## 3 Methodology
### Lidar Point Cloud Mapping
#### 3.2.1 Polarized Lidar Odometry Factor
In our approach, the roll angle transformation threshold \(\varepsilon_{roll}=1^{\circ}\), pitch angle transformation threshold \(\varepsilon_{pitch}=1^{\circ}\), yaw angle transformation threshold \(\varepsilon_{yaw}=1^{\circ}\), and translation transformation threshold \(\varepsilon_{trans}=0.5m\) are predefined. Figure 7: Flow chart of polarized Lidar odometry. 3. Feature Extraction  
The feature description of the polarized matrix uses the method of extracting polarized edge features and polarized planar features. The curvature of each point cloud is calculated based on the polarized matrix, and the edge and planar feature points are screened out. Select an equal number of matrix points on both sides of the point cloud \(p_{k}\), which must be in the same matrix row as the point, and calculate the curvature of the point cloud according to the point cloud curvature calculation formula [40; 41]:  
\[c_{k}=\left(\frac{1}{|\mathbf{S}|}\right)\times\left|\sum\
olimits_{j\in \mathbf{S},j\
eq k}\left(r_{j}-r_{k}\right)\right|^{2}, \tag{15}\]  
\[ \begin{cases}\mathbb{F}_{n}^{\mathrm{e}}=\left\{p_{k}|c_{k}>\varepsilon^{ \mathrm{e}}\right\}\\ \mathbb{F}_{n}^{\mathrm{p}}=\left\{p_{k}|c_{k}\leq\varepsilon^{\mathrm{p}} \right\}.\end{cases}  \tag{16}\]  
where when the \(c_{k}\) is greater than the edge feature point curvature threshold \(\varepsilon^{\mathrm{e}}\), the point is an edge feature point; when it is less than or equal to the planar feature point curvature threshold \(\varepsilon^{\mathrm{p}}\), the point is a surface feature point. The edge feature point curvature threshold is \(\varepsilon^{\mathrm{e}}=1.0\) and the surface feature point curvature threshold is \(\varepsilon^{\mathrm{p}}=0.1\) in our method. 4. Feature scan-matching  
The scan-matching of the nearest node uses the L-M algorithm. Based on the initial pose value, the feature point cloud in the current laser frame is mapped to the global coordinate system. Historical keyframes with a Euclidean distance to the current laser frame less than or equal to the Euclidean distance threshold \(\varepsilon_{dis}\) are selected, i.e., \(d_{ni}\leq\varepsilon_{dis}\). The feature point cloud of these historical keyframes is then mapped to the global coordinate system according to their poses to obtain the local map \(\mathbf{M}_{\varepsilon}\):  
\[\mathbf{M}_{\varepsilon}=\left\{\mathbf{M}_{n}^{\mathrm{e}},\mathbf{M}_{n}^{ \mathrm{p}}\right\}, \tag{17}\]  
\[\mathbf{M}_{n}^{\mathrm{e}}=\left\{r_{n}^{\mathrm{e}}\cup r_{n-1}^{\mathrm{e}} \cup\cdots\cup r_{n-i}^{\mathrm{e}}|d_{ni}\leq\varepsilon_{dis}\right\}, \tag{18}\]  
\[\mathbf{M}_{n}^{\mathrm{p}}=\left\{r_{n}^{\mathrm{p}}\cup r_{n-1}^{\mathrm{p}} \cup\cdots\cup r_{n-i}^{\mathrm{p}}|d_{ni}\leq\varepsilon_{dis}\right\}. \tag{19}\]  
where \(d_{ni}\) represents the Euclidean distance between the \(n\)th frame and the \(i\)th frame of Lidar. In our method, the Euclidean distance threshold is \(\varepsilon_{dis}=20.0\) m.  
The point-line matching method is used for matching edge feature points. The point cloud \(p_{k}\) is regarded as an edge feature point in the current laser frame, and the nearest five edge feature points are found in the local map. If these five edge feature points can be fitted into a straight line, the match is successful, and these successfully matched edge feature points \(r_{n}^{\mathrm{e}}\) are retained. The point-surface matching method is used for matching planar feature points. The point cloud \(p_{k}\) is regarded as a planar feature point in the current laser frame, and the nearest five planar feature points are found on the local map. If these five planar feature points can be fitted into a plane, the match is successful, and these successfully matched planar feature points \(r_{n}^{\mathrm{p}}\) are retained.