• Laser & Optoelectronics Progress
  • Vol. 60, Issue 15, 1506003 (2023)
Jin Chen1, Shiwu Xu1,2,*, Fen Wei2, and Longteng Zhang3
Author Affiliations
  • 1Concord University College, Fujian Normal University, Fuzhou 350117, Fujian, China
  • 2Key Laboratory of Opto-Electronic Science and Technology for Medicine, Ministry of Education, Fujian Normal University, Fuzhou 350007, Fujian, China
  • 3School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, Fujian, China
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    DOI: 10.3788/LOP222011 Cite this Article Set citation alerts
    Jin Chen, Shiwu Xu, Fen Wei, Longteng Zhang. Design and Performance Analysis of Positioning and Orientating System for Visible Light Communication[J]. Laser & Optoelectronics Progress, 2023, 60(15): 1506003 Copy Citation Text show less

    Abstract

    A three-dimensional (3D) positioning and orientating method based on an adaptive parameter and adaptive mutation particle swarm optimization is proposed in this study to solve the 3D positioning and orientating problem in visible light communication. First, a hybrid 3D visible light positioning (VLP) model based on a ranging model in a complex environment is analyzed, and the positioning problem is transformed into an optimization problem of the joint probability density function. Second, an adaptive parameter and adaptive mutation particle swarm optimization method are designed by calculating the fuzzy closeness between the solution of the particle and the optimal solution of the population. Finally, the theoretical lower bound of the positioning and orientating error of the proposed 3D VLP model, called the Cramer-Rao lower bound (CRLB), is accurately analyzed using mathematical methods. The results show that the time complexity of the proposed algorithm is low, and the positioning and orientating errors are close to the CRLB. The average positioning and average orientating convergence errors of the proposed algorithm are 5.99 cm and 6.65°, respectively, which are significantly better than those of four other iterative-based VLP algorithms.
    hix,u=Arr+1Tsg2πdi2cosθircosϕi
    θi=arccosx-piTυix-pi2υi2
    ϕi=arccos-x-piTux-pi2u2
    ψi=Pthix,u=Cr+1x-piTυirx-piTux-pi2r+3υi2ru2
    ψi,LOS=ψi+ni
    Pi,LOS=12πσLOS2exp-ψi,LOS-ψi22σLOS2
    ψi,NLOS=ψi+ni+εi
    Pi,NLOS=12πσLOS2+σNLOS2·exp-ψi,NLOS-ψi-u22σLOS2+σNLOS2
    zi=ψi+ξiNψi+biu,σ2
    Pi=12πσexp-zi-ψi-biu22σ2
    Lα;z=i=1MPi=12πMσ-M·exp-i=1Mzi-ψi-biu22σ2
    α=argαmaxLα;z,s.t.0bi1
    vjt+1=wvjt+c1R1βjLBt-βjt+c2R2βGBt-βjt
    βjt+1=βjt+vjt+1
    βjt=βj1t,βj2t,βj3t,βj4t,βj5t,βj6tT
    djGBt=12βGB1:3tβj1:3tβGB1:3tβj1:3t+βGB4:6tβj4:6tβGB4:6tβj4:6t,jGB
    wjt=wmin,       if  j = GBdjGBtwmax-wmin1-tTmax+wmin, else
    c1jt=djGBtcmax-cmin1-tTmax+cmin
    c2jt=cmax-djGBtcmax-cmin1-tTmax
    vjt+1=wjtvjt+c1jtR1βjLBt-βjt+c2jtR2βGBt-βjt
    σ2=1NP-1j=1NPdjGBt-Smeant2,jGB
    Smeant=1NP-1j=1NPdjGBt,jGB
    δjkt=exp(-σ2)djGBt1-tTmax,jGB
    if          R3t<δjktthen   βjkt=R4tβkmax-βkmin+βkmin
    lnLα;z=-M2ln2π-Mlnσ-i=1Mzi-ψi-biu22σ2
    lnLα;zαm=-12σ2i=1M2zi-ψi-biu-ψiαm=1σ2i=1Mzi-ψi-biuψiαm
    2lnLα;zαmαn=1σ2·i=1M-ψiαmψiαn+zi-ψi-biu2ψiαmαn
    E2lnLα;zαmαn=-1σ2i=1Mψiαmψiαn
    xψi=ψix1,ψix2,ψix3T, uψi=ψiu1,ψiu2,ψiu3T
    Iα=-E2lnLα;zαmαn6×6=1σ2i=1Mψiαmψiαn6×6=1σ2i=1MxψixψiTxψiuψiTuψixψiTuψiuψiT
    xψi=Cr+1υi2ru2xx-piTυirx-piTux-pi2r+3=Cr+1υi2ru2×rx-piTυir-1x-piTuυix-pi2r+3+x-piTυirux-pi2r+3-r+3x-piTυirx-piTux-pix-pi2r+5
    uψi=Cr+1x-piTυirυi2rx-pi2r+3ux-piTuu2=Cr+1x-piTυirυi2rx-pi2r+3u22I3×3-uuTu23x-pi
    Eα˜-α22traceIα-1
    Jin Chen, Shiwu Xu, Fen Wei, Longteng Zhang. Design and Performance Analysis of Positioning and Orientating System for Visible Light Communication[J]. Laser & Optoelectronics Progress, 2023, 60(15): 1506003
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