Cramér-Rao-Type Bounds for Localization

1 The localization problem is fundamentally important for sensor networks. This paper 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 3 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.