# A Comprehensive Evaluation Algorithm of Multi-Point Relay Based on Link-State Awareness for UANETs
## 3 Proposed Algorithm
### Evaluation Parameters  
#### 3.1.1 Awareness of Mobility  
Considering the impact of node mobility in the network from the dimensions of time and space, we propose three measurement parameters: link duration, stability degree of link, and average neighbor set change rate. 1. Link Duration  
Given the propensity for drone nodes to move at high speeds, they frequently venture beyond the communication range of a node, leading to link disconnections. In light of this, we introduce the concept of _link duration_ (LD), defined as the period from the establishment of a connection between two nodes in the network until the disconnection of the link. This metric serves to quantify the stability and reliability of network connections in dynamic environments. As shown in Figure 4, we establish a three-dimensional Cartesian coordinate system with node \(i\) as the reference center, where node \(j\) moves around node \(i\). At time \(t_{1}\), node \(j\) establishes a link connection with node \(i\) at point \(B\), and then moves along the \(\overrightarrow{V}\) direction to point \(C\) at time \(t_{2}\). At the next moment, it will disconnect from node \(i\), which will have exceeded the communication range of node \(j\). Assuming that the measured coordinates of the drone node \(i\) and node \(j\) are \((x_{i},y_{i},z_{i})\) and \((x_{i},y_{i},z_{i})\), and the velocities are \((v_{ix},v_{iy},v_{iz})\) and \((v_{jx},v_{iy},v_{jz})\), respectively, the relative position vector \(\overset{\rightarrow}{OB}\) between node \(i\) and node \(j\) is denoted as \((d_{x},d_{y},d_{z})\), and the relative velocity vector \(\overset{\rightarrow}{OC}\) between node \(i\) and node \(j\) is denoted as \((v_{x},v_{y},v_{z})\). The expressions are as follows, where \(\alpha\) is the angle between the relative position vector \(\overset{\rightarrow}{OB}\) and the relative velocity vector \(\overset{\rightarrow}{OC}\), and \(\beta\) is its complementary angle:  
\[\cos\alpha=\frac{\overset{\rightarrow}{OB}\cdot\overset{\rightarrow}{V}}{| \overset{\rightarrow}{OB}|\cdot|\overset{\rightarrow}{V}|} \tag{1}\]  
\[\cos\beta=-\cos\alpha=-\frac{\overset{\rightarrow}{OB}\cdot\overset{ \rightarrow}{V}}{|\overset{\rightarrow}{OB}|\cdot|\overset{\rightarrow}{V}|} \tag{2}\]  
The LD between node \(i\) and node \(j\) called \(LD_{ij}\) is expressed as:  
\[LD_{ij}=\frac{-(v_{x}d_{x}+v_{y}d_{y}+v_{z}d_{z})+\sqrt{(v_{x}^{2}+v_{y}^{2}+v_ {z}^{2})R^{2}-[(v_{x}d_{y}-d_{x}v_{y})^{2}+(v_{x}d_{z}-d_{x}v_{z})^{2}+(v_{y}d_ {z}-d_{y}v_{z})^{2}]}}{v_{x}^{2}+v_{y}^{2}+v_{z}^{2}} \tag{3}\]  
When two connected nodes maintain consistency in their movement direction and speed, the link maintenance time is longer, making the link less likely to disconnect. Conversely,  
Figure 4: The schematic diagram of relative motion between drone node \(i\) and node \(j\). the link is more prone to disconnection if there is inconsistency in their movement. Therefore, selecting neighbors with larger LD values results in longer link connection times along their paths, ensuring more stable and reliable data transmission. 2. Stability Degree of Link  
Link duration assesses link stability by gauging the current or anticipated motion state of the link. However, to further enhance the evaluation of link stability, we propose the _stability degree of link_ (SDL), which quantifies the fluctuation level of relative node positions. By leveraging SDL, we can enhance packet delivery rates, diminish data retransmission instances, elevate routing success rates, and ultimately enhance network performance. Before defining link stability, we first provide the definition of distance variation based on the Chebyshev inequality in statistical theory, which can reflect the fluctuation of distance between node \(i\) and node \(j\).