## 1 Introduction  
Light detection and ranging technology (LiDAR) is a laser-based remote sensing measurement technology. Its principle is to aim the laser at the surface of the object, calculate the time it takes for the laser to return to the starting point, and then calculate the distance [1; 2; 3]. This technology is commonly used in geographic information systems (GIS) to generate digital elevation models (DEMs) or digital surface models (DSMs) for 3D modeling [4; 5; 6; 7; 8]. As an active remote sensing method, LiDAR can be used for carbon dioxide retrieval [9], aerosol detection [10], boundary layer detection [11], and target classification [12]. With the maturity of hardware production technology and the rapid development of related data processing software, LiDAR has made great research progress and has shown great advantages in many aspects. Compared with traditional measurement methods, which require a lot of field control, aerial triangulation, long mapping period and low precision to obtain the topographic surface, LiDAR can observe the ground around the clock [13; 14; 15]. In addition, when the LiDAR scans a work area that is occluded by vegetation or shaded by vegetation, it can more directly and effectively obtain 3D information of surface targets [16; 17; 18; 19]. As the cost and size of scanners have decreased, LiDAR has had new applications. In forestry science [20; 21], LiDAR data have been used for tree and canopy height measurements and large-scale biomass estimation. In geological disaster monitoring [22; 23], airborne LiDAR can be used to predict areas prone to landslides, providing reference for safety assessments. In route planning [24; 25], LiDAR can also be used for pedestrian wayfinding to ensure the accessibility of routes in urban environments. In archaeological applications [26; 27], archaeologists have enhanced the visualization of high-resolutiondigital elevation models generated by airborne LiDAR by combining perception and interpretation, and discovering numerous new settlement sites of ancient communities and new archaeological ground features. Point cloud ground filtering is an important link in LiDAR data processing that can effectively distinguish ground points from non-ground points to obtain real ground point coordinates and improve the accuracy of DTMs [28; 29; 30]. However, point cloud filtering is generally difficult due to the diversity of terrain and features, and the features displayed by LiDAR data are often very complex [31]. The International Society for Photogrammetry and Remote Sensing (ISPRS) team analyzed the point cloud data structure and listed some difficult objects in filtering when testing the filtering method [32]. Traditional point cloud filtering methods include the mathematical morphology method [33], terrain slope method [34], and irregular triangulation method [35]. Many studies have explored the optimization and improvement of traditional filtering methods [36; 37; 38; 39; 40]. With the wide application of various machine learning methods, some scholars have gradually integrated point cloud filtering into machine learning. For instance, [PERSON] et al. [41] used fully convolutional networks for terrestrial and multiclass classification of airborne laser scanner point clouds, providing highly accurate classification results in a computationally efficient manner. An Airborne LiDAR Building-Extraction Method Based on the Naive Bayes-RANSAC Method for Proportional Segmentation of Quantitative Features [42] proposed by [PERSON] et al. [PERSON] et al. [43] proposed a point cloud classification method based on ICSF and weighted weakly correlated random forests with a particular focus on the extraction of urban LiDAR point cloud buildings, which has improved the accuracy and efficiency of point cloud classification. Many mature methods are being used in urban point cloud filtering research [44; 45]. However, these methods have a poor filtering effect for forest areas.