# A Dependable Localization Algorithm for Survivable Belt-Type Sensor Networks
## 3 Hop-Distance Estimation Correction
### Correcting the Accumulated Values  
In the framework of standard DV-Hop algorithm, the estimated distances of the target node to the anchor nodes in the range of the surrounding hop are very easy to identify as the same, which makes it difficult to determine the distances between the adjacent nodes. A large number of measured statistical results show that if the cumulative number of hops are used to estimate the distances between the target nodes and any anchor nodes, the estimated results are greater than the actual physical distance between them [21; 35]. In the algorithm process, an appropriate correction method must be added in its framework when the estimation distances and coordinate calculation are carried out. In this way, it is possible to avoid the accumulation of errors between the anchor nodes and the positioning target node due to the accumulation of the positioning information. It also can reduce the accuracy of the positioning accuracy due to the blurring of the hops-distance estimation. Our purpose is to consider the differences between the distance between adjacent nodes (anchor nodes and neighbor nodes) and network connectivity. To improve the accuracy of positioning estimation is our ultimate goal. Based on the above reasons, an auxiliary distance correction estimation method based on the optimization of connectivity among nodes is proposed without adding additional communication overhead. Let the average hop distance of the network be expressed as \(d_{i}\), and its expression can be defined as:  
\[d_{i}=\frac{\sum\limits_{i\
eq j}md_{ij}}{\sum\limits_{i\
eq j}h_{ij}} \tag{4}\]  
In Equation (4), \(md_{ij}\) represents the cumulative hops distance between the anchor and the target, and \(h_{ij}\) represents the minimum value of the direct hops between the two. According to the principle that in the network the communication radius of nodes is greater than the distance between nodes, we uniformly collect the average distance per hop of multiple recent anchors received by the target node, and then weighted processing of them is normalized. Firstly, \(\theta_{m}\) is defined as the average distance error between nodes \(m\) and \(n\). \[\theta_{m}=\frac{\sum\limits_{n\
eq n}\left|d_{est(m,n)}-d_{r(m,n)}\right|/h_{ mm}}{M-1} \tag{5}\]  
In Equation (5), \(d_{est(m,n)}\) represents the estimated distance between nodes \(m\) and \(n\). \(d_{r(m,n)}\) represents the actual distance between them. Assuming that the target node receives the data sent by the \(k\) anchor nodes at this time, the average hop-distance weighting coefficient from the \(m^{\text{th}}\) anchor node is expressed as:  
\[\eta_{m}=\frac{1}{\theta_{m}}/\sum\limits_{k=1}^{n}\frac{1}{\theta_{k}} \tag{6}\]  
In summary, when the member nodes of the network receive the distance value represented by the average hop per hop (\(h\)) through broadcasting, the distance estimation to the corresponding anchor node is expressed as \(d_{est(i,j)}\). It is shown in Equation (7):  
\[d_{est(i,j)}=\eta_{m}\sum\limits_{i\
eq j}h_{ij}\times d_{i} \tag{7}\]  
According to the principle of simplicity, we only select the last three anchor node information, and \(\lambda_{m}\) is normalized. In a network, a single node can send test packets(\(S\)) to determine the neighbor relationship. We define \(\gamma\) as the threshold for the packet rate, which needs to meet the condition \(1/S\leq\gamma\leq 1\). When node \(i\) receives the packet scent by node \(j\), if it is determined that the following relationship exists, node \(i\) and \(j\) can be determined as neighbors. A significant increase in the reliability of the node's neighbor distance makes it possible to have a unique relationship between the different unknown nodes and its recent anchor nodes. Based on it, we can eliminate some information from interfering nodes or false anchors. After removing the tampered beacon information and eliminating the interfering nodes, we can obtain the relative accurate node distance, so as to correctly compute the node location.