Abstract

We propose and experimentally demonstrate a practical visible light position (VLP) system using repeated unit cells and machine learning (ML) algorithms. ML is employed to increase the positioning accuracy. Algorithms of the 2nd-order regression ML model and the polynomial trilateral ML model are discussed. More than 80% of the measurement data have position error within 4 cm when using the 2nd-order regression ML model, while the position error is within 5 cm when using the polynomial trilateral ML model.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. H. Haas, “Visible light communication,” Proc. OFC, 1–72 (2015).
  2. C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).
  3. Z. Wang, C. Yu, W. D. Zhong, J. Chen, and W. Chen, “Performance of a novel LED lamp arrangement to reduce SNR fluctuation for multi-user visible light communication systems,” Opt. Express 20(4), 4564–4573 (2012).
    [Crossref] [PubMed]
  4. H. H. Lu, Y. P. Lin, P. Y. Wu, C. Y. Chen, M. C. Chen, and T. W. Jhang, “A multiple-input-multiple-output visible light communication system based on VCSELs and spatial light modulators,” Opt. Express 22(3), 3468–3474 (2014).
    [Crossref] [PubMed]
  5. B. Janjua, H. M. Oubei, J. R. D. Retamal, T. K. Ng, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, H.-C. Kuo, G.-R. Lin, J.-H. He, and B. S. Ooi, “Going beyond 4 Gbps data rate by employing RGB laser diodes for visible light communication,” Opt. Express 23(14), 18746–18753 (2015).
    [Crossref] [PubMed]
  6. C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
    [Crossref]
  7. Y. F. Liu, Y. C. Chang, C. W. Chow, and C. H. Yeh, “Equalization and pre-distorted schemes for increasing data rate in in-door visible light communication system,” Proc. OFC 2011, paper JWA083.
    [Crossref]
  8. C. H. Yeh, H. Y. Chen, C. W. Chow, and Y. L. Liu, “Utilization of multi-band OFDM modulation to increase traffic rate of phosphor-LED wireless VLC,” Opt. Express 23(2), 1133–1138 (2015).
    [Crossref] [PubMed]
  9. K. Liang, C. W. Chow, and Y. Liu, “RGB visible light communication using mobile-phone camera and multi-input multi-output,” Opt. Express 24(9), 9383–9388 (2016).
    [Crossref] [PubMed]
  10. C. W. Chow, R. J. Shiu, Y. C. Liu, X. L. Liao, K. H. Lin, Y. C. Wang, and Y. Y. Chen, “Using advertisement light-panel and CMOS image sensor with frequency-shift-keying for visible light communication,” Opt. Express 26(10), 12530–12535 (2018).
    [Crossref] [PubMed]
  11. S. Wu, H. Wang, and C. H. Youn, “Visible light communications for 5G wireless networking systems: from fixed to mobile communications,” IEEE Netw. 28(6), 41–45 (2014).
    [Crossref]
  12. R. Faragher and R. Harle, “An analysis of the accuracy of Bluetooth low energy for indoor positioning applications,” Proc. ION GNSS+ 2014, 201–210.
  13. J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51(12), 68–73 (2013).
    [Crossref]
  14. M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor positioning system using visible light and accelerometer,” J. Lightwave Technol. 32(19), 3306–3316 (2014).
    [Crossref]
  15. H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
    [Crossref]
  16. C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
    [Crossref]
  17. C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
    [Crossref]
  18. Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
    [Crossref]
  19. C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2006).

2018 (1)

2016 (2)

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

K. Liang, C. W. Chow, and Y. Liu, “RGB visible light communication using mobile-phone camera and multi-input multi-output,” Opt. Express 24(9), 9383–9388 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (4)

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

H. H. Lu, Y. P. Lin, P. Y. Wu, C. Y. Chen, M. C. Chen, and T. W. Jhang, “A multiple-input-multiple-output visible light communication system based on VCSELs and spatial light modulators,” Opt. Express 22(3), 3468–3474 (2014).
[Crossref] [PubMed]

S. Wu, H. Wang, and C. H. Youn, “Visible light communications for 5G wireless networking systems: from fixed to mobile communications,” IEEE Netw. 28(6), 41–45 (2014).
[Crossref]

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor positioning system using visible light and accelerometer,” J. Lightwave Technol. 32(19), 3306–3316 (2014).
[Crossref]

2013 (2)

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51(12), 68–73 (2013).
[Crossref]

2012 (2)

C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).

Z. Wang, C. Yu, W. D. Zhong, J. Chen, and W. Chen, “Performance of a novel LED lamp arrangement to reduce SNR fluctuation for multi-user visible light communication systems,” Opt. Express 20(4), 4564–4573 (2012).
[Crossref] [PubMed]

Armstrong, J.

J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51(12), 68–73 (2013).
[Crossref]

Chang, C. H.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Chang, G. K.

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

Chen, C. Y.

Chen, H. Y.

C. H. Yeh, H. Y. Chen, C. W. Chow, and Y. L. Liu, “Utilization of multi-band OFDM modulation to increase traffic rate of phosphor-LED wireless VLC,” Opt. Express 23(2), 1133–1138 (2015).
[Crossref] [PubMed]

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

Chen, J.

Chen, J. H.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Chen, M. C.

Chen, W.

Chen, Y. Y.

Cheng, C. J.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Chi, Y.-C.

Chow, C. W.

C. W. Chow, R. J. Shiu, Y. C. Liu, X. L. Liao, K. H. Lin, Y. C. Wang, and Y. Y. Chen, “Using advertisement light-panel and CMOS image sensor with frequency-shift-keying for visible light communication,” Opt. Express 26(10), 12530–12535 (2018).
[Crossref] [PubMed]

K. Liang, C. W. Chow, and Y. Liu, “RGB visible light communication using mobile-phone camera and multi-input multi-output,” Opt. Express 24(9), 9383–9388 (2016).
[Crossref] [PubMed]

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

C. H. Yeh, H. Y. Chen, C. W. Chow, and Y. L. Liu, “Utilization of multi-band OFDM modulation to increase traffic rate of phosphor-LED wireless VLC,” Opt. Express 23(2), 1133–1138 (2015).
[Crossref] [PubMed]

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

Chu, M. T.

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

Faragher, R.

R. Faragher and R. Harle, “An analysis of the accuracy of Bluetooth low energy for indoor positioning applications,” Proc. ION GNSS+ 2014, 201–210.

Haas, H.

H. Haas, “Visible light communication,” Proc. OFC, 1–72 (2015).

Han, S.

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

Harle, R.

R. Faragher and R. Harle, “An analysis of the accuracy of Bluetooth low energy for indoor positioning applications,” Proc. ION GNSS+ 2014, 201–210.

He, J.-H.

Ho, S. W.

Hsu, C. W.

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

Janjua, B.

Jhang, T. W.

Kim, D.

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

Kim, H.

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

Kuo, H.-C.

Lee, C. H.

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

Li, C. Y.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Liang, K.

K. Liang, C. W. Chow, and Y. Liu, “RGB visible light communication using mobile-phone camera and multi-input multi-output,” Opt. Express 24(9), 9383–9388 (2016).
[Crossref] [PubMed]

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

Liao, X. L.

Lin, C. Y.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Lin, G.-R.

Lin, K. H.

Lin, Y. P.

Liu, S.

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

Liu, Y.

K. Liang, C. W. Chow, and Y. Liu, “RGB visible light communication using mobile-phone camera and multi-input multi-output,” Opt. Express 24(9), 9383–9388 (2016).
[Crossref] [PubMed]

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).

Liu, Y. C.

Liu, Y. F.

C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).

Liu, Y. L.

Lu, F.

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

Lu, H. H.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

H. H. Lu, Y. P. Lin, P. Y. Wu, C. Y. Chen, M. C. Chen, and T. W. Jhang, “A multiple-input-multiple-output visible light communication system based on VCSELs and spatial light modulators,” Opt. Express 22(3), 3468–3474 (2014).
[Crossref] [PubMed]

Neild, A.

J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51(12), 68–73 (2013).
[Crossref]

Ng, T. K.

Ooi, B. S.

Oubei, H. M.

Retamal, J. R. D.

Sekercioglu, Y. A.

J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51(12), 68–73 (2013).
[Crossref]

Shiu, R. J.

Son, Y.

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

Tsai, C.-T.

Vellambi, B. N.

Wan, Z. W.

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Wang, H.

S. Wu, H. Wang, and C. H. Youn, “Visible light communications for 5G wireless networking systems: from fixed to mobile communications,” IEEE Netw. 28(6), 41–45 (2014).
[Crossref]

Wang, H. Y.

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

Wang, H.-Y.

Wang, Y. C.

Wang, Z.

Wu, J. T.

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

Wu, P. Y.

Wu, S.

S. Wu, H. Wang, and C. H. Youn, “Visible light communications for 5G wireless networking systems: from fixed to mobile communications,” IEEE Netw. 28(6), 41–45 (2014).
[Crossref]

Yang, S.

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

Yasir, M.

Yeh, C. H.

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

C. H. Yeh, H. Y. Chen, C. W. Chow, and Y. L. Liu, “Utilization of multi-band OFDM modulation to increase traffic rate of phosphor-LED wireless VLC,” Opt. Express 23(2), 1133–1138 (2015).
[Crossref] [PubMed]

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

Youn, C. H.

S. Wu, H. Wang, and C. H. Youn, “Visible light communications for 5G wireless networking systems: from fixed to mobile communications,” IEEE Netw. 28(6), 41–45 (2014).
[Crossref]

Yu, C.

Zhong, W. D.

IEEE Commun. Mag. (1)

J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51(12), 68–73 (2013).
[Crossref]

IEEE Netw. (1)

S. Wu, H. Wang, and C. H. Youn, “Visible light communications for 5G wireless networking systems: from fixed to mobile communications,” IEEE Netw. 28(6), 41–45 (2014).
[Crossref]

IEEE Photon. Soc. Newslett. (1)

C. W. Chow, C. H. Yeh, Y. Liu, and Y. F. Liu, “Digital signal processing for light emitting diode based visible light communication,” IEEE Photon. Soc. Newslett. 26, 9–13 (2012).

IEEE Photonics J. (1)

C. W. Hsu, J. T. Wu, H. Y. Wang, C. W. Chow, C. H. Lee, M. T. Chu, and C. H. Yeh, “Visible light positioning and lighting based on identity positioning and RF carrier allocation technique using a solar cell receiver,” IEEE Photonics J. 8(4), 1 (2016).
[Crossref]

J. Lightw. Tech. (1)

H. Kim, D. Kim, S. Yang, Y. Son, and S. Han, “An indoor visible light communication positioning system using a RF carrier allocation technique,” J. Lightw. Tech. 31(1), 134–144 (2013).
[Crossref]

J. Lightwave Technol. (2)

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor positioning system using visible light and accelerometer,” J. Lightwave Technol. 32(19), 3306–3316 (2014).
[Crossref]

C. H. Chang, C. Y. Li, H. H. Lu, C. Y. Lin, J. H. Chen, Z. W. Wan, and C. J. Cheng, “A 100-Gb/s multiple-input multiple-output visible laser light communication system,” J. Lightwave Technol. 32(24), 4723–4729 (2014).
[Crossref]

Opt. Eng. (1)

Y. Liu, C. W. Hsu, H. Y. Chen, K. Liang, C. W. Chow, and C. H. Yeh, “Visible-light communication multiple-input multiple-output technology for indoor lighting, communication, and positioning,” Opt. Eng. 54(12), 120502 (2015).
[Crossref]

Opt. Express (6)

Other (5)

Y. F. Liu, Y. C. Chang, C. W. Chow, and C. H. Yeh, “Equalization and pre-distorted schemes for increasing data rate in in-door visible light communication system,” Proc. OFC 2011, paper JWA083.
[Crossref]

C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2006).

C. W. Hsu, S. Liu, F. Lu, C. W. Chow, C. H. Yeh, and G. K. Chang, “Accurate indoor visible light positioning system utilizing machine learning technique with height tolerance,” Proc. OFC2018, Paper M2K.2.
[Crossref]

R. Faragher and R. Harle, “An analysis of the accuracy of Bluetooth low energy for indoor positioning applications,” Proc. ION GNSS+ 2014, 201–210.

H. Haas, “Visible light communication,” Proc. OFC, 1–72 (2015).

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Figures (6)

Fig. 1
Fig. 1 (a) Proposed VLP architecture using repeated trilateral unit cells. (b) VLP inside a unit cell.
Fig. 2
Fig. 2 Experimental VLP performances when using (a) the 2nd order regression ML model and (b) the polynomial trilateral ML model without optical background noises.
Fig. 3
Fig. 3 Experimental VLP performances when using (a) the 2nd order regression ML model and (b) the polynomial trilateral ML model with optical background noises.
Fig. 4
Fig. 4 Experimental CDF against position error when using (a) the 2nd order regression ML model and (b) the polynomial trilateral ML model respectively without optical background noises.
Fig. 5
Fig. 5 Experimental CDF against position error when using (a) the 2nd order regression ML model and (b) the polynomial trilateral ML model respectively with optical background noises.
Fig. 6
Fig. 6 Experimental down-converted NRZ signals without and with the background noises.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

f ^ = w (0) + i=1 D w (i) p i + i=1 D j=1 D w (ij) p i p j =Φ W ML
{ f x = w x (0) + w x (1) p 1 + w x (2) p 2 + w x (3) p 3 + w x (11) p 1 2 +...+ w x (22) p 2 2 + w x (23) p 2 p 3 + w x (33) p 3 2 f y = w y (0) + w y (1) p 1 + w y (2) p 2 + w y (3) p 3 + w y (11) p 1 2 +...+ w y (22) p 2 2 + w y (23) p 2 p 3 + w y (33) p 3 2
Φ= [ ϕ p (1), ϕ p (2),..., ϕ p (N)] T , ϕ p (i)=[1, p 1 (i), p 2 (i),..., p 2 (i) p 3 (i), p 3 2 (i)]
 t= [ x 1 , x 2 ,, x N y 1 , y 2 ,, y N ] T = [ t 1 , t 2 ,, t N ] T
p(t| Φ,W,β)= n=1 N Ν( t n |   ϕ p (n)W , β 1 )
lnp(t| Φ,W,β)=β n=1 N { t n ϕ p (n)W } ϕ p (n) T  = 0
W ML =( Φ T Φ ) 1 Φ T t
f ^ = w (0) + w (1) p+ w (2) p 2 =Φ W ML
Φ=[1,p, p 2 ] T ,t= [ d(1),d(2),,d(N) ] T
{ d 1 2 = ( x e x 1 ) 2 + ( y e y 1 ) 2 + ( z e z 1 ) 2 d 2 2 = ( x e x 2 ) 2 + ( y e y 2 ) 2 + ( z e z 2 ) 2 d 3 2 = ( x e x 3 ) 2 + ( y e y 3 ) 2 + ( z e z 3 ) 2

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