Efficient Beacon Placement Algorithms for Time-of-Flight Indoor Localization

Abstract

Beacon-based time-of-flight indoor localization systems have shown great promise for applications ranging from indoor navigation to asset tracking. In large-scale deployments, a major practical challenge is determining the placement of a minimal number of beacons that ensures full coverage -- each point in the domain has line-of-sight paths to enough beacons to uniquely localize itself. Three beacons with line-of-sight paths are always enough, but two beacons within line of sight may also work, given a favorable geometry. In this paper, we propose two beacon placement algorithms that leverage the floor plan geometry with provable theoretical guarantees. First, we present a greedy algorithm using properties of sub-modular functions to place O(OPT · ln m) beacons, where m is the number of discrete location points in the region that need to be localized, and OPT is the size of the optimal solution. Second, we present a random sampling algorithm that places O (OPT · log(OPT)) beacons while localizing all targets. We evaluate our algorithms on both real-world and randomly generated floor plans. Our algorithms place on an average 6 ~ 23% and 12% fewer beacons in real-world topologies and randomly generated floor plans respectively, as compared to prior work. We also present a study where we ask users to attempt to place nodes manually and discover that even humans that are well versed on the coverage problem find it hard to balance the trade-off between the number of beacons and area localized.