## 1 Introduction  
A wireless sensor network (WSN) is formed of numerous sensors that observe the network field and connect wirelessly among each other [1]. WSNs are used in many applications such as in the army, health, field monitoring, air pollution monitoring systems, and object tracking [2]. The collected data of these applications are not meaningful without knowing the location of the source [3]. The mechanism of locating sensor nodes is defined as localization. There are classic methods to obtain the positions of unknown sensor nodes, such as GPS, which is usually utilized as an accurate method for localization. However, it wastes a lot of power and comes with a very high cost. Moreover, GPS is not able to function in all environments, such as closed areas [4]. To overcome the problems of GPS, we use localization methods that use nodes called anchor nodes located via GPS or by placing them in predetermined positions, which are then used to find the positions of other unknown nodes in the network. Although this solution is effective, it has been observed, however, that the accuracy of this solution depends on the number of anchor nodes [5; 6], but raising the number of anchor nodes means increasing the power utilization and cost. Taking all these problems into consideration has led researchers to propose path planning models using one mobile anchor node rather than many stationary anchor nodes. Finding the position using one mobile anchor node is more precise and there is less cost and lower power consumption [7; 8; 9; 10; 11]. The mobile anchor node moves through the network field in a predefined path and starts sending messages to unknown sensor nodes that are posited in the field [12]. The messages contain information related to each point it stops at. The success of path planning models depends on designing the most efficient path for the mobile anchor node that guarantees covering all sensor nodes in the network field. Moreover, it has to achieve high position accuracy while reducing the power consumption of the mobile node.  
In paper, a new path model for mobile anchor aided localization in WSNs is proposed. The proposed path model achieves high localization accuracy and low power consumption and path length. An air pollution monitoring system framework is built in simulation and in realtime using Node MCU (ESP8266 Wi-Fi module and (ESP32 (Wi-Fi-Bluetooth) module) hardware to apply and inspect the proposed localization models in comparison to previously proposed models in literature. The main contributions of this paper are:  
1. Introducing two path models for mobile anchor-based localization in WSN.
2. Solving the problem of having three pausing points on one straight line for the mobile anchor node (collinearity problem).
3. Finding the average localization error, standard deviation of error, power consumption, and path length as evaluation metrics for the proposed path models.
4. Finding the average localization error, standard deviation of error, power consumption, and path length as evaluation metrics for the proposed path models.
5. Comparing the proposed models with previously proposed models in literature using simulation and a hardware realtime model.  
The rest of this paper is organized as follows. In Section 2, the work related to localization algorithms based on mobility is presented. In Section 3, the path modeling design is introduced. Section 4 presents the results of the model evaluation. In Section 5, the conclusions and future work are provided.