# An Improved MbICP Algorithm for Mobile Robot Pose Estimation
## 3 Results
### Evaluation Method  
The first experiment compared the accuracy and convergence of the improved MbICP algorithm with those of the original MbICP algorithm in matching partially overlapped scans. Before introducing more details regarding the experiment, we first explain the evaluation factors of the accuracy and convergence. Given two scans that were acquired in the same sensor location, we precisely know that the ground truth of the pose estimate is (0, 0, 0\({}^{\circ}\)). To quantitatively compare the algorithms' accuracy, a random displacement \(\delta\) is added to the initial pose estimate, and one scan is also roto-translated by this value. This transformed scan is treated as the object scan, which is marked as \(S_{obj}\), while the other scan is treated as the reference scan, which is marked as \(S_{ref}\). After matching, the pose estimation is determined and statistical analysis can be performed. The translational and rotational deviation between the pose estimation from the algorithm and the ground truth is used as the evaluative factor of the algorithm's accuracy. The smaller the deviation, the more closely \(S_{obj}\) fits \(S_{ref}\) and the better the accuracy of the algorithm. In addition, the number of iterations can intuitively represent the algorithm's convergence. Figure 10: (**a**) Rejection result without the resampling step (red dots-reference scan, blue dots-object scan, black lines-correspondences); (**b**) rejection result with the resampling step (red dots-reference scan, blue dots-object scan, black lines-correspondences). We conducted the first experiment by matching two partially overlapping scans with the improved algorithm and standard algorithm. To obtain experimental scans, we recorded data taken by UTM-30 LX laser range finder in a corner by artificially adding or removing the trashcan in the field of view without moving the sensor. This way we acquired a pair of scans that partially overlap, one of which with the presence of the trashcan is shown in Figure 11a and the other is shown in Figure 11b. The scan with this trashcan was roto-translated with a given transformation (500 mm, 500 mm, 15\({}^{\circ}\)) and then used as the object scan, while the scan without the trashcan was treated as the reference scan (as shown in Figure 12a). The matching result from the standard algorithm is depicted in Figure 12b, which is far from satisfactory because of obvious deviation between two scans. The distance between the estimated pose and the ground truth was (75.75 mm, 34.69 mm, 2.71\({}^{\circ}\)), demonstrating awful accuracy. However, the matching result from the improved algorithm was relatively satisfactory because the two scans closely matched (as shown in Figure 12c). The deviation between the estimated pose and ground truth was nearly zero, demonstrating high accuracy. The improved algorithm also exhibited a faster convergence rate (18 iterations) because of the resampling step, while the standard algorithm satisfied the convergence condition after 22 iterations (Figure 12d). Figure 11: Two partially overlapping scans taken by sensor at the same location: (**a**) The first scan was captured with the presence of a trashcan; (**b**) the second scan was captured without the presence of a trashcan. Figure 12: _Cont._  
Another group of experiments was conducted to quantitatively evaluate the algorithms' accuracy in matching scans with different overlapping ratios. Given an overlapping percentage \(\eta\%\) and two identical scans, one scan had \(1-\eta\%\) of the points artificially removed, while the other scan remained unchanged from the object scan. Thus, we obtained pairs of scans with an overlapping percentage \(\eta\), which varied from 60% to 100%. These scans were acquired under different scenarios, such as stairs and corners, where overlapping frequently occurs because of range holes and rotation, and corridors, where dynamic obstacles are common (as shown in Figure 13).