## 1 Introduction  
With the advantages of being low-cost, easy to implement, self-organizing, and highly reliable, multi-sensor fusion networks are widely used for such applications as non-cooperative tracking [1; 2], forest fire detection [3], industrial process control [4], water quality detection [5], and machine health monitoring [6], and object state detection [7; 8]. These sensor networks are composed of a group of cooperating low-power, low-precision, inexpensive sensor nodes equipped with limited transmission range transceivers, a small data processing unit, constrained memory, and limited available energy. However, due to dense sensor node deployment and the infrequent occurrences of the targets for each sensor node, too much energy will be consumed when the targets are absent if wake-up control is not utilized [9; 10]. The fact that power consumption constraints exist for sensor nodes using un-rechargeable batteries [11] means that it is essential to balance conflicting performance requirements adaptively between energy consumption and target sensing. The most widely used technique for lifetime optimization of multi-sensor networks is sensor wake-up control (WC) [12], which is used to adaptively determine the \"wake up\" or \"sleep\" states of each node. A \"wake up\" sensor node is in charge of collecting and processing the measurementsand transferring them to its neighbors or fusion center, while a \"sleep\" sensor node closes its sensing, communication, and processing modules for energy saving purposes. Currently, two different research methods are employed improve the energy efficiency of the WC of multi-sensor networks. The first mainly focuses on designing different channel assignments [13; 14; 15], power controls [16], sampling rates [17], and MAC/routing protocols [13; 14; 18]. These methods are usually classified as being in the wireless communication research field of sensor networks, which mainly emphasizes the back-end network protocol design of the system. The second focus of research is primarily interested in establishing different models of multi-sensors themselves and developing corresponding control algorithms. These research methods usually belong to the information fusion field of sensor networks, which theoretically emphasizes the front-end sensor model and fusion algorithm exploration of the system. Further, for the WC strategies viewed from the information fusion field, classical WC scheduling strategies can be divided into three categories: surveillance-oriented, tracking-oriented, and topology-oriented. In the surveillance-oriented category, all sensor nodes are set to randomly \"sleep\" and \"wake\" independently, with the aim of achieving homogeneous wide-area coverage with even energy consumption [19; 20]. For the tracking-oriented WC method, the sensor nodes in the vicinity of the predicted target location are woken up successively along the predicted target track, and, during this process, one or more clusters are formed, and one sensor node will be chosen as the cluster leader in each cluster, which is in charge of gathering target information and controlling the nodes' states [21; 22; 23; 24; 25]. The authors of [22] utilized a PSO algorithm and duty cycling technology in order to let the selected sensors perform tasks. The authors of [23] proposed a sensor selection strategy based on a multi-objective optimization method to save energy. However, the performance of this method is restricted by localization accuracy of the sensor nodes, as low node localization will lead to poor target positioning and therefore improper wake up clusters. The third category is the topology-oriented WC strategy [26; 27; 28; 29; 30; 31; 32], which gathers nodes together to form a cluster, in which the node states of \"wake\" and \"sleep\" change dynamically. The elected cluster leader keeps the \"wake\" state to detect the target. A new cluster with two heads was proposed in [27] to track the targets collaboratively to enhance the robustness and network lifetime.