# Scan Matching by Cross-Correlation and Differential Evolution
## 6 Results
 \\ \hline \multicolumn{10}{c}{**75 mm**} \\ \hline
25 th & 3.5 & 2.7 & 5.4 & 4.6 & 3.6 & 7.0 & 0.18 & 0.02 & 0.08 & 11.0 & 2.1 & 2.8 \\
50 th & 6.1 & 6.4 & 9.7 & 8.1 & 7.8 & 12.7 & 0.40 & 0.08 & 0.19 & 15.0 & 5.2 & 11.9 \\
75 th & 11.9 & 15.7 & 22.5 & 15.9 & 20.9 & 30.0 & 0.78 & 0.26 & 0.36 & 49.0 & 14.0 & 38.4 \\ \hline \multicolumn{10}{c}{**150 mm**} \\ \hline
25 th & 1.7 & 9.9 & 7.9 & 1.2 & 6.6 & 5.1 & 0.11 & 0.12 & 0.09 & 2.5 & 6.7 & 1.7 \\
50 th & 3.8 & 22.2 & 11.4 & 2.5 & 13.6 & 7.5 & 0.25 & 0.40 & 0.17 & 4.9 & 12.1 & 5.1 \\
75 th & 13.8 & 38.4 & 25.4 &The absolute and the relative rotation errors of all scan matching experiments are shown in Figure 7. The box plots clearly demonstrate that the proposed CORR algorithm achieves better (i.e., lower) error values for all observed translation error percentiles. The median relative error value of the CORR method is 2.8% while the standard ICP algorithm has relative error of 9.6%. Similarly to its performance on translation, the RMSE method performs the worst of the three compared scan matching strategies with median relative rotation error of 28.4%. Figure 7a also reveals some important information about the nature of rotation errors of the ICP and CORR methods. The rotation outliers, that is, scan matching cases with high absolute rotation error, are concentrated in the proximity of 90\({}^{\circ}\) and 180\({}^{\circ}\) values. The false alignments are caused by the tendency of both algorithms to converge to local rotation optima which is typically situated around 90\({}^{\circ}\), 180\({}^{\circ}\) and 270\({}^{\circ}\). This situation is illustrated in the following pair of figures. Figure 8a shows a wrong alignment at a local rotation optimum of 180\({}^{\circ}\), while Figure 8b shows the correct alignment. The relatively high number of rotation outliers in results obtained by the CORR method indicate its higher sensitivity to rotation errors, compared to the ICP algorithm. Figure 6: A boxplot visualization of the absolute (**a**) and the relative (**b**) translation error of all scan matching experiments (section Total of Table 2). Figure 7: A boxplot visualization of the absolute (**a**) and the relative (**b**) rotation error of all scan matching experiments (section Total of Table 2). Comparisons of translation and rotation errors of scan matching experiments in relation to the length of the robot trajectory between the scans are shown, respectively, in Figures 9 and 10. It can be seen that the ICP algorithm provides the best alignment for scans taken after the robot traveled between 75 mm to 450 mm. The error of scan alignment by ICP starts to rise for scans taken after the robot traveled 750 mm or more. Its accuracy deteriorates even more when matching laser range scans taken after the robot traveled long distances, that is, 1500 mm or 3000 mm. Based on the executed scan matching experiments, the proposed scan matching method (CORR) has for scans spaced 75 mm to 450 mm only slightly worse results than the ICP, still sufficient for practical indoor localization. However, the CORR algorithm shows superior results when matching laser range scans taken after the robot traveled long distances of 750 mm or more. In these cases, it provides significantly better localization than the standard ICP algorithm. Figure 8: An example of scan alignment by the CORR method: (**a**) Incorrect alignment due to a rotation error. (**b**) Correct alignment. Figure 9: Absolute (**a**) and relative (**b**) translation errors of scan matching experiments for laser range scans taken after robot movement of 75–3000 mm. Figures 9 and 10 also illustrate the convergence of the proposed approach. In contrast to the ICP, RMSE and CORR are both stochastic methods with random initialization. They were outperformed by the ICP for scans taken when the robot traveled between 75 and 750 mm in terms of minimum and average absolute and translation and rotation errors.