Towards Optimal Beacon Placement for Range-Aided Localization

TL;DR

This paper introduces an information theoretic method for optimally placing a limited number of beacons to minimize localization error, using a submodular optimization approach with provable guarantees.

Contribution

It formulates beacon placement as a submodular optimization problem based on MAP estimation, providing a flexible, rigorous, and efficient solution with theoretical guarantees.

Findings

The method outperforms benchmarks in simulated scenarios.

The approach guarantees near-optimal solutions via greedy algorithms.

Open source implementation is provided for reproducibility.

Abstract

Range-based localization is ubiquitous: global navigation satellite systems (GNSS) power mobile phone-based navigation, and autonomous mobile robots can use range measurements from a variety of modalities including sonar, radar, and even WiFi signals. Many of these localization systems rely on fixed anchors or beacons with known positions acting as transmitters or receivers. In this work, we answer a fundamental question: given a set of positions we would like to localize, how should beacons be placed so as to minimize localization error? Specifically, we present an information theoretic method for optimally selecting an arrangement consisting of a few beacons from a large set of candidate positions. By formulating localization as maximum a posteriori (MAP) estimation, we can cast beacon arrangement as a submodular set function maximization problem. This approach is probabilistically rigorous, simple to implement, and extremely flexible. Furthermore, we prove that the submodular structure of our problem formulation ensures that a greedy algorithm for beacon arrangement has suboptimality guarantees. We compare our method with a number of benchmarks on simulated data and release an open source Python implementation of our algorithm and experiments.