## 1 Introduction  
Wireless sensor networks (WSNs) are a form of network formed by freely organizing and combining tens of thousands of sensor nodes through wireless communication technology. It is a wireless network composed of several static or mobile sensors in a self-organizing and multi-hop way, aimed at exchanging the information processed by cooperative detection of perceived objects in the coverage area of the transmission network to users [1, 2]. The wireless sensor has a far-reaching impact on human life and production as it integrates sensors, micro-electro-mechanical systems, and network communication technology [3, 4, 5]. At present, it has attracted significant attention from academia and industry and has become the focus and highlight of international competition. Localization technology is an essential supporting technology in wireless sensor networks where the estimated location information is crucial. A wide range of applications that require these easy-to-deploy, low-cost sensorswell suited in WSNs includes military, agricultural, intelligent transportation, and environmental protection [6; 7; 8; 9; 10; 11]. Although GPS can locate accurately, it is unrealistic to equip all micro sensor nodes with GPS in WSNs due to their high price and limited usage environment. Also, the localization accuracy of GPS in indoor and other complex environments may not be satisfactory [6]. Therefore, it is a challenging task to design an intelligent and effective localization algorithm under restricted conditions. Presently, research aims to take advantage of the interaction and connection between sensor nodes to achieve the goal of localization [12; 13; 14]. On the basis of the need to measure the distance between the actual nodes in the localization process, it can divide the localization algorithm into a range-based localization algorithm and a range-free localization algorithm [15; 16]. The former needs to measure the absolute distance or azimuth between adjacent nodes and utilize the actual distance between nodes to calculate the localization of unknown nodes; such algorithms include time-of-arrival (TOA) [17], time-difference of arrival (TDOA) [18], angle of arrival (AOA) [19], and received signal strength indicator (RSSI) [20]. Regarding the latter, it is based on the network connectivity between nodes, utilizing the estimated distance between nodes to calculate the localization of nodes without measuring the actual distance between them; it includes algorithms Centroid [21], Distance Vector-Hop (DV-Hop) [22], Amorphous [23], Multi-Dimensional Scaling-programming (MDS-MAP) [24], and Approximate Point in Triangle Test (APIT) [25]. Range-free algorithms have the advantages of being low-cost, with low power consumption robust anti-measurement noise ability, and has simple hardware equipment; they can provide acceptable localization accuracy and, consequently, have attracted much attention in recent years [26]. DV-Hop, as one of the distributed localization methods based on distance vector routing and localization, is an algorithm that has attracted significant attention due to its simplicity and low equipment requirements [27]. There are two types of sensor nodes in WSNs: the anchor node with a known location, and the unknown node, the one to be located [28; 29]. The purpose of the localization algorithm is to calculate the location of the unknown nodes in various ways. DV-Hop comprises three steps: the first step is that all nodes in the network get a hop-count value from the anchor nodes; next is calculated the average distance per hop for all anchor nodes; then, the estimated distance is obtained by multiplying the average distance per hop and the minimum hop-count value. Finally, the third step is to compute the localization of the unknown node according to the least-squares method [30; 31], when the unknown node retrieves an estimated distance from three or more anchor nodes.