Estimation bounds for localization

The localization problem is fundamentally important for sensor networks. We study the Cramer-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is anchored localization in which we know true positions of at least 3 nodes. 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, we derive a CRB-like bound 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.