## 1 Introduction  
Wireless Sensor Networks (WSNs) are network structures consisting of many small, low-cost sensor nodes that enable information obtained from the Region of Interest (ROI) to be transmitted wirelessly and adapted to many environments. Examples of WSNs application areas include military, health, home, environmental, and industrial applications [1]. Many factors affect the design and performance of WSNs. One of the most important of these factors is localization. Localization can be defined as the process of locating sensor nodes whose locations are unknown in a particular coordinate system. Most localization methods require the location information of some nodes in the network in order to locate the other nodes. The nodes that are known are generally called anchors, beacons, or references in the literature. Ordinary sensors that are the target of localization through the localization process are called Unknown Nodes (UNNs) [2]. For the data collected from the ROI to be meaningful, the sensors' locations must be known. Accurate sensor position information will also be beneficial for geographic routing algorithms. Device costs should be low as many sensors are used in most WSN applications. In addition, in some implementations, the network will need to be organized without general human management. The sensors may need to work for years or even decades without batteries requiring replacement. Hence, adding a Global Positioning System (GPS) to each device on the network is not energy and cost-efficient in most applications. It is also limited to GPS outdoor applications. Local Positioning Systems (LPSs), on the other hand, use high-capacity base stations deployed in each coverage area, which is a cost burden for most low-configuration WSNs [3]. Depending on the distance measurement method used, localization schemes can be divided into range-based localization schemes and range-free localization schemes. In range-based localization schemes, the distance or angle between the UNN and the Anchor Node (AN) is measured using particular equipment types. The location of the UNN is calculated using these measurement values [4]. Typical range-based schemes include Time of Arrival (ToA), Time Difference of Arrival (TDoA), Angle of Arrival (AoA), and Received Signal Strength Indicator (RSSI) [5]. In range-free localization schemes, it is not necessary to measure physical properties such as distance and angle. These schemes deal with connection information between UNNs and ANs. For example, the number of hops between a UNN and AN can be counted and converted into physical distances. Some examples of range-free schemes are Approximate Point in Triangle (APIT), Centroid, Amorphous, and DV-HOP algorithms. In general, range-based schemes give more accurate results than range-free schemes. However, the structure of range-free schemes is more straightforward; their cost is cheaper and they do not require extra hardware [6]. Due to the disadvantages mentioned above of GPS for localization in WSNs, approaches generally using as few GPS devices as possible have been studied in the literature. Therefore, it would be more logical to periodically broadcast location information with one or several mobile anchors (MA) equipped with GPS units and position UNNs as shown in Figure 1. On the other hand, unknown static nodes do not move once they are deployed for detection tasks [7]. Since MA's Mobile Anchor Node Assisted Localization (MANAL) architecture does not have energy constraints like UNNs, its movement trajectory can be carefully designed to improve its localization accuracy. In a network localized with static anchors, a static anchor is not reused after localization. As a result, there will be an extra load for each static anchor not used in the WSN. Compared to a sensor node, a robot is quite large, making it easier to mount the robot's GPS unit. Hence, MANAL scenarios are more efficient than static scenarios [8].