Multi-scale Anchor-free Distributed Positioning in Sensor Networks

Positioning is one of the most fundamental problems in sensor networks: Given the network’s connectivity graph and some additional local information on measured distances and/or angles, the goal is to recover the nodes’ positions. Varying the assumptions regarding the nature and the quality of the measurements, there has been extensive research for both hardness results and practical, distributed, positioning schemes. This paper addresses these issues for a setting that appears to be most likely in real-world scenarios in the future – nodes can roughly measure distances and relative angles. We will show that this problem is NP-hard like most positioning problems even for arbitrarily small errors. We will also propose an algorithm combining robustness to erroneous measurements and scalability in a completely distributed fashion and provide simulation results for networks of up to 128k nodes with varying errors.