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A New Range-Free and Storage-Efficient Localization Algorithm Using Neural Networks in Wireless Sensor Networks

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Abstract

Wireless Sensor Network is one of the new technologies that have gotten more attention in the past few years. The localization problem is one of the most important topics in these types of the networks. The traditional positioning techniques cannot be used in these networks due to the hardware restrictions of the sensor nodes. Lately, some positioning methods which use soft computing approaches such as neural networks, are proposed for solving the localization problem. In this paper, we propose a new range-free localization algorithm which uses the neural networks for this purpose. This method utilizes Particle swarm optimization (PSO) algorithm to optimize the number of neurons of hidden layers of neural networks. The objective function considers both localization accuracy and storage overhead, simultaneously. The proposed algorithm is implemented and simulated in isotropic networks with and without coverage hole, and anisotropic networks. The obtained result show, in the different environmental conditions, the proposed algorithm has a less localization error rate and less storage requirement than the analogous methods.

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Authors and Affiliations

  1. Department of Computer Engineering, Yazd University, Yazd, Iran

    Seyed Saber Banihashemian, Fazlollah Adibnia & Mehdi A. Sarram

Authors
  1. Seyed Saber Banihashemian
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  2. Fazlollah Adibnia
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  3. Mehdi A. Sarram
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Corresponding author

Correspondence to Fazlollah Adibnia.

Appendix 1

Appendix 1

To determine the furthest corner from a location class, we can divide the area into four small rectangles that have the same dimensions as it is shown in Fig. 11. The furthest corner from a location class is in the opposite rectangle as it is demonstrated for the location class A in the Fig. 11.

Fig. 11
figure 11

Division of deployment area to four smaller rectangles

Full size image

Therefore, the average distance of a location class to furthest corner in a 2-d rectangular area is the probability that a class location is in one of these small rectangles and mean of distances of a location class in the small rectangle to furthest corner. This probability can be formulated as follows:

$$\begin{aligned} \overline{\hbox{max} P\_error} &= \frac{1}{4}*\frac{1}{{\frac{{N_{x} }}{2}*\frac{{N_{y} }}{2}}}*\mathop \sum \limits_{i = 1}^{{\frac{{N_{x} }}{2}}} \mathop \sum \limits_{j = 1}^{{\frac{{N_{y} }}{2}}} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {N_{x} ,N_{y} } \right)} \right] \hfill \\ &\quad+ \frac{1}{4}*\frac{1}{{\frac{{N_{x} }}{2}*\frac{{N_{y} }}{2}}}*\mathop \sum \limits_{{i = \frac{{N_{x} }}{2} + 1}}^{{N_{x} }} \mathop \sum \limits_{j = 1}^{{\frac{{N_{y} }}{2}}} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {1,N_{y} } \right)} \right] \hfill \\ &\quad + \frac{1}{4}*\frac{1}{{\frac{{N_{x} }}{2}*\frac{{N_{y} }}{2}}}*\mathop \sum \limits_{i = 1}^{{\frac{{N_{x} }}{2}}} \mathop \sum \limits_{{j = \frac{{N_{y} }}{2} + 1}}^{{N_{y} }} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {N_{x} ,1} \right)} \right] \hfill \\ &\quad + \frac{1}{4}*\frac{1}{{\frac{{N_{x} }}{2}*\frac{{N_{y} }}{2}}}*\mathop \sum \limits_{{i = \frac{{N_{x} }}{2} + 1}}^{{N_{x} }} \mathop \sum \limits_{{j = \frac{{N_{y} }}{2} + 1}}^{{N_{y} }} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {1,1} \right)} \right] \hfill \\ \end{aligned}$$
(19)

The above equation can be further summarized as follows:

$$\begin{aligned} \overline{\hbox{max} P\_error} &= \frac{1}{{N_{x} *N_{y} }}*\mathop \sum \limits_{i = 1}^{{\frac{{N_{x} }}{2}}} \mathop \sum \limits_{j = 1}^{{\frac{{N_{y} }}{2}}} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {N_{x} ,N_{y} } \right)} \right] \hfill \\ &\quad + \frac{1}{{N_{x} *N_{y} }}*\mathop \sum \limits_{{i = \frac{{N_{x} }}{2} + 1}}^{{N_{x} }} \mathop \sum \limits_{j = 1}^{{\frac{{N_{y} }}{2}}} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {1,N_{y} } \right)} \right] \hfill \\ &\quad + \frac{1}{{N_{x} *N_{y} }}*\mathop \sum \limits_{i = 1}^{{\frac{{N_{x} }}{2}}} \mathop \sum \limits_{{j = \frac{{N_{y} }}{2} + 1}}^{{N_{y} }} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {N_{x} ,1} \right)} \right] \hfill \\ &\quad + \frac{1}{{N_{x} *N_{y} }}*\mathop \sum \limits_{{i = \frac{{N_{x} }}{2} + 1}}^{{N_{x} }} \mathop \sum \limits_{{j = \frac{{N_{y} }}{2} + 1}}^{{N_{y} }} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {1,1} \right)} \right] \hfill \\ \end{aligned}$$
(20)

The formulas mentioned in above equation can be considered as the same formula (because the average distance of a location class in a small rectangle is equal for all four small rectangles), so the equation can be presented as follows:

$$\overline{\hbox{max} P\_error} = \frac{4}{{N_{x} *N_{y} }}*\mathop \sum \limits_{i = 1}^{{\frac{{N_{x} }}{2}}} \mathop \sum \limits_{j = 1}^{{\frac{{N_{y} }}{2}}} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {N_{x} ,N_{y} } \right)} \right]$$
(21)

The above equation can be transformed to:

$$\overline{{\hbox{max} P_{error} }} = \frac{1}{{\frac{{N_{x} }}{2}*\frac{{N_{y} }}{2}}}*\mathop \sum \limits_{i = 1}^{{\frac{{N_{x} }}{2}}} \mathop \sum \limits_{j = 1}^{{\frac{{N_{y} }}{2}}} dist\left[ {\left( {C_{x}^{i} ,C_{y}^{j} } \right),\left( {N_{x} ,N_{y} } \right)} \right]$$
(22)

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Banihashemian, S.S., Adibnia, F. & Sarram, M.A. A New Range-Free and Storage-Efficient Localization Algorithm Using Neural Networks in Wireless Sensor Networks. Wireless Pers Commun 98, 1547–1568 (2018). https://doi.org/10.1007/s11277-017-4934-4

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