## 5 Localization Employing a Single Anchor Node  
An individual anchor node is employed to find the locality of movable target nodes, as described above. The unknown target nodes are dispersed in an arbitrary manner. The whole sensor area is partitioned into circles and is inside the span of the anchor node. The anchor node sends out a beacon wave that assists the movable target nodes in locating them separately. When the movable target nodes come inside the span of an anchor node, they first observe the beacon signal and then accumulate the anchor node's RSS information. After gathering RSS data, the distance between the anchor and target node is calculated. On the basis of these estimations, the anchor node is projected at a 60\({}^{\circ}\) angle with six virtual anchors (two of which will be chosen, as at least three reference nodes are necessary) to examine the location of movable target nodes. Every node in this study is considered to have the same hardware specifications and transmission range.  
The following steps are involved in locating target nodes:  
1. The region of 15 \(\times\) 15 m\({}^{2}\) is set up including the 'N' target nodes and an individual anchor node.
2. When mobile target nodes drop inside the span of an individual anchor node, each target node keeps a record of distances among the anchor and the target node, as well as two virtual anchors in the vicinity (as at least three reference nodes are needed to discover unknown target nodes). Figure 5 depicts the notion of anchor node, virtual anchor node, and target node.
3. The position of unknown nodes is evaluated using mLebTLBO.  
The distance between each moving target and the anchor node is illustrated in Figure 5. There are two virtual anchor nodes for each anchor node (as three reference nodes are being taken to compute 2D position).  
\[d_{i}=\sqrt{(x_{t}-x)^{2}+(y_{t}-y)^{2}} \tag{14}\]  
Here \((x_{t},\ y_{t})\) denotes the position of the target node, and \((x,y)\) denotes the present locality of the anchor node. The centroid calculation (15) along with its representation is illustrated in Figure 6.  
\[x_{c},\ y_{c}=\left(\frac{x+xv_{1}+xv_{2}}{3},\ \frac{y+yv_{1}+yv_{2}}{3}\right) \tag{15}\]  
Figure 5: Sensor field representation.  
Figure 7 depicts the use of mLebTLBO to obtain the parameters of a target node denoted by \((x_{s},y_{s})\). The goal is to reduce the actual and calculated distance between evaluated and actual node co-ordinates, which is expressed statistically in Equation (16):  
\[f(x_{s},\ y_{s})=\frac{1}{M}\sum\biggl{(}\sqrt{\left(x_{e}-x_{i}\right)^{2}+ \left(y_{e}-y_{i}\right)^{2}}-\dot{d_{i}}\biggr{)}^{2} \tag{16}\]  
where \((x_{e},y_{e})\) denotes the calculated position of the target node, \((x_{i},y_{i})\) denotes the position of beacon node \(i\) in the vicinity of the target node, and \(M\) is the total count of beacons (\(M>3\) in this study).  
The error in localization is estimated using Equation (17) and is illustrated in Figure 8.  
\[E_{t}=\frac{1}{N_{L}}\sum\sqrt{\left(x_{e}-x_{t}\right)^{2}+\left(y_{e}-y_{t} \right)^{2}} \tag{17}\]  
Figure 6: Centroid calculation.  
Figure 7: mLebTLBO implementation around centroid.  
The optimal positioning of the target node is determined for mLebTLBO until the termination criterion is met.