## 2 Related Works  
The mobile anchor needs to approach an unknown node to receive the radio signal while performing the positioning. [PERSON] et al. had the mobile anchor use the random waypoint model to travel within the deployment area [25]. However, this method is inefficient when the size of the deployment area in which positioning is to be carried out is known in advance. [PERSON] et al. used a mobile anchor to locate the target nodes on the basis of received signal strength (RSS) and angle of arrival (AoA) [38]. They also applied artificial intelligence technologies such as particle swarm optimization (PSO), hybrid PSO (HPSO), and the firefly algorithm (FA) to optimize the positioning of the target nodes. However, their study was focused on the positioning of the targets, and it did not address methods for scheduling the route of the mobile anchor. The simplest way for the mobile anchor to efficiently scan the whole area is to schedule a route with less overlapping of the radio signal. To this end, [PERSON] et al. proposed the SCAN method [26]. In this method, a single mobile anchor travels along a single dimension, for example, in the direction of the x-axis or y-axis. Let the communication range of the sensor nodes be R. The resolution of the mobile anchor's SCAN trajectory, which indicates the distance between two neighboring segments, should be 2R at most. Furthermore, all sensors will be able to receive the beacon signal emitted by the mobile anchor. When an unknown node receives the mobile anchor's beacon signal from more than three different locations, range-based positioning technology is applied to compute the location of the unknown node. Using the SCAN trajectory introduces the problem of beacon collinearity in cases when the resolution is greater than the transmission range. To solve this problem, [PERSON] et al. also proposed the DOUBLE SCAN trajectory and the HILBERT trajectory. The DOUBLE SCAN trajectory requires the mobile anchor to scan the deployment area along both the x-axis and y-axis directions. This comes at the cost of doubling the traveling distance required by the mobile anchor. The HILBERT trajectory divides the two-dimensional space into 4n squares. The centers of those squares are connected using 4n line segments. The length of each line segment is the edge length of one square. This comes at the cost of the additional time required to schedule the connection of these line segments and the additional travel distance compared to when using SCAN. To solve the problem of three-point collinearity, [PERSON] et al. varied the resolution of the mobile anchor's SCAN trajectory to increase the chances that the beacon signal would be overhead [28]. [PERSON] et al. also proposed a similar method with the use of two mobile anchors moving simultaneously in opposite directions in order to scan the deployment area [27]. [PERSON] et al. proposed a localization method for the mobile anchor based on trilateration (LMAT) [29]. LMAT uses a mobile anchor that scans the deployment area in a trajectory shaped like an equilateral triangle and periodically broadcasts its current position to locate the unknown nodes. [PERSON] et al. proposed an enhanced method employing the localization method for the mobile anchor based on trilateration (LMAT) and the SCAN algorithm, referred to as SLMAT [30], in order to reduce the size of the triangular trajectory used by LMAT. SLMAT computes the visiting points using LMAT in order to guarantee that the regular triangle formed by the beacons is able to cover all of the unknown nodes. These points will be collinear, and SLMAT postpones the positioning operation of the mobile anchor until the mobile anchor is moving on the neighboring line segments. [PERSON] et al. proposed the Z-curve method [35], which is an extension of the HILBERT method. When using the Z-curve method, the deployment area is divided into multiple squares according to the radio range. Then, each square is cut into four sub-squares.