Fig. 2: Omnidirectional radiation pattern- (a) Ideal pattern, and (b) Irregular pattern.
Therefore the erroneous nature, of the DV-Hop algorithm and its various improvements, is because of the poor distance estimation between anchor node and the unknown node. This distance is impractical because it is calculated with the support of an inadequately estimated hop size and moreover it (i.e. distance) is far away from a Euclidean distance. The proposed method in this paper is based upon the fact that the minimum distance estimation in-between anchor node and an unknown node is a close approximation of Euclidean distance in-between the two (i.e. an anchor node and an unknown node).
Consequently, to localize a node with more accuracy, a model should focus on two points- 1) approximated correction of hop size, and 2) obtain Euclidean distance up to a maximum possible extent. The proposed model ODR thrust upon these two points. To examine the proposed ODR significance, it is closely studied about a recent projected Improved DV-Hop (IDV) algorithm by S. Shen et al. [18]. The algorithm [18] employs hyperbolic function based upon the distance equations of an unknown node and an anchor node, as explained below.
4. Improved DV-Hop Algorithm (IDV) [18]
In this algorithm, localization has been improved by modifying the hop size. The correction factor \((\varnothing_{p})\) for hop size of an arbitrary anchor node \({}^{\prime}p^{\prime}\) is obtained by calculating a difference of the distance values obtained as per DV-Hop distance estimation method and the actual distance in-between every anchor node pair, shown by the following equation-
\begin{equation} \varnothing_{p}=\frac{\sum_{p\neq s}\left(\left|\left({H_{\text{size}}}_{p}\times H_{\text{coun}t_{\text{ps}}}\right)-d_{\text{ps}}\right|\right)}{\sum_{p\neq s}H_{\text{coun}t_{\text{ps}}}};\ \forall\ p\neq s\ and\ p,s\ \epsilon\ A_{n};\nonumber \\ \end{equation}
where \(d_{\text{ps}}\) is an actual distance between anchor nodes\({}^{\prime}p^{\prime}\) and \({}^{\prime}s^{\prime}\).
Further to convert the hop size into the distance, IDV [18] does not consider all the anchor nodes. Instead, it finds out the hop counts which must be traversed from the unknown node to have at least three anchor nodes only. To find out the minimum number of hop counts, it employs probability based upon anchor nodes density per unit area.
Though the suggested modifications by IDV [18] can reduce the localization error considerably it draws some shortfalls also. The hop size correction factor \({}^{\prime}\varnothing_{p}^{\prime}\) contributes a noteworthy complexity of the order of\({}^{\prime}m^{2}{}^{\prime}(if\ there\ are\ ^{\prime}m^{\prime}\ number\ of\ anchor\ nodes\ only)\). Further, the localization accuracy is dependent upon a degree of the randomness of the nodes’ distribution. The degree of randomness of the distribution of nodes will affect its performance. Because by keeping the same number of anchor nodes and unknown nodes; the anchor node’s density value will remain the same but it doesn’t ensure that at every instance at a distance of fix hop counts from every unknown node there will be at least three anchor nodes always. It implies that IDV [18] is less robust and unable to keep the computational complexity low but at the same time it localizes with improved accuracy in the case of dense networks only at the cost of poor latency.
The proposed model ODR in this paper improves the hop size also but with a computation requirement of the order of \({}^{\prime}m^{\prime}\) only. The ODR localizes with high accuracy and robust in comparisons to IDV [18] because it does not depend upon any of the terms which are predetermined as the density of a node of IDV [18]. Further ODR localization can calculate approximated Euclidean distance whereas IDV [18] is dependent upon the distance values obtained through discrete calculation of hop count and hop size.
5. Proposed Work: The proposed algorithm ODR has three steps. Its first step is the same as that of the DV-Hop algorithm. In the second step, the hop size is improved by calculating average hop size error. The improved hop size and the centroid of the minimum hop distant anchor nodes are used to find an approximated region in which the unknown node should exist. The approximated region is calculated by using the routing table of the respective anchor nodes. This approximated region assists to calculate a base distance which is a minimum possible distance between the unknown node and the anchor nodes\((A_{n}-K)\); where \({}^{\prime}A_{n}^{\prime}\ \)is a set of all anchor nodes and ‘K’ is a set of anchor nodes at a minimum hop distance from the unknown node. This base distance is a probable straight line distance between an anchor node and an unknown node. The straight line distance overcomes the drawback of the zigzag distance measured by DV-Hop and IDV algorithms. In the third step, we localize the unknown node. The base distance calculated in the second step is not a complete distance between the unknown node and the anchor nodes\((A_{n}-K)\). To make it complete we add a respective comprehensive distance value in the base distance and which is known as complete distance. Further by using linear optimization we try to minimize the comprehensive distance to get high localization accuracy.
Here we explain all the steps of ODR one by one.