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On the Noise Effect of Fingerprinting-Based Positioning Error in Underwater Visible Light Networks^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. System Model

## 3. Fingerprinting UVLP Algorithm

#### 3.1. Step I. Database Construction

#### 3.2. Step II. Likely Position Detection

**Remark**

**1.**

**Remark**

**2.**

#### 3.3. Step III. Position estimation

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of a reference UVLC network, comprised of ${L}_{N}=4$ LED transmitters and a centralized RF IoUT sensor node. Wearable battery-powered photodetectors are assumed to be placed on the diver’s wetsuit.

**Figure 2.**Map of different LED transmitter scenarios deployed in the seabed following a grid structure. Green, blue and red stars refer to ${L}_{N}=[4,6,8]$, respectively. The case of ${L}_{N}=2$ overlaps with two LEDs of the $({L}_{N}=6)$ LED configuration.

**Figure 3.**MSE of the position estimation behavior versus the noise standard deviation for different network configurations and water types, i.e., (

**a**) pure, (

**b**) clear, (

**c**) coastal and (

**d**) harbor water. We assume a beam angle of ${50}^{\circ}$.

**Figure 4.**MSE of the position estimation behavior versus the noise standard deviation for different network configurations and water types, i.e., (

**a**) pure, (

**b**) clear, (

**c**) coastal and (

**d**) harbor water. We assume a beam angle of ${80}^{\circ}$.

**Figure 5.**Comparison of MSE trends for different values of noise standard deviation computed for different user positions, for (

**a**) variable and (

**b**) fixed position along z-direction, i.e., $z=4$ m.

**Figure 7.**Average MSE comparison of fingerprint to triangulation approaches versus the number of APs and for different water types, i.e., (

**a**) pure, (

**b**) clear, (

**c**) coastal and (

**d**) harbor water. We assume a beam angle of ${60}^{\circ}$.

**Figure 8.**Maximum achievable estimation error (m) versus the vertical distance, for different water types.

Parameter | Values |
---|---|

LED Power | 10 W |

Beam angle | ${[50,80]}^{\circ}$ |

Monitoring space $\mathcal{S}$ $({l}_{x}\times {l}_{y}\times {l}_{z})$ | 10 m × 10 m × 10 m |

PD field of view (FOV), ${\psi}_{C}$ | ${60}^{\circ}$ |

Refractive index, n | $1.5$ |

Optical filter gain, ${T}_{s}\left(\psi \right)$ | 1 |

Effective PD area, ${A}_{e}$ | 1 cm${}^{2}$ |

Noise standard deviation ${\sigma}_{n}$ | $[0,{10}^{-6}]$ |

Number of LEDs | $[2,4,6,8]$ |

Extinction coefficient, c | $[0.056,0.150,0.305,2.170]$ m${}^{-1}$ |

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## Share and Cite

**MDPI and ACS Style**

Hammouda, M.; Vegni, A.M.; Loscrí, V. On the Noise Effect of Fingerprinting-Based Positioning Error in Underwater Visible Light Networks. *Sensors* **2021**, *21*, 5398.
https://doi.org/10.3390/s21165398

**AMA Style**

Hammouda M, Vegni AM, Loscrí V. On the Noise Effect of Fingerprinting-Based Positioning Error in Underwater Visible Light Networks. *Sensors*. 2021; 21(16):5398.
https://doi.org/10.3390/s21165398

**Chicago/Turabian Style**

Hammouda, Marwan, Anna Maria Vegni, and Valeria Loscrí. 2021. "On the Noise Effect of Fingerprinting-Based Positioning Error in Underwater Visible Light Networks" *Sensors* 21, no. 16: 5398.
https://doi.org/10.3390/s21165398