# A Dependable Localization Algorithm for Survivable Belt-Type Sensor Networks
## 4 Simulation and Analysis
### Relative Error of Positioning Accuracy  
_Error\({}_{ave}\)_ is the ratio of the target positioning error to the communication radius of the node itself. It is defined as the relative error of positioning accuracy and its expression is (25):  
\[ \begin{array}{l}Error_{ave}=\frac{\sum\limits_{i=1}^{n}\Delta r_{i}}{N\times R _{c}}\times 100\%\\ =\frac{\sum\limits_{i=1}^{n}\sqrt{\left(x_{i,ent}-x_{i,renal}\right)^{2}+ \left(y_{i,ent}-y_{i,renal}\right)^{2}}}{N\times R_{c}}\end{array}  \tag{25}\]  
In Equation (25), the coordinates of the target node are denoted as \((x_{i,est},y_{i,est})\), the coordinates of the real position of the target node are denoted by \((x_{i,real},y_{i,real})\), \(N\) is the number of unknown target nodes, and \(R_{t}\) is the communication radius of the normal node. It can be seen from Figure 7 that the error of the average positioning accuracy for the target is maintained at 27% when the number of anchor nodes is about 11 and the other network conditions are unchanged. If the number of anchor nodes increases from 3 to 13, the algorithm positioning error basically displays decreasing trend. The standard DV-Hop has the largest positioning error because it does not use other corrective measures. However, when the number of anchor nodes reaches 13 or 14, the trend of positioning accuracy error is almost smooth. As the band network continues to extend along the edge, the difference between adjacent anchor nodes is narrowing, and their correction to distance estimation is weakening. In addition, when the anchor nodes increase to a certain percentage, the network connectivity no longer significantly changes. Therefore, when the number of anchor nodes reaches 13 or so, the positioning error basically becomes stable. When the number of anchor nodes is further increased, the positioning accuracy of the DV-Distance algorithm is slightly decreased. That is because the DV-Distance algorithm must use the RSSI signal as an auxiliary estimation parameter. When the signal transmission is within a certain distance range, its amplitude change, resulting in increased signal fluctuations. The number of anchor nodes can increase the source of information needed for locating. But on the other hand, it also introduces more error sources to some extent. When such a node reaches a certain number, it can lead to an increase in cumulative errors and relatively negative effects on the elevation of positioning accuracy. The simulation data curve in Figure 7 shows that the relative positioning accuracy error of DV-Distance and proposed algorithm is significantly lower in general. When the number of nodes is less than 13, the precision of the proposed algorithm is slightly higher than that of DV-Distance algorithm. According to the simulation process, the proposed algorithm only needs to be carried out two iterations, the initial value is approaching the real value quickly. It shows some advantages: the convergence speed is faster, the computation is small. The confidence interval of the simulation results is shown in Figure 8.  
Figure 7: Localization error vs. Number of anchors. It can be seen from Figure 9, from the perspective of qualitative analysis, that the communication radius of a node can determine the number of its neighbors and number of connections. As the communication radius of the target node increases, it can be searched and acquired the location information for more anchor nodes within its communication range. At the same time, the radius of node communication increases, which can also make its own positioning coverage increase. In that way, the node can obtain more adjacent node location information, so the estimation accuracy can be improved. DV-Distance algorithm uses RSSI signal as auxiliary positioning parameters. If the distance between nodes is more than 20 m, the signal fading curve will show large fluctuations.