# A Lidar-Inertial Navigation System for UAVs in GNSS-Denied Environment with Spatial Grid Structures
## 1 Introduction  
Automated intelligent UAVs, which have the ability to autonomously sense the location, have been widely used in inspection, survey, and other tasks in GNSS-denial environments [1, 2]. A reliable navigation system [3] is a fundamental guarantee for the safe flight of UAV systems in these environments [4]. Therefore, many lidar-inertial navigation systems have been proposed [5, 6, 7, 8], which calculate the pose using line and plane features. However, the working environment of these navigation systems determines whether they can achieve high-precision UAV pose estimation [9]. The lack of plane and line features in the common spatial grid structure of industrial scenes creates significant challenges for the autonomous navigation system of UAVs. The critical problem of the autonomous navigation scheme of UAVs based on lidar is the point cloud registration of lidar. This is the process of obtaining the relative pose from the changes in the two frame point clouds of the lidar. A typical method used in this process is the iterative closest point (ICP) method [10]. The ICP method is generally divided into two steps. The first step is to calculate the matching relationship between two scans. The second step is to calculate the optimal transfer matrix to minimize the cost function of the distance between matching points. However, when the point cloud is sparse, accurate matching points cannot be found, and when the point cloud is dense, the matching relationship between points is difficult to calculate in real-time. In order to solve theseproblems, many ICP variants using higher dimensional information in the environment have been proposed. This method extracts features such as lines, curves, and planes from point clouds [11; 12] and constructs cost functions of point-to-line [13], point-to-plane [14], and plane-to-plane [15]. A low drift, real-time lidar navigation system LOAM [16] was first proposed. The front end of this navigation system extracts plane features and corner features. These features form a feature point set. In the feature point set, the UAV pose change is solved by minimizing the cost function of the distance from point-to-line and point-to-plane. Due to this feature-based odometer algorithm, it can be solved in real-time in most airborne computers. Many subsequent navigation systems have been improved on this basis. LIOSAM [17] presents a factor-graph-based, lidar-inertial, loose-coupling method in the front end. It uses the high-precision position and attitude estimated by the lidar to correct the measurement bias of IMU. It also uses high-frequency IMU measurement to predict the lidar's motion, providing information for point cloud distortion removal and pose estimation solution. Then F-LOAM [18] improved the lidar navigation system. It constructs a new cost function of point-to-line and point-to-plane matching, which results in a faster and more accurate lidar pose estimation solution. These navigation systems based on plane and corner features are reliable in most artificial environments. However, there is a significant risk of failure when they work in an environment lacking a clear plane and straight edge, such as woods [19], the moon surface [20], etc. Due to the significant difference in resolution between the horizontal and vertical directions of the surrounding lidar, when the number of feature points is insufficient, it will lead to large errors in motion estimation and failure of system positioning. Spatial grid structures are now widely used in industrial and living scenes, mainly including grid structure and shell structure, because of their light weight, strong shape adaptability, and high structural strength. The lidar navigation system used for UAVs is faced with the above problems when it is applied in GNSS-denied environments full of spatial grid structures [21], such as stadiums, terminals, aircraft hangars, factory workshops, coal sheds, and warehouses.