Cramer–Rao Lower Bound Attainment in Range-Only Positioning Using Geometry: The G-WLS
Daniele Fontanelli, Farhad Shamsfakhr, Luigi Palopoli
Abstract
The positioning problem addressed in this paper amounts to finding the planar coordinates of a device from a collection of ranging measurements taken from other devices located at known positions. The solution based on Weighted Least Square is popular, but its accuracy depends from a number of factors only partially known. In this paper, we explore the dependency of the uncertainty from the geometric configuration of the anchors. We show a refinement technique for the estimate produced by the WLS that compensates for the effects of geometry on the WLS and reduces the target uncertainty to a value very close to the Cramer Rao Lower Bound. The resulting algorithm is called Geometric WLS (G-WLS) and its application is particularly important in the most critical conditions for WLS (i.e., when the target is far apart from the anchors). The effectiveness of the G-WLS is proved theoretically and is demonstrated on a large number of experiments and simulations.