# Tracking Method of GM-APD LiDAR Based on Adaptive Fusion of Intensity Image and Point Cloud
## 3 The Adaptive Fusion of KCF and Kalman Filter
### Target Occlusion Judgment  
Judging the occlusion state of the target at the current moment is the key to the effective fusion of the two algorithms. In this paper, PSLR [23] and ISS [24] are used to effectively judge the occlusion state of the target. The PSLR is a physical quantity describing the degree of prominence of the main lobe relative to the sidelobe, which can be used to evaluate the matching degree of the two target signals of the related operation. It can be defined as:  
\[PSLR=\frac{\max(f(z))-\mu}{\sigma} \tag{29}\]  
where \(\max(f(z))\) is the response value of the main lobe; \(\mu\) and \(\sigma\) are the mean and variance of all sidelobes, respectively. When the target is out of occlusion, the response graph has only the main lobe which is close to the ideal two-dimensional Gaussian distribution. When the target is in occlusion, multiple sidelobes appear in the response graph, and the contrast between sidelobe and peak value decreases, as shown in Figure 4:The average PSLR value of the first five frames when the target is out of occlusion is taken as the standard response value \(\mu_{PSLR}\), as shown in Equation (30). When the target is in full occlusion, the peak response is not 0. Through experimental tests, 0.3 \(\mu_{PSLR}\) and 0.8 \(\mu_{PSLR}\) are defined as the low and high threshold of the occlusion detection mechanism, respectively. \[\mu_{PSLR}=\frac{1}{5}\sum\limits_{i=1}^{5}PSLR_{i} \tag{30}\]  
where \(i\) is the image ordinal. In the tracking process, the appearance characteristic information of the target is easy to change with the change of the scene. In order to adapt to the change of motion scene, the appearance model is adaptively updated with the PSLR. \[\left\{ \begin{array}{l}\alpha^{i}=\left(1-\gamma^{i}\right)\alpha^{i-1}+ \gamma^{i}\alpha^{i}\\ \gamma^{i}=\left\{\begin{array}{ll}0&PSLR<T_{L}\\ \frac{PSLR^{i}}{\mu_{PSLR}}\times\beta&otherwise\end{array}\right.\end{array} \right. \tag{31}\]  
where \(\alpha\) is the coefficient of the correlation filter, \(\gamma^{i}\) is the adaptive parameter that varies with the PSLR value in each frame, and \(\beta\) is a constant with the value of 0.025. When the target is too close to the complex background or there is a texture similar to the target in the background, the response of the filter may be interfered by the background, which affects the accuracy of the PSLR. In order to enhance the robustness of the detection mechanism, the ISS detection algorithm is used to extract the key points of the point cloud target, and then the number of key points under different occlusion conditions is used as the evaluation criteria for occlusion state. The specific process is as follows:  
Let the quantity of point cloud target be \(N\), and the coordinate \(p_{i}\) of any point is \((x_{i},y_{i},z_{i})\). Step 1: Set a search radius \(r_{f}\) for each point \(p_{i}\) of the point cloud;  
Step 2: Calculate the weights \(w_{ij}\) of each point \(p_{i}\) within the radius \(r_{f}\) of the point \(p_{i}\):  
\[w_{ij}=\frac{1}{|p_{j}-p_{i}|}\quad,\ \Big{|}p_{j}-p_{i}\Big{|}<r_{f} \tag{32}\]  
Step 3: Calculate the covariance matrix for point \(p_{i}\):  
\[\text{cov}(p_{i})=\frac{\sum\limits_{|pi-p|<r_{f}}w_{ij}(p_{j}-p_{i})(p_{j}-p _{i})^{T}}{\sum\limits_{|pi-p|<r_{f}}w_{ij}} \tag{33}\]  
Figure 4: 2D target response graph. Step 4: Calculate all eigenvalues \((\lambda_{i}^{1},\lambda_{i}^{2},\lambda_{i}^{3})\) of the covariance matrix \(\text{cov}(p_{i})\) in Step 3 and arrange them in descending order;  
Step 5: Set threshold values \(\varepsilon_{1}\) and \(\varepsilon_{2}\), and the points satisfying Equation (34) are regarded as ISS feature points. \[ \begin{cases}\frac{\lambda_{i}^{2}}{\lambda_{i}^{1}}\leq\varepsilon_{1}\\ \frac{\lambda_{i}^{3}}{\lambda_{i}^{2}}\leq\varepsilon_{2}\end{cases}  \tag{34}\]  
Step 6: Repeat all the steps above until you have traversed all the points.