# A Low Complexity Persistent Reconnaissance Algorithm for FANET
## 2 System Model and Problem Statement
### System Model  
In recent years, three main strategies have been used to achieve drone swarms' persistent surveillance [8; 11; 12; 13; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]: (i) on-duty UAV replacement scheme based on recharging stations [13; 19; 25]; (ii) energy-efficiency path planning [20; 21; 22; 23; 24; 25; 26; 27]; and (iii) novel structures of UAV teaming [8; 11; 18; 22]. UAV distribution's hierarchical architecture helps plan efficient and adaptive surveillance missions when the surveillance map changes due to weather or invisible factors. The hierarchical structure intends to divide the surveillance task into different platforms such as ground stations, high-altitude UAVs, and UAV sensing swarms. Each platform is in charge of different functions such as control, motion coordination, data transmission, package routing, etc. We assume that the FANET in this study consists of a high-altitude UAV \(A\), as its airborne command and control platform, i.e., ACP, and set \(U\) of drone swarms in low-altitude to perform reconnaissance missions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Acronym** & **Description** \\ \hline TA\&CRFOOTNOTE:]Footnote *: footnotemark: [ENDFOOTNOTE] & Dynamic threat avoidance and continuous reconnaissance FANET operation \\ UAV & Unmanned aerial vehicle \\ TARFC & Threat avoidance and reconnaissance FANET construction algorithm \\ FANET & Flying ad hoc network \\ ACP & Airborne command and control platform \\ LoS & Line-of-sight \\ PSO & Particle swarm optimization \\ TED & Total edit distance \\ AUDS & Anti-UAV defensive system \\ MUs & Monitoring UAVs \\ RUs & Relay UAVs \\ PDF & Probability density function \\ KKT & Karush–Kuhn–Tucker method \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of acronyms. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Description** \\ \hline \(A\) & The ACP of FANET \\ \(U\) & Set of low-altitude drone swarms \\ \(R\) & Set of all RUs \\ \(M\) & Set of all MUs \\ \(x_{i}\) & Location of node \(i\) \\ \(V\) & Node Set \\ \(X_{V}\) & Set of locations of all nodes in \(V\) \\ \(\varepsilon_{m}\) & The MU assigned to mission \(m\) \\ \(\rho(m)\) & Routing path for mission \(m\) \\ \(p\) & Set of all active links \\ \(f\) & Overall performance function \\ \(f^{C}\) & Network connectivity function \\ \(f^{C}_{ij}\) & Wireless connectivity quality between \(i\) and \(j\) \\ \(f^{I}\) & FANET threat metric \\ \(r_{thr}\) & Threatened radius of UAV \\ \(\varphi(x)\) & Threat PDF in related areas \\ \(r^{C}\) & Maximum communication radius between UAV \\ \(r^{S}\) & Minimum safety radius between UAV \\ \(t\), \(\tau\) & Time \\ \(\dot{\varphi}(t)\) & FANET in time \(t\) \\ \(N\) & Node set in graph theory model \\ \(\sigma(t)\) & Edge set in graph theory model \\ \(P_{N}(t)\) & Nodes’ position set in graph theory model \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of variables. If there is any ambiguity, all UAVs are referred to as nodes of the network throughout this article. We identify a node \(i\)'s location by \(x_{i}\in\mathbb{R}^{3}\), and a set of all the nodes' locations in set \(V\) by \(X_{V}=\left\{x_{i}\right\}_{i\in V}\). To simplify the model, we presume that each UAV can only carry out one reconnaissance operation at a time and that each target that is being scouted should be covered by at least one UAV. As a consequence, we make the assumption that the number of targets to be scouted is not larger than the number of drones that are currently accessible. In our FANETs, the ACP can either hover over the given location or fly around the periphery of the area of interest, while drone swarms have controllable mobility. Therefore, drone movement can be managed by themselves or by the ACP to achieve excellent performance in both network and mission-related factors. Considering the radio propagation model, [PERSON]'s free space model [28], the most popular propagation model, is used in this article. According to this radio propagation model, all nodes have the same transmission radius.