Revisiting the Cramer-Rao Bound for Localization Algorithms

Acquiring position information by means of ad-hoc networks and in particular wireless sensors networks (WSNs) received a lot of attention in the past years. Survey works, such as [1], [2], show a large number of techniques/algorithms that can be used to solve the localization problem. The techniques used are often borrowed from other fields of science and modified to fit the context of wireless sensor networks [3–5]. In order for results established in other fields of science to hold for the problem at hand, particular care must be taken to ensure that the assumptions are still valid. Even the slightest mismatch in the underlying assumptions could render the well-known techniques useless and lead to wrong results. In this paper, we address the usage of lateration [6] and the associated Cramer-Rao Bound (CRB) [3], concepts borrowed from GPS localization [7]. Via a series of counter-examples, we show how these concepts fail to deliver the expected results when applied to the field of WSNs. The goal of this paper is to bring forward the idea that a foundation based on geometrical considerations – rather than estimation theory – should be employed when studying the basic mechanisms and boundaries for localization in WSNs.