## 2 Algorithm for Tracking Target Trajectories  
The radar system operation process can be divided into two main stages: radar signal processing and radar data processing. These stages are closely related, but they have different functionality, purpose, and methods used. This division helps to better understand the functionality of the systems and their modeling. The first stage of radar signal processing (radar signal processing stage) analyses the received echo signal to extract useful information. The main processes include the following:  
* Signal pre-filtering. Used to suppress noise and interference occurring in the radar channel. * CFAR (Constant False Alarm Rate). Adaptive false alarm control algorithms that highlight potential targets against a background of interference. * Target Detection. Using corrected thresholds after CFAR, target coordinates, amplitudes and other characteristics are extracted. These processes are part of primary processing, where radar signals are analyzed to extract target-related data during a single radar scan. The next stage is the data processing stage, which focuses on using the detected information to analyze the trajectories and behavior of targets. The key tasks in this stage are the following:  
* Trajectory initialization. Combining multiple observations to form a track. * Updating and maintaining the tracks. Using Kalman filters or other methods to refine target position based on new data. * Motion prediction. Extrapolation of target position into the future based on mathematical models. This stage is referred to as secondary processing, where multiple radar scans are analyzed to determine continuous target trajectories. These processing stages are tightly integrated into the overall algorithm for tracking target trajectories, as shown in Figure 1.  
According to [21], the number of pulses transmitted by the radar to the target is determined by the antenna's rotation speed and the repetition rate of the probing pulses. For each range cell, a decision is made regarding the presence or absence of a target during each probing period. When a target is detected, a message is generated containing information such as the target's coordinates and other relevant data. This stage is referred to as \"primary processing\", as it involves collecting data from a single radar during one scan. Following this, the process of determining the target's trajectory and locking onto it for tracking begins. At this stage, data from multiple radar scans are processed to identify and correlate observations related to the same target, forming a continuous trajectory--a single data set for each target. This is referred to as \"secondary processing\" of radar information. The block diagram of the algorithm for tracking a target's trajectory using data from one radar is shown in Figure 1.  
Figure 1 illustrates the initial stage of the target detection process. A radar target typically generates several signals above the detection threshold across adjacent cells. These signals, along with their amplitudes, are used for interpolation to achieve more precise measurements. The following methods are employed to perform this task:  
* Sliding window method (interpolation);
* Center of mass correlation (weighted averaging);
* Comparison with a database using ray shape (angular coordinate), impulse response (range), and Doppler filter shape (Doppler velocity). The next phase of target trajectory tracking involves adaptive stabilization of the false alarm rate. The radar cross-section (RCS) distribution of air targets overlaps with the distribution of interference from scattering surfaces, increasing the number of false alarms as interference signals exceed the average detection threshold. To address this, an adaptive detection threshold is formed to stabilize the false alarm rate. Once a target is detected, its trajectory is identified according to a specific algorithm. The trajectory is confirmed after the target is detected in three or more consecutive radar scans.