## 3 Network Model and Problem Formulation  
Let \(N=\{N_{1},N_{2},N_{3},\ldots N_{n}\}\) be the set of sensor nodes, and each node is assumed to have constant transmission parameters and also to have equal participation in the deployed environment. Let \(U=\{U_{N1},U_{N2},U_{N3}\ldots U_{Nn}\}\) be the set of unknown nodes, set where the location of the nodes is not known. The unknown set of nodes may be operating with the sensor nodes to estimate the sensor pair in the neighbor nodes, determined as \(N_{SN}=\{N_{SN1},\ N_{SN2},\ N_{SN3},\ldots\ldots N_{SN_{n}}\}\). Hence, the sensor node is united to form a parametric assumption \(N=U\cup N_{SN}\). By combining the operating parameters with the unknown locations and the coverage, the node coverage optimization is calculated [2]. The node coverage is estimated using the N pairs N (Xm, Yn), where the adjacent nodes are marked with \(U=m-1,m-2,m-3\) and the nearest hop nodes are estimated using the \(U=n-1,n-2,n-3\). The hop distance is estimated using the distance between the N pairs of the sensor nodes and hop = NUI\(\cup\). In addition, the distance denoted as \(hd_{m,\ n}^{est}\) and the probable actual attained distance are estimated using the \(hd_{m,n}^{act}\).  
In order to enhance network coverage among the nodes in a wireless sensor network (WSN), the position of the sensor nodes is determined using the hop distance. The error variation in the received signal strength is assumed to be minimal in count in the determined place. The number of sensor nodes increases when the hops are increased with the sensor pairs. The distance metrics between the different sensor nodes and the adjacent nodes have been obtained using the formula \(U=n-1,n-2,n-3\) estimated nodes. The proposed localization and node optimization have been applied to WSN using the bat and the Q learning algorithms. In the proposed system, the received signal strength is used to enhance the localization of the unknown nodes. The average error distance between the sensor nodes and neighbor nodes is estimated using the sensor nodes. The shortest distance between the sensor and unknown nodes is estimated by measuring the distance in the reception parameters. Nm is assumed to be of the'm' segments in the measurable distance, and the segment is completed with the localization values. The estimation accuracy of the proposed method is estimated with the Est\({}_{\text{Am}}\) for the m-segment sensor nodes in the WSN. The average distance error AVG\({}_{\text{disterror}}\) is the error where the process of the sensor nodes and the unknown nodes estimation is performed using the anchor sensor nodes to estimate the localization of unknown nodes in the network. Table 1 outlines the list of notations used in the proposed system.  
\begin{table}
\begin{tabular}{c l} \hline \hline \multicolumn{1}{c}{**Parameters**} & \multicolumn{1}{c}{**Details**} \\ \hline N & Sensor nodes group \\ \hline \([\text{N}_{1}\text{N}_{2}\text{N}_{3},\ldots\text{Nn}]\) & Set of sensor nodes \\ \hline U & Unknown nodes \\ \hline \(\text{N}_{\text{SN}}\) & Neighbor nodes \\ \hline \(N=U\cup N_{SN}\) & Coverage optimization \\ \hline N (Xm, Yn) & Node coverage \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations used in the proposed system.