## 4 Modeling the Target Tracking Process Using Kalman Filters
However, it should be noted that GERT networks can more precisely model complex systems with multiple dependencies and probabilistic scenarios. In contrast, the advantage of Markov networks lies in their higher accuracy for tasks with fewer complex dependencies when strictly defined. For the comparative study, the models described in [24; 25] were chosen as prototypes. Among the possible comparison metrics, the authors selected the Kullback-Leibler divergence (KL-divergence) and the Wasserstein distance. Both metrics are widely used in statistical analysis and information theory, making them reliable tools for distribution analysis. Figures 9 and 10 present the comparison results as curves of the cumulative distribution function (CDF) and probability density function (PDF) of the radar system's \"interaction\" time with the tracking object, respectively. Figures 9 and 10 illustrate that the GERT model demonstrates a more gradual change in cumulative probability, which is due to the probabilistic structure of network processes and their multiple pathways--characteristic of GERT modeling. Meanwhile, the hidden Markov model (HMM) and Markov models show a sharper accumulation of probability, reflecting their more straightforward probabilistic trajectories. Additionally, the GERT results appear smoother and less abrupt compared to HMM. Further research is needed to gain a deeper understanding of the reasons for these differences. Table 2 presents a comparison of the developed GERT model with prototype models [24; 25; 26; 27], evaluated through KL-divergence and Wasserstein distance, highlighting the probabilistic and temporal accuracies of each model under varying interference intensities. As part of this study, a comparison of the GERT, Kalman filter, Markov, and HMM approaches was conducted to analyze radar systems under jamming conditions. The primary focus was on their individual advantages. GERT enables the modeling of temporal and probabilistic dependencies at the macro level, providing an overall structure for processes. At the same time, the Kalman filter ensures high accuracy at the micro level, minimizing the impact of noise when refining trajectories. Comparative metrics such as KL-divergence and Wasserstein distance were used for quantitative analysis, highlighting differences in probability distributions between the models. These results emphasize the unique features and application areas of each model. Based on the comparison results between the GERT model, the Markov model, and the HMM, several conclusions can be drawn regarding their characteristics and differences:  
* At \(\lambda=9\), the KL-divergence for the Markov model is 0.0001, indicating a high similarity with the GERT model. This is also observed for other \(\lambda\) values, except for \(\lambda=0.2\), where a significant increase in KL-divergence is observed as the intensity decreases;
* The KL-divergence for HMM is significantly higher, indicating a greater discrepancy between GERT and HMM. This suggests that HMM is better suited for describing more complex dynamics but may not always align with GERT, especially at lower \(\lambda\) values;
* Low values of the Wasserstein distance between GERT and the Markov model (e.g., 0.0016 at \(\lambda=9\) and 0.0066 at \(\lambda=5\)) indicate a close match in distributions, consistent with the low KL-divergence;
* The Wasserstein distance between GERT and HMM is also noticeable (e.g., 0.1037 at \(\lambda=9\) and 0.0832 at \(\lambda=5\)), confirming that HMM differs more from GERT than the Markov model;
* As the intensity value, \(\lambda\), decreases, both the KL-divergence and Wasserstein distance increase for all models. This may indicate that as \(\lambda\) decreases, the models become less similar, possibly due to changes in the structure of the data they are modeling;