Cramer-Rao Lower Bound Attainment in Range-Only Positioning Using Geometry: The G-WLS

The positioning problem addressed in this article 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 (WLS) is popular, but its accuracy depends from a number of factors only partially known. In this article, 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 proven theoretically and is demonstrated on a large number of experiments and simulations.

Automated summary

This article addresses the positioning problem using weighted least square (WLS) method, examining the impact of geometric configuration of anchors on the uncertainty and introducing a refinement technique (G-WLS) to improve accuracy. The effectiveness of G-WLS is proven theoretically and demonstrated through experiments and simulations.