# Indoor Visible-Light 3D Positioning System Based on GRU Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. Visible-Light Positioning Model

#### 2.1. System Model

_{i}; ${\alpha}_{i}\left(i=1,2,3\right)$ is the azimuth angle of PD

_{i}; $\theta $ is the central angle of the arc between point $O$ and PD

_{i}; and $\beta \left(0<\beta <90\xb0\right)$ is the elevation angle of PD

_{i}, which can be expressed as the following.

_{i}and the position $\left({x}_{0},{y}_{0},{z}_{0}\right)$ of the top center point $O$ is

_{i}, and $H$ is the vertical distance between point $O$ and PD

_{i}. $L$ and $H$ can be expressed as the following.

#### 2.2. Channel Model

## 3. GRU Neural Network Model

## 4. Positing Process

#### 4.1. Construction of Fingerprint Database

#### 4.2. Data Preprocessing

#### 4.3. Selection of Performance Indicators

#### 4.4. Building the GRU Network Model

## 5. Simulation Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Liu, H.; Darabi, H.; Banerjee, P.; Liu, J. Survey of wireless indoor positioning techniques and systems. IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.)
**2007**, 37, 1067–1080. [Google Scholar] [CrossRef] - Zhuang, Y.; Yang, J.; Li, Y.; Qi, L.; El-Sheimy, N. Smartphone-based indoor localization with bluetooth low energy beacons. Sensors
**2016**, 16, 596. [Google Scholar] [CrossRef] [PubMed] - Ruiz, A.R.; Granja, F.S.; Honorato, J.C.; Rosas, J.I. Accurate pedestrian indoor navigation by tightly coupling foot-mounted IMU and RFID measurements. IEEE Trans. Instrum. Meas.
**2011**, 61, 178–189. [Google Scholar] [CrossRef] - Yan, D.; Kang, B.; Zhong, H.; Wang, R. Research on positioning system based on Zigbee communication. In Proceedings of the 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), Chongqing, China, 12–14 October 2018; pp. 1027–1030. [Google Scholar]
- Monica, S.; Ferrari, G. UWB-based localization in large indoor scenarios: Optimized placement of anchor nodes. IEEE Trans. Aerosp. Electron. Syst.
**2015**, 51, 987–999. [Google Scholar] [CrossRef] - Lin, P.; Hu, X.; Ruan, Y.; Li, H.; Fang, J.; Zhong, Y.; Zheng, H.; Fang, J.; Jiang, Z.L.; Chen, Z. Real-time visible light positioning supporting fast moving speed. Opt. Express
**2020**, 28, 14503–14510. [Google Scholar] [CrossRef] [PubMed] - Chizari, A.; Jamali, M.V.; Abdollahramezani, S.; Salehi, J.A.; Dargahi, A. Visible light for communication, indoor positioning, and dimmable illumination: A system design based on overlapping pulse position modulation. Optik
**2017**, 151, 110–122. [Google Scholar] [CrossRef] - Bakar, A.H.; Glass, T.; Tee, H.Y.; Alam, F.; Legg, M. Accurate visible light positioning using multiple-photodiode receiver and machine learning. IEEE Trans. Instrum. Meas.
**2020**, 70, 7500812. [Google Scholar] [CrossRef] - Tran, H.Q.; Ha, C. Improved visible light-based indoor positioning system using machine learning classification and regression. Appl. Sci.
**2019**, 9, 1048. [Google Scholar] [CrossRef] - Zhang, S.; Zhong, W.D.; Du, P.; Chen, C. Experimental demonstration of indoor sub-decimeter accuracy VLP system using differential PDOA. IEEE Photonics Technol. Lett.
**2018**, 30, 1703–1706. [Google Scholar] [CrossRef] - Liu, R.; Liang, Z.; Yang, K.; Li, W. Machine learning based visible light indoor positioning with single-LED and single rotatable photo detector. IEEE Photonics J.
**2022**, 14, 7322511. [Google Scholar] [CrossRef] - Hao, X.; Sun, W.; Chen, J.; Yu, C. Vertical measurable displacement approach for altitude accuracy improvement in 3D visible light positioning. Opt. Commun.
**2021**, 490, 126914. [Google Scholar] - Alonso-González, I.; Sánchez-Rodríguez, D.; Ley-Bosch, C.; Quintana-Suárez, M.A. Discrete indoor three-dimensional localization system based on neural networks using visible light communication. Sensors
**2018**, 18, 1040. [Google Scholar] [PubMed] - Jia, C.; Yang, T.; Wang, C.; Sun, M. High-Accuracy 3D Indoor Visible Light Positioning Method Based on the Improved Adaptive Cuckoo Search Algorithm. Arab. J. Sci. Eng.
**2022**, 47, 2479–2498. [Google Scholar] - Hsu, L.S.; Chow, C.W.; Liu, Y.; Yeh, C.H. 3D Visible Light-Based Indoor Positioning System Using Two-Stage Neural Network (TSNN) and Received Intensity Selective Enhancement (RISE) to Alleviate Light Non-Overlap Zones. Sensors
**2022**, 22, 8817. [Google Scholar] [CrossRef] - Zhang, Z.; Chen, H.; Zeng, W.; Cao, X.; Hong, X.; Chen, J. Demonstration of Three-Dimensional Indoor Visible Light Positioning with Multiple Photodiodes and Reinforcement Learning. Sensors
**2020**, 20, 6470. [Google Scholar] [CrossRef] [PubMed] - Zhao, H.-X.; Wang, J.-T. A novel three-dimensional algorithm based on practical indoor visible light positioning. IEEE Photonics J.
**2019**, 11, 6101308. [Google Scholar] [CrossRef] - Chen, Y.; Guan, W.; Li, J.; Song, H. Indoor real-time 3-D visible light positioning system using fingerprinting and extreme learning machine. IEEE Access
**2019**, 8, 13875–13886. [Google Scholar] [CrossRef] - Nguyen, N.T.; Suebsomran, A.; Sripimanwat, K.; Nguyen, N.H. Design and simulation of a novel indoor mobile robot localization method using a light-emitting diode positioning system. Trans. Inst. Meas. Control
**2016**, 38, 305–314. [Google Scholar] [CrossRef] - Wang, Z.; Liang, Z.; Li, X.; Li, H. Indoor Visible Light Positioning Based on Improved Particle Swarm Optimization Method with Min-Max Algorithm. IEEE Access.
**2022**, 10, 130068–130077. [Google Scholar] [CrossRef] - Li, H.; Wang, J.; Zhang, X.; Wu, R. Indoor visible light positioning combined with ellipse-based ACO-OFDM. IET Commun.
**2018**, 12, 2181–2187. [Google Scholar] [CrossRef] - Seguel, F.; Krommenacker, N.; Charpentier, P.; Soto, I. A novel range free visible light positioning algorithm for imaging receivers. Optik
**2019**, 195, 163028. [Google Scholar] - Ghassemlooy, Z.; Popoola, W.; Rajbhandari, S. Optical Wireless Communications: System and Channel Modelling with Matlab
^{®}; CRC Press: Boca Raton, FL, USA, 2019. [Google Scholar] - Fan, K.; Komine, T.; Tanaka, Y.; Nakagawa, M. The effect of reflection on indoor visible-light communication system utilizing white LEDs. In Proceedings of the 5th International Symposium on Wireless Personal Multimedia Communications, Honolulu, HI, USA, 27–30 October 2002; Volume 2, pp. 611–615. [Google Scholar]
- Tran, H.Q.; Ha, C. Fingerprint-based indoor positioning system using visible light communication—A novel method for multipath reflections. Electronics
**2019**, 8, 63. [Google Scholar] [CrossRef] - Bengio, Y.; Simard, P.; Frasconi, P. Learning long-term dependencies with gradient descent is difficult. IEEE Trans. Neural Netw.
**1994**, 5, 157–166. [Google Scholar] [PubMed] - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] - Cho, K.; Van Merriënboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y. Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv
**2014**, arXiv:1406.1078. [Google Scholar]

**Figure 10.**Cumulative distribution of positioning errors for LOS and LOS + NLOS links in 3D visible-light positioning system.

**Figure 13.**Comparison chart of 2D positioning results on different positioning heights under LOS + NLOS link.

Positioning Algorithm | Mean Squared Error | Average Error (m) | Maximum Error (m) | Training Parameters | Training Time (s) |
---|---|---|---|---|---|

SimpleRNN | 0.08891 | 1.02182 | 1.99923 | 5475 | 147.86 |

GRU | 0.00038 | 0.02666 | 0.75596 | 16,923 | 172.91 |

LSTM | 0.00045 | 0.03554 | 0.46776 | 21,675 | 234.57 |

Number of Network Layers | Mean Squared Error | Average Error (m) |
---|---|---|

1 | 0.00483 | 0.11334 |

2 | 0.00082 | 0.04432 |

3 | 0.00203 | 0.08636 |

4 | 0.00231 | 0.07098 |

5 | 0.00467 | 0.14691 |

Batch Size | Mean Squared Error | Average Error (m) | Training Time (s) |
---|---|---|---|

16 | 0.00714 | 0.15795 | 2015.49 |

32 | 0.00143 | 0.08539 | 1036.73 |

64 | 0.00176 | 0.07599 | 617.59 |

128 | 0.00082 | 0.04432 | 388.47 |

256 | 0.00106 | 0.06665 | 247.98 |

Learning Rate | Mean Squared Error | Average Error (m) |
---|---|---|

0.005 | 0.00091 | 0.04544 |

0.010 | 0.00082 | 0.04432 |

0.015 | 0.00151 | 0.07569 |

0.020 | 0.00193 | 0.08529 |

0.025 | 0.00724 | 0.18912 |

**Table 5.**The effect of the proposed learning rate decay strategy and the learning rate setting of 0.1 on the accuracy of the model.

Learning Rate | Mean Squared Error | Average Error (m) | Training Time (s) |
---|---|---|---|

0.01 | 0.00075 | 0.04131 | 169.09 |

$lr$ | 0.00038 | 0.02660 | 172.91 |

Parameter | Value |
---|---|

Number of neurons in the GRU layer | 24 |

Number of neurons in the dense layer | 1 |

Batch size | 128 |

Number of iterations | 950 |

Learning rate | Equation (37) |

Optimizer | Adam |

Parameter | Value |
---|---|

Room size (length × width × height) | 4 m × 4 m × 3 m |

Height of positioning space | 0–1.7 m |

(Training, testing) partition | (0.18, 0.24) m |

LED position (x, y, z) | (1, 2, 3); (3, 2, 3) |

$\mathrm{LED}\text{}\mathrm{semi}-\mathrm{angle}\text{}\mathrm{at}\text{}\mathrm{half}-\mathrm{power}\text{}({\varphi}_{1/2}$) | 30° |

Amplitude of LED signal | 10 V |

Frequency of LED signal | 4 KHz and 5 KHz |

$\mathrm{Effective}\text{}\mathrm{area}\text{}\mathrm{of}\text{}\mathrm{PD}\text{}({A}_{PD}$) | 10^{−4} m^{2} |

$\mathrm{Azimuth}\text{}\mathrm{angle}\text{}\mathrm{of}\text{}\mathrm{PDs}\text{}({\alpha}_{1},{\alpha}_{2},{\alpha}_{3}$) | 0°, 135°, 225° |

Radius of the robot receiver model ($r$) | 0.15 m |

Arc length from PD to the top center point ($l$) | 0.05 m |

$\mathrm{Gain}\text{}\mathrm{of}\text{}\mathrm{optical}\text{}\mathrm{filter}\text{}{T}_{s}$($\psi $) | 1 |

Refractive index of optical concentrator ($n$) | 1.5 |

$\mathrm{FOV}\text{}\mathrm{of}\text{}\mathrm{PD}\text{}({\psi}_{FOV}$) | 90° |

Refractive index ($\rho $) | 0.8 |

$\mathrm{Reflection}\text{}\mathrm{surface}\text{}\mathrm{element}\text{}\mathrm{area}\text{}(\Delta A$) | 0.0225 m^{2} |

Filter sampling frequency | 15 KHz |

Type of filter | Butterworth bandpass filter |

**Table 8.**Performance comparison of 3D indoor visible-light localization models under different links.

Link | Mean Squared Error | Average Error (m) |
---|---|---|

LOS | 0.00045 | 0.02687 |

LOS + NLOS | 0.00038 | 0.02660 |

**Table 9.**Comparison of 2D positioning errors at different positioning heights for LOS and LOS + NLOS links.

Height (m) | LOS | LOS + NLOS | ||
---|---|---|---|---|

Average Error (m) | Maximum Error (m) | Average Error (m) | Maximum Error (m) | |

0 | 0.01672 | 0.08093 | 0.01771 | 0.08095 |

0.24 | 0.01324 | 0.08719 | 0.01347 | 0.06899 |

0.48 | 0.01420 | 0.08867 | 0.01384 | 0.09652 |

0.72 | 0.01752 | 0.13633 | 0.01614 | 0.14298 |

0.96 | 0.01976 | 0.23178 | 0.01946 | 0.22707 |

1.20 | 0.02436 | 0.22531 | 0.02308 | 0.24067 |

1.44 | 0.03169 | 0.18135 | 0.03071 | 0.18333 |

1.68 | 0.07747 | 1.01654 | 0.07839 | 0.75597 |

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**MDPI and ACS Style**

Yang, W.; Qin, L.; Hu, X.; Zhao, D.
Indoor Visible-Light 3D Positioning System Based on GRU Neural Network. *Photonics* **2023**, *10*, 633.
https://doi.org/10.3390/photonics10060633

**AMA Style**

Yang W, Qin L, Hu X, Zhao D.
Indoor Visible-Light 3D Positioning System Based on GRU Neural Network. *Photonics*. 2023; 10(6):633.
https://doi.org/10.3390/photonics10060633

**Chicago/Turabian Style**

Yang, Wuju, Ling Qin, Xiaoli Hu, and Desheng Zhao.
2023. "Indoor Visible-Light 3D Positioning System Based on GRU Neural Network" *Photonics* 10, no. 6: 633.
https://doi.org/10.3390/photonics10060633