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

• Published in: IEEE transactions on instrumentation and measurement Vol. 70; pp. 1 - 14
• Main Authors: Fontanelli, Daniele, Shamsfakhr, Farhad, Palopoli, Luigi
• Format: Journal Article
• Language: English
• Published: New York IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Cramer-Rao bounds; Cramer–Rao lower bound (CRLB); Distance measurement; estimation algorithms; indoor positioning; Lower bounds; mobile robot estimation; Mobile robots; Position measurement; ranging-based positioning; Ultra wideband technology; ultrawide band (UWB); Uncertainty; uncertainty analysis
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2021.3122521

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.