Localization of Networks on 3D Terrain Surfaces

Xuan Li, Buri Ban, Yang Yang, Miao Jin

Abstract: The majority of current research on sensor network localization focuses on wireless sensor networks deployed on two-dimensional (2D) plane or in three-dimensional (3D) space, very few on the 3D terrain surface. However, many real-world applications require large-scale sensor networks deployed on the surface of a complex 3D terrain. Compared with planar and 3D network localization, terrain surface network localization generates unique and fundamental hardness. We explore 3D surface network localization with terrain models. A digital terrain model (DTM), available to the public with a variable resolution of up to one meter, is a 3D representation of a terrain's surface. It is commonly built using remote sensing technology or from land surveying and can be easily converted to a triangular mesh. Given a sensor network deployed on the surface of a 3D terrain with one-hop distance information available, we can extract a triangular mesh from the connectivity graph of the network. The constraint that the sensors must be on the known 3D terrain's surface ensures that the triangular meshes of the network and the terrain's surface overlap and approximate the same geometric shape. The basic idea of the localization algorithms is to map the two triangular meshes extracted from the connectivity graph of a sensor network and the DTM of its deployed terrain surface to the plane. The two meshes mapped to the plane can be easily aligned if the location information of anchor nodes is available. We introduce a fully distributed algorithm to construct a well-aligned mapping between the two triangular meshes in the plane based on anchor nodes information. However, accidents may happen on anchor nodes. We then introduce an anchor-free algorithm to extract feature points with geometric properties intrinsic to surface distances and independent of the embedding of the two meshes in 3D. The matched feature points induce transformations to align the two meshes in the plane. With the aligned triangular meshes of a network and its deployed terrain surface, each sensor node of the network can easily locate reference grid points from the DTM of the terrain to calculate its own geographic location. We carry out extensive simulations under various scenarios to evaluate the overall performance of the proposed algorithms with different factors such as the one-hop distance measurement error, the resolution of a DTM, and the performance of the algorithm in the situation of connectivity only.