Wireless Sensor Networks Localization Methods: Multidimensional Scaling vs. Semidefinite Programming Approach

📝 Abstract

With the recent development of technology, wireless sensor networks are becoming an important part of many applications such as health and medical applications, military applications, agriculture monitoring, home and office applications, environmental monitoring, etc. Knowing the location of a sensor is important, but GPS receivers and ophisticated sensors are too expensive and require processing power. Therefore, the localization wireless sensor network problem is a growing field of interest. The aim of this paper is to give a comparison of wireless sensor network localization methods, and therefore, multidimensional scaling and semidefinite programming are chosen for this research. Multidimensional scaling is a simple mathematical technique widely-discussed that solves the wireless sensor networks localization problem. In contrast, semidefinite programming is a relatively new field of optimization with a growing use, although being more complex. In this paper, using extensive simulations, a detailed overview of these two approaches is given, regarding different network topologies, various network parameters and performance issues. The performances of both techniques are highly satisfactory and estimation errors are minimal

💡 Analysis

With the recent development of technology, wireless sensor networks are becoming an important part of many applications such as health and medical applications, military applications, agriculture monitoring, home and office applications, environmental monitoring, etc. Knowing the location of a sensor is important, but GPS receivers and ophisticated sensors are too expensive and require processing power. Therefore, the localization wireless sensor network problem is a growing field of interest. The aim of this paper is to give a comparison of wireless sensor network localization methods, and therefore, multidimensional scaling and semidefinite programming are chosen for this research. Multidimensional scaling is a simple mathematical technique widely-discussed that solves the wireless sensor networks localization problem. In contrast, semidefinite programming is a relatively new field of optimization with a growing use, although being more complex. In this paper, using extensive simulations, a detailed overview of these two approaches is given, regarding different network topologies, various network parameters and performance issues. The performances of both techniques are highly satisfactory and estimation errors are minimal

📄 Content

Wireless Sensor Networks Localization Methods: Multidimensional Scaling vs. Semidefinite Programming Approach Biljana Stojkoska, Ilinka Ivanoska, Danco Davcev,

1 Faculty of Electrical Engineering and Information Technologies – Skopje, Karpoš II bb, 1000 Skopje, Macedonia {biles@feit.ukim.edu.mk, ilinka_iv@yahooo.com, etfdav@feit.ukim.edu.mk}

Abstract. With the recent development of technology, wireless sensor networks are becoming an important part of many applications such as health and medical applications, military applications, agriculture monitoring, home and office applications, environmental monitoring, etc. Knowing the location of a sensor is important, but GPS receivers and sophisticated sensors are too expensive and require processing power. Therefore, the localization wireless sensor network problem is a growing field of interest. The aim of this paper is to give a comparison of wireless sensor network localization methods, and therefore, multidimensional scaling and semidefinite programming are chosen for this research. Multidimensional scaling is a simple mathematical technique widely-discussed that solves the wireless sensor networks localization problem. In contrast, semidefinite programming is a relatively new field of optimization with a growing use, although being more complex. In this paper, using extensive simulations, a detailed overview of these two approaches is given, regarding different network topologies, various network parameters and performance issues. The performances of both techniques are highly satisfactory and estimation errors are minimal.
Keywords: Wireless Sensor Networks, Semidefinite programming, multi- dimensional scaling, localization techniques 1 Introduction New technologies bring new possibilities, however, in the same time new questions are being opened. The area of wireless sensor networks solves a great amount of new problems. A wireless sensor network (WSN) is a network consisting of distributed sensor devices that cooperatively monitor physical or environmental conditions at different locations. The development of wireless sensor networks was originally

motivated by military applications. However, wireless sensor networks are now used in many industrial and civilian application areas, including industrial process monitoring and control, machine health monitoring, environment and habitat monitoring, healthcare applications and traffic control. Today, wireless sensor networks has become a key technology for different types of smart environments, and the aim is to enable the application of wireless sensor networks for a wide range of industrial problems. Wireless networks are of particular importance when a large number of sensor nodes have to be deployed. A fundamental problem in wireless sensor networks is localization i.e. the determination of the geographical locations of sensors. Localization is a challenge when dealing with wireless sensor nodes, and a problem which has been studied for many years [1]. Nodes can be equipped with a Global Positioning System (GPS), but this is a costly solution in terms of money and power consumption. The localization issue is important where there is an uncertainty about some positioning. If the sensor network is used for monitoring the temperature in a remote forest, nodes may be deployed from an airplane and the precise location of most sensors may be unknown. An effective localization algorithm can then use all the available information from the nodes to compute all the positions. Most existing localization algorithms were designed to work well in wireless sensor networks. The performance of localization algorithms depend on critical sensor network parameters, such as the radio range, the network topology i.e. the density of nodes, the anchor-to-node ratio, and it is important that the solution gives adequate performance over a range of reasonable parameter values. In this paper we give an overview of two completely different localization approaches: Multidimensional scaling and Semidefinite programming. We present analysis and simulations of the algorithms, demonstrating the accuracy compared to each other, regarding different sensor network parameters.
The Multidimensional scaling approach is an algorithm using connectivity information for computing the nodes’ localization with the help of some linear transformations [2]. The MDS-MAP algorithm first uses connectivity to roughly estimate the distance between each pair of nodes, then, multidimensional scaling (MDS) is used to find possible node locations that fit the estimations, and finally, it is optimized by using the anchors positions [3]. In section 2 we describe the classical MDS approach used in the simulations.
Section 3 describes the Semidefinite programming (SDP) relaxation based method for the position estimation problem in sensor networks [4][5]. The basic idea behind the tec

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