3-D Localization With Coplanar Anchors

The performance of 3-dimensional (3-D) localization is significantly degraded when anchors are placed near the same plane. It can be interpreted as a large noise sensitivity or inversion of a singular matrix. This letter presents an alternative algebraic multilateration algorithm using a virtual anchor, which removes the necessity of an inversion of the singular matrix. Through the mathematical analysis, we reveal that the convergence of this algorithm relies on sensor geometries. The proposed algorithm is validated via simulation and field experiments, which shows that this method could achieve reliable results by having proper sensor geometries.