## 7 Conclusions  
This study developed a mathematical model for radar operation, allowing visualization and formalization of complex processes, including probabilistic dependencies and time characteristics, particularly at the initial stages of target acquisition and tracking. The model's key feature is its integrated approach to accounting for these characteristics. Analytical assessments of the system's probabilistic, time, and spatial characteristics were obtained. Additionally, as part of this study, a Kalman filter-based model was developed and integrated to refine the trajectories predicted by the GERT model. The Kalman filter ensures precise smoothing of noisy measurements and minimizes deviations from the true trajectory of the object. This enables the GERT model to serve as a tool for primary probabilistic analysis, while the Kalman filter performs the functions of trajectory refinement and improving prediction accuracy. Such a combined use of models provides a more comprehensive description and understanding of the dynamics of radar system interactions with objects. The analysis of the Kalman filter demonstrated its high efficiency in conditions of significant noise and uncertainty. At the same time, the GERT model continues to play an important role in accounting for the temporal and probabilistic characteristics of the system, as well as in forming the initial conditions for further data refinement. The combined use of the GERT model and the Kalman filter allows for both the probabilistic nature of the system to be considered and measurement errors to be minimized, which is particularly critical for tracking systems operating in interference-heavy environments. The study of the target trajectory tracking algorithm's block diagram based on data from a single radar suggests that prioritizing performance indicators is crucial. The choice of probabilistic and time indicators led to the formulation of the concept of GERT-network modeling for radar-object interaction. A mathematical model of radar operation under interference conditions was then developed, yielding distribution function curves, \(\Phi(x)\), and probability distribution density, \(\varphi(x)\), along with polynomial coefficients for different generating function intensities. The comparative study with prototype models illustrated that models based on Markov network technologies align reasonably well with the GERT model, particularly at high values of the parameter \(\lambda\). However, as \(\lambda\) decreases, there is an increase in both KL-divergence and Wasserstein distance, indicating limited accuracy under these conditions. Thus, the proposed GERT model proves to be more accurate and effective. The comparison with HMM revealed that while this model can account for hidden states, its complexity may lead to discrepancies with the GERT model, especially under low \(\lambda\) conditions. The model can be utilized to enhance the efficiency of collision warning systems, object tracking, and improve tracking systems' performance in high interference environments. In the future, it may be possible to expand the model using fuzzy GERT networks and neural networks, making it more adaptive to changing operational conditions. Supervision and conceptualization: S.S. and V.D. ; methodology: S.S.; experiments, result visualization, and analysis: M.K.-K., P.M., Y.T., V.V., O.V. and V.B. ; verification of theoretical and experimental conclusions: S.S.; writing--original draft: V.D. and S.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The raw data supporting the conclusions of this article will be made available by the authors on request.