ToA-Based Localization of Far-Away Targets: Equi-DOP Surfaces, Asymptotic Bounds, and Dimension Adaptation
Raghunandan M. Rao, Aditya V. Padaki, Boon Loong Ng, Yi Yang, M. S. Kang, Vuk Marojevic
Abstract
This paper studies the Dilution of Precision (DOP) in the Time-of-arrival (ToA)-based localization of targets outside the anchors’ convex hull. In the far-away target regime, we derive a closed-form expression of the DOP that reveals a linear asymptotic scaling law. We characterize the asymptotic DOP bounds, and equi-DOP surfaces/contours in 3D/2D localization scenarios, which quantifies the reliability of location estimates on the target's trajectory. Motivated by vehicular applications, we propose a range-aided dimension adaptation scheme. Here the localization dimension is adapted in real-time using a single range measurement such that the maximum/root-mean-square (rms) DOP does not exceed a threshold. Since high-accuracy localization of far-away targets is infeasible due to linear DOP scaling with distance, this scheme prioritizes high-dimensional tracking of nearby targets while monitoring far-away targets with range-only measurements.