#
Two-Phase Framework for Indoor Positioning Systems Using Visible Light ^{†}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Visible Light Positioning Systems

## 3. Two-Phase Positioning Framework

#### 3.1. Model Framework

#### 3.2. Coarse Phase

#### 3.2.1. Modulations

#### Pulsed Modulation

#### Muti-Carrier Modulations

#### 3.2.2. Multiple Access

#### Time Division Multiplexing (TDM)

#### Frequency Division Multiplexing (FDM) & Wavelength Division Multiplexing (WDM)

#### Code Division Multiplexing (CDM)

#### 3.3. Fine Phase

#### 3.4. Fine Phase-Triangulation Based Positioning Using AoA

#### 3.5. Fine Phase-Trilateration Based Positioning Using ToF or RSS

- RF Channel: $\chi ={G}_{T}{G}_{R}\frac{{\lambda}^{2}}{16{\pi}^{2}}$, where ${G}_{T}$ is the gain of the transmit antenna, ${G}_{R}$ is the gain of the receive antenna, $\lambda $ is the wavelength of the RF signal.
- VLC Channel: $\chi =T\left({\varphi}_{k,j}\right){A}_{{R}_{j}}g\left({\theta}_{k,j}\right)$, where $T\left({\varphi}_{k,j}\right)$ angle of emission dependent transmit optics, ${A}_{{R}_{j}}$ is the effective area of the photodetector, $g\left({\theta}_{k,j}\right)$ is the angle of incidence dependent concentration optics at the receiver.

## 4. Results

#### 4.1. Coarse

#### 4.1.1. Coarse Phase-Proximity-Based Positioning with Time Division Multiplexing

#### 4.1.2. Coarse Phase-Proximity-Based Positioning with Frequency Division Multiplexing

#### 4.1.3. Coarse Phase-Proximity-Based Positioning with Code Division Multiplexing

#### 4.2. Fine

#### 4.3. Two-Phase

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Model Description: (

**a**) Indoor Environment Model with 12 Source Luminaries and 169 Discrete Receiver Positions in a 4 m by 4 m by 3.5 m room without Obstructions; and (

**b**) iVisible Light Channel Geometry Model for the kth source Luminaire with Q LED’s Transmitting Modulated Data to the jth Receiver in an Indoor Space.

**Figure 3.**Model Description: (

**a**) Illumination Pattern for Candidate Indoor Environment; and (

**b**) Aggregate SNR Distribution over Candidate Indoor Environment for a ${R}_{b}=20$ Mbps.

**Figure 4.**Pulsed Modulations Illustrating Power and Bandwidth Tradeoffs for L-PPM and M-PAM relative to OOK [38].

**Figure 5.**Model Description: (

**a**) Time Division Multiplexing among 4 Timeslots; (

**b**) Frequency Division Multiplexing among 4 Frequencies; (

**c**) Code Division Multiplexing among 4 Spreading Codes.

**Figure 6.**Two Source-Single Receiver Geometry Illustration for Azimuth and Elevation Angle of Arrival Measurement with Local Coordinate Frame.

**Figure 8.**Illustration of Coarse Proximity-based Positioning with Time Division Multiplexing for OOK, 2-PPM, and 4-PAM pulsed modulations under the Spatial SNR Room Distribution.

**Figure 9.**Illustration of Coarse Proximity-based Positioning with Frequency Division Multiplexing for DCO-OFDM and ACO-OFDM modulations under the Spatial SNR Room Distribution.

**Figure 10.**Illustration of Coarse Proximity-based Positioning with Code Division Multiplexing for OOK, 2-PPM, and 4-PAM pulsed modulations under the Spatial SNR Room Distribution.

**Figure 11.**Model Description: (

**a**) Empirical CDF of Euclidean Distance Error for Time Division Multiplexing using Coarse Phase Proximity Positioning; (

**b**) Empirical CDF of Euclidean Distance Error for Orthogonal Frequency Division Multiplexing using Coarse Phase Proximity Positioning; (

**c**) Empirical CDF of Euclidean Distance Error for Code Division Multiplexing using Coarse Phase Proximity Positioning.

**Figure 12.**Fine Phase Positioning Performance in Candidate Room using Angle of Arrival Measurement, Geometric Constrained Optimized Triangulation Positioning Algorithm and Time Division Multiplexing.

**Figure 13.**Fine Phase Positioning Performance in Candidate Room using Angle of Arrival Measurement, Geometric Constrained Optimized Triangulation Positioning Algorithm and Orthogonal Frequency Division Multiplexing.

**Figure 14.**Fine Phase Positioning Performance in Candidate Room using Time of Flight Measurement, Geometric Constrained Optimized Triangulation Positioning Algorithm and Time Division Multiplexing.

**Figure 15.**Fine Phase Positioning Performance in Candidate Room using Received Signal Strength Measurement, Least Squares Trilateration Positioning Algorithm and Time Division Multiplexing.

**Figure 16.**Fine Phase Positioning Performance in Candidate Room using Received Signal Strength Measurement, Least Squares Trilateration Positioning Algorithm and Orthogonal Frequency Division Multiplexing.

**Figure 17.**Fine Phase Positioning Performance in Candidate Room using Received Signal Strength Measurement, Least Squares Triangulation Positioning Algorithm and Code Division Multiplexing.

**Figure 18.**Model Description: (

**a**) Two-Phase Precision with TDM Multiplexing; (

**b**) Two-Phase Precision with OFDM Multiplexing; (

**c**) Two-Phase Precision with CDM Multiplexing.

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

Optical Tx Power $({P}_{T})$ | 1.924 | W |

Lambertian Mode $(m)$ | 1 | - |

Effective Area of Rx $({A}_{R})$ | 0.81 | ${\mathrm{cm}}^{2}$ |

Electron Charge $(q)$ | $1.6\times {10}^{-19}$ | C |

Background Light Current $({I}_{BG})$ | $5100\times {10}^{-6}$ | A |

Speed of Light $(c)$ | $3.0\times {10}^{8}$ | m/s |

Noise PSD $({N}_{0})$ | $1.632\times {10}^{-21}$ | W/Hz |

Optical / Electrical Efficiency $({R}_{OE})$ | 0.53 | - |

Source Orientation Vector $()$ | ${[0,0,-1]}^{T}$ | - |

Rx Azimuth Angle $()$ | $0-\pi $ | rad |

Rx Elevation Angle $()$ | $0-\pi $ | rad |

Rx Orientation Vector $()$ | ${[0,0,1]}^{T}$ | |

Vertical Range $({z}_{k}-{z}_{j})$ | 2.2 | m |

Symbol Rate $({R}_{S})$ | 20 | symbols/s |

Source Bandwidth $(B)$ | 20 | MHz |

Field of View $(FoV)$ | $0-\pi $ | rad |

Wall Reflectivity $({\eta}_{R})$ | 0.6 | - |

Coarse Phase Multiplexing Scheme | Benefits | Drawbacks |
---|---|---|

OFDM | Better suited for high data rate communication, Asynchronous | Complex Modulator and Demodulator |

TDM | Simplistic | Requires Network Infrastructure, Highly Accurate Clocks, Synchronous |

CDM | Asynchronous | Multiple Access Interference, Codes are not fully orthogonal |

**Table 3.**Coarse Phase Positioning Performance for Pulsed Modulations using Time Division Multiplexing.

Pulsed Modulation Using TDM | Mean Positioning Error [m] | Median Positioning Error [m] | Mode Positioning Error [m] | Standard Deviation Positioning Error [m] |
---|---|---|---|---|

OOK | 0.315 | 0.3149 | 0.0065 | 0.1437 |

2PPM | 0.315 | 0.3149 | 0.0065 | 0.1437 |

4PAM | 0.315 | 0.3149 | 0.0065 | 0.1437 |

**Table 4.**Coarse Phase Positioning Performance for Multicarrier Modulations using Orthogonal Frequency Division Multiplexing.

Multicarrier Modulation Using OFDM | Mean Positioning Error [m] | Median Positioning Error [m] | Mode Positioning Error [m] | Standard Deviation Positioning Error [m] |
---|---|---|---|---|

ACO-OFDM | 0.305 | 0.3029 | 0.0056 | 0.1232 |

DCO-OFDM | 0.305 | 0.3029 | 0.0056 | 0.1232 |

**Table 5.**Coarse Phase Positioning Performance for Pulsed Modulations using Code Division Multiplexing.

Pulsed Modulation Using CDM | Mean Positioning Error [m] | Median Positioning Error [m] | Mode Positioning Error [m] | Standard Deviation Positioning Error [m] |
---|---|---|---|---|

OOK | 0.3406 | 0.3258 | 0.0121 | 0.1643 |

2PPM | 0.3404 | 0.3278 | 0.0285 | 0.1515 |

4PAM | 0.3321 | 0.3205 | 0.0095 | 0.1578 |

Coarse Phase Multiplexing Scheme | Mean Pos. Error [m] | Median Pos. Error [m] | Mode Pos. Error [m] | Std Dev. Pos. Error [m] | 90 Percent Precision |
---|---|---|---|---|---|

OFDM-ALL | 0.305 | 0.3029 | 0.0056 | 0.1232 | 0.498 |

TDM-ALL | 0.315 | 0.3149 | 0.0065 | 0.1437 | 0.5085 |

CDM-4PAM | 0.3321 | 0.3205 | 0.0095 | 0.1578 | 0.563 |

CDM-2PPM | 0.3404 | 0.3278 | 0.0285 | 0.1515 | 0.565 |

CDM-OOK | 0.3406 | 0.3258 | 0.0121 | 0.1643 | 0.575 |

Performance Metric | Average Positioning Error [m] | Median Positioning Error [m] | Std Dev Positioning Error [m] |
---|---|---|---|

CDM with RSS | 0.1142 | 0.0931 | 0.1050 |

OFDM with AOA | 0.0778 | 0.0422 | 0.1191 |

OFDM with RSS | 0.0608 | 0.0260 | 0.1252 |

TDM with AOA | 0.1213 | 0.0985 | 0.1014 |

TDM with RSS | 0.1059 | 0.0803 | 0.1067 |

TDM with TOF | 0.0616 | 0.0276 | 0.1249 |

**Table 8.**Two Phase: Coarse/Fine Positioning Average, Median, and Standard Deviation of Positioning Error.

Performance Metric | Average Positioning Error [m] | Median Positioning Error [m] | Std Dev Positioning Error [m] |
---|---|---|---|

CDM with RSS | 0.1413 | 0.0997 | 0.0704 |

OFDM with AOA | 0.0988 | 0.0452 | 0.0790 |

OFDM with RSS | 0.0826 | 0.0328 | 0.0880 |

TDM with AOA | 0.1403 | 0.1207 | 0.0539 |

TDM with RSS | 0.1254 | 0.0975 | 0.0627 |

TDM with TOF | 0.0833 | 0.0309 | 0.0877 |

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**MDPI and ACS Style**

Prince, G.B.; Little, T.D.C. Two-Phase Framework for Indoor Positioning Systems Using Visible Light ^{†}. *Sensors* **2018**, *18*, 1917.
https://doi.org/10.3390/s18061917

**AMA Style**

Prince GB, Little TDC. Two-Phase Framework for Indoor Positioning Systems Using Visible Light ^{†}. *Sensors*. 2018; 18(6):1917.
https://doi.org/10.3390/s18061917

**Chicago/Turabian Style**

Prince, Gregary B., and Thomas D. C. Little. 2018. "Two-Phase Framework for Indoor Positioning Systems Using Visible Light ^{†}" *Sensors* 18, no. 6: 1917.
https://doi.org/10.3390/s18061917