## 3 Proposed Method
### Node Collaborative Scheduling Algorithm (NCS)  
Although the DGS algorithm can largely exploit the advantages of the disk coverage model, the disk coverage model also possesses certain limitations and such data are not captured when the sensed points are outside the disk. Therefore, we use a node collaboration algorithm [32] to reconstruct the points that are not sensed by the sensor nodes by deeply excavating the spatial correlation between the nodes, which greatly increases the coverage of the network. Apart from that, we further propose a node collaborative scheduling algorithm with the same coverage rate threshold, fewer nodes can be scheduled to work. The node collaboration coverage model function expression is shown in (2). \[\xi(p)=\sqrt{ \begin{array}{c}\frac{1}{T}\times\sum\limits_{t=1}^{T}\left( \left(u^{t}(p)-\hat{u}^{t}(p)\right)^{2}\right)\end{array} } \tag{2}\]  
\(\xi(p)\) is the time-averaged root mean square error (RMSE) of the reconstructed spatial point \(p\), and \(u^{t}(p)\) and \(\hat{u}^{t}(p)\) denote the perceived true and estimated values of the spatial point \(p\), respectively. We define that a spatial point \(p\) is considered to be a valid reconstructed sensing point when the RMSE of the reconstructed point \(p\) is lower than a set threshold \(\lambda\). \(\lambda\) is usually given by the demand of the actual project and represents the reconstructed quality of the spatial point \(p\). Figure 6 shows an example of a node collaboration coverage model. \(S1\), \(S2\), \(S3\), \(S4\) are the sensor nodes, the green circle represents the coverage range of the disk model, \(R\) is the sensing radius of the sensor nodes, \(P1\), \(P2\), \(P3\) are the three spatial points, and the yellow area is the coverage of the nodes after collaborative coverage. Obviously, the disk coverage model can only sense \(P1\) and \(P2\) located within the sensing radius and it does not have the ability to sense \(P3\), which can be sensed by the node collaboration coverage model. Figure 5: The schematic of the DGS protocol. We divide the monitoring area of \(S\times S\) into several reconstructed subregions with edge length \(a\). The whole reconstructed subregion is within the range of the variable range. When two or more nodes are located within the range of the variable range, the nodes can collaborate with each other, while when the distance between the nodes exceeds the range of the variable range, it is considered that there is no spatial correlation between the nodes to collaborate with each other. In the reconstructed subregion, five reference points are set. Equations (3) and (4) reflect the coordinates of these five reference points. \[HC=\{0.2a,0.8a,0.5a,0.2a,0.8a\} \tag{3}\]  
\[VC=\{0.2a,0.2a,0.5a,0.8a,0.8a\} \tag{4}\]  
\(HC\) is the horizontal coordinates of the five reference points and \(VC\) is the vertical coordinates of the five reference points. In a reconstructed subregion, five nodes nearest to the corresponding reference points are scheduled to work together, and these five reference points are chosen because when the sensor nodes' positions are completely overlapped with these five reference points, the collaborative coverage can completely cover the whole reconstructed subregion, and the coverage range is the biggest at this time. In addition, when the nodes are unevenly distributed, the nodes scheduled to work together can also have a high coverage rate. The network always ensures that each reconstructed subregion can reach the coverage rate threshold, when the reconstructed subregion fails to reach the coverage rate threshold, nodes closer to the center of the reconstructed subregion will be gradually added to collaborate until the subregion coverage rate threshold is met, and when the coverage of the whole network fails to reach the coverage rate threshold, all remaining nodes will be mobilized to carry out the work. The ERG-NCS algorithm is shown in Algorithm 3.