Beacon deployment strategy for guaranteed localization in wireless sensor networks

Abstract

In wireless sensor networks, beacons are always treated as infrastructures for localization. After beacons are deployed, non-beacon nodes can be located by simple schemes such as multilateration and multidimensional scaling (MDS). Deploying as many beacons as needed is an efficient way to improve localization accuracy where a global positioning system does not work well or a higher location accuracy is required. With more beacons to be deployed, the configuration of beacons' positions will have to be done manually. Therefore position auto-configuration using measured distances between these beacons can save a lot of efforts for the deployment. One challenge of this auto-configuration is that the positions should be uniquely determined based on the measured distances. In graph theory, it is a problem of unique realization in which the positions of vertices are determined by edges between them. Addressing this problem is one major aspect of this paper. To determine whether the topology of a network is a unique realization, this paper proposes a novel category of topology named Uniquely Determined Topology, with which edges in a d-dimensional space can be reduced from $$d+1$$d+1 to d in each extension, which is less strict and more suitable for beacon deployment. The other aspect of this paper is to improve localization accuracy of the deployed beacons. In MDS and curvilinear component analysis, a shortest-path algorithm is adopted to approximately reconstruct the distance matrix between each two nodes, and our proposed Uniquely Determined Topology has a feature that a distance calculation model can be adopted to replace the shortest-path algorithm, therefore that the local distance matrix can be reconstructed more accurately. Theoretical analysis shows that it has a low computational complexity to determine whether a deployment is a Uniquely Determined Topology. Simulations show the advantages of the improved localization scheme, in that they do not depend on the connectivity level of the networks, and they can provide accurate localization when the estimation accuracy of distances is high.