# A Dependable Localization Algorithm for Survivable Belt-Type Sensor Networks
## 4 Simulation and Analysis
### Relative Error of Positioning Accuracy
At this moment, the communication radius can no longer directly improve the positioning accuracy, the overall positioning accuracy and the proposed improvement algorithm is basically close, but it uses additional hardware that can measure distance which greatly increases the communication consumption and reduces efficiency, so the positioning cost is also affected. The confidence interval of the simulation results is shown in Figure 10.  
At a certain time, we gradually increase the number of unknown randomly distributed target nodes. The relationship between node number and location accuracy is shown in Figure 11. We see that the error of proposed algorithm is significantly smaller than the DV-Distanc  
Figure 8: The confidence interval of the data I.  
Figure 10: The confidence interval of the data II. Figure 9: Localization error vs. Node communication radius. algorithm and CDV-Hop algorithm. On the whole, the larger number of nodes is beneficial to improve the accuracy of the distance estimation between nodes. That is because the localization algorithm using network connectivity (hop number) is designed based on the relationship between the number of hops and distances between nodes. The network connectivity will directly influence the accuracy of the algorithm. The confidence interval of the simulation results is shown in Figure 12.  
Network connectivity affects the accuracy of the algorithm directly. The better the network connectivity, the more accurate the distance between each hop. Connectivity refers to the existence of at least one direct path between any two nodes in the network, enabling efficient communication [16]. According to the basic theory of graph theory [26; 27], the minimum node degree of the network is expressed as \(D_{\min}(G)\):  
\[D_{\min}(G)=\min\{D(v)\} \tag{26}\]  
In Equation (26): \(v\) represents a node in the network, and \(D(v)\) represents the number of neighbor nodes that can communicate with the node directly. In the network the connectivity of any node with node \(N\) and the remaining \(N-1\) nodes can be expressed as \(K\), and the relationship can be expressed as (27):  
\[E(K)=(N-1)p_{x} \tag{27}\]  
In Equation (27): \(p_{x}\) is the probability of any two nodes being connected when the communication distance is fixed. The increase in connectivity index \(p_{x}\) indicates that the number of hops between nodes decreases, and the average positioning error decreases with the increase of node density. The reason is that although the node position is relatively dispersed, its probability density function is continuous. When the node density increases, the discrete function approximates the continuous function. This can make the error smaller, thus improving the positioning accuracy. The better the connectivity, the closer to the true value for each hop estimate. When calculating the coordinates, the gradient method can be used to make the evaluation more accurate, so the estimation accuracy is higher. However, due to the number of anchor nodes has not changed, other nodes lead to an increase in its proportion, the whole error curve is not always showing a downward trend. Figure 7:0 Localization error vs. Total number of sensor nodes. Figure 7:1 The confidence interval of the data III.