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Indoor Visible Light Positioning: Overcoming the Practical Limitations of the Quadrant Angular Diversity Aperture Receiver (QADA) by Using the Two-Stage QADA-Plus Receiver^{ †}

^{1}

^{2}

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^{†}

## Abstract

**:**

## 1. Introduction

- Detailed discussion of the potential sources of error for the QADA and how adopting the two-stage system will lead to better performance.
- Description of reference points and their importance in precise indoor positioning.
- In depth analysis of the impact of luminaire size and shape on the QADA receiver.
- Triangulation results for the QADA that show how noise, luminaire shape and size and room dimensions impact on positioning accuracy.

## 2. Indoor Positioning with QADA and QADA-Plus

#### 2.1. QADA Design

#### 2.2. QADA-Plus

#### 2.3. Reference Points

## 3. QADA Triangulation Algorithm

## 4. Analysis and Limitations of QADA

#### Light Spot Centroid Estimation

_{n}is the spectral irradiance, A is the area of a PD quadrant, Δλ is the optical bandwidth and B is the electrical bandwidth.

## 5. AOA Estimation for QADA

#### 5.1. Angle of Arrival Accuracy for a Point Source

#### 5.2. Impact of Luminaire Size and Shape on AOA Estimation

#### 5.2.1. Varying Luminaire Size

#### 5.2.2. Varying Luminaire Shape

## 6. Triangulation Simulations Using QADA

#### 6.1. Triangulation in the Absence of Noise

#### 6.2. Triangulation in the Presence of Noise

#### 6.3. Triangulation with Fewer Samples

## 7. Discussion and Conclusions

#### 7.1. Accuracy of QADA as a Stand-Alone Sensor

#### 7.2. Other Sources of QADA Error

#### 7.3. Reference Points

#### 7.4. Image Sensor Stage of QADA-Plus

#### 7.5. QADA-Plus

## 8. Patents

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**QADA-plus in a typical smartphone. The inset shows the QADA sensor located next to the standard front-facing camera.

**Figure 5.**Image captured by smartphone camera showing four luminaires with a single red reference point each.

**Figure 7.**Light spot overlapping the quadrant PD. In (

**a**), finding x

_{1}uses the ratio of the red and blue segments and in (

**b**), finding y

_{1}use the ratio of the orange and purple segments.

**Figure 9.**Two different room configurations used for the simulations. In (

**a**) the vertical distance between the transmitter and the receiver is 1.5 m and in (

**b**) the vertical distance between the transmitter and the receiver is 3.0 m.

**Figure 10.**rMSE for incident angle detection (

**a**) for polar angle detection (

**b**). The transmitted power is 3 W, the vertical distance from the transmitter to the receiver is 1.5 m and each estimate is the average of 20,000 samples.

**Figure 11.**rMSE for incident angle detection (

**a**) for polar angle detection (

**b**). The transmitted power is 1 W, the vertical distance from the transmitter to the receiver is 3.0 m and each estimate is the average of 20,000 samples.

**Figure 12.**Single trial absolute error for incident angle detection (

**a**) and polar angle detection (

**b**). In (

**c**), the large errors in the center of (

**b**) have been removed to show additional detail. The transmitted power is 1 W, the vertical distance from the transmitter to the receiver is 3.0 m and each estimate is the average of 20,000 samples.

**Figure 13.**Absolute error in incident angle estimation (

**a**), and in polar angle estimation (

**b**), for a square luminaire with side length 10 cm.

**Figure 14.**Absolute error in incident angle estimation and in polar angle estimation for a square luminaire with side length 10 cm, (

**a**,

**b**), and for a square luminaire with side length 30 cm, (

**c**) and (

**d**).

**Figure 15.**(

**a**) Absolute error in incident angle estimation, and (

**b**) in polar angle estimation for a circular luminaire with diameter 30 cm.

**Figure 16.**(

**a**) Absolute error in incident angle estimation, and (

**b**) in polar angle estimation for a rectangular light with dimensions 30 cm × 60 cm.

**Figure 17.**Room configurations for triangulation simulations. In (

**a**), square luminaires with side length 30 cm are used, in (

**b**), circular luminaires with diameter 30 cm are used and in (

**c**), rectangular luminaires with dimensions 30 cm × 60 cm were used. In all cases, the centers of the luminaires are 75 cm from the edges of the room.

**Figure 18.**Positioning error for square luminaires with side length 30 cm, (

**a**,

**c**), and circular luminaires with diameter 30 cm, (

**b**,

**d**). Errors in two-dimensions are shown in (

**a**,

**b**) and errors in three-dimensions are shown in (

**c**,

**d**).

**Figure 19.**Positioning error for rectangular luminaires with dimensions 30 × 60 cm. Errors in two-dimensions are shown in (

**a**) and errors in three-dimensions are shown in (

**b**).

**Figure 20.**Positioning error in the presence of noise with point source transmitters. Errors in two-dimensions are shown in (

**a**) and errors in three-dimensions are shown in (

**b**). Each estimate is the average of 20,000 samples.

**Figure 21.**Positioning error in the presence of noise with square luminaires and a vertical distance of 1.5 m. Errors in two-dimensions are shown in (

**a**) and errors in three-dimensions are shown in (

**b**). Each estimate is the average of 20,000 samples.

**Figure 22.**Positioning error in the presence of noise with square luminaires, room dimensions 6 m × 6 m and a vertical distance of 3 m. Errors in two-dimensions are shown in (

**a**) and errors in three-dimensions are shown in (

**b**). Each estimate is the average of 20,000 samples.

**Figure 23.**3-dimensional positioning error in the presence of noise with square luminaires and room dimensions 6 m × 6 m. In (

**a**) the vertical distance is 4 m and in (

**b**) the vertical distance is 5 m. Each estimate is the average of 20,000 samples.

**Figure 24.**3-dimensional positioning error in the presence of noise with square luminaires and room dimensions 6 m × 6 m × 5 m. Position estimates are calculated using (

**a**) a single sample, (

**b**) 100 samples and (

**c**) 1000 samples. Note that these figures are on different scales.

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

Quadrant PD size | 5 mm × 5 mm |

Aperture height | 2.5 mm |

QADA FOV | 90° |

Responsivity | 0.25 A/W |

Electrical bandwidth | 1 MHz |

Optical bandwidth | 300 nm |

Noise Equivalent Power | 1.9 × 10^{−14} $\mathrm{W}/\sqrt{\mathrm{Hz}}$ |

Spectral irradiance | 6.2 × 10^{−6} W/(nm·cm)^{2} |

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**MDPI and ACS Style**

Cincotta, S.; He, C.; Neild, A.; Armstrong, J.
Indoor Visible Light Positioning: Overcoming the Practical Limitations of the Quadrant Angular Diversity Aperture Receiver (QADA) by Using the Two-Stage QADA-Plus Receiver. *Sensors* **2019**, *19*, 956.
https://doi.org/10.3390/s19040956

**AMA Style**

Cincotta S, He C, Neild A, Armstrong J.
Indoor Visible Light Positioning: Overcoming the Practical Limitations of the Quadrant Angular Diversity Aperture Receiver (QADA) by Using the Two-Stage QADA-Plus Receiver. *Sensors*. 2019; 19(4):956.
https://doi.org/10.3390/s19040956

**Chicago/Turabian Style**

Cincotta, Stefanie, Cuiwei He, Adrian Neild, and Jean Armstrong.
2019. "Indoor Visible Light Positioning: Overcoming the Practical Limitations of the Quadrant Angular Diversity Aperture Receiver (QADA) by Using the Two-Stage QADA-Plus Receiver" *Sensors* 19, no. 4: 956.
https://doi.org/10.3390/s19040956