# Difference DV_Distance Localization Algorithm Using Correction Coefficients of Unknown Nodes
## 1 Introduction  
In recent years, the advantages of wireless communication technology, sensors, and embedded technology have significantly propelled the development of wireless sensor networks (WSNs) which have already been widely applied to some key fields [1; 2], such as environmental monitoring, traffic management, national defense, and so on, in order to achieve real-time acquisition and perception of various object information in monitoring areas. Generally, the smart sensor nodes are often randomly and unevenly distributed, and the topology of WSNs may sometimes change dynamically, and thus it is difficult to determine the positions for all the sensor nodes. But, the position information of sensor nodes is indispensable and the monitoring without position information is also meaningless. Besides that, the position information of sensor nodes can help design the top-level route protocols [3; 4; 5]. Therefore, localization algorithm for sensor nodes is one of the key technologies is WSNs [6]. WSNs consist of a large number of sensor nodes, and the Figure 1 shows an example of network structure. Each node can be classified as either an unknown nodes or as an anchor node. Traditionally, anchor nodes can be localized by using Global Positioning System (GPS) or BeiDou Navigation Satellite System (BDS). However, it is impossible for the use of GPS/BDS on each node, because it requires higher hardware or deployment costs, which are not acceptable in large-scale WSNs. Therefore,there are only a few of anchor nodes compared to the number of unknown nodes in WSNs, and most unknown nodes have to estimate distances from anchor nodes over multi-hop environments. When the positions of anchor nodes in WSNs are already given, Node localization refers to the process of computing the positions of unknown nodes after mathematical or physical model have been established through information exchange and calculation. At present, there are many kinds of self-localization algorithms, which can be divided into two categories, that is, range-based localization algorithm [7] and range-free localization algorithm [8]. Range-based algorithms use absolute point-to-point distance or angle information to calculate distance between neighboring sensor nodes, but the range-free algorithms do not need absolute range information. In range-free localization algorithms, for example, centroid localization [9], APIT [10], DV_Hop [11], and amorphous [12], nodes have no ability to measure the distances or angles to their neighbors and instead use connectivity or hop information to compute their positions. They are simpler and do not require extra hardware for measurement. The DV_Hop is a typical range-free based localization algorithm due to its simplicity, cost-effectiveness, and robustness, and its basic idea is to calculate the estimated distances by the product of the average distance per hop and the hop numbers from unknown nodes to anchor nodes. On the basis of original DV_Hop algorithm, [PERSON] [13] uses the least square method to modify the average distance per hop between anchor nodes. In reference [14], weighting coefficients are introduced into the correlation matrix of estimated distance, and a new localization algorithm with the weighted hyperbolic localization is proposed. [PERSON] [15] proposes an improved weighted centroid DV_Hop localization algorithm, which improves the accuracy after selecting appropriate anchor nodes and replaces maximum likelihood localization by centroid localization, besides that a weighted scheme is also used so that the influence of different anchor nodes can be taken into consideration. In order to further improve localization accuracy, the differential evolution (DE) algorithm, which performance is verified superior to the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, is used to optimize the weighted square error of the estimated distance [16], so that the global optimal solution can be obtained.