A Tractable Analysis of the Improvement in Unique Localizability Through Collaboration

TL;DR

This paper mathematically analyzes how collaboration among devices significantly improves their ability to uniquely localize themselves, especially in cellular networks, by deriving probabilistic conditions using stochastic geometry.

Contribution

It provides the first analytical expressions quantifying the localization improvement due to device collaboration under various shadowing and frequency reuse scenarios.

Findings

Collaboration drastically increases the probability of unique localizability.

Short-distance device collaboration yields significant localization improvements.

Analytic expressions are derived for different shadowing and frequency reuse scenarios.

Abstract

In this paper, we mathematically characterize the improvement in device localizability achieved by allowing collaboration among devices. Depending on the detection sensitivity of the receivers in the devices, it is not unusual for a device to be localized to lack a sufficient number of detectable positioning signals from localized devices to determine its location without ambiguity (i.e., to be uniquely localizable). This occurrence is well-known to be a limiting factor in localization performance, especially in communications systems. In cellular positioning, for example, cellular network designers call this the hearability problem. We study the conditions required for unique localizability and use tools from stochastic geometry to derive accurate analytic expressions for the probabilities of meeting these conditions in the noncollaborative and collaborative cases. We consider the scenario without shadowing, the scenario with shadowing and universal frequency reuse, and, finally, the shadowing scenario with random frequency reuse. The results from the latter scenario, which apply particularly to cellular networks, reveal that collaboration between two devices separated by only a short distance yields drastic improvements in both devices' abilities to uniquely determine their positions. The results from this analysis are very promising and motivate delving further into techniques which enhance cellular positioning with small-scale collaborative ranging observations among nearby devices.