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

TL;DR

This paper introduces a Fisher-information framework for optimal anchor placement in wireless localization within mixed LOS/NLOS environments, providing new criteria and algorithms for robust, region-wide target localization.

Contribution

It develops a unified model coupling anchor geometry with a physically grounded path-loss law, deriving optimality conditions and practical algorithms for multi-target anchor placement.

Findings

Optimal anchor placement coincides under A-, D-, and E-optimality in specific conditions.

Proposes mixed-integer second-order cone programs for robust, region-wide anchor placement.

Provides theoretical guarantees and practical algorithms for multi-target localization in complex environments.

Abstract

We develop a unified Fisher-information framework for localization in environments with both Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) paths, focusing on diffraction-dominated NLOS propagation characteristic of Outdoor-to-Indoor (O2I) signal propagation. The model couples anchor geometry with a physically grounded path-loss law that is continuous across the LOS/NLOS boundary and serves as an optimization objective for our optimal anchor placement problem. As the first step, we analyze single-target anchor placement and derive the classical A-, D-, and E-optimality criteria. Under a specific path-loss assumption, these criteria collapse to a polygon-closure condition in the complex plane: A-, D-, and E-optimal designs coincide, yielding necessary and sufficient conditions for optimal placement. Next, we extend the notion of optimal anchor placement with respect to a single target to optimality over a feasible region (multi-target setting) using a general formulation that explicitly includes a realistic path loss model. This is achieved by recasting the anchor placement as a combinatorial anchor-selection problem with provable guarantees. Next, we specify E- and D-optimal objectives over multiple targets in a predefined feasible target region and show that E-optimality straddles A-optimality (within a constant factor), while D-optimality provides looser bounds. These insights yield two practical algorithms, both mixed-integer second-order cone programs (MISOCP) with exact E-optimal and exact D-optimal objectives that produce robust, region-wide designs under mixed LOS/NLOS conditions.