Fast computation of Cramer-Rao Bounds for TOA – An application to network-based positioning simulations

Abstract

As part of a larger scope work that studies network-based positioning, that employs timing measures, this article proposes a methodology to add Cramer-Rao Bounds (CRBs) information to the propagation model. Moreover, it enables a very quick computation of CRBs for timing, avoiding the growing computational effort resulting from Fisher’s matrix formulation and its inversion for each required position at the simulation stage, assuring at the same time the reliability of the required data in the study of positioning using space-time diversity. This methodology considers the variability of the propagation conditions in terms of delay spread (DS) and Signal-to-Noise ratio (SNR) in a realistic scenario. It also coordinates the operation of concurrent models within simulation, and finally performs bi-exponential regression and interpolation procedures on pertinent operational regions for CRBs. Properly validated models provide simple closed expressions that ease the operational region discrimination and its integration to the positioning simulation platform.