This thesis studies range-based WSN localization problem in 3D environments that induce coplanarity. In most real-world applications, even though the environment is 3D, the grounded sensor nodes are usually deployed on 2D planar surfaces. Examples of these surfaces include structures seen in both indoor (e.g. floors, doors, walls, tables etc.) and outdoor (e.g. mountains, valleys, hills etc.) environments. In such environments, sensor nodes typically appear as coplanar node clusters. We refer to this type of a deployment as a planar deployment. When there is a planar deployment, the coplanarity causes difficulties to the traditional range-based multilateration algorithms because a node cannot be unambiguously localized if the distance measurements to that node are from coplanar nodes. Thus, many already localized groups of nodes are rendered ineffective in the process just because they are coplanar. We, therefore propose an algorithm called Coplanarity Based Localization (CBL) that can be used as an extension of any localization algorithm to avoid most flips caused by coplanarity. CBL first performs a 2D localization among the nodes that are clustered on the same surface, and then finds the positions of these clusters in 3D. We have carried out experiments using trilateration for 2D localization, and quadrilateration for 3D localization, and experimentally verified that exploiting the clustering information leads to a more precise localization than mere quadrilateration. We also propose a heuristic to extract the clustering information in case it is not available, which is yet to be improved in the future.
Aspnes @cite_46 investigated the localization and localizability of a network in 2010. They defined the term and showed that it is sufficient and necessary condition for a WSN graph to be localized in 2D. Even though global rigidity is defined for all dimensions, the sufficient and necessary conditions for a WSN to be localized in 3D have not been found yet.
@cite_46
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In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly