On optimal anchor node placement in sensor localization by optimization of subspace principal angles

In sensor network self-localization, anchor nodes provide a convenient means to disambiguate scene translation and rotation, thereby affording estimates in an absolute coordinate system. However, localization performance depends on the positions of the anchor nodes relative to the unknown-location nodes. Conventional wisdom in the literature is that anchor nodes should be placed around the perimeter of the network. In this paper, we show analytically why this strategy works well universally. We demonstrate that perimeter placement forces the information provided by the anchor constraints to closely align with the subspace that cannot be estimated from inter-node measurements: the subspace of translations and rotations. Examples quantify the efficacy of perimeter placement of anchors.