Range-Based Localization for Sparse 3-D Sensor Networks

Localization plays a pivotal role in wireless sensor networks. Many range-based localization algorithms have been proposed for 2-D sensor networks or densely deployed 3-D sensor networks. However, range-based localization in sparse 3-D sensor networks is still a challenging problem, because the sparseness of the network makes it difficult to obtain a proper order of nodes to be sequentially localized. The patch-and-stitching localization strategy can conquer the sparseness problem in 2-D networks, but for 3-D networks it is still unknown how to uniquely merge two patches when there are not enough common nodes. In this paper, we solve this challenging problem by deriving the conditions under which two subnetworks can be uniquely merged. In the proposed approach, we treat the translation parameters as unknowns and form a set of equations with which the unknowns can be uniquely solved. The novelty of our algorithm also lies in that we exploit both common nodes and connecting edges among adjacent subnetworks to merge them, resulting in very high chances that two subnetworks can be merged. We conduct extensive simulation experiments to evaluate the performance of the proposed algorithm. The results show that the proposed algorithm could localize more than 90% of nodes in sparse 3-D networks with average node degree of 11 and anchor ratio of 5%, while the best existing solution can localize only 52% of nodes in the same situation.