Lower bounds for Arrangement-based Range-Free Localization in Sensor Networks

TL;DR

This paper establishes tight bounds on the minimum number of location-aware entities needed for arrangement-based, range-free localization in sensor networks, improving understanding of localization efficiency without distance estimation.

Contribution

It provides the first tight upper and lower bounds on the size of arrangement-based colanders for localization, including expected sizes for uniform distributions.

Findings

Derived tight bounds on colander size for localization accuracy

Analyzed expected colander size in uniform distributions

Enhanced understanding of range-free localization limits

Abstract

Colander are location aware entities that collaborate to determine approximate location of mobile or static objects when beacons from an object are received by all colanders that are within its distance $R$. This model, referred to as arrangement-based localization, does not require distance estimation between entities, which has been shown to be highly erroneous in practice. Colander are applicable in localization in sensor networks and tracking of mobile objects. A set $S \subset {\mathbb R}^2$ is an $(R,\epsilon)$-colander if by placing receivers at the points of $S$, a wireless device with transmission radius $R$ can be localized to within a circle of radius $\epsilon$. We present tight upper and lower bounds on the size of $(R,\epsilon)$-colanders. We measure the expected size of colanders that will form $(R, \epsilon)$-colanders if they distributed uniformly over the plane.