Open Access

Cramér-Rao-Type Bounds for Localization

EURASIP Journal on Advances in Signal Processing20062006:094287

https://doi.org/10.1155/ASP/2006/94287

Received: 31 May 2005

Accepted: 1 December 2005

Published: 27 May 2006

Abstract

The localization problem is fundamentally important for sensor networks. This paper, based on "Estimation bounds for localization" by the authors (2004 © IEEE), studies the Cramér-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is anchored localization in which the estimated positions of at least nodes are known in global coordinates. We show some basic invariances of the CRB in this case and derive lower and upper bounds on the CRB which can be computed using only local information. The second is anchor-free localization where no absolute positions are known. Although the Fisher information matrix is singular, a CRB-like bound exists on the total estimation variance. Finally, for both cases we discuss how the bounds scale to large networks under different models of wireless signal propagation.

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Authors’ Affiliations

(1)
Electrical Engineering and Computer Sciences, University of California

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Copyright

© Chang and Sahai. 2006