## 4 The Proposed Tracking Anchor Based Clustering Method
### Tracking Anchor Determination
The sensing range and communication range of each sensor are identically fixed to 20 m and 40 m. The size of the data packet is 4000 bits. For the determination of the tracking anchors, the maximum iteration is 300, and we terminate the iteration when \(\left|\frac{\mu(t)-\mu(t-1)}{\mu(t-1)}\right|<\varepsilon\). The quantity \(\varepsilon\) is a small value, controlling the convergence of the membership \(\mu\). In our experiments, \(\varepsilon=0.01\), that is, our results obtained converged to the 0.01 specification level for comparing the two different methods [32; 33]. The simulation lasted for 5000 time steps. As for the target, we simulate a scenario where the target moves based on a Gauss-Markov mobility model [34] in the surveillance area. Initially, a random speed and direction are assigned to each target. At each time step \(t\), the movement parameters of the target are updated by:

\[v_{t}=\eta v_{t-1}+(1-\eta^{2})\overline{v}+\sqrt{1-\eta^{2}}v_{t-1}^{G}\, \tag{26}\]

\[\theta_{t}=\eta\theta_{t-1}+(1-\eta)\overline{\theta}+\sqrt{1-\eta^{2}}\theta _{t-1}^{G}\, \tag{27}\]

where \(v_{t}\) and \(\theta_{t}\) are the current speed and direction of the target at time \(t\); \(\overline{v}\) and \(\overline{\theta}\) are constants denoting the mean value of speed and direction; \(v_{t-1}^{G}\) and \(\theta_{t-1}^{G}\) are random variables from a Gaussian distribution, and \(\eta\in(0,\ 1)\) is a parameter that is used to vary the randomness of target motion. Therefore, the position of the target is calculated as follows:

\[\left\{ \begin{array}{l}x_{t}=x_{t-1}+v_{t-1}\cos(\theta_{t-1})\\ y_{t}=y_{t-1}+v_{t-1}\sin(\theta_{t-1})\end{array} \right.. \tag{28}\]

According to Equation (28), we can obtain the future position of the target in simulation. Not limited to this, different target motion models and prediction methods can be used in practical applications. ### Performance Analysis

We consider multiple vital metrics to measure the energy efficiency of different clustering methods for target tracking. First, we compared the residual energy of sensor nodes, and the average results of this metric are shown in Figure 9. Moreover, Figure 10 presents the total energy consumption during network operation. It can be seen that our proposed \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Network Scale (\(m^{2}\)) & \(500\times 500\) \\ Node Number & 200–500 \\ Sink Coordinates (\(m\)) & (250, 250) \\ Initial Energy (J) & 1 \\ \(E_{dec}\) (\(nI/bit\)) & 50 \\ \(\varepsilon_{fs}\) (\(pI/bit/m^{2}\)) & 10 \\ \(\varepsilon_{mp}\) (\(pI/bit/m^{4}\)) & 0.0013 \\ Data Packet Size (bit) & 4000 \\ Transmission Round (s) & 0.5 \\ Sensing Radius \(R_{s}\) (\(m\)) & 20 \\ Communication Radius \(R_{c}\) (\(m\)) & 40 \\ Maximum Iteration \(I_{\max}\) & 300 \\ Change Rate Threshold \(\varepsilon\) & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. clustering method TACM displays better results in both metrics compared with other methods. At the 1000-th time step, the average residual energy is 0.64 joules for TACM, 0.57 joules for EEDC, 0.43 joules for EEAOC, and 0.14 joules for HCTT. Moreover, the total energy consumption is 145 joules for TACM, 169 joules for EEDC, 224 joules for EEAOC, and 343 joules for HCTT. The energy consumption of TACM is the lowest, which is achieved by introducing the tracking anchors to liberate nodes from the heavy workload of serving as fixed CHs. HCTT and EEAOC make structural adjustments on the static cluster as the target moves, so the communication overhead caused by CH rotation cannot be avoided. Although EEDC does not require static clusters as support, the selection of candidate CHs in an omnidirectional manner will result in energy waste, and the results show that its energy consumption is higher than that of TACM. In Figure 11, the number of activated sensor nodes in the network is presented, and Table 2 gives the average values in 1000 time steps.