Utilizing hyperplanar substructures to perform efficient range-based WSN localization
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A wireless sensor network (WSN) consists of multiple wireless sensor nodes that communicate each other to fulfill a particular task. In this paper, we emphasize on the networks whose deployments admit lower dimensional substructures, such as collinear groups in 2D, or coplanar groups in 3D. When these groups are given as a part of the input, we describe an algorithm to utilize this information to perform a low-cost localization. In emergency situations such as fire, earthquake etc. inside a building, wireless sensor networks might be very crucial to provide critical information and help the rescue teams to move very quickly by decreasing their burden of exploring the environment. Thus, it is very important to develop a system that provides information quickly and without consuming too much energy. We observe that in these type of environments, sensor nodes tend to form hyperplanar groups. A hyperplane is a subspace of one dimension less than its ambient space, and accordingly, a hyperplanar group of sensor nodes is a group of nodes that sit on the same hyperplane. When we consider a floor of a building, the nodes can be deployed on the corridors to form collinear groups, and when we consider the whole building, the sensor nodes will sit on the floors to form coplanar groups. Therefore, we study range-based WSN localization problem in 3D environments that induce hyperplanar groupings. First, we show that it is an -hard problem to obtain hyperplanar groups, even if we are given the equations of the hyperplanes. Then, we describe an algorithm that assumes each sensor node is aware of its hyperplanar group, and performs a localization when the sensor nodes are deployed in the corridors on each floor of a building. In this case, grouping information allows us to localize a network, which cannot be localized by conventional range-based localization algorithms.
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