## 5 Analysis of Energy Consumption  
This section considers the energy consumption of the proposed scheme in Section 3. It is often the case that inter-sensor communication costs are greater by orders of magnitude than local computation and sensing costs with respect to energy expenditures [22, 32, 33]. Therefore, the computational cost in a wireless sensor network is usually neglected compared to the communication cost. In addition, the problem of energy waste in idle listening mode can be solved by periodic listen and sleep. Moreover, based on the data sheet of CC2420 [34], the energy consumption of receive mode is about 59.1 mW, the energy consumption of transmit mode is about 52.2 mW, and the energy consumption of idle listening mode is about 1.2 mW. Accordingly, we focus on the comparison of power consumption for communication with the scheme of [5]. The total power requirements include both the power required to transmit messages and the power required to receive (or process) messages. Suppose that the energy needed to transmit for sensors with omnidirectional antennas is \(E_{T}\), which depends on the transmitting range \(R\), and the energy needed to receive is \(E_{R}\). When the target broadcasts a message with \(L_{id}=0\), its neighboring sensor, say sensor \(i\), becomes an active sensor and broadcasts a \(Hello\) message with a random waiting time \(LWT_{i}^{(j)}\) for being a task leader at time step \(j\). As the active sensor \(i\) claims to be a leader, the \(L_{id}\) is updated and broadcasted from target. As a result, the number of transmissions and receptions for tasking leader selection (Phase I) are  
\[S_{T}^{c}(j) = 1+N_{t}(j) \tag{16}\] \[S_{R}^{c}(j) = \sum_{i\in(I_{A}^{(j)}\bigcup L_{id}^{(j)})}|I_{N_{i}}|+2N_{t}(j) \tag{17}\]  
where \(L_{id}^{(j)}\) is a leader ID at time step \(j\), \(I_{N_{i}}\) is the index set of vicinal sensors of sensor \(i\), and \(N_{t}(j)\) is the number of transmissions of vicinal sensors of the target at time step j. Afterward, the active sub-cluster members of the leader are selected according to the extra backoff time \(BT_{m}\), which transmit the \(Position\) messages to the leader. Thus, the number of transmissions yields the sub-cluster size \(|M(j)\bigcap I_{N_{L_{id}^{(j)}}}|\) and the number of receptions is \(|I_{N_{i}}|(\forall i\in M(j)\bigcap I_{N_{L_{id}^{(j)}}})\), where the \(M(j)\) is the set of sub-cluster members at time step \(j\). Since the fused estimate \(f(j)\) is routed to the clusterhead in a multi-hop manner, the number of transmissions is \(N_{i}^{H}(\forall i\in(I_{A}^{(j)}\bigcap I_{N_{L_{id}^{(j)}}})^{c})\), where \(N_{i}^{H}\) is number of hops for sensor \(i\) to perform estimation reporting. Finally, the clusterhead disseminates \(f(j)\) to the base station. Furthermore, if the clusterhead receives a message from the leader for incorporating supplementary estimates, it may assign a desired number of supplementary members to be supplementary sub-cluster members for the tracking task. Therefore, the number of transmissions and receptions for selecting tasking members (Phase II) and delivering the position estimate (Phase III) are  
\[S_{T}^{p}(j) = |M(j)\bigcap I_{N_{L_{id}^{(j)}}}|+\sum_{i\in(I_{A}^{(j)}\bigcap I _{N_{L_{id}^{(j)}}})^{c}}N_{i}^{H}+\sum_{i\in M^{\prime}}N_{i}^{H}+1 \tag{18}\]  
\[S_{R}^{p}(j) = \sum_{i\in(M(j)\bigcap I_{N_{L_{id}^{(j)}}})}|I_{N_{i}}|+(\sum_{i \in(I_{A}^{(j)}\bigcap I_{N_{L_{id}^{(j)}}})^{c}}+\sum_{i\in M^{\prime}})\sum _{h=1}^{N_{i}^{H}}N_{I_{R_{i}}^{(h)}} \tag{19}\]  
where \(M^{\prime}=\{i:\operatorname*{argmin}_{i}\sum N_{i}^{H},i\in M(j)\bigcap(I_{A }^{(j)}\bigcap(I_{N_{L_{id}^{(j)}}}\bigcup L_{id}^{(j)}))^{c}\}\) and \(I_{R_{i}}^{(h)}\) is index set of relay ID for sensor \(i\) at hop \(h\).