## 2 Materials and Methods
### Algorithm for Dynamic Weighting Between Estimates of Kalman Filter and GERT Model  
The task of the next stage of the research is to formalize an approach to dynamic control of the target state filtering process under conditions of variable measurement reliability. As part of the task, it is necessary to determine the dependence between the current statistical characteristics of the measurement process and the level of confidence in local and global estimates of the object state. Special attention should be paid to the construction of a functional weighting mechanism between the Kalman filter estimate and the results of predictive analysis, which reflects the current state of the interference situation. The proposed approach involves the formation of a combined estimate of the target position and velocity by adaptive linear fusion of the Kalman filter and GERT model output data. The GERT model in this architecture represents the radar tracking process as a network of probabilistic phase transitions between key system states such as detection, stable tracking, degradation, and loss. Each state is connected by arcs assigned with transition probabilities and time distributions based on system dynamics and interference conditions. While the Kalman filter provides real-time local estimation of the target's coordinates using current measurements, it is sensitive to signal loss, incorrect noise parameters, and unmodeled dynamics. The GERT model complements this by simulating the likelihood of system transitions to undesirable states (e.g., tracking failure), enabling the intelligent module to anticipate potential degradation. This predictive insight is used to proactively adjust the fusion coefficient \(\alpha\)(t), decreasing reliance on the Kalman estimate when instability is likely, and increasing trust in it when conditions are stable. Thus, GERT does not improve Kalman filtering directly but adds robustness to the overall system by shaping the confidence weighting dynamically based on risk estimation. This cooperation results in more stable performance under variable and degraded conditions. Formally, the final coordinate estimate \(\hat{x}_{comb}\) is defined as:  
\[\hat{x}_{comb}=\alpha(t)\cdot\hat{x}_{KF}+(1-\alpha(t))\cdot\hat{x}_{GERT}, \tag{1}\]  
where \(\hat{x}_{KF}\) is the coordinate estimate from the Kalman filter,  
\(\hat{x}_{GERT}\) is the coordinate forecast based on the GERT network,  
\(\alpha(t)\) is the weighting coefficient of confidence in the Kalman filter, which changes in time according to the current situation. In this work, a one-dimensional (1D) kinematic model is used to describe the target motion along the \(x\)-axis. This simplification is commonly adopted in simulation studies and methodological papers to improve readability and focus on algorithmic behavior [18]. It allows for the integration of the Kalman filter, the GERT model, and the learning module to be illustrated without introducing vector notation at this stage. Nonetheless, the model is easily generalizable to multidimensional cases. For example, in real radar tracking scenarios involving motion in three-dimensional space (\(x\), \(y\), \(z\)), the same architecture can be applied independently to each coordinate or reformulated as a vector state-space model with coupled dynamics [19; 20]. The proposed framework is thus not limited to 1D, but serves as a scalable prototype for more complex tracking configurations. The construction of the adaptation algorithm is based on taking into account the phase structure of the support system functioning (see Figure 1), in which transitions between states of stable support, signal loss, and its recovery are possible. Under these conditions, the reliability of  
The intelligent adaptive module, implemented as a combination of fuzzy logic and neural network, is responsible for analyzing relevant indicators (errors, filter instability, interference level, tracking loss prediction, etc.) and forming the Kalman filter value.