## 2 The Proposed Method
### Quantitative Evaluation  
In order to verify the performance of the proposed method in the low-texture environment with dynamic target interference, we elaborately selected two low-texture scenes: the first one was an open-loop scene, the other one was a closed-loop scene. The open-loop scene was a classroom corridor in our university. As shown in Figure 7, the corridor was 35.3 m long and 2.8 m wide. The closed-loop experiment was carried out in a looped classroom corridor 65 m long and 3.9 m wide, which is presented in Figure 8.  
Figure 8: Evaluation experiments in closed-loop scene. (**a**) A map created by Cartographer with LiDAR only; (**b**) a map created by Cartographer with LiDAR+IMU fusion; (**c**) a map created by the proposed method. Figure 6: The edge and wall representation in a grid map (the more blurriness in a map, the lower quality it is). (**a**) A submap with more blurries (lower quality); (**b**) A submap with less blurries (higher quality). Figure 7: Maps built in open-loop scene (inside the corridor area, the darker the area was, the more blurry it was, that is, the lower quality it will be). (**a**) A map built with Cartographer with LiDAR only; (**b**) a map built with Cartographer with LiDAR+IMU fusion; (**c**) a map built with the proposed method. We operated the mobile robot along a predefined trajectory to build the map. At the same time, some students moved around the robot elaborately to simulate the interference of moving obstacles. We carried out three kinds of experiments in the open-loop and closed-loop environment. Figure 7 shows the mapping results with the open-loop scene. The first map was built by Cartographer with LiDAR only [40]. The second map was built by Cartographer with LiDAR+IMU fusion. The third map was built by the proposed method. The results of the open-loop scenes are shown in Figure 7. The results for the closed-loop scene are shown in Figure 8.  
As shown in Figure 7, the experiments in the open-loop scene show that though the map built with LiDAR and IMU is improved, because of the existence of the moving obstacles, there are still many noise data in the final map. However, with the proposed method, these noise data are removed. In order to compare the accuracy of three maps for the open-loop scene, we measured the length of the same segment in the corridor, and the estimated lengths with three methods are shown in Table 1. We can see from Figure 7 and Table 1 that the accuracy and stability of the map are greatly improved with the proposed method. The experiments for the closed-loop scene in Figure 8 show the performances of the three methods (Cartographer without IMU, Cartographer with IMU, and the proposed). In Figure 8a, because the low texture of the environment leads to large error drifting in the front-end stage, after the optimization in the back-end stage, the result map still has inconsistencies. There are also many blurs inside the corridor caused by the moving persons during the experiments. Because the LiDAR-only method cannot recognize the moving objects, it takes all the data for scan matching, then the points located on the moving objects are noise data, which lead to the DA error and map updating error too. Comparatively, as shown in Figure 8b, by fusing with IMU, the fusion-based Cartographer method improves the DA error greatly, but it still cannot remove the moving object effectively, which leads to the blurs inside the corridor of the map. For the proposed method, benefiting from the prediction of IMU and SPA algorithm in the front-end stage, the closed-loop optimization, and large error removing in the back-end stage, the proposed method outperformed the others, as illustrated in Figure 8c.