## 6 Simulation
### Network Energy Consumption  
The simulation is performed with different density of nodes, considering the number of messages transmitted and received involved in clustering and target localization. In order to evaluate the network performance, several models for measuring the energy dissipation per transmitted bit have been proposed [36,37]. Here, the energy model presented in [36] is applied to describe the energy dissipation. Assume the hardware energy dissipation is as follows [36]:  
\[E_{Tx} = \left\{\begin{array}{ll}tE_{elec}+t\varepsilon_{fs}d^{2},&d<d_{o }\\ tE_{elec}+t\varepsilon_{mp}d^{4},&d\geq d_{o}\end{array}\right. \tag{24}\] \[E_{Rx} = tE_{elec} \tag{25}\]  
where \(E_{Tx}\) and \(E_{Rx}\) are energy consumption of a transmitter and a receiver, respectively, \(t\) is the data packet size, \(E_{elec}\) denotes the energy consumption of the electronic circuitry, \(\varepsilon_{fs}\) and \(\varepsilon_{mp}\) depend on distance \(d\) between the transmitter and the receiver for maintaining an acceptable bit-error rate, and \(d_{o}\) is a threshold of the transmission. The values of simulation parameters are detailed in Table 3[36].  
Figure 16: The typical runs of sub-cluster formation (**left**); the frequency of leader handoff (**right**).  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline \(E_{elec}\) & 50 nJ/bit \\ \(\varepsilon_{fs}\) & 10 pJ/bit/m\({}^{2}\) \\ \(\varepsilon_{mp}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ \(d_{o}\) & Transmission range \(R\) \\ Energy for data aggregation & 5 nJ/bit/signal \\ Data packet size \(t\) & 2048 bits \\ \hline \hline \end{tabular}
\end{table}
Table 3: The Values of Simulation Parameters [36].  
Figures 17 and 18 show the accumulated energy consumption comparison between the TCAT scheme and the method in [5]. Observe that the number of transmissions/receptions grows nearly linearly as the tracking sub-cluster size increases. Referring to Figure 17, compared with a network with \(N_{S}=100\) and \(1\leq n\leq 3\), a network with a larger scale (e.g., \(N_{S}=500,1000\)) may have a larger cluster size, which may lead to a higher number of transmission/reception for data gathering at each round and result in a faster network resource depletion. Nonetheless, the performance of TCAT is still superior to that of the approach in [5].  
Given \(n\) = 2, \(N_{S}=100\), and \(R/R_{e}=1\), Figure 12(right) shows that the tracking accuracy of TCAT is comparable to that of [5]. Moreover, as depicted in Figure 18(left), the energy consumption of transmissions with TCAT is about \(26.4\%\) less than that of [5] and in Figure 18(right) the energy consumption of receptions with TCAT is about \(25\%\) less than that of [5], which implies that the scheme in [5] may lead to a fast network energy depletion. Accordingly, the TCAT provides better network service characteristics compared to the protocol of [5].  
Figure 17: The number of transmission/reception: the communication cost.  
Figure 18: The comparison of accumulated network energy consumption.  
Observe that in Figures 12 and 18, although the performance of TCAT with \(n=1\) leads to a lower network energy consumption, compared with those of TCAT with \(n=2\sim 4\), it results in a larger target localization error. Moreover, due to high correlation of sensing data in time and spatial domains, the sub-cluster with \(n>2\) members may lead to undesired sensing redundancy. Therefore, considering the trade-off between performance and network energy consumption, the TCAT with \(n=2\) may be a good choice for the tracking task.