## 4 Proposed Methods
### Proposed Method for Virtual Data Generation Using PSQ  
The received signal strength indicator value obtained at a fixed node (FN) is divided into log scales using the suggested incremental segmentation method to produce a virtual coordinate of the mobile node (MN). By limiting the amount of labeled training data, PSQ-based localization aims to solve the costs and difficulties of acquiring labeled data while  
Figure 2: Proposed system flow chart. The asterisks are how we calculate the point-by-point Euclidean distance to split each zone.  
perhaps avoiding overfitting issues that could arise with deep learning-based localization. In order to enhance the effectiveness of supervised learning, these technologies make use of both created and acquired data.  
In a segmentation and conquest strategy, a given problem is divided into two or more subproblems, which are typically taken directly from the original problem. It is possible to segment subproblems into smaller ones or use the solutions to a segmented subproblem directly to calculate solutions to a given problem. This method divides small cases into smaller ones until a solution is found. The segmentation and conquering algorithm uses a top-down methodology in which answers to the child problem are used to calculate answers to the parent problem.  
In this study, the log scale of the RSSI signal was gradually divided using a threshold determination technique to produce data for the center values at 25 points and 16 zones on the 5 \(\times\) 5 grid. A conceptual diagram of the PSQ algorithm employed in this study is shown in Figure 3. For the binary segmentation process to create four node values and intermediate values in the segmented zone, a 3 m \(\times\) 3 m space must be divided into four 1.5 m \(\times\) 1.5 m intervals.  
To estimate the coordinates of \((x_{e},\ y_{e})\) for PSQ, one zone is divided into four regions. If each \(x\)-coordinate is from \(x_{0}\) to \(x_{1}\) and the \(y\)-coordinate is from \(y_{0}\) to \(y_{1}\), it is divided into four zones (Zones 1 to 4), each of which is defined in the same way as Equation (3). The symbols used in this study are shown in Table 1.  
\[\begin{cases}\begin{aligned} Zone\ 1:\left(x_{0}\leq x \leq\frac{x_{1}+x_{0}}{2}\right),\ \left(\frac{y_{1}+y_{0}}{2}\leq x\leq y_{1}\right)\\ Zone\ 2:\left(\frac{x_{1}+x_{0}}{2}\leq x\leq x_{1}\right),\ \left(\frac{y_{1}+y_{0}}{2}\leq x \leq y_{1}\right)\\ Zone\ 3:\left(x_{0}\leq x\leq\frac{x_{1}+x_{0}}{2}\right),\ \left(y_{0}\leq x \leq\frac{y_{1}+y_{0}}{2}\right)\\ Zone\ 4:\left(\frac{x_{1}+x_{0}}{2}\leq x\leq x_{1}\right),\ \left(y_{0} \leq x\leq\frac{y_{1}+y_{0}}{2}\right)\end{aligned}\end{cases} \tag{3}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Definition** \\ \hline \(x_{0,1}\) & \(x\)-coordinate of the fixed node \\ \(y_{0,1}\) & \(y\)-coordinate of the fixed node \\ \((x_{e},\ y_{e})\) & Expected coordinates of \((x,\ y)\) \\ \([Q]\) & Curve equation in matrix form \\ \([B]\) & Control points coordinate \\ \(\left[E^{k}\right]\) & Error of the \(k\)th value \\ \([B]^{f}\) & Converted control point matrix \\ \([T]_{k}\) & Translation matrix of the selected cell \(k\). \\ \((u_{e},\ v_{e})\) & Expected parametric values of \((u,\ v)\) \\ \((x_{m},\ y_{m})\) & Converting coordinates form RSSI \\ \hline \hline \end{tabular}
\end{table}
Table 1: Symbols used in the study.  
Figure 3: Conceptual diagram of PSQ algorithm. (The arrows represent the flow of data).  
The measured area was divided into 4 zones, as depicted in Figure 4, and 4 subdivided cells were chosen as selection regions.