## 3 System Model
### Environment Model  
In the urban environment depicted in Figure 1, multiple UAVs engage in collaborative search operations to locate anomalous radiation source targets. We construct an intelligent  
\begin{table}
\begin{tabular}{p{56.9 pt} p{142.3 pt} p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Reference** & **Main Contributions** & **Key Limitations** & **Proposed Solutions** \\ \hline
[27] & \(\bullet\) & Centralized training, distributed execution age and efficiency & \(\bullet\) & The focus is on reducing search overlap and coverage, without using multiple UAVs for precise triangulation & \(\bullet\) & Cooperative triangulation strategy \\ \hline
[28] & \(\bullet\) & Multi-Agent DRL framework  
+++ ==WARNING: Truncated because of repetitions==
spectrum game platform for multi-UAV cooperation, integrating it with reinforcement learning framework to train and evaluate multi-UAV models. The target search area is characterized as a rectangular two-dimensional plane with dimensions \(X\times Y\), further divided into grids. Let \(\mathcal{T}=\{0,1,\ldots,T\}\) denote the discrete time horizon. In the defensive reconnaissance process, the red team has multiple UAVs with sensing and localization capabilities, while the blue team has one anomalous radiation source. Each UAV is assigned a unique identifier. The red team's UAVs have movement and scan rotation capabilities, equipped with both sensing and localization abilities. Initially, the red team's UAVs are distributed across the map at a fixed altitude \(H\). The blue team's radiation source is randomly placed in certain critical areas of the urban map, hovering to gather intelligence, also at a fixed altitude \(H\). The red team's UAVs perform sensing and detection operations in the defense area to locate the blue team's radiation source. When three or more red team's UAVs successfully detect the target simultaneously, a three-point localization process is triggered. The UAVs then continue to track and localize the target. The urban electromagnetic spectrum model employs a layered information table design, including position information table \(PT\), sensing information table \(ST\), and radiation propagation table \(RT\). The position table \(PT\) records the positions of UAVs and environmental information, where the positions of UAVs are marked with their unique identifiers (positive integers), obstacles are marked as \(-1\), and actionable areas are marked as \(0\). The sensing table \(ST\) records detection states, with \(0\) for undetected areas, \(1\) for detected areas without radiation source, and \(5\) for areas with detected radiation signals. The radiation propagation table \(RT\) is derived from the received power [30]. To model the radiation signal propagation and detection in our system, we first establish the relationship between transmitted and received power based on the Friis transmission equation. The received power (\(P_{r}\)) equals the transmitted power (\(P_{t}\)) minus the free-space path loss (L):  
\[P_{r}=P_{t}-[20\log_{10}(d)+20\log_{10}(f)+20\log_{10}(4\pi/c)], \tag{1}\]  
where \(d\) represents the propagation distance, \(c\) is the speed of light (\(3\times 10^{8}\) m/s), and \(f\) denotes the signal frequency (\(2.4\) GHz). This equation enables us to calculate the expected signal strength at given distance from the radiation source, which is crucial for the detection and localization process. Figure 1: Urban electromagnetic spectrum model, consisting of UAV teams, multi-layered information tables, and electromagnetic sensing systems. Building upon the signal propagation model in Equation (1), we define the sensing mechanism for each UAV. In the sensing process, each UAV \(i\) has a directional sensing matrix \(B_{i}\). The sensing result \(ST_{i}\) of UAV \(i\) at position \((x_{i},y_{i})\) is defined as follows:  
\[ST_{i}=B_{i}\times RT, \tag{2}\]  
where \(B_{i}\) represents the sensor's directional detection pattern (weights in different directions).