Secure and Robust Localization in a Wireless Ad Hoc Environment

Abstract

We study the problem of accurate localization of static or mobile nodes in a wireless ad hoc network using the distance estimates of a group of untrusted anchors within the communication range of the nodes. Some of the anchors may be malicious and may independently lie about the distance estimate. The malicious anchors may also collude to lie about the distance estimates. In both cases, accurate node localization may be seriously undermined. We propose a scheme that performs accurate localization of the nodes in the network despite the presence of such malicious anchors. We also show how to identify most of these malicious anchors. In the case where measurements are error free, we derive a critical threshold <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> for the number of malicious anchors that can be tolerated in the localization process without undermining accuracy. We also show how to correctly localize a node and identify all the malicious anchors in this setting. In the presence of measurement errors, we propose a convex optimization-based localization scheme that can accurately localize a node, as long as the number of malicious anchors in its communication range is no more than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> . Simulation results show that our schemes are very effective. When the measurements are error prone and the number of malicious anchors is no more than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> , our scheme localizes a node with an error less than 8% and is also able to identify a significant number of malicious anchors. Our schemes guarantee that a true anchor is not identified as malicious.