Frame Theory and Optimal Anchor Geometries in Wireless Localization

We revisit the problem of describing optimal anchor geometries that result in the minimum achievable MSE by employing the Cramer Rao Lower bound. Our main contribution is to show that this problem can be cast onto the whelm of modern Frame Theory, which not only provides new insights, but also allows the straightforward generalization of various classical results on the anchor placement problem. For example, by employing the frame potential for single-target localization we see that the directions of the anchors, as seen from the target, should optimally be as orthogonal as possible and that the existence of an optimal geometry for an arbitrary number of anchors is governed by a fundamental inequality. Furthermore, the frame-theoretic approach allows for simple derivation of some properties on optimal anchor placement that prove to be useful in a tractable approach for the more complex, multi-target anchor placement problem. In a more general sense, the paper builds a refreshing bridge between the classical problem of wireless localization and the powerful domain of Frame Theory, with far-reaching potential.