Cooperative Localization in Visible Light Networks: Theoretical Limits and Distributed Algorithms

TL;DR

This paper develops a theoretical framework and distributed algorithms for cooperative localization in visible light networks, enhancing indoor positioning accuracy by leveraging multiple LED transmitters and VLC units.

Contribution

It introduces a set-theoretic approach to cooperative localization, deriving bounds, formulating a quasiconvex feasibility problem, and proposing distributed algorithms with convergence guarantees.

Findings

Cooperative localization improves positioning accuracy.

Algorithms converge to true locations in various scenarios.

Numerical results validate the effectiveness of the proposed methods.

Abstract

Light emitting diode (LED) based visible light positioning (VLP) networks can provide accurate location information in indoor environments. In this manuscript, we propose to employ cooperative localization for visible light networks by designing a VLP system configuration that involves multiple LED transmitters with known locations (e.g., on the ceiling) and visible light communication (VLC) units equipped with both LEDs and photodetectors (PDs) for the purpose of cooperation. First, we derive the Cram\'er-Rao lower bound (CRLB) and the maximum likelihood estimator (MLE) for the localization of VLC units in the proposed cooperative scenario. To tackle the nonconvex structure of the MLE, we adopt a set-theoretic approach by formulating the problem of cooperative localization as a quasiconvex feasibility problem, where the aim is to find a point inside the intersection of convex constraint sets constructed as the sublevel sets of quasiconvex functions resulting from the Lambertian formula. Next, we devise two feasibility-seeking algorithms based on iterative gradient projections to solve the feasibility problem. Both algorithms are amenable to distributed implementation, thereby avoiding high-complexity centralized approaches. Capitalizing on the concept of quasi-Fej\'er convergent sequences, we carry out a formal convergence analysis to prove that the proposed algorithms converge to a solution of the feasibility problem in the consistent case. Numerical examples illustrate the improvements in localization performance achieved via cooperation among VLC units and evidence the convergence of the proposed algorithms to true VLC unit locations in both the consistent and inconsistent cases.