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.