## 3 Model for Predicting the Health of an Unmanned Aerial Vehicle Data-Link System
### Constructing a Bayesian Network Root Node Prediction Model
Both the line-of-sight communication and the non-line-of-sight communication have an impact on the telemetry link and the telecontrol link. Therefore, now we can construct the telecontrol link node and the telemetry link node with the parent node as the line-of-sight communication and the non-line-of-sight communication links. Finally, the leaf node is constructed. The DAG for the UAV data-link system is shown in Figure 4.  
In the BN probability prediction model of the UAV-data-link system, \(R_{xi}(t)\)\(R_{\text{Mj}}(\text{t})\) and \(R_{L}(t)\) are used to represent the health state of root node \(X_{i}=(i=1,2\cdots p)\), the intermediate node \(M_{j}(j=1,2\cdots q)\) and the leaf node \(L\) at time \(t\) respectively. For the \(p\) root nodes, the probability of health status is solved by the prediction model of each corresponding device and discretized according to the unsupervised equal-width interval method with a time sequence to achieve the state prediction in the future \(T\) time; that is, the \(p\times n\) order health state probability prediction matrix [36]:  
\[H_{p\times n}=\left( \begin{array}{ccc}H_{1,1}&\cdots&H_{1,n}\\ \vdots&\ddots&\vdots\\ H_{p,1}&\cdots&H_{p,n}\end{array} \right). \tag{6}\]  
With a certain time sequence \(T=(t+\varsigma,t+2\varsigma\cdots t+n\varsigma)\). The elements \(H_{i,\tau}(i=1,2,\cdots p,\tau=1,2\cdots n)\) represent root node \(X_{i}\) to be in the health state at the \(\tau\)th predicted point. Assigning the prior probability of the root node according to the probability prediction matrix. The probability of the root node \(X_{i}\) at time \(t\) is \(P(RX_{i}(t))=H(R_{i}(t)),i=1,2,\cdots,p\). For the solution of the state probability of intermediate nodes, it is assumed that the parent-node set \(F=\{R_{1},R_{2},\cdots R_{i}\}\) exists for the node \(M_{j}\). According to the assumption of independent conditions, the probability prediction of the intermediate nodes at time \(t\) can be solved based on:  
\[P\big{(}M_{j}(t)\big{)}=\sum_{F}P\left(R_{M_{j}}(t),Rx(t)\,\right). \tag{7}\]  
Based on the probability of the root node and intermediate node, the predicted probability of the leaf node in health state can be further solved according to:  
\[RL(t) = \sum P(Rx1(t),Rx2(t),\cdots,Rxp(t),RM1(t),RM2(t)\cdots RMq(t),RL(t))\] \[= \sum_{Pa(L)}P(RL(t)|RPa(L)(t))\cdot\sum_{Pa(M_{j})}P(RM1(t)|RPa(M 1)(t))\cdots\] \[\sum_{Pa(M_{q})}P(RMq(t)|RPa(M_{q})(t))\cdots P(Rx1(t))\cdots P( Rxp(t))\]  
where, \(Pa(*)\) is the parent node of the node \"\((*)\)\". According to the above formula, the JT estimation algorithm traverses the DAG and the state of the system node \(L\) can be predicted. By the probability prediction matrix \(R_{p\times n}=(R(t),R(t+\varsigma),R(t+2\varsigma)\cdots R(t+n\varsigma))\) of the root node, the corresponding prediction sequence of probability at system level will be obtained to achieve continuous prediction of health state. Figure 4: Directed acyclic graph of UAV data-link. LOS: line-of-sight; NLOS: non-line-of-sight; UAV-RS: UAV repeater satellite; G-RS: ground data terminal repeater satellite. A Bayesian Network Model of an Unmanned Aerial Vehicle Data-Link System Considering the Bit Error Rate  
In addition to the possible degradation of hardware equipment performance and accidental failure, the health status of the UAV data-link system can be affected by the health status of UAV data-links. Such as the bit error rate (BER), packet loss rate, path loss, UAV speed and weather and channel capacity will affect the health status of UAV data-links. It can be expressed as follows:  
\[h=f(x_{1},x_{2},x_{3}\cdots x_{n}), \tag{8}\]  
where \(h\) indicates the health status of UAV data-links, \(x_{i}\) is a factor that affects the health status of UAV data-links, such as \(x_{1}\) is UAV speed, \(x_{2}\) is the weather \(x_{3}\) is bit error rate (BER) and so forth. We introduce the bit error rate as a factor affecting the health status of the UAV data-inks in the following paper.