Distance and Position Estimation in Visible Light Systems with RGB LEDs

TL;DR

This paper investigates the theoretical limits and practical estimators for distance and position estimation in visible light positioning systems using RGB LEDs, analyzing different scenarios of channel knowledge.

Contribution

It derives CRLB bounds and ML estimators for various scenarios, highlighting the advantages of RGB LEDs in VLP accuracy.

Findings

CRLB bounds quantify estimation accuracy limits.

ML estimators approach CRLB performance at high power.

RGB LEDs improve positioning accuracy.

Abstract

In this manuscript, distance and position estimation problems are investigated for visible light positioning (VLP) systems with red-green-blue (RGB) light emitting diodes (LEDs). The accuracy limits on distance and position estimation are calculated in terms of the Cramer-Rao lower bound (CRLB) for three different scenarios. Scenario~1 and Scenario~2 correspond to synchronous and asynchronous systems, respectively, with known channel attenuation formulas at the receiver. In Scenario~3, a synchronous system is considered but channel attenuation formulas are not known at the receiver. The derived CRLB expressions reveal the relations among distance/position estimation accuracies in the considered scenarios and lead to intuitive explanations for the benefits of using RGB LEDs. In addition, maximum likelihood (ML) estimators are derived in all scenarios, and it is shown that they can achieve close performance to the CRLBs in some cases for sufficiently high source optical powers.