Statistical Analysis of Geometric Algorithms in Vehicular Visible Light Positioning

TL;DR

This paper compares geometric algorithms for vehicular visible light positioning, analyzing their statistical performance under channel noise, and finds that bearing-based methods excel laterally while range-based methods are better longitudinally.

Contribution

Introduces two new geometric VLP algorithms, compares them with existing methods, and provides a theoretical performance analysis using Cramer-Rao bounds.

Findings

Bearing-based algorithms are more accurate laterally.

Range-based algorithms are more accurate longitudinally.

All algorithms' performance is bounded by derived Cramer-Rao limits.

Abstract

Vehicular visible light positioning (VLP) methods find relative locations of vehicles by estimating the positions of intensity-modulated head/tail lights of one vehicle (target) with respect to another (ego). Estimation is done in two steps: 1) relative bearing or range of the transmitter-receiver link is measured over the received signal on the ego side, and 2) target position is estimated based on those measurements using a geometric algorithm that expresses position coordinates in terms of the bearing-range parameters. The primary source of statistical error for these non-linear algorithms is the channel noise on the received signals that contaminates parameter measurements with varying levels of sensitivity. In this paper, we present two such geometric vehicular VLP algorithms that were previously unexplored, compare their performance with state-of-the-art algorithms over simulations, and analyze theoretical performance of all algorithms against statistical channel noise by deriving the respective Cramer-Rao lower bounds. The two newly explored algorithms do not outperform existing state-of-the-art, but we present them alongside the statistical analyses for the sake of completeness and to motivate further research in vehicular VLP. Our main finding is that direct bearing-based algorithms provide higher accuracy against noise for estimating lateral position coordinates, and range-based algorithms provide higher accuracy in the longitudinal axis due to the non-linearity of the respective geometric algorithms.