# Indoor Intruder Tracking Using Visible Light Communications

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## Abstract

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## 1. Introduction

- A VLC-based system for adversary target tracking inside buildings. A minimax filter is proposed to overcome possible failures of classical tracking methods in the case of an intelligent adversarial target. To the best knowledge of the authors, this is the first comprehensive study of adversary target tracking inside buildings using a VLC system.
- The simulation is based on a realistic channel model that takes multipath propagation, mobility of objects and shadowing into consideration.
- We examined the performance of the minimax filter against the Kalman filter, which is used as a benchmark, for the VLC-based tracking system, in terms of tracking accuracy and calculation complexity performance. The results showed that the minimax filter provided marginal tracking accuracy compared to the Kalman filter. However, both filters had a similar level of calculation complexity.
- This is the first study to compare the performance of both Kalman and minimax filters for RF- and VLC-based intruder tracking, taking into consideration the inherent differences in noise and position measurement accuracy. VLC is expected to provide more accurate position measurements in comparison to RF. Hence, the conclusion drawn in the RF domain is not necessarily applicable to VLC. For example, in RF, minimax is necessary to track the adversary target as Kalman filter is inadequate [2]. However, this study shows that the Kalman filter was adequate for intruder tracking with the VLC system.

## 2. System Description

#### 2.1. Indoor Channel Model

#### 2.2. Target Movement Model

## 3. Filter Design

#### 3.1. Minimax Filter

#### 3.2. Kalman Filter

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A schematic of the proposed indoor intruder tracking using visible light communication (VLC) showing three possible ray paths: line of sight (LOS), reflection from walls and furniture and blocked rays.

**Figure 2.**The actual and estimated (using minimax and Kalman filters) trajectories of the random paths of three different intruders, tracked using VLC.

**Figure 3.**The estimated position error as a function of time for different power levels using a Kalman filter, assuming an ideal source.

**Figure 4.**The estimated position error as a function of time for different power levels using a minimax filter, assuming an ideal source.

**Figure 5.**Relation between the estimation error, the received power, the shot noise and the total measurement noise using (

**a**) Kalman filter and (

**b**) minimax filter.

**Figure 6.**Position estimation error of the minimax verses the Kalman filters using line of sight (LOS) and shadowing.

**Figure 8.**Comparison between the position estimation errors from minimax and Kalman filters using RF and VLC.

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

${P}_{R}$ | Optical power by individual LED | 20 mW |

${n}_{LED}\times \phantom{\rule{3.33333pt}{0ex}}{n}_{LED}$ | Number of LEDs in the array | $60\times \phantom{\rule{3.33333pt}{0ex}}60$ |

${\mathsf{\Phi}}_{c}$ | Semi-angle | ${60}^{\circ}$ |

$\gamma $ | Photodiode (PD) responsivity | $0.54$ A/W |

${\mathsf{\Psi}}_{c}$ | The receiver field of view | ${60}^{\circ}$ |

${A}_{r}$ | Receiver area | $1\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-4}$ m${}^{2}$ |

${C}_{pd}$ | Capacitance of PD per unit area | $1.12\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$Fm${}^{-2}$ |

${I}_{2}$ | Noise bandwidth factor | 0.562 |

${I}_{3}$ | Noise bandwidth factor | 0.0868 |

${B}_{w}$ | Noise bandwidth | 100 MHz |

${G}_{\nu}$ | Open-loop voltage gain | 10 |

$\mathsf{\Gamma}$ | FET channel noise factor | 1.5 |

${g}_{m}$ | FET transconductance | 30 mS |

${I}_{bg}$ | Background current (silicon PD) | 10 nA |

$\rho $ | Reflection coefficient | 0.8 |

**Table 2.**The received power, the total noise covariance and the total measurement noise R, according to the simulation results.

Received Power (dBm) | Shot Variance ${\mathit{\sigma}}_{\mathbf{total}}^{2}$ (dB) | Measurement Noise R (dB) |
---|---|---|

19 | −119 | $-119\times I$ |

−1 | −139.4 | $-132.6\times I$ |

−21 | −158.8 | $-133.8\times I$ |

Algorithm Line | Complexity |
---|---|

${\mathit{x}}_{\mathit{k}+\mathbf{1}}={\mathbf{Ax}}_{\mathit{k}}+{\mathbf{Bw}}_{\mathit{k}}+{\mathsf{\Delta}}_{\mathit{k}}$ | $O({N}^{2})$ |

${\mathit{P}}_{\mathit{k}+\mathbf{1}}=\mathit{F}{\mathit{P}}_{\mathit{k}}{\mathit{F}}^{\mathbf{T}}+\mathit{B}\mathit{Q}{\mathit{B}}^{\mathbf{T}}+\mathit{K}\mathit{R}{\mathit{K}}^{\mathbf{T}}-\mathit{L}\mathit{S}{\mathit{L}}^{\mathbf{T}}$ | $O({N}^{2.376})$ |

$\mathit{F}=(\mathit{A}-\mathit{K}\mathit{C}+\mathit{L}\mathit{G})$ | $O({N}^{2.376})$ |

${\mathit{\varphi}}_{\mathit{k}}^{-\mathbf{1}}={\mathit{P}}_{\mathit{k}}^{-\mathbf{1}}+{\mathit{C}}^{\mathbf{T}}{\mathit{R}}^{-\mathbf{1}}\mathit{C}-{\mathit{G}}^{\mathbf{T}}{\mathit{S}}^{-\mathbf{1}}\mathit{G}$ | $O({N}^{2})$ |

$\mathit{K}=\mathit{A}{\mathit{\varphi}}_{\mathit{k}}{\mathit{C}}^{\mathbf{T}}{\mathit{R}}^{-\mathbf{1}}$ | $O({N}^{2.376})$ |

$\mathit{L}=\mathit{A}{\mathit{\varphi}}_{\mathit{k}}{\mathit{G}}^{\mathbf{T}}{\mathit{S}}^{-\mathbf{1}}$ | $O({N}^{2.376})$ |

$\widehat{{\mathit{x}}_{\mathit{k}+\mathbf{1}}}=\mathit{A}\widehat{{\mathit{x}}_{\mathit{k}}}+\mathit{K}({\mathit{y}}_{\mathit{k}}-\mathit{C}\widehat{{\mathit{x}}_{\mathit{k}}})$ | $O({N}^{2})$ |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alsalami, F.M.; Ahmad, Z.; Zvanovec, S.; Haigh, P.A.; Haas, O.C.L.; Rajbhandari, S.
Indoor Intruder Tracking Using Visible Light Communications. *Sensors* **2019**, *19*, 4578.
https://doi.org/10.3390/s19204578

**AMA Style**

Alsalami FM, Ahmad Z, Zvanovec S, Haigh PA, Haas OCL, Rajbhandari S.
Indoor Intruder Tracking Using Visible Light Communications. *Sensors*. 2019; 19(20):4578.
https://doi.org/10.3390/s19204578

**Chicago/Turabian Style**

Alsalami, Farah M., Zahir Ahmad, Stanislav Zvanovec, Paul Anthony Haigh, Olivier C. L. Haas, and Sujan Rajbhandari.
2019. "Indoor Intruder Tracking Using Visible Light Communications" *Sensors* 19, no. 20: 4578.
https://doi.org/10.3390/s19204578