Coarse-to-Fine Partitioning Algorithm for Angle-of-Arrival Estimation in Visible Light Positioning Using Liquid Crystal Display

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Abstract
Coarse-to-fine partitioning (CFP) algorithm is proposed for angle-of-arrival (AoA) estimation with a controllable liquid crystal display (LCD) in front of a photodetector (PD). By electrically switching each pixel of the LCD in transparent or opaque, the position of the aperture through which the incident light passes is controlled to estimate the AoA of the incident light to the PD. The size of the aperture needs to be a certain size to maintain the accuracy of the AoA estimation, which consists of a region of several pixels. In the conventional algorithm, with a fixed size of the aperture equal to the size of resolution unit, the entire surface of the LCD was exhaustively searched horizontally and vertically. In our CFP algorithm, the entire surface is partitioned into two or three equal-area regions, and the intensities observed at the PD when pixels consisting of each of such regions are alternately switched to transparent mode are compared. Among them, the region with the highest intensity observed is chosen as the next candidate region through which the incident light passes. This process is iteratively applied, partitioning the candidate region from coarse to fine, until the region reaches the resolution size. For the LCD consisting of 2560 × 1440 pixels with the resolution unit size of 10 × 10 pixels, to estimate the AoA, our CFP algorithm requires 30 searches while the conventional algorithm requires 400 searches. Experimental results show that although intensity measurements are repeated fifteen times for each search to stabilize the intensity measurement values in both of the conventional algorithm and our CFP algorithm, our algorithm estimates it with the error less than one degree. Furthermore, by adding another PD into the system, from the AoA estimation for the two PDs with our CFP algorithm, the distance estimation to the light source from 200 mm to 900 mm is experimentally shown with a relative error of 4.5$\%$.
Funding Information
  • Grant-in-Aid for Scientific Research (JP22K04092)

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