# Cloud-Assisted UAV Data Collection for Multiple Emerging Events in Distributed WSNs
## 3 Mathematical Model and Algorithm Analysis
### Outline of Our Algorithm  
In the paper, we focus on emerging events surveillance in ground WSN, and use the UAV to enhance the data collection scheme. Figure 1 shows the schematic of the approach. The overall system includes a cloud computing platform, a UAV, sensor nodes and cluster heads. The process in our approach after the occurrence of specific events can be divided into two phases. The operation of the mechanism can be described by the following steps: cloud based mission planning and UAV data collection.  
In the first step, if there are emerging events in the monitored area, the related and simple information is sent to the base station. Next, the cloud computing platform identifies the event-related clusters based on the position of the WSN clusters and the coverage of events. Meanwhile, the algorithm in the cloud is used to optimize the visiting sequence of clusters in the WSN. Then, the flight mission is scheduled to the UAV.  
In the second phase, to save energy and shorten the flying time, optimal parameters for dynamic flying must be decided in advance. In this phase, issues such as rate of packet loss and data acquisition integrity of the wireless communication channel are addressed at the same time.  
Figure 1: Topology of a hierarchical Unmanned Aerial Vehicles-Wireless Sensor Networks (UAV-WSN).  
the event \(U_{1}\), so the cluster correlation coefficient for \(C_{2}\) and \(U_{1}\)\(\Phi_{21}=1\). In the same way, the cluster correlation coefficient \(\Phi_{11}=0\), as in cluster \(C_{1}\) no sensor could detect the event \(U_{1}\). So, the overall correlation matrix \(\Delta^{3\times 3}=\left[\begin{array}{ccc}0&0&0\\ 1&1&1\\ 0&1&1\end{array}\right]\).  
Let \(Sc(f)\) and \(Sr(f)\), be sums of the \(f\)th column and row respectively. From this, we can obtain the following Lemmas.  
**Lemma 1**.: _Given multiple events occurring in a cluster \(i\), we have \(Sr(i)>\)1._  
**Proof.** For any cluster \(i\) which senses the event \(j\), we have a cluster coefficient \(\Phi_{ij}=1\). We assume that there are \(L=\{1,2,\ldots,l\}\) events occurring in the cluster \(i\). Namely, \(\|L\|=l>1\). We can obtain the sum of the cluster correlation as \(\Sigma_{j=1}^{l}\Phi_{ij}=\|L\|\). Since \(L\subseteq U_{M}\), we get that the value of \(Sr(i)\geq l>1\).  
**Definition 2**.: _Integrity of data acquisition: Let \(\epsilon_{a}(j)\) and \(\epsilon_{a}(j)\) be the number of received and total messages, respectively, of the event \(j\) in the cluster \(a\). \(\partial_{a}\) (\(j\)) is the ratio of \(\epsilon_{a}(j)\) and \(\epsilon_{a}(j)\), namely:_  
\[\partial_{a}(j)=\frac{\in_{a}\ (j)}{\epsilon_{a}(j)} \tag{5}\]  
_So, the data acquisition integrity (\(\ell(j)\)) of the event of \(j\) in WSN is given by:_  
\[\ell(j)=\frac{\Sigma_{a=1}^{n}\in_{a}\ (j)}{\Sigma_{a=1}^{n}\epsilon_{a}(j)} \tag{6}\]  
**Definition 3**.: _Total Flying Score: Let \(F_{s}\) be the total flying score. \(D_{f}\) is the total distance flown by the aerial vehicle to gather data for an event. So, at a given moment (\(t\)), \(F_{s}\) is the sum of the results of \(\alpha_{a}(j)\) multiplied by the event priority and divided by the total flying distance. \(F_{s}\) can be written as:_  
\[F_{s}=\frac{\sum\limits_{a\in j\in M}\alpha_{a}(j)\cdot w_{j}}{D_{f}} \tag{7}\]  
Figure 2: Modelling of Event correlation coefficient.