}{c r r r r r r r r r r r} \hline \hline \begin{tabular}{c} **Per-** \\ **Cen-** \\ **tile** \\ \end{tabular}  & \begin{tabular}{c} **Absolute** **Translation Error** \\ **(mm)** \\ **ICP** \\ \end{tabular}  & \begin{tabular}{c} **Relative** **Translation Error** \\ **RMSE** \\ \end{tabular}  & \begin{tabular}{c} **Absolute** **Rotation Error** \\ **(\%)** \\ **RMSE** \\ \end{tabular}  & \begin{tabular}{c} **Relative** **Rotation Error** \\ **CORR** \\ \end{tabular}  & \ \begin{tabular}{c} **Relative** **Error** \\ **(\%)** \\ **RMSE** \\ \end{tabular}  & \begin{tabular}{c} **Relative** **Error** \\ **CORR** \\ \end{tabular}