## 3 Mathematical Model of Radar Operation Under Interference Conditions
Metrics such as the probability of detection, false alarm rate, and mean time to track loss are used to evaluate and optimize the model's performance. The interaction between a radar and an object emitting active jamming can be represented through a GERT network with a discrete set of states and time intervals. The number of states in the network is determined by the decision-making algorithms used within the radar system:  
\[\frac{k}{x}+\frac{x}{n}-h, \tag{1}\]  
where \(k/x\) is establishing the object's trajectory criterion;  
\(x/n\) is object trajectory detection confirmation criterion;  
\(h\) object tracking reset criterion. Equation (1) formalizes the criteria governing object trajectory detection, confirmation, and reset in a probabilistic GERT network framework. The model time increment, \(dt\), is determined based on the radar's time characteristics. Specifically, the time interval, \(dt\), can be set equal to the period during which the radar interacts with the object. Figure 2 presents a generalized GERT network that illustrates the radar's operation during its initial interaction with the tracked object, following an arbitrary algorithm described by the expression (1). In Figure 2 the transitions, nodes, and connections are defined as follows:  
* Transition (1-2): Represents the process of detecting an echo signal from the tracked object;
* Transition (2-3): Records the event of forming a sufficient set of echo signals to establish a trajectory;
* Transition (2-1): Indicates the failure of the radar to use the set of echo signals to establish a trajectory;
* Connection (3-4): Formalizes the process of establishing the trajectory of the tracked object;
* Transition (4-6): Illustrates the final detection of the trajectory of the tracked object;
* Connection (4-5): Formalizes the radar's failure to complete the target task of final detection of the trajectory;
* Transition (5-4): Shows a return to the process of establishing the trajectory of the tracked object;
* Transition (6-7): Describes the ongoing tracking of the object;
* Transition (6-1): Formalizes the radar's failure in tracking the object;
* Nodes S1 and S7: Represent the \"initial state of the system\" and the \"state characterizing successful tracking of the object\", respectively;
* Nodes S2 to S6: Record the states of \"forming a sufficient set of echo signals to establish a trajectory\", \"establishing a trajectory of the tracked object\", \"failure to establish a trajectory\", \"final detection of the trajectory\", and the \"tracking of the object\". When considering the possibility of transferring the tracked object for servicing to the monitoring and execution system, it is important to recognize that the time during which tracking may fail is limited by the radar's preparation time for the initial data on the tracked object. A key feature of this GERT network is that the tracking process, before the object's transfer for servicing, can be represented as a sequence of intermediate states corresponding to events where tracking does not fail during a specified time interval \(dt\)  
Figure 2: Generalized GERT network of radar operation in interaction with the tracking object at the initial stage. This must be considered in the mathematical description of transition (5-6). Reaching the final state of the chain, which corresponds to no failures in tracking during the specified time, indicates the successful transfer of the tracked object for servicing to the monitoring and execution system. The use of the method of combining and describing fictitious states in GERT network modeling technology also allows for the analysis of the noise immunity of a radar system with a variable coverage period.