# Multi-UAVs Communication-Aware Cooperative Target Tracking
## 2 Problem Description and System Model
### Communication Model  
In the traditional cooperative tracking algorithm, the widely used communication model is the \"disk model\". The disk model assumes that there is a clear communication distance \(d\) between UAVs. If the distance of two UAVs is less than \(d\), communication between them is 100% successful; otherwise, they cannot communicate with each other. The model is an ideal model which does not take thecomplexity of actual communication into account. When we studied UAVs network topology [20], this model could be used to simplify the problem, but when we estimated the target state in the target tracking problem, the disk model could not meet the accuracy requirements. Therefore, this paper introduces communication noise, based on communication signal to noise ratio, so it can be compared with the observed noise covariance and process noise covariance. There are several methods to handle communication between UAVs. The method proposed in Reference [9] took the reliability of multi-hop networked communication into account. It built a function of SNR to describe the probability of communication between node \(i\) and node \(j\) and then established an objective function with the expected value. The work in Reference [11] considered real communication and proposed the concept of \"communication noise\" to describe communication between two UAVs. In this paper, we used the concept of communication noise and applied the form of Fisher information matrix (FIM) to add communication noise to the objective function. Then, we proposed a new method to put communication noise into the FIM and get control input for each UAV. A local filter was designed for each UAV platform (the extended Kalman filter is used in this paper) to get a better estimate of the target state. \(\hat{x}_{i}[k],e_{i}[k],P_{i}[k]\) represents the state estimate of the \(i\)-th UAV, its corresponding estimate errors, and its error co-variance matrix, respectively. Each UAV sends the estimated value of the target state and its corresponding covariance matrix to its neighbors. \(\hat{x}_{j\mu}[k]\) represents the reception value of the \(i\)-th UAV from the \(j\)-th UAV and \(P_{j,i}[k]\) the corresponding covariance matrix:  
\[ \begin{array}{l}\hat{x}_{j,i}[k]=\hat{x}_{j}[k]+c_{j,i}[k]\\ P_{j,i}[k]=P_{j}[k]+L_{j,i}[k]\end{array}  \tag{5}\]  
where \(c_{j\mu}[k]\) and \(L_{j,i}[k]\) contain the error and its corresponding covariance matrix caused by communication noise [11]. The communication noise covariance matrix can be calculated with the following Equation (6):  
\[\sum_{j\mu}{[k]}=\overline{c_{\mu i}[k]c_{\mu i}^{T}[k]}=\psi(SNR_{j,i}[k]). \tag{6}\]  
A wireless transmission is degraded by several factors, among which distance-dependent path loss, fading, and receiver thermal noise are the most critical. One of the most fundamental parameter of a communication channel is the received signal-to-noise ratio (SNR). \(SNR_{j,i}[k]\) represents the SNR from node \(j\) to node \(i\) at time \(k\). We can calculate SNR with the following equation:  
\[SNR_{j,i}[k]=\frac{Power_{j}\cdot Gain_{ji}}{N_{i}}. \tag{7}\]  
In addition, for a distance-dependent path loss without fading, we have:  
\[Gain_{ji}=\frac{C_{ji}|h_{ji}[k]|^{2}}{d_{ji}^{n_{p}}} \tag{8}\]  
where \(Power_{j}\) in (7) represents the transmission signal power, \(N_{i}=\sigma_{\rm T}^{2}=E(|n_{thermal}|^{2})\) the noise power at the receiver, \(Gain_{ji}\) the channel gain, \(h_{ji}[k]\) the attenuation factor for the communication environment, \(d_{ji}\) the distance between the \(i\)-th UAV and the \(j\)-th UAV, and \(C_{ji}\) the communication environment impact factor. SNR determines the effectiveness of communication. Then, we can rewrite Equation (7) as the following:  
\[ \begin{array}{l}SNR_{j,i}[k]=\frac{\alpha_{ji}[k]}{d_{ji}^{n_{p}}[k]}\\ \alpha_{ji}[k]=\frac{Power_{j}C_{ji}|h_{ji}[k]|^{2}}{N_{i}}\end{array}  \tag{9}\]  
where \(\alpha_{ji}[k]\) is an intermediate variable. In a fading environment, however, the SNR is a random variable.