## 3 Distributed Target Tracking Systems
### Phase IV: Sub-Cluster Member Reselection and Leader Handoff
\begin{table}
\begin{tabular}{l} \hline \hline
1. Target broadcasts a message with \(L_{id}=0\). \\
2. Determine the active sensors \(I_{A}^{(j)}\) and the leader \(L_{id}\) at time step \(j\). \\  (a) \(L_{id}=\operatorname*{argmin}_{i}LWT_{i}^{(j)},i\in I_{A}^{(j)}\); \(M=L_{id}\). \\  (b) \(BT_{i}=LWT_{i}+bf_{i},i\in I_{CA}\); \(I_{CA}=I_{A}^{(j)}\bigcap C_{L_{id}}\). \\
3. Find the sub-cluster members: \\   while(\(I_{CA}\
eq\emptyset\)) \\  (i) if(\((S=I_{N_{L_{id}}})==0\)), \(S=(I_{N_{L_{id}}}\bigcap I_{CA})^{c}\). \\  (ii) \(\widehat{M}=\operatorname*{argmin}_{i}BT_{i}^{(j)}\), \(i\in S\). \\  (iii) Send the position estimate to the leader or clusterhead. \\  (iv) \(M=M\bigcup\widehat{M}\); \(S=(S\bigcap M)^{c}\); \(I_{CA}=(I_{CA}\bigcap\widehat{M})^{c}\). \\  (v) if(\(|M|==n\)), break. \\ \end{tabular} \\
4. Estimation Fusion: \\  (a) Leader sends the global fused estimate \(f(j)\) to the clusterhead. \\  (b) The clusterhead disseminates the \(f(j)\) to the base station. \\
5. Perform leader handoff (renewing sub-cluster members): \\  (a) \(N_{P}=|H_{P}|\), \(H_{P}=\{i:d(T_{j},i)\leq R,i\in M\}\). \\  (b) if(\(N_{P}<n\)), \(j=j+1\) and go to Step 1. \\  (c) if(\(d(P_{L_{id}},f(j))>\Re\)) \\  \(M=(M\bigcap L_{id})^{c}\), \\  \(K=\{i:\operatorname*{argmin}_{i}d(P_{i},f(i))\leq\Re\), \(i\in C_{L_{id}}\}\), \\  \(L_{id}=\operatorname*{argmax}_{k}N_{s}(k)\), \(k\in K\), \\   if(\(L_{id}==0\)), \(j=j+1\); go to Step 1. \\   end \\  (d) \(I_{CA}=(C_{L_{id}}\bigcap M)^{c}\). \\  (e) \(N_{E}=|H_{E}|\), \(H_{E}=\{i:d(O_{L_{id}},P_{i})\leq\triangle R\), \(i\in M\}\). \\  (f) while(\(N_{E}<n\)) \\  (i) \(\widehat{M}=\operatorname*{argmin}_{i}d(O_{L_{id}},P_{i})\leq R,i\in I_{CA}\). \\  (ii) \(N_{E}=N_{E}+1\); \(M=M\bigcup\widehat{M}\); \(I_{CA}=(I_{CA}\bigcap\widehat{M})^{c}\). \\  (iii) if(\(I_{CA}==0\)), break. \\   end \\  (g) if(\(N_{E}<n\)), \(j=j+1\); go to Step 1. \\  (h) Target broadcasts a message with \(L_{id}\) at time step \(j+1\). \\  (i) Go to Step 4. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Procedures of the TCAT model for target tracking. a new sub-cluster member. If any of the above conditions holds, the leader and target will sequentially broadcast a _Handoff_ message with \(L_{id}=0\) to trigger a leader reselection process as depicted in Phases I and II. Figure 9 shows an example of leader handoff procedure from time step 23 to time step 24. In Figure 9(left), a handoff procedure is triggered by condition 2. Afterwards, as shown in Figure 9(right), a new leader and its associated sub-cluster members are formed. Due to the cluster-based network topology, the handoff schemes can be further divided into two categories: (1) intra-cluster leader handoff and (2) inter-cluster leader handoff. Since the clusterhead collects the supplementary estimates and receives the estimate from the leader, it may monitor the \(d(P_{i},f(j))\), \(N_{P}\), and \(N_{E}\). If condition 1 holds, then an intra-cluster leader handoff is performed and the clusterhead may assign a cluster member to be a new leader. Otherwise, an inter-cluster leader handoff is triggered and the operations move to Phase I and II. The procedures of the TCAT model for cooperative target tracking are detailed in Table 2. Note that \(I_{N_{i}}\) is the index set of vicinal sensors of sensor \(i\), \(T_{j}\) is the true position of target at time step \(j\), and \(C_{i}\) is the set of cluster members of sensor \(i\).