## 4 Modeling the Target Tracking Process Using Kalman Filters
The interference intensity (\(\lambda\)) ranges from 0.1, representing low external jamming, to 1, indicating high interference, which allows  
Figure 4: Comparison of trajectory predictions generated by the GERT model and Kalman filter, highlighting their complementary performance in interference conditions. Figure 3: Structural diagram of the relationship between the GERT model and the Kalman filter. the model to simulate various environmental conditions. The modeled target moves at a velocity of 200 m/s, characteristic of a maneuverable airborne object. The radar operates at a scan rate of 10 Hz, which is typical for medium-range detection systems and ensures frequent updates of tracking data. To account for the effects of noise and variability, the noise covariance parameters (\(Q\) and \(R\)) are adjusted to reflect real-world sensor imperfections and process fluctuations. Additionally, the GERT network incorporates probabilistic states to model key radar processes, such as signal detection, trajectory establishment, and tracking. These states are interconnected through transitions that account for time delays and uncertainties introduced by interference conditions. This comprehensive parameter set enables a detailed analysis of radar system performance in challenging environments. Figure 4 illustrates the process of object tracking using the Kalman filter and the GERT model, as well as their interaction for processing measurement data. The blue line represents the true position of the object at each time step, serving as a reference trajectory. This ideal position shows where the object is located at each moment in time without the influence of noise and uncertainty. The orange points on the graph represent noisy measurements of the object's position, simulating data obtained from real sensors. These measurements deviate randomly from the true position due to noise, which is characteristic of any real observation system. Nevertheless, the measurements remain close enough to the true trajectory, allowing the Kalman filter to effectively use them for correcting the object's position. The red dashed line demonstrates the object position estimates generated using the Kalman filter. This filter smooths the noisy measurements, minimizing deviations and bringing the estimates closer to the true trajectory. The results of the Kalman filter exhibit high accuracy, as its estimates closely match the reference trajectory. The green dash-dotted line shows the mean trajectory predicted by the GERT model. This trajectory is based on probabilistic transitions and temporal characteristics determined by the GERT model. While it generally aligns with the true trajectory, the GERT predictions are less accurate due to their probabilistic nature. The green shaded area around the GERT mean line represents the model's uncertainty zone, showing the range of possible object positions. The expanded uncertainty zone highlights that the GERT model provides a broader, more generalized representation of the object's position, unlike the Kalman filter, which minimizes noise. The combined use of the GERT model and the Kalman filter demonstrates their complementary nature. The GERT model accounts for the probabilistic characteristics of the system and provides an initial understanding of the possible range of object positions. The Kalman filter, in turn, refines the trajectory based on incoming measurement data, delivering precise estimates. This combined approach is particularly useful for tracking tasks where both high accuracy and consideration of system uncertainties are required. The graph clearly illustrates the differences between the approaches, their advantages, and their respective limitations. Experiments and Results: Research of the Probability-Time Characteristics of the Interaction Channel Between the Radar and the Object That Puts Up Active Interference  
Consider an example of radar-object interaction in the presence of active interference from the object.