## 3 Dynamic Object Identification and Tracking
### Object Identification  
We process data from a radar sensor, applying clustering and filtering operations to extract valuable information about detected objects. The code is implemented as a ROS node, which subscribes to a scan topic to receive radar data. The radar (IWR6843 ISK) provides detailed information for each detected point, including point ID, \(X\) and \(Y\) coordinates, and timestamps. To group these points into meaningful clusters, we utilize the DBSCAN clustering algorithm, which categorizes points based on their spatial proximity. As shown in Figure 2, DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a clustering algorithm that groups data points based on local density. It relies on two key parameters: \(\epsilon\), which defines the neighborhood radius, and \(\text{min\_samples}=5\), is the minimum number of points required within this radius to form a cluster. By sequentially scanning data points and expanding clusters based on density, DBSCAN effectively identifies clusters while filtering out noise. Its efficiency, with a computational complexity of \(O(N\log N)\), makes it well suited for clustering and tracking tasks. Each cluster represents a potential object within the radar's field of view. To ensure accurate object separation and prevent multiple objects from being grouped into a single cluster, we set an object size of 0.4 m as the clustering radius parameter, as depicted in Figure 3a. For each detected cluster, the algorithm computes its centroid by taking the average of the coordinates \((x,y,z)\) of all core points within the cluster:  
\[\textbf{c}=\left(\frac{1}{k}\sum_{j=1}^{k}x_{j},\frac{1}{k}\sum_{j=1}^{k}y_{j},\frac{1}{k}\sum_{j=1}^{k}z_{j}\right) \tag{5}\]  
where \(k\) represents the total number of core points in the cluster, and \((x_{j},y_{j},z_{j})\) are the coordinates of the \(j\)-th core point. This method condenses each cluster into a single representative point, indicating its central position. \begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{3}{c}{Radar System Specifications} \\ \hline Radar model & - & Texas Instrument IWR6843 ISK \\ Maximum detection range for cars & \(R_{\text{max,car}}\) & 175 m \\ Maximum detection range for pedestrians & \(R_{\text{max,ped}}\) & 98 m \\ Range resolution & \(d_{\text{Res}}\) & 0.039–0.044 m \\ Azimuth field of view & \(\theta_{\text{az}}\) & \(\pm 60^{\circ}\) \\ Elevation field of view & \(\theta_{\text{el}}\) & \(\pm 20^{\circ}\) \\ Azimuth angular resolution & \(\Delta\theta_{\text{az}}\) & \(20^{\circ}\) \\ Elevation angular resolution & \(\Delta\theta_{\text{el}}\) & \(58^{\circ}\) \\ Maximum radial velocity & \(v_{\text{max}}\) & 9.59 m/s \\ \hline \multicolumn{3}{c}{Radar Data from ROS Package} \\ \hline Scanned points per frame & \(N_{\text{points}}\) & Variable \\ Point coordinates & \((X,Y)\) & Provided \\ Timestamp precision & \(t_{\text{stamp}}\) & Seconds and nanoseconds \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Radar system specifications and data parameters. Figure 2: Illustration of the DBSCAN clustering algorithm. The image highlights core points (yellow), border points (blue), and noise points (orange). Figure 3: Detailed view of the object detection process using a radar sensor. Each step highlights a specific aspect of the detection and tracking pipeline. (**a**) Clustering based on the maximum size of an object. (**b**) The real center of the object vs. the center of the observed points from the radar. (**c**) A window is created for each detected object and records the history of center points from the radar. (**d**) Overall dynamic object detection process using radar. However, the inherent randomness in radar detection often results in discrepancies between the detected center points and the actual center of objects, as illustrated in Figure 3b. To address this, we apply the weighted moving average filter Equation (6).