## 2 Materials and Methods  
### Overview of the Proposed Framework  
The overview of the proposed framework is depicted in Figure 1. The boxes painted in blue are inherited from our previous work LC-LIO in [33] where we developed a factor graph-based LIO scheme. The yellow ones represent the main contributions in this paper. As receiving the 3D point clouds and the IMU ego-motion measurements, the LiDAR factor and IMU factor are constructed via scan-matching [43] and IMU pre-integration [44] respectively, and then jointly optimized in the sliding window based local FGO. A globally consistent map consisting of registered 3D points is incrementally generated with each local optimization accomplished. For more details about the LIO adopted in this paper, the full paper [33] is recommended. The GNSS raw data produced by the rover and station are firstly processed by RTKLIB [7] to obtain GNSS-RTK solutions. For each of the epochs, the surrounding local map is extracted from the global map. The mean elevation angle mask could be calculated according to the 3D point cloud map, after which GNSS-RTK availability is assessed. Given a predefined threshold, those with heavy mean elevation angle masks, indicating encirclement by skyscrapers, towering trees, etc., are supposed to be unreliable and excluded. Others with small mean elevation angle masks are in relatively open areas and are assumed to be reliable. A global FGO is executed for the fusion of LiDAR factor, IMU factor and GNSS-RTK factor created by reliable GNSS-RTK. A continuous and accurate georeferenced position is finally achieved.  
Before diving into the expanded introduction of the proposed method, the coordinates involved are clarified as follows:  
* The LiDAR frame \({}^{l}\{\cdot\}\): Originated at the geometric center of the LiDAR.
* The IMU frame \({}^{b}\{\cdot\}\): Originated at the geometric center of the IMU.
* The GNSS measurement frame \(\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{ \mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{\mathit{ \mathit{  }}}}}}}}}}}}}}\): Originated at the GNSS measurement with the orientation of the axes consistent with that of the LiDAR frame.
* The local world frame \({}^{w}\{\cdot\}\): Coincide with the initial LiDAR frame.
* The east-north-up (ENU) frame \({}^{n}\{\cdot\}\): Originated at the initial vehicle position with the x-axis, y-axis, and z-axis pointing to the east, north, and up respectively.  
In this paper, matrices are denoted in upper-case and bold letters. Vectors are denoted in lowercase and bold letters. Variable scalars are denoted as lower-case and italic letters. Poses under different frames could be transferred via multiplication rules defined in the 3D Special Euclidean group (SE(3)) [45]. Concretely, \({}^{n}\mathbf{T}_{w}\) represents the transformation matrix from the local world frame to the ENU frame. Following the Equation (1), the \(i\)-th map points \({}^{w}\mathbf{f}_{i}\in\mathbb{R}^{3}\) under the world frame would be transformed to the ENU frame and denotes as \({}^{n}\mathbf{f}_{i}\):  
\[{}^{n}\mathbf{f}_{i}={}^{n}\mathbf{T}_{w}{}^{w}\mathbf{f}_{i}. \tag{1}\]