Optimization-based Secure Multi-hop Localization in Wireless Ad Hoc Networks

The problem of localizing nodes without GPS based on a small fraction of anchor nodes which are aware of their positions is considered to be an important service for applications in wireless ad hoc networks. With an adversary trying to mislead nodes about their estimated locations, several approaches aiming to defeat attackers by means of robustness instead of cryptographic measures have been proposed in the past. Nevertheless, these robust techniques focus on single-hop based localization. Hence, we investigate the impact of employing the well-known Least Median of Squares (LMS) algorithm in the context of the multi-hop based DV-hop approach. We argue that in this case LMS is no longer able to meet its requirements. We examine the source of this behavior and show that LMS leads to more accurate results when using the median to obtain average hop lengths in DV-hop. Furthermore, we investigate the feasibility of performing lateration using the l1-norm instead of the typically employed l2-norm, as well as the possibility of enhancing the robustness of LMS using lateration based on the l1-norm. Contrary to our expectations, the l1-norm only results in a slight, neglectable advantage compared to the computationally less expensive l2-norm lateration. Digital Object Identifier 10.4230/OASIcs.KiVS.2011.182