## 2 Materials and Methods
### Structural Model of Interaction of the GERT Model, Kalman Filter and Intelligent Module  
The task of this stage is to determine the logical structure of the phase transition of the radar system from the moment of target detection to entering a stable tracking mode. Such a task arises due to the fact that at the initial stage of radar operation there are no complete data on the target trajectory. The system can transit between the phases of detection, loss of tracking, or its restoration; the characteristics of the observations remain unstable. To take into account these features, it is necessary to formalize the sequence of states and possible transitions between them. The purpose of the task is to build a generalized logical-structural scheme that reflects typical scenarios of system behavior in conditions of incomplete measurements and to justify its use as a basis for the further adaptation of tracking algorithms. The expected result is the selection of key phases, a description of possible transition trajectories between them, and the identification of points at which the need for adaptive system response arises. The proposed intelligent method for tracking air targets at the initial stage of radar operation in a complex interference environment is based on the integration of three key subsystems: the GERT model, the Kalman filter, and the intelligent adaptation module. Such an architecture allows for the combining of the probabilistic-temporal analysis of processes with local recursive trajectory refinement and dynamic parameter control in real time. At the first stage, the GERT model performs the function of forming a probabilistic assessment of the process of detection and initial target capture. It reflects possible trajectories of transitions between system states (detection, loss, confirmation of tracking, etc. ), taking into account the influence of intentional interference, time delays, and the probability of successful transitions at each stage. As a result, the GERT model generates not only the expected target location area, but also provides generalized time characteristics that are used as initialization conditions for launching the Kalman filter. At the second stage, the Kalman filter accepts initial information about the object's state from the GERT model and refines the coordinates and parameters of the target's motion based on the incoming noisy measurements. The recursive structure of the filter allows for prediction errors to be minimized, as well as for constant updating of the object's state based on new data. The third component of the system is an intelligent adaptation module that controls the method parameters depending on the situation. In particular, it assesses the level of interference on the input signals, analyzes the reliability of the predictions, compares current estimates with historical data and, using a machine learning model or fuzzy logic rules, makes decisions on:  
* changing the Kalman filter parameters (covariance matrices, smoothing coefficients);
* dynamic weighting between the GERT and Kalman filter estimates;
* switching between tracking modes (stability/accuracy);
* signaling about the risk of tracking loss. The information flow in the system involves two-way interactions between all components. Data on the state of the object are supplied to the Kalman filter and the intelligent module. Control signals (for example, changing the filtering parameters) are generated by the artificial intelligence unit. These affect both the Kalman filter and GERT (for example, to update the probabilities when confirming the loss of the target). The general structural diagram of the interactions of the method components is presented in Figure 1. It indicates the main blocks, data transmission directions, and control signals. Data arrows indicate the transmission of measurements, forecasts, and status updates; the control arrows indicate parameter modifications and changes in the processing mode.