Localization and routing in sensor networks by local angle information

Abstract

Location information is useful both for network organization and for sensor data integrity. In this article, we study the anchor-free 2D localization problem by using local angle measurements. We prove that given a unit disk graph and the angles between adjacent edges, it is NP-hard to find a valid embedding in the plane such that neighboring nodes are within distance 1 from each other and non-neighboring nodes are at least distance √2/2 away. Despite the negative results, however, we can find a planar spanner of a unit disk graph by using only local angles. The planar spanner can be used to generate a set of virtual coordinates that enable efficient and local routing schemes such as geographical routing or approximate shortest path routing. We also proposed a practical anchor-free embedding scheme by solving a linear program. We show by simulation that it gives both a good local embedding, with neighboring nodes embedded close and non-neighboring nodes far away, and a satisfactory global view such that geographical routing and approximate shortest path routing on the embedded graph are almost identical to those on the original (true) embedding.