## 2 Algorithm for Tracking Target Trajectories
This is called the \"trajectory detection criterion\", which is selected to avoid creating false trajectories. The detected marks are evaluated against the target motion hypothesis and the speed range for which the radar is designed. At this stage, the use of radar noise immunity indicators is critical. These include probabilistic, temporal, and spatial metrics under various interference conditions. The next step involves smoothing and extrapolating the trajectory. Based on previous target marks and the current scan, a smoothed estimate of the target's current position and velocity is generated. This estimate is then used to extrapolate the target's position for the next scan. An \(\alpha\)-\(\beta\) filter (Kalman filter) is applied for extrapolation, considering jamming resistance metrics, such as accuracy in determining target coordinates and tracking stability under varying jamming conditions. The final stages of the algorithm include trajectory tracking and updating. Trajectory data are stored in trajectory files. The main file contains information on all tracked trajectories, including measured coordinates, Doppler frequency, signal amplitude, timestamps, smoothed coordinates and velocities, extrapolated values for the next survey. When a target mark is associated with an existing trajectory, the trajectory is updated. During this stage, temporal noise immunity metrics are analyzed to optimize the target acquisition and trajectory update times. If a target mark from the current survey cannot be associated with a tracked trajectory, a tracking strobe with expanded dimensions is created for the next survey. If target marks are absent in multiple surveys, the trajectory is reset. The criteria for resetting a trajectory may differ depending on the radar system. Spatial noise immunity indicators, such as tracking stability in varying noise environments, are also considered when resetting a trajectory. The analysis of the algorithm indicates its relevance to studying radar noise immunity metrics, which encompass probabilistic, temporal, and spatial indicators. Prioritizing a specific set of indicators allows researchers to focus on certain areas of mathematical modeling and assess the effectiveness of the selected approach. References [2; 17; 18; 22] reveal a broad range of characteristics used in the mathematical formalization of radar system operations. 1. Probabilistic indicators: - probability of target detection; - probability of false alarm; - probability of correct classification; - probability of failure; - probability of failure to search for an object within given time; - probability of failure of capture the object within given time; - probability of failure to track an object within a given time; - probability of failure to transfer an object to the control and execution system within a given time. 2. Time indicators: - mean time between failures; - mean time to restore;  
Figure 1: Block diagram of the algorithm for tracking a target’s trajectory using data from a single radar. system response time;  
- data processing delay time;  
- timeframes for failure in searching, capturing, tracking, and transfer with a certain probability. 3. Spatial indicators:  
- detection zone;  
- accuracy of coordinate determination;  
- resolution;  
- insensitivity zone;  
- spatial zones and radar suppression ranges. Several indicators pertain to the radar's performance during key operations such as object search, capture, tracking, and transfer to the control and execution system.