Optimal Anchor Placement for Wireless Localization in Mixed LOS and NLOS Scenarios

Abstract

This paper develops a general optimal experimental design framework for anchor placement in localization and related estimation problems whose Fisher information matrix (FIM) can be expressed as a weighted sum of rank-one matrices. Within this framework, anchor locations are selected to optimize Cramér--Rao lower bound (CRLB)-based performance measures, while accounting jointly for measurement geometry and information strength. As a challenging motivating application, we consider localization in diffraction-dominated non-line-of-sight (NLOS) outdoor-to-indoor (O2I) environments, where the direct path is severely attenuated or blocked. Although diffraction-based time-of-arrival (TOA) measurements can provide useful positioning information, optimal anchor placement is less intuitive than in conventional line-of-sight (LOS) settings because both the measurement directions and their information strengths depend on the propagation environment. The proposed $S_n,r_n$ -based FIM representation compactly captures this interaction between geometry and signal strength. For a single target, it yields a polygon-closure interpretation and characterizes the conditions under which A-, D-, and E-optimal anchor geometries coincide. We then extend the framework to region-wide anchor placement by constructing a precomputed anchor--target dictionary and formulating min--max E- and D-optimal anchor-selection problems as mixed-integer second-order cone programs. Numerical results demonstrate the resulting anchor layouts, localization bounds, and computational tradeoffs in a mixed-LOS/NLOS O2I environment. While the analysis is instantiated and evaluated for diffraction-based O2I localization, its underlying results apply broadly to estimation and anchor-placement problems with weighted rank-one-sum FIMs.

Accepted at Transactions of Signal Processing pending final submission