## 4 Proposed Methods
### Estimated Location Compensation Using B-Spline Surface Equation  
When a potential area is chosen, the coordinates are derived by applying the B-spline curved expression in the standard cell to calculate the parameters \(u\) and \(v\). Standardized and numbered from 0 to 1, the \(u\) and \(v\) parameters are used to calculate coordinate values by transforming them into particular cells. Using curved equations in two dimensions in selected cells, such as employing LUTs, has been suggested to monitor the location. Since data must be compared and cell locations must be computed using linear proportional equations, tracking locations with LUTs is laborious. B-spline surface equation data can be saved as a surface and utilized in place of LUTs to resolve this issue. The equation for the B-spline surface is as follows:  
\[Q(u,\ v)=\sum\
olimits_{i=0}^{m}\sum\
olimits_{j=0}^{n}B_{i,j}S_{i,j}(u,\ v) \tag{4}\]  
\(B_{i,j}\) represents the control points of B-spline equation, and \(S_{i,j}\) is the basis function for parameters \(u\) and \(v\). This surface equation can be represented in matrix form as follows:  
\[[Q]=[S][B] \tag{5}\]  
The node coordinate value \([Q]\) is represented in this curve equation. Control point coordinate \([B]\) computed coordinates are as follows when using Equation (6):  
\[[B]=[S]^{-1}[Q] \tag{6}\]  
If the data was generated using a rectangular polygon net of dimensions \(m\times n\), the matrix [D] can be represented as \(m\times n\times 2\), effectively removing the height variable equation on the 3-D coordinate axis. To solve the problem, an ideal algorithm must be used. The control point acts as the interpolation, making sure that each data coordinate on the surface of the curve is traversed. Each node must be supplied with the variable parameters \(u\) and \(v\) in order to acquire interpolation data using the provided data coordinates. The two variable parameters \(u\) and \(v\) have an acceptable range that is determined by:  
\[0\leq u\leq 1.0,\ 0\leq v\leq 1.0 \tag{7}\]  
To perform curve interpolation and ensure the calculation of the control point \(B_{i,j}\), it is necessary to meet the requirements of the following equation:  
\[E_{i,j}^{k+1}=E_{i,j}^{k}+\left(Q_{i,j}-\sum\
olimits_{i=0}^{m}\sum \
olimits_{j=0}^{n}B_{i,j}S_{i,j}(u,\ v)\right) \tag{8}\]The control value of \(E_{i,j}^{k}\) is the error of the kth value in solving the equation. The operation is repeated until the error value is below the given common difference. The disparities between data that has been measured and calculated make up the objective function. In the B-spline curved expression, the control point \([B]\) is converted into the selected cell as follows:  
\[[B]^{\prime}=[T]_{k}[B] \tag{9}\]  
Here, \([B]^{\prime}\) is the converted control point matrix, and \([T]_{k}\) is the moving translation matrix of the selected cell \(k\).  
In the given B-spline Equation (6), the expecting (\(u_{e}\), \(v_{e}\)) value may be calculated as follows:  
\[(\mathrm{x}_{e},\,\mathrm{y}_{e})=\sum_{i=0}^{m}\sum_{j=0}^{m}Bt_{ij}S_{i,j}( u_{e},\,\,v_{e}) \tag{10}\]  
\[u_{e}=\frac{x_{m}-x_{0}}{x_{1}-x_{0}} \tag{11}\]  
\[u_{e},\,v_{e}=0\,\,if\,\,u,\,v<0\,\,and\,\,u_{e},\,\,v_{e}=1\,\,if\,\,u,\,v>1 \tag{12}\]  
Here, \(x_{m}\) and \(y_{m}\) are values obtained by converting RSSI signals received from four FNs into distances. If each \(x\)-coordinate ranges from \(x_{0}\) to \(x_{1}\) and the \(y\)-coordinate ranges from \(y_{0}\) to \(y_{1}\), it is divided into four zones (Zones 1 to 4). These divisions are determined based on RSSI signals received from the four FNs that have been converted into coordinate values of \(x_{m}\) and \(y_{m}\). The \(x\) coordinates are \(x_{0}\) to \(x_{1}\) and the \(y\) coordinates are \(y_{0}\) to \(y_{1}\). Within the divided area, the \((x_{e},\,y_{e})\) coordinates are calculated by \(u_{e},v_{e}\) parameters.