Localization in Wireless Sensor Networks Using Quadratic Optimization

The localization problem in a wireless sensor network is to determine the coordination of sensor nodes using the known positions of some nodes (called anchors) and corresponding noisy distance measurements. There is a variety of different approaches to solve this problem such as semi-definite programming (SDP) based, sum of squares and second order cone programming, and between them, SDP-based approaches have shown good performance. In recent years, the primary SDP approach has been investigated and a variety of approaches are proposed in order to enhance its performance. In SDP approaches, errors in approximating the given distances are minimized as an objective function. It is desirable that the distribution of error in these problems would be a delta distribution, which is practically impossible. Therefore, we may approximate delta distribution by Gaussian distribution with very small variance. In this paper, we define a new objective function which makes the error distribution as similar as possible to a Gaussian distribution with a very small variance. Simulation results show that our proposed method has higher accuracy compared to the traditional SDP approach and other prevalent objective functions which are used such as least squares. Our method is also faster than other popular approaches which try to improve the accuracy of the primary SDP approach.Comment: 11 pages, 9 figure

A State-of-the-Art Survey on Multidimensional Scaling Based Localization Techniques

Current and future wireless applications strongly rely on precise real-time localization. A number of applications such as smart cities, Internet of Things (IoT), medical services, automotive industry, underwater exploration, public safety, and military systems require reliable and accurate localization techniques. Generally, the most popular localization/ positioning system is the Global Positioning System (GPS). GPS works well for outdoor environments but fails in indoor and harsh environments. Therefore, a number of other wireless local localization techniques are developed based on terrestrial wireless networks, wireless sensor networks (WSNs) and wireless local area networks (WLANs). Also, there exist localization techniques which fuse two or more technologies to find out the location of the user, also called signal of opportunity based localization. Most of the localization techniques require ranging measurements such as time of arrival (ToA), time difference of arrival (TDoA), direction of arrival (DoA) and received signal strength (RSS). There are also range-free localization techniques which consider the proximity information and do not require the actual ranging measurements. Dimensionality reduction techniques are famous among the range free localization schemes. Multidimensional scaling (MDS) is one of the dimensionality reduction technique which has been used extensively in the recent past for wireless networks localization. In this paper, a comprehensive survey is presented for MDS and MDS based localization techniques in WSNs, Internet of Things (IoT), cognitive radio networks, and 5G networks.Comment: Accepted in IEEE Communications Surveys and Tutorial