# An Efficient Indoor Positioning Method with the External Distance Variation for Wireless Networks
## 4 Results  
Simulation environment in this paper is about a 100 m \(\times\) 100 m using the MMSE algorithm to locate the area formed by the circle as shown in Figures 9 and 10. Figures 9 and 10 are either defined as a small area and a large area, respectively, for comparison for two MSEs. Furthermore, in Figures 9 and 10, three to six fixed reference nodes are used to estimate the small range and the large range, respectively. When more reference nodes are used to estimate for results, the MSE is decreased. Figure 11 compares the MSE of three to six fixed and randomly deployed 40 reference nodes. The more reference nodes there are, the more MSE decreases, and the lower the MSE of the fixed reference node. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Deployment** & **Three From Four Mechanism** & **Strengthen the Selection Mechanism** \\
**Reference Nodes** & & **Mechanism** \\ \hline
10 reference nodes & 77.086 & 67.61 \\
20 reference nodes & 60.31 & 56.87 \\
30 reference nodes & 50.32 & 49.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of conditions added and choosing three from four mechanisms. Figure 8: The relationship between variation and MSE after strengthening the selection mechanism. In Figure 12, the random selection of reference nodes (\(\sigma=3\)) is added to a small range. The random selection of three reference nodes (\(\sigma=3\)) is higher than the fixed three (\(\sigma=4\)) MSEs. Because three random reference nodes may be selected as reference nodes that are very close to each other and will increase the MSE. When there are four at random, the MSE will be a little bit higher than the fixed three (\(\sigma=3\)) because the original three reference nodes are very close and the MSE will be very high. If one more reference node supports positioning, the MSE will be lower than the original three reference nodes. Figure 10: Three, four, five, and six reference nodes for a large range. Figure 9: Three, four, five, and six reference nodes for a small range. In Figure 13, the method of randomly selecting reference nodes (\(\sigma=3\)) is added in a large range. Although the fixed three (\(\sigma=4\)) and the random three (\(\sigma=3\)) are compared with the random three (\(\sigma=3\)), the random three (\(\sigma=3\)) are worse. The reference nodes 4, 5, and 6 are both fixed and random. Figure 11: Comparison of three to six fixed and random reference nodes. Figure 12: Comparison of the estimated small range of fixed reference nodes and random reference nodes. The analysis method is based on the center coordinates (50, 50). As shown in Figure 14, the square extended outward is defined as the first circle to the third circle. The change of MSE around the center point can be explored. As shown in Figure 15, the MSE of the center point coordinates (50, 50) is the lowest, and the MSE will increase. Therefore, the MSE of the outermost periphery (the first circle) is the highest, whereas the fixed reference node is higher than the MSE of the random deployment reference node. Figure 14: Simulation range is about 100 m \(\times\) 100 m.  
Figure 13: Comparison of the estimation of a large range of fixed reference nodes and random reference nodes. However, by analyzing the fixed three, four, five, and six reference nodes through the 3D graph to estimate the small area, the difference between them can be more clearly observed. As shown in Figure 16, when the three reference nodes are fixed to estimate the nodes, the closer they are to the center point, the lower the MSE, and the highest relative to the outermost node. Therefore, from Figures 16-19, it is shown that the lowest MSE is the center point coordinates (50, 50), and that the highest MSE is around a small area. The more reference nodes are located, the MSE of the node will decrease. Figure 16: Three reference nodes to estimate the small range. Figure 15: Comparison between center point and directly selected reference node. Figure 8:0 Four reference nodes to estimate the small range.