# Robust Localization of the Mobile Robot Driven by Lidar Measurement and Matching for Ongoing Scene
## 3 Localization of Mobile Robot in Ongoing Scene
### Localization of Artificial Landmarks and Generated Buildings Based on Adaptive Weights
#### 3.2.2 Robust Localization Based on Adaptive Weights
\begin{array}{ll}W_{f,s}=d_{k}\cdot b^{i-1},i=1,2,\cdots,k \quad LiDAR\_sensor\\ W_{f,l}=V_{s,m}/\left(V_{s,l}+V_{s,m}\right)\quad Artificial\_reflector\\ W_{f,m}=V_{s,l}/\left(V_{s,l}+V_{s,m}\right)\quad Ongoing\_building\\ \end{array} \right.. \tag{23}\]  
From Equation (23), considering that the noise of Lidar changes slowly with the working location, the paper uses the weighting coefficient of the evanescent memory index as the weight coefficient of Lidar to compensate for the noise. Therefore, the parameter \(d_{k}\) is expressed as  
\[\left\{ \begin{array}{ll}\sum\limits_{i=1}^{k}d_{k}\cdot b^{i-1}=1\\ d_{k}=\frac{1-b}{1-b^{b}}\\ \end{array} \right.. \tag{24}\]  
In the Formula (24), the parameter \(b\) is a forgetting factor of the weighting coefficient, and \(b\in[0,1]\). In this article, \(b=0.98\), and \(k\) is the numbers of working locations at different time. The parameters \(V_{s,l}\) and \(V_{s,m}\) represent the covariance value of point clouds to reflectors and the minimum mean value of adjacent matching buildings, respectively. When the features of artificial landmarks in the scene are extracted, the observation weighting value \(W_{f,l}\) is inversely proportional to the covariance \(V_{s,l}\) of Lidar points of artificial landmarks. When the covariance \(V_{s,l}\) of the scanned points is smaller, the distribution of the extracted points is relatively concentrated, and the corresponding weighting value \(W_{f,l}\) is larger. On the contrary, the covariance \(V_{s,l}\) is the larger, the weighting value \(W_{f,l}\) of the corresponding points is the smaller. Similarly, when \(V_{s,m}\) is smaller, the weighting value \(W_{f,m}\) of corresponding matching points is larger, and the larger \(V_{s,m}\) is, the weighting value \(W_{f,m}\) of corresponding matching points is smaller. The specific equations of corresponding to the parameters \(V_{s,l}\) and \(V_{s,m}\) are as follows:  
\[\left\{ \begin{array}{ll}V_{s,l}=\frac{1}{n-1}\sum_{i=1}^{n}\left(x_{li}- \overline{x_{l}}\right)\left(y_{li}-\overline{y_{l}}\right)\\ V_{s,m}=\frac{1}{k}\sum_{j=1}^{k}d_{\min}\left(m_{pi,j},m_{pi\left(i+1,j\right) }\right)\\ \end{array} \right. \tag{25}\]  
where the parameter \(\left(x_{li},y_{li}\right)\) represents the \(i\)-th coordinate value of Lidar points that scanned to the reflector, \(\left(\overline{x_{l}},\overline{y_{l}}\right)\) is the mean value of Lidar points that attached to surface of reflectors. \(d_{\min}\left(m_{pi,i},m_{pi\left(i+1\right),j}\right)\) represents the minimum distance of optimal matching by ICP algorithm between the position \(pi\) and position \(p(i+1)\) of mobile robot. Then, the parameters \(i\) and \(j\) indicate the index of Lidar points on reflectors and matching buildings, respectively. Similarly, \(n\) represents the extracted Lidar points of artificial landmarks, \(k\) indicates the number of matching Lidar points corresponding of two adjacent locations. At this time, the distribution range of parameter \(i\) is [1, n] and the parameter \(j\) is [1, k].