Target tracking assisted by multiple cluster heads in wireless sensor networks

　　Where ci represents the trend factor, and its initial value is 1. The trend factor indicates which cluster head node the target will tend to move towards in the future. If it tends to cluster head node i, the reserve cluster head nodes around cluster head node i will monitor the target node information earlier. The trend factor is determined by the number of reserve cluster heads received by the auxiliary cluster head.

　　Initially, the main cluster head is the sentinel node that discovers the target; when the target is lost, the recovery mechanism is used to track the target and re-establish the tracking mechanism. At this time, the main cluster head is the cluster head node that discovers the target. Except for the above two cases, the main cluster head compares the thresholds of the current auxiliary cluster heads and selects the node with a larger threshold as the main cluster head of the next stage. After the main cluster head is selected, its adjacent cluster head node serves as the auxiliary cluster head, and the adjacent cluster head node of the auxiliary cluster head serves as the reserve cluster head to establish a tracking mechanism, as shown in Figure 2.

　　The three cluster heads complete different tasks. The main cluster head mainly completes the fusion of node information in the cluster and performs weighted fusion of the auxiliary cluster head information to form the final positioning position; the auxiliary cluster head receives the information sent by the nodes in the cluster for initial positioning and sends the positioning result to the main cluster head; the reserve cluster head is prepared to monitor the target on the one hand and prevent the target from being lost on the other hand, and its nodes in the cluster are in a dormant state. When the reserve cluster head senses the target information, it informs the auxiliary cluster head. The auxiliary cluster head regards the reserve cluster head as a node in the cluster, integrates the information from the reserve cluster head, and records the number of reserve cluster heads as the value of the trend factor when electing the main cluster head.

　　3 Target Tracking Algorithm

　　3.1 Target Monitoring Model

　　The entire monitoring area is divided into many virtual cells using a grid structure. The sensor nodes in each cell form a cluster. When the energy of the cluster head node is less than a certain threshold, the cluster head is replaced, and each node has two states: monitoring and sleeping.

　　Energy saving is an important evaluation index in the study of wireless sensor networks. Many scholars study tracking algorithms based on energy factors. In order to save the energy of sensor nodes, most nodes should be in a dormant state when no target appears, and only a small number of nodes are needed to monitor whether the target appears. This paper sets a sentinel node (acted by the cluster head node at the border) at the border of the monitoring area to detect whether a target enters the monitoring area. The border cluster head periodically generates a number between 0 and N randomly. If the number is greater than N/2 (N is the total number of border nodes), the cluster head node is a sentinel node. In order to prevent the sentinel node from running out of energy, cluster head election is required. The relationship between the remaining energy of the sentinel node and a certain threshold is compared to decide whether to elect a cluster head. The sentinel node is in a listening state, and the non-border cluster head node and the nodes in the cluster are in a dormant state. When the target appears, the sentinel node wakes up its neighboring cluster head node as an auxiliary cluster head, and the auxiliary cluster head node wakes up its non-primary and auxiliary cluster head nodes as reserve cluster heads to establish a monitoring mechanism.

　　During the communication process, the sensor nodes only need to communicate with adjacent nodes. Assuming that the side length of the grid is r, the communication radius is 2r; the auxiliary cluster head node and the main cluster head node need to locate the target, so the sensor perception radius is 2r. The cluster head election adopts the strategy of literature 11, and each sensor node has simple computing capabilities. The tracking algorithm monitoring model is shown in Figure 2.

　　3.2 Target Detection and Positioning

　　After the sentinel node finds the target, it immediately wakes up the neighboring cluster head node, and the neighboring cluster head node successively wakes up the nodes in the cluster for monitoring. Initially, the sentinel node establishes a tracking mechanism as the main cluster head node, and then the main cluster head. The auxiliary cluster head cooperates with the nodes in its cluster to start monitoring the signals emitted by the target and positioning.

　　Sensor nodes can determine the distance between each other through the transmitted signals. The algorithms that can measure distance include TOA (Time Of Arrival) algorithm, TDOA (Time Difference Of Arrival) algorithm, AOA (Angle Of Arrival) algorithm and RSSI (Received Signal Strength) algorithm. Since the sensor node itself will send out RSSI signals and the distance value can be obtained independently according to the strength of the signal, this paper adopts the RSSI algorithm, in which the sensing node calculates the distance dij between the target and the measured received signal carrier power as follows:

　　Where d0=1 m, P0=-30 dBm, α=3.

　　After receiving the target signal, the nodes in the cluster send the information to the cluster head node, which uses multilateral measurement to calculate the coordinates of the target. Assume that at time t, there are k sensor nodes in the cluster head node i, whose coordinates are (x1, y1), (x2, y2), ..., (xk, yk), and the distances to the target node (x, y) are d1, d2, ..., dk, respectively. According to the polygon positioning model, we have:

　　Due to the presence of ranging error, a random error vector ξ is added (ξ is n-1 dimension), and AX + ξ = b is obtained. The least squares algorithm is used to obtain the value of X when ξ is minimum. Let Q(X) = ξ2 = AX – b2, and take the derivative of X to obtain the estimated position of the target:

　　The coordinates of the target node are preliminarily calculated through formula (5), and then the auxiliary cluster head sends the positioning information to the main cluster head node. The main cluster head fuses the information from n-1 auxiliary cluster heads and calculates the average through formula (6) to obtain the final target location.

　　The three types of cluster heads transform into each other in the whole network. The main cluster head judges the difference between two adjacent signals received. If the signal difference is less than zero, it means that the target is far away from the main cluster head node. At this time, the main cluster head node sends a message to re-elect the main cluster head. The auxiliary cluster head that receives this message calculates its own threshold Ti and sends it to the main cluster head node. The main cluster head node selects the node with the largest threshold as the next main cluster head node, retreats to the auxiliary cluster head node, and updates the tracking mechanism. When the auxiliary cluster head node and its cluster nodes cannot receive the target signal, the cluster nodes of the auxiliary cluster head sleep and become the reserve cluster head. If the reserve cluster head receives the target signal and the tracking mechanism updates one of its neighboring nodes to become the main cluster head node, the reserve cluster head is converted into an auxiliary cluster head and wakes up the nodes in the cluster for positioning. However, when the reserve cluster head finds that its neighboring cluster head node is a reserve cluster head or a common cluster head, it stops working and becomes a common cluster head node.