## 4 The Proposed Tracking Anchor Based Clustering Method
### Tracking Anchor Determination
The algorithm for tracking anchor determination based on RFCM is shown below (Algorithm 1):  
```
0: Node Number \(N\), Tracking Anchor Number \(K\)
0: Tracking Anchor Locations, Node Membership
1: Parameter Initialization: \(I_{max}\), Fuzzifier \(m\), Thresholds \(\delta\) and \(\varepsilon\)
2: Initialize Population \(\mathcal{A}=\{a_{1},\ \dots,\ \ a_{i},\ \dots,\ \ a_{K}\}\)
3:Repeat
4: For Each \(a_{i}\) in \(\mathcal{A}\)do
5: Calculate \(\mu_{ij}\) for \(K\) anchors and \(N\) nodes using Equation (10)
6: Endfor
7: If\(\mu_{ij}\) and \(\mu_{kj}\) be the two highest membership of \(s_{j}\) and \(\left|\mu_{ij}-\mu_{kj}\right|\leq\delta\)then
8:\(s_{j}\in\overline{A}(\beta_{i})\) and \(s_{j}\in\overline{A}(\beta_{k})\)
9: Else
10:\(s_{j}\in\underline{A}(\beta_{i})\)
11: Endif
12: Modify \(\mu_{ij}\) considering lower and boundary regions
13: Compute new anchors as Equation (11)
14:Until \(I=I_{max}\) or \(\left|\mu(t)-\mu(t-1)\right|<\varepsilon\)
15:For each sensor in the network do
16: Assigned as a member to the anchors with maximum \(\mu\)
17:Endfor

### Node Activation

Activation of nodes requires scheduling instructions provided by anchors. By using RFCM, we obtain tracking anchors, along with their lower approximation regions and boundary regions. According to the membership relationship, we build a membership table of the anchor for common sensors. The membership table has \(N\) rows and \(K\) columns, which refer to \(N\) sensors and \(K\) anchors, respectively. The value of the \(j\)-th row and the \(i\)-th column of the member table is \(MT(j,i)\), where \(MT(j,i)\) is equal to 0 or 1, indicates that the sensor \(s_{j}\) belongs to \(a_{i}\)'s lower approximation region or boundary region. Furthermore, \(MT(j,i)=0\) indicates that \(s_{j}\) is far away from \(a_{i}\) without any membership relationship. According to the properties mentioned in Section 4.1, sensors can be divided into two types: one belongs to the lower approximation region of an anchor. Since they do not belong to any other anchors, they only have one '1' in their rows on the membership table. Another belongs to the boundary regions of multiple anchors, apparently with multiple occurrences of '1' in its row. The activation rules for the sensors are given with the help of the membership table: A sensor will be activated when it can receive the \"Node Activation\" messages sent by all the anchors corresponding to the column with the value \"1\" in its row. Following this rule, we specifically analyze two sensor scheduling scenarios in the tracking process:

1. The target is located in the lower approximation region of a certain anchor. As shown in Figure 5, only the sensors in the lower approximate region will be activated because they have received a \"Node Activation\" message from the only anchor to which they belong. 2. The target is located in the overlapping boundary region of multiple anchors. As shown in Figure 6, the nodes in the lower approximation regions and the overlapping boundary region of the two anchors will be activated. The overlapping boundary region of the two anchors can be used as a transition region to ensure the continuity of the tracking process. Figure 5: Sensor Activation Scenario (1). ### Cluster Formation

We consider the future-position estimation mechanism as technical support, which is commonly used by traditional dynamic clustering algorithms [8]. As the target moves in the surveillance area, the tracking anchors near the predicted target position will send activation messages to sensors. The activated sensors will form a cluster. The CH will be selected among them using a delayed broadcast message. Assuming that the target's next position is predicted to belong to the scheduling region of some anchors, the sink will send an \"Anchor Scheduling\" message to them. Note that this message is relayed by other anchors in the network because most sensors are sleeping.