# Application of Kalman Filter to Improve 3D LiDAR Signals of Autonomous Vehicles in Adverse Weather
## 6 Research Results  
The above experimental test data (LiDAR point cloud data) were input into the software for calculation. The results under normal weather conditions are displayed in Figure 14. The results for rain are shown in Figure 15. The neighbor point cloud segmentation algorithm described in this research filtered out some noise, as shown in Figure 16. Finally, after passing through the Kalman filter, excess noise was filtered out, as shown in Figure 17. The resultant image obtained after using the algorithm is very similar to that obtained under normal weather conditions. Figure 12: Simulated dense smoke. Figure 13: Simulated rain and dense smoke. Figure 16: Filter results from the neighboring point cloud segmentation algorithm: (**a**) 3D view and (**b**) top view. Figure 14: (**a**) 3D view and (**b**) top view under normal weather conditions. Figure 15: (**a**) 3D view and (**b**) top view for a simulated rainy day. Next, the resultant improvement under heavy smoke conditions is explained. Figure 14 shows the 3D view and top view obtained in the normal situation. The influence of dense smoke can be seen on the image displayed in Figure 18. The lower corner is seriously affected by the interference of dense smoke. The improvement obtained by using the first nearest neighbor segmentation algorithm is shown in Figure 15.0 The result of improving the filtering model through the Kalman filter is shown in Figure 15.1 Although the process described in this study cannot restore the signal to that of normal weather, there was a significant improvement, and a lot of noise could be filtered out. The third type of weather examined is the influence of both rain and heavy smoke, as shown in Figure 15.2 The results after processing with the nearest neighbor segmentation algorithm are shown in Figure 15.3 Although it was not possible to filter out all of the noise, it was possible to filter out most of it. Further improvement was obtained after Kalman filtering, as shown in Figure 15.4 The improvement is obvious, resulting in restoration of the four corners of the space. A lot of noise has been filtered out. Figure 15.5 (a) 3D view and (b) top view of filtering results after neighboring point cloud segmentation. Figure 15.6 (a) 3D view and (b) top view of Kalman filter filtering results. Figure 15.7 (a) 3D view and (b) top view of filtering results after neighboring point cloud segmentation. The point cloud model data discussed in this research include an environmental frame with an \(x\)-axis, \(y\)-axis, and \(z\)-axis. The point cloud is located within the environmental frame. In the process of nearest neighbor point cloud segmentation within the environmental frame, a number of sampling circles were used to sample the point cloud. Two adjacent sampling circles overlap locally. When the number of point clouds obtained within the sampling circle was greater than a critical judgment value, the sampling circle was retained. The sampling circle has a radius of 2 cm. The critical judgment value is 10. When the number of point clouds in the sampling circle was less than the critical judgment value, the point cloud was filtered out as noise. In addition, Kalman filtering was used to improve the spatial model data to filter and output low-noise environment model data. As a result, the interference of environmental noise on LiDAR sensing was reduced. Kalman filtering was especially helpful to filter out the noise caused by dense smoke. In order to understand the improvement demonstrated in the experiments, error analysis was conducted. For each weather condition and the improved results, the same number of point clouds were used for comparison, as shown in Figure 15.8 The results show that the nearest neighbor segmentation algorithm and Kalman filter have lower RMSE values. Figure 15.9 (**a**) 3D view and (**b**) top view after Kalman filtering. Figure 16.0 (**a**) 3D view and (**b**) top view of filtering results after neighboring point cloud segmentation.