Abstract

This paper discusses the time-of-arrival (TOA) based indoor visible light communication (VLC) positioning system in a non-line-of-sight environment. The propagation delay is assumed to be gamma distributed. The generalized Cramer–Rao lower bound for multipath propagation is derived as the theoretical accuracy limitation. The performance of the positioning system is affected by the shape parameter and the scale parameter of gamma distribution. The influences on positioning accuracy of multipath effects are analyzed through discussing the physical meaning of the gamma distribution parameters. It is concluded that the lower bound of positioning accuracy is attained when variance of the non-line-of-sight propagation-induced path lengths is zero. The simulation result proves that the theoretical positioning accuracy is in the order of centimeters with the given scenario.

© 2015 Chinese Laser Press

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References

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  1. R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.
  2. M. Nakajima and S. Haruyama, “Indoor navigation system for visually impaired people using visible light communication and compensated geomagnetic sensing,” in 1st IEEE International Conference on Communications in China (ICCC) (2012), Vols. 524–529, pp. 15–17.
  3. X. Zhang, J. Duan, Y. Fu, and A. Shi, “Theoretical accuracy analysis of indoor visible light communication positioning system based on received signal strength indicator,” J. Lightwave Technol. 32, 3578–3584 (2014).
  4. T. Q. Wang, Y. A. Sekercioglu, and A. Neild, “Position accuracy of time-of-arrival based ranging using visible light with application in indoor localization systems,” J. Lightwave Technol. 31, 3302–3308 (2013).
    [Crossref]
  5. Y. Qi, “Wireless geolocation in a non-line-of-sight environment,” Ph.D. dissertation (Princeton University, 2003).
  6. J. B. Carruthers and S. M. Carroll, “Statistical impulse response models for indoor optical wireless channels,” Int. J. Commun. Syst. 18, 267–284 (2005).
    [Crossref]
  7. L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
    [Crossref]
  8. J. Grubor, S. Randel, K. D. Langer, and J. W. Waleski, “Broadband information broadcasting using LED-based interior lighting,” J. Lightwave Technol. 26, 3883–3892 (2008).
    [Crossref]
  9. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
    [Crossref]
  10. Q. Jeffery, F. Greg, B. Patrick, and E. Eric, “Quantifying the indoor light environment-testing for light stability in retail & residential environments,” in International Conference on Digital Printing Technologies NIP & Digital Fabrication Conference (2004), pp. 689–698.

2014 (1)

2013 (1)

2009 (1)

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

2008 (1)

2005 (1)

J. B. Carruthers and S. M. Carroll, “Statistical impulse response models for indoor optical wireless channels,” Int. J. Commun. Syst. 18, 267–284 (2005).
[Crossref]

2004 (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

Campbell, K. C.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Carroll, S. M.

J. B. Carruthers and S. M. Carroll, “Statistical impulse response models for indoor optical wireless channels,” Int. J. Commun. Syst. 18, 267–284 (2005).
[Crossref]

Carruthers, J. B.

J. B. Carruthers and S. M. Carroll, “Statistical impulse response models for indoor optical wireless channels,” Int. J. Commun. Syst. 18, 267–284 (2005).
[Crossref]

Duan, J.

Eric, E.

Q. Jeffery, F. Greg, B. Patrick, and E. Eric, “Quantifying the indoor light environment-testing for light stability in retail & residential environments,” in International Conference on Digital Printing Technologies NIP & Digital Fabrication Conference (2004), pp. 689–698.

Faulkner, G. E.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Fu, Y.

Greg, F.

Q. Jeffery, F. Greg, B. Patrick, and E. Eric, “Quantifying the indoor light environment-testing for light stability in retail & residential environments,” in International Conference on Digital Printing Technologies NIP & Digital Fabrication Conference (2004), pp. 689–698.

Grubor, J.

Haruyama, S.

M. Nakajima and S. Haruyama, “Indoor navigation system for visually impaired people using visible light communication and compensated geomagnetic sensing,” in 1st IEEE International Conference on Communications in China (ICCC) (2012), Vols. 524–529, pp. 15–17.

Honda, Y.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Jeffery, Q.

Q. Jeffery, F. Greg, B. Patrick, and E. Eric, “Quantifying the indoor light environment-testing for light stability in retail & residential environments,” in International Conference on Digital Printing Technologies NIP & Digital Fabrication Conference (2004), pp. 689–698.

Jung, D.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Kawano, H.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Kitano, Y.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Komine, T.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

Langer, K. D.

Lee, K.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Matsukawa, Y.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Minh, H. L.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Murai, R.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Nakagawa, M.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

Nakajima, M.

M. Nakajima and S. Haruyama, “Indoor navigation system for visually impaired people using visible light communication and compensated geomagnetic sensing,” in 1st IEEE International Conference on Communications in China (ICCC) (2012), Vols. 524–529, pp. 15–17.

Neild, A.

O’Brien, D. C.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Oh, Y.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Patrick, B.

Q. Jeffery, F. Greg, B. Patrick, and E. Eric, “Quantifying the indoor light environment-testing for light stability in retail & residential environments,” in International Conference on Digital Printing Technologies NIP & Digital Fabrication Conference (2004), pp. 689–698.

Qi, Y.

Y. Qi, “Wireless geolocation in a non-line-of-sight environment,” Ph.D. dissertation (Princeton University, 2003).

Randel, S.

Sakai, T.

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

Sekercioglu, Y. A.

Shi, A.

Waleski, J. W.

Wang, T. Q.

Won, E. T.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Zeng, L.

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

Zhang, X.

IEEE J. Sel. Areas Commun. (1)

L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27, 1654–1662 (2009).
[Crossref]

IEEE Trans. Consum. Electron. (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

Int. J. Commun. Syst. (1)

J. B. Carruthers and S. M. Carroll, “Statistical impulse response models for indoor optical wireless channels,” Int. J. Commun. Syst. 18, 267–284 (2005).
[Crossref]

J. Lightwave Technol. (3)

Other (4)

Q. Jeffery, F. Greg, B. Patrick, and E. Eric, “Quantifying the indoor light environment-testing for light stability in retail & residential environments,” in International Conference on Digital Printing Technologies NIP & Digital Fabrication Conference (2004), pp. 689–698.

Y. Qi, “Wireless geolocation in a non-line-of-sight environment,” Ph.D. dissertation (Princeton University, 2003).

R. Murai, T. Sakai, H. Kawano, Y. Matsukawa, Y. Kitano, Y. Honda, and K. C. Campbell, “A novel visible light communication system for enhanced control of autonomous delivery robots in a hospital,” in IEEE/SICE International Symposium on System Integration (SII) (2012), Vols. 510–516, pp. 16–18.

M. Nakajima and S. Haruyama, “Indoor navigation system for visually impaired people using visible light communication and compensated geomagnetic sensing,” in 1st IEEE International Conference on Communications in China (ICCC) (2012), Vols. 524–529, pp. 15–17.

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Figures (3)

Fig. 1.
Fig. 1. Experimental data and gamma fitting of RMS delay spread in rooms with different sizes.
Fig. 2.
Fig. 2. G-CRLB versus the emitted optical power with different values of a and b .
Fig. 3.
Fig. 3. G-CRLB versus the background spectral irradiance with different values of a and b .

Equations (26)

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r ( t ) = α · R · x ( t τ ) + n ( t ) ,
α = m + 1 2 π · h m + 1 d m + 3 · S ,
x ( t ) = A · ( 1 + cos ( 2 π f t ) ) · ( 1 + cos ( 2 π t / T TOA ) ) 0 t T TOA ,
θ = ( l 1 , l 2 , , l M ) T .
τ z ^ = τ z + ξ , for z Z .
τ z = 1 c · ( ( x z x ) 2 + ( y z y ) 2 + l z ) , for z Z ,
f ( τ z ^ | θ ) z = 1 Z exp { 1 2 σ z 2 ( τ z ^ τ z ) 2 } .
E [ ( θ ^ θ ) · ( θ ^ θ ) T ] J 1 1 ,
J 1 = E [ ( θ ln f ( τ z ^ | θ ) ) · ( θ ln f ( τ z ^ | θ ) ) T ] = E [ θ τ z · ( τ z ln f ( τ z ^ | θ ) ) · ( τ z ln f ( τ z ^ | θ ) ) T · ( θ τ z ) T ] = H · J τ z · H T .
H = 1 c ( 1 0 0 1 0 ) M × Z .
J τ z = 4 π 2 β 2 α 2 R 2 E ( 1 σ 1 2 0 0 1 σ Z 2 ) Z × Z .
J 1 = 4 π 2 · f 2 · R 2 · E · α 2 3 c 2 ( 1 N 01 0 0 1 N 0 M ) M × M = f 2 · R 2 · E · ( m + 1 ) 2 · h 2 ( m + 1 ) · S 2 3 · N 0 i · c 2 · d i 2 ( m + 3 ) i { 1 , , M } ,
J 1 1 3 N 0 i · c · d i ( m + 3 ) f · R · E · ( m + 1 ) · h ( m + 1 ) · S ,
β 2 1 3 f 2 .
G ( l | a , b ) = a b Γ ( b ) exp ( a · l ) · l b 1 , l θ ,
E [ ( θ ^ θ ) · ( θ ^ θ ) T ] J 2 1 ,
J 2 = J D + J P .
J D = J 1 , J P = E [ ( θ ln p θ ( θ ) ) · ( θ ln p θ ( θ ) ) T ] = E [ l log G ( l | a , b ) ] 2 = a 2 + a b · ( b 1 ) 2 Γ ( b ) 0 exp ( a l ) · l b 3 d l + 2 a b + 1 · ( b 1 ) Γ ( b ) 0 exp ( a l ) · l b 2 d l .
J P = E [ l log G ( l | a , b ) ] 2 = a 2 .
J P = E [ l log G ( l | a , b ) ] 2 .
J P = E [ l log G ( l | a , b ) ] 2 = a 2 b 2 ( 4 b 7 ) .
J P = ( a 1 2 b 1 2 ( 4 b 1 7 ) 0 0 a M 2 b M 2 ( 4 b M 7 ) ) .
J 2 = J 1 + J P = f 2 · R 2 · E · ( m + 1 ) 2 · h 2 ( m + 1 ) · S 2 3 · N 0 i · c 2 · d i 2 ( m + 3 ) + a i 2 b i 2 ( 4 b i 7 ) i { 1 , , M } .
J 2 1 1 f 2 · R 2 · E · ( m + 1 ) 2 · h 2 ( m + 1 ) · S 2 3 · N 0 i · c 2 · d i 2 ( m + 3 ) + a i 2 b i 2 ( 4 b i 7 ) i { 1 , , M } .
1 f 2 · R 2 · E · ( m + 1 ) 2 · h 2 ( m + 1 ) · S 2 3 · N 0 i · c 2 · d i 2 ( m + 3 ) + a i 2 b i 2 ( 4 b i 7 ) J 1 3 N 0 i · c · d i ( m + 3 ) f · R · E · ( m + 1 ) · h ( m + 1 ) · S .
N 0 = 2 · q · R · p · S · Δ λ ,

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