## 4 The Proposed Tracking Anchor Based Clustering Method
### Tracking Anchor Determination
The anchor receiving the message will broadcast a \"Node Activation\" message to the nodes in its lower approximation region and boundary region, as described in Section 4.2. Activated nodes will broadcast a \"Cluster Formation\" message by themselves after waiting for a while. The sensor that broadcasts the message first becomes the CH, and the sensor that receives the message becomes the CM. The length of delay time is related to the distance to the target's predicted position and the residual energy of the sensor, which can be given by:

\[t_{delay}=T_{\text{min}}+(T_{\text{max}}-T_{\text{min}})*(\eta\frac{d}{e})+T_{ rand}\;, \tag{16}\]

where \(T_{\text{min}}\) and \(T_{\text{max}}\) denote the minimal and maximum delay timer values; \(d\) is the distance from a sensor to the target; \(e\) denotes the residual energy; \(\eta\) is a parameter that can nondimensionalize distance and energy and \(T_{rand}\) is a random delay timer value, which is set to prevent multiple sensors from becoming CHs at the same time. In each round, the CMs send sensing data to CH. Then CH will fuse the data and forward them to the sink. When the target moves out of the current cluster, the system will activate the sensors to form the next tracking cluster in advance to ensure continuous tracking of the target. This process continues until the target moves out of the monitoring range or the network dies. Figure 6: Sensor Activation Scenario (2). ### State Scheduling for CMs

To improve the effectiveness of the network, we further schedule the working state of the CMs in the current tracking cluster. During the tracking process, it is not necessary for all CMs to send sensing data to CH. Therefore, we can find ways to reduce the energy consumption caused by redundant data transmission. We first set the activated CMs to have two working states: sensing state and sensing-transmitting state. The sensor in the sensing state only has the sensing module turned on and will not send data to the CH. On the other hand, the sensor in the sensing-transmitting state will sense and transmit data to the CH. By setting redundant nodes to be in the sensing state, we can reduce energy consumption and extend network life. Considering tracking quality and node coverage redundancy, we transform the problem of determining the optimal working status of CMs into a linear 0-1 programming problem. We define the variable \(x\) to represent the two working states of the CMs:

\[x=\left\{ \begin{array}{ll}0,&\mbox{\it sensor\ works\ in\ sensing\ state}\\ 1,&\mbox{\it sensor\ works\ in\ sensing\ -transmitting\ state}\end{array} \right.. \tag{17}\]

Apparently, the CMs working in the sensing-transmitting state will consume more energy than the CMs working in the sensing state because of the data transmission. To reduce and balance energy consumption, we need to schedule as few CMs as possible to work in the sensing-transmitting state and ensure that they are the ones with more energy remaining. Therefore, the objective function \(F(x)\) is defined as:

\[F(x)=\sum_{j=1}^{n}e_{j}x_{j}\, \tag{18}\]

where \(n\) is the number of the CMs in the cluster, and \(e_{j}\) is the energy currently consumed by sensor \(s_{j}\). We can achieve the purpose of reducing and balancing energy consumption by minimizing \(F(x)\). Then there are the constraints. First, it is necessary to ensure that the data transmitted by the CMs meet the requirements of tracking quality, so the number of CMs in the sensing-transmitting state should be greater than or equal to the minimum number required in specific tracking applications, which is defined as \(n_{0}\). The constraint is given by:

\[\sum_{j=1}^{n}x_{j}\geq n_{0}. \tag{19}\]

Moreover, in a large-scale network with randomly deployed nodes, the sensing coverage of some nodes will overlap with each other. When the target sensing source is generated in the overlapped part, multiple nodes will sense the same signal, and several identical data packets will be transmitted to CH, resulting in data redundancy.