## 2 The Proposed Method
### Qualitive Evaluation  
In this section, some state-of-the-art 2D LiDAR-based SLAM, such as HectorSLAM and Cartographer, are evaluated qualitatively with the proposed method. Figure 10 shows the maps of Cartographer (LiDAR-only) and the proposed fusion methods in the outdoor environment, which were conducted at the outdoor square road behind the Siyuan building in the university. The left is the map with LiDAR-only used, the right is obtained with the fusion-based method. Figure 11 shows the maps with Cartographer; the experiments were conducted on the first floor of teaching buildings No. 9 and No. 1. There were some persons passing by during the experiment process, which led to the blurs in the result map. As aforementioned in Figure 6, many blurs remain in the map with LiDAR-only; comparatively, the map generated by the proposed method is sharper and clearer. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Segment**} & \multirow{3}{*}{ \begin{tabular}{c} **Actual** \\ **Value** \\ \end{tabular}  } & \multirow{3}{*}{**LiDAR**} & \multirow{3}{*}{ \begin{tabular}{c} **Relative** \\ **Error** \\ **(LiDAR)** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Relative Error** \\ **\& IMU** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Relative Error** \\ **(LiDAR** \\ \& IMU)** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **LiDAR** \\ **\& IMU** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Relative Error** \\ **\& IMU** \\ \end{tabular}  } & \multirow{3}{*}{\ \begin{tabular}{c} **Relative Error** \\ **(LiDAR** \\ \& IMU)** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Relative Error** \\ **\& Static Map/** \\ **Proposed** \\ **Method** \\ \end{tabular}  } \\ \hline A & \(11.0\) & \(10.4\) & \(-5.5\%\) & \(10.8\) & \(-1.8\%\) & \(11.1\) & \(+0.9\%\) \\ B & \(42.8\) & \(38.3\) & \(-10.5\%\) & \(42.9\) & \(+0.2\%\) & \(42.9\) & \(+0.2\%\) \\ C & \(1.8\) & \(1.6\) & \(-11.1\%\Figure 11: The map generated with the proposed method in indoor environment. (**a**) mapping result of first floor of teaching building No. 9; it is a closed-loop classroom corridor, but we deliberately arranged to not use the last section data, and the mapping result is acceptable. (**b**) mapping results of the first floor of teaching building No.1. Figure 10: Closed-loop experiment in outdoor environment. (**a**) Cartographer (LiDAR only); (**b**) the proposed method. We used some open datasets [48] to evaluate the proposed fusion-based method, and the results are presented in Figures 12-14. In all these three figures, the left one shows the results with Cartographer of LiDAR only, and the right one shows the results with the proposed method. In Figure 12 the left map shows larger accumulated error indicated by large ellipse. In Figure 12, there is more blurriness in the map generated by Cartographer of LiDAR only. In Figure 13, the map generated by the proposed method is sharp with less blurriness. Figure 15 shows the experiment results obtained by HectorSLAM, Cartographer (LiDAR-only), and the proposed method with \"Team_Hector_MappingBox_Dagstuhl_Neubau.bag\" (first raw in the figure) and \"Team_Hector_MappingBox_L101_Building.bag\" (second raw in the figure) respectively; other datasets obtained the same results. In these experiments, the map with HectorSLAM seems not convergent and leads to inconsistencies. On the other hand, the maps built by Cartographer (LiDAR only) (Figure 15e) and the proposed method (Figure 15f) show not much difference in this case. This is because the environment is not a low-texture one. Figure 14: Map built by Cartographer (LiDAR only) (**a**) and the proposed method (**b**) with file b0-2014-08-14-13-36-48.bag [48]. Figure 15: Evaluation results with HectorSLAM, Cartographer (LiDAR only) and the proposed method. The first raw is the generated maps with “Team_Hector_MappingBox_Dagstuhl_Neubau.bag” file. They are (**a**) HectorSLAM; (**b**) Cartographer (LiDAR only); (**c**) the proposed method respectively.