A Reversed Visible Light Multitarget Localization System via Sparse Matrix Reconstruction

Abstract

A reversed indoor multitarget localization system employing compressive sensing (CS) theory is proposed for the first time in terms of visible light positioning (VLP). Unlike conventional VLP systems, where targets process the received light signals to localize themselves, our system works reversely by using multiple photodiodes (PDs) mounted on the ceiling to localize mobile targets that carry light emitting diodes. By utilizing its nature of sparsity, the problem of multitarget localization is formulated as a problem of sparse matrix reconstruction, and a 3-step workflow is developed to solve the problem. In this workflow, first, a sensing matrix is redesigned by using QR decomposition to enable CS theory. Next, the conventional l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization (l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> M) algorithm which is highly vulnerable to noise in solving a localization problem is theoretically analyzed and subsequently improved by adopting a reweighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> M approach. Finally, a subgrid localization algorithm is proposed to overcome a common unpractical assumption of on-grid locations, tackle the false peak problem in sparse matrix reconstruction, and ultimately improve the localization precision. The feasibility of our system and supporting algorithms is verified through extensive simulations. Our system demonstrates a good positioning accuracy of 7.4 cm by using 25 PDs when SNR = 20 dB. We also investigate the impact of various factors on the positioning performance, and the obtained results provide an insightful reference paving the way to a practical system design.