# An Improved MbICP Algorithm for Mobile Robot Pose Estimation
## 3 Results
### Evaluation Method
We repeated each matching experiment 10 times with these two algorithms for each overlapping percentage and each scenario (a total of 400 runs), and the common parameters were identical. Figure 12: (**a**) Object scan (blue) and reference scan (red); (**b**) matching result from the standard MbICP algorithm (red dots-reference scan, blue dots-transformed object scan); (**c**) matching result from the improved MbICP algorithm (red dots-reference scan, blue dots-transformed object scan); (**d**) iteration process. Figure 13: _Cont._  
We first discuss the results in terms of robustness. A scan match was considered a failure when the solution was larger than 0.1 m in translation and 3.14\({}^{\circ}\) in rotation. Solutions with an error below the threshold were used in a follow-up precision analysis. _True Positives_ (converged to the right solution), _False Positives_ (converged to an incorrect solution), _True Negatives_ (not converged but the solution is correct) and _False Negatives_ (not converged and the solution is incorrect) are frequently used robustness characteristics. For the standard algorithm, the true positives decreased and the false positives increased as the overlapping percentage decreased, as shown in Table 1. Thus, the robustness of the standard algorithm was influenced by non-overlapping areas between scans. The improved algorithm showed good robustness because all the solutions were true positives despite a decrease in the overlapping percentage, as shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Overlapping Ratio (\%)**} & \multicolumn{4}{c}{**Solutions (\%)**} \\ \cline{2-5}  & **True Positive** & **False Positive** & **True Negative** & **False Negative** \\ \hline
90 & 100 & 0 & 0 & 0 \\
80 & 90 & 10 & 0 & 0 \\
70 & 70 & 25 & 0 & 5 \\
60 & 55 & 37.5 & 0 & 7.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Solutions that were generated by the standard algorithm. Figure 13: **(a)** Scans obtained in corridor 1 (red dots-reference scan, blue dots-object scan); **(b)** scans obtained near stairs (red dots-reference scan, blue dots-object scan); **(c)** scans obtained in corridor 2 (red dots-reference scan, blue dots-object scan); **(d)** scans obtained in the corner (red dots-reference scan, blue dots-object scan). \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Overlapping Ratio (\%)**} & \multicolumn{4}{c}{**Solutions (\%)**} \\ \cline{2-5}  & **True Positive** & **False Positive** & **True Negative** & **False Negative** \\ \hline
90 & 100 & 0 & 0 & 0 \\
80 & 100 & 0 & 0 & 0 \\
70 & 92.5 & 7.5 & 0 & 0 \\
60 & 90 & 7.5 & 0 & 2.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Solutions that were generated by the improved algorithm. We calculated the deviation between the estimated pose and ground truth to indicate the precision (only using _True Positives_), as shown in Table 3. Both algorithms were accurate when two scans perfectly overlapped but experienced increasing deviation in their translation and rotation as the overlap ratio decreased. However, the improved algorithm was more accurate than the standard algorithm when the scans partially overlapped. Moreover, a decline in the overlap ratio substantially decreased the performance of the standard algorithm but had no significant effect on the improved algorithm.