## 2 Related Work  
Extensive research on proposing localization methods in wireless sensor networks has recently been published. Most of this research can be categorized based on reliance on the type of surroundings as follows: range-based techniques or range-free techniques. Range-based techniques rely on the features of the surroundings, such as received signal strength indicator (RSSI), time of arrival (TOA), and angle of arrival (AOA).  
In [13; 14; 15], the authors proposed a number of range-based techniques. On the other side, range-free techniques as in [16; 17] rely on connectivity information such as the number of hops among the sensor nodes. Although this categorization is effective in the case of static anchor nodes and static unknown sensor nodes, it does not however take into consideration the case of the mobile anchor node or mobile unknown sensor nodes. Thus, another category based on node mobility was proposed.  
This categorizes sensor nodes into four classes, as in Figure 1: static sensor nodes, static anchor nodes--for example, as presented in [18; 19; 20]; static sensor nodes, mobile anchor nodes--for example, as presented in [8; 21; 22; 23; 24]; mobile sensor nodes, static anchor nodes--for example, as presented in [5; 25; 26; 27]; and mobile sensor nodes, mobile anchor nodes--for example, as presented in [28; 29].  
The main focus of localization algorithms depending on mobile anchor node path design is to find the best path model for the mobile node which achieves the required goals, such as whole coverage area, low position error, short path length, and low power consumption. Some of the existing path length models will be listed in this section.  
In [30], the authors proposed SCAN and HILBERT models, which are the first proposed path models. SCAN is an elementary model; in this model, the mobile node moves directly in one extent, the \(x\) axis line or \(y\) axis line. The resolution in this path model is defined as the interval between two anchor stop points in each line. The strength of SCAN model is that it is easy to implement, though it does not solve the collinearity problem. To solve the problem of collinearity, HILBERT was proposed. In the HILBERT path model, the network field is divided into four equivalent sub-fields and links the stop points between these sub-fields. Using the information from non-collinear pausing points, the unknown nodes can estimate their positions with higher position accuracy than the SCAN model. The point of weakness for the HILBERT path mode is that it cannot apply full coverage area because the unknown nodes that are set at the margin of the network field cannot receive sufficient information to determine their positions. This problem affects the value of the position error.  
In [31], the authors presented an effective path model for the mobile anchor node called the LMAT path model. In this path model, the mobile node traverses through the symmetrical triangles and regularly transmits messages at each edge of the triangle. The unknown nodes estimate their positions using the calculated distance between themselves and the mobile anchor node via RSSI. This model solves the collinearity problem and reduces the position error. However, the position error on the border is high, and the path length of the mobile node is high.  
In [32], the authors presented a new path model called Z-curve path model. This model solves the collinearity problem and has a short path length. Moreover, it can deal with obstacles in the network field. However, this advantage causes higher energy consumption by the mobile anchor node.  
In [33], the authors proposed a path model called the H-Curve path model. This model, as shown in Figure 2, solves the collinearity problem, achieves high results of position accuracy, has short path length. However, it does not deal with the obstacles and has a high number of pausing points for the mobile node.  
Figure 1: Classification of node mobility.  
Figure 2: H-Curve path model.