## 3 Dynamic Object Identification and Tracking
### Evaluating Tracking Performance Using the MOTA Metric  
This section employs the Multiple Object Tracking Accuracy (MOTA) metric to evaluate the system's precision and the ability to maintain consistent object tracking over time. It measures how accurately the system associates detected objects, denoted as \(O_{i}\), with their corresponding tracks, represented by hypotheses \(H_{i}\)[47]. At each frame \(i\), the system generates a hypothesis \(H_{i}\) based on the detected objects, either associating them with existing tracks or initializing new ones as necessary. This association process is crucial for ensuring tracking continuity and accuracy. Any discrepancies between the generated hypotheses and the actual object states result in tracking errors, quantified in the MOTA calculation. MOTA evaluates three types of errors relative to the ground truth. The error ratios are defined as follows:  
\[\bar{m}=\frac{\sum_{t}\text{Miss}_{t}}{\sum_{t}g_{t}} \tag{15}\]  
where \(\bar{m}\) represents the ratio of missed ground-truth objects, \(\text{Miss}_{t}\) is the number of misses at time \(t\), and \(g_{t}\) is the number of ground-truth objects at time \(t\). \[\bar{f}_{p}=\frac{\sum_{t}\text{FP}_{t}}{\sum_{t}g_{t}} \tag{16}\]  
where \(\bar{f}_{p}\) denotes the ratio of false positives, and \(\text{FP}_{t}\) is the number of false positive detections at time \(t\). \[\text{mme}=\frac{\sum_{t}\text{MME}_{t}}{\sum_{t}g_{t}} \tag{17}\]  
where mme is the ratio of ID mismatches, with \(\text{MME}_{t}\) representing the ID switches at time \(t\). Figure 4: Tracking process: Overview of the steps involved in object recognition and tracking. (**a**) Real-world test environment. (**b**) Radar point cloud visualization. (**c**) Clustering radar detections within windows. (**d**) Object tracking. Each colored line represents the trajectory of a human participant during the test. The \"ground truth\" refers to the true state of the environment, including the actual number and positions of objects, against which the system's performance is evaluated. It serves as a benchmark to measure how well the system can detect and track objects accurately over time. The MOTA score is computed by summing these errors and normalizing them by the total number of ground-truth objects, as expressed in Equation (18). This metric provides a comprehensive assessment of the system's tracking performance and accuracy. The following pseudocode outlines the implementation of the bird's-eye-view object tracking system, which plays a crucial role in calculating the MOTA metric. This system processes radar data to track multiple objects by mapping their positions, updating trajectories, and visualizing their movements in real-time. \[\text{MOTA}=1-\frac{\text{FP}+\text{Miss}+\text{MME}}{\text{Total Ground Truth Objects}}\times 100 \tag{18}\]  
This metric enables a detailed evaluation of the system's tracking capabilities across multiple test scenarios. Algorithm 3 outlines the process of updating object tracks and calculating the Multiple Object Tracking Accuracy (MOTA) metric. It leverages a Kalman filter for prediction and correction, combined with the Hungarian algorithm for optimal assignment of detections to existing tracks. The algorithm handles errors such as false positives, missed detections, and ID switches, which are essential for evaluating the system's tracking performance. MOTA provides a comprehensive measure of the system's accuracy in maintaining object trajectories over time.