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In this paper, we propose a novel probabilistic localization approach that relies on a Metropolis-Hastings (MH) algorithm-based Bayesian approach to visible light communication (VLC) systems. Due to the usage of the MH algorithm from Markov chain Monte Carlo methods, the positioning capability of the proposed approach becomes more robust against varying channel propagation conditions and measurement uncertainties. The validity of the proposed approach is demonstrated by numerical analyses based on simulations in 3-D indoor environments in a comparative manner with the least square (LS) and the differential LS algorithms-based localization solutions, while circumventing the shortcomings of LS-based approaches. Addressing the short range challenge in the VLC-based positioning system, an efficient hybrid localization framework is also developed for multi-tier heterogeneous networks (HetNets), jointly considering VLC and radio frequency networks. Our methodology mainly considers independent positioning solution branches that each estimate the target location by utilizing the MH-based Bayesian approach. Based on simulation results, the proposed framework for multi-tier HetNets provides a robust performance. Overall, we show that with the new VLC localization scheme, the performance in the short range is enhanced, while with HetNets the effectiveness of the localization in the long range is improved.

A Bayesian Perspective on RSS Based Localization for Visible Light Communication With Heterogeneous Networks Extension