# An Indoor Visible Light Positioning System Using Tilted LEDs with High Accuracy

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## Abstract

**:**

## 1. Introduction

_{p}i.e., typically in a range of 10 to 45 cm, depending on the fingerprint database [8,9,10]. In the scene analysis technique, the estimation process of the relative position can be obtained by comparing the measured value with a pre-measured location of each position and then matching it to determine the real position. However, the measurement can be affected by the distributions of base stations, i.e., transmitters (Txs), shadowing and blocking, as well as the absolute location (i.e., probabilistic and correlation) dependency on pattern recognition techniques [9]. A VLP using two photodiodes (PDs) and an image sensor (IS) was proposed in [7,8,11]. Note, visible light communication (VLC) with IS (composed of a large PD array) naturally fits well with multiple inputs multiple-output systems in indoor and outdoor applications. In IS-based VLP, image-processing techniques can be used to determine the position but at the cost of increased complexity [12]. Note that, in VLP the transmission speeds (i.e., data rates) of the PD and IS are not critical at all since the aim is to achieve positioning with high accuracy [13]. Most research reported on VLP has focused on the investigation of geometrical properties using triangulation/trilateration, fingerprinting, or proximity methods to determine the transmission distance based on establishing a one-to-one relationship between the target location and its received signal strength (RSS). In such works, the analyses were based on the intensity modulation, angle of arrival [9], time of arrival [10], time difference of arrival [14], time of flight (TOF), and direct detection. In VLP systems, linear least square (LLS) or non-linear least square (NLLS) algorithms are often used for the position estimation [15,16,17].

^{2}). Alternatively, the highest root mean square (RMS) delay spread of 6.5% in comparison with the case with no people was observed for an empty hall. The results also revealed that, the corridor with the maximum RMS delay of 2% at the people density > 0.16 people/m

^{2}is the most robust against the people’s movement compared with the other two where the problem of shadowing or blockage could be readily avoided. Another concern with the user’s mobility is the processing time required that needs considering with respect to the speed of movement for the receiver (Rx).

_{p}; whereas in [23], it was shown that, the channel capacity can be significantly improved by carefully selecting the Rx’s tilting angle ${\theta}_{\mathrm{Rx}}$. However, the initial research demonstrated that in VLP ${\theta}_{\mathrm{Rx}}$ usually results in increased ε

_{p}(i.e., lower accuracy).

_{p}increased (i.e., in the order of centimeters) with ${\theta}_{\mathrm{Tx}}$. In [25], a 4-LED VLP system using an artificial neural network (ANN) was proposed to improve the positioning accuracy, which is impacted by the random and unknown static Tx tilt angle with a maximum variation of 2°. It was shown that ANN offered improved performance compared with standard trilateration, achieving localization errors below 1 cm for the line-of-sight (LoS) channel. In Addition, an RSS-based localization algorithm with multidimensional LED array was proposed in [26], where the design of the lamp structure was introduced to exploit the direction of the LED in a LoS environment. The authors showed that, the proposed system achieved a RMS error of 0.04 and 0.06 m in two- and three-dimensional localization, respectively for the LED with a tilt angle of 15°. While in [27], an angle diversity Tx (ADT) together with accelerometers was proposed for uplink three-dimensional localization in a LoS environment. ADT was a combination of 19 or 37 LEDs (LEDs array), which were placed on the ground, and PDs located on the ceiling. The results showed that, an average localization error of less than 0.15 m.

_{F}, y

_{F}, z

_{F}) coordinates without violating the acceptable uniformity range of the light distribution in the illuminated region. Note, F is selected at the center of the receiving plane in this work, and alignment is achieved with respect to the Tx normal ${\widehat{t}}_{k}$.

_{R}points at various Rx locations for two different scenarios. Note, the Rx locations are within a squared shape region centered at F with a side length D

_{r}. The polynomial regressions (PRs) are fitted with the PR points for the full and half rooms of areas of 6 × 6 and 3 × 3 m

^{2}, which is termed as scenarios S1 and S2, respectively-. The study is carried out using the LLS algorithm for position estimation, which is a low complexity solution. Hence, we offer a significant accuracy improvement by up to ~66% compared with a link without Tx’s tilt. We show ε

_{p}of 1.7, and 1.3 cm for S1 and S2, respectively, and for z

_{F}of 0 m (i.e., the height of F from the floor level). Furthermore, we investigate z

_{F}with respect to ε

_{p}and we show that, the lowest ε

_{p}of 1.3 and 0.8 cm were for S1 and S2, respectively.

## 2. Proposed Visible Light Positioning (VLP) System Model

_{R}. For NLoS links, reflection from near and far walls should be considered, which contributes to the degradation of PA. For example, Figure 1 illustrates a system with two Txs aligned with respect to F (i.e., shown as the tilted Tx normal ${\widehat{t}}_{k}$), which is used to investigate the impact of reflections from walls on the accuracy of VLP). Here, the aim is to maximize P

_{R}from the LoS paths to improve accuracy at F, which is initially set at the center of the receiving plane (i.e., ${x}_{F},{y}_{F},$ and ${z}_{F}$ are all set to zero). The tilting orientation is estimated based on the position of F, which is given by:

_{k}, y

_{k}, z

_{k}), which is associated with the world coordinate system (WCS), with ${\widehat{t}}_{k}$ of $\left[{\mathrm{sin}\theta}_{\mathrm{Tx},k}\text{}\mathrm{cos}{\alpha}_{k},{\text{}\mathrm{sin}\theta}_{\mathrm{Tx},k}\text{}\mathrm{sin}{\alpha}_{k},\text{}-{\mathrm{cos}\theta}_{\mathrm{Tx},k}\right]$ where ${\theta}_{\mathrm{Tx},k},\text{}{\alpha}_{k}$ are the tilting and azimuth angles, respectively and k is 1, …, 4. Note that, in this work, as a reference, an empty room is considered to study the impact of Tx’s tilting on the positioning accuracy. The proposed system can be utilized for positioning purposes where the positioning accuracy is a major concern. However, if indoor positioning system uses the already existing wireless communication network architectures, then high accuracy may no longer be critical. Therefore, there exists always a trade-off between accuracy and other system requirements including scalability, complexity, coverage, etc.

_{r}and $\mathcal{R}$ are the PD’s active area and responsivity, respectively. ${T}_{s}\left(\phi \right)$ and $g\left(\phi \right)$ are the gains of the optical filter and the concentrator at the Rx, respectively. Note, ${T}_{s}\left(\phi \right)$ and $g\left(\phi \right)$ are set to unity, φ < 90° and d ≫ $\sqrt{{A}_{r}}$.

_{r}, y

_{r}, z

_{r}). We have also specified the dedicated region, which is a square shape centered at the point F and located at the receiving plane. The receiving positions are considered inside this region only. All the other key system parameters are given in Table 1.

## 3. Positioning Algorithm

#### 3.1. Distance Estimation Using Polynomial Regression

_{j}is the coefficient of the fitted polynomial at jth degree polynomial and ${P}_{R,\text{}k}$ is the total received power at Rx from kth Tx. Note, ${d}_{k}$ is computed using (11), which is then substituted into (9) to determine ${r}_{k}$.

#### 3.2. Linear Least Square (LLS) Estimation

_{k}, y

_{k}, z

_{k}) and the Rx is located at (x

_{r}, y

_{r}, z

_{r}). A closed-form solution using the LLS estimation method is given by:

## 4. Results and Discussion

#### 4.1. Impact of the Transmitter (Tx) Tilting on the Radiation Pattern

#### 4.2. Polynomial Fitting

_{R,k}and the PR (polynomial regression) method as outlined in Section 3.1. The accuracy and precision of fitting are measured by the coefficient of determination R

^{2}, which is a statistical measure of how close the data are to the fitted regression line, and the standard deviation. Note, PR is considered for various data points and categorized into two scenarios S1 and S2 based on the room dimensions. For scenarios S1 and S2, the PRs are fitted with the P

_{R,k}points for the full and half rooms of areas of 6 × 6 and 3 × 3 m

^{2}, respectively. The deviation of P

_{R,k}points is impacted mainly by the reflections wherein the data near the walls imply a larger estimation error as stated previously in the literature [19,32]. Therefore, 3600 samples (a full room with a 1 cm grid size) are considered for the polynomial fitting for S1, while for S2 we only have considered 900 samples (an inner half room). A stabilized residual sum of squares is achieved with the polynomial order j of 4. The polynomial coefficients of the fitted curve and R

^{2}are estimated for both S1 and S2.

_{R,k}points for the full and half rooms, respectively. Figure 5a shows that, the P

_{R,k}points span between 0 and 4.2 mW, and are uniformly distributed for both S1 and S2. However, Figure 5b depicts that the P

_{R,k}points for S1 are more scattered with a smaller span of 0.5 to 3.2 mW, which corresponds to the corner of the room. In S2, the P

_{R,k}points are more focused towards S2 due to tilting of the Tx, thus the fitting data points are considered for S2 only. From the results obtained, both R

^{2}and the standard deviation are positively affected with tilting of the Tx, i.e., higher R

^{2}value of 0.98 and lower standard deviation of 0.98 is achieved for the tilted Tx as compared with a lower R

^{2}value of 0.96 and higher standard deviation of 1.01 in the case of no tilted Tx, see Figure 5b. Table 3 shows the estimated polynomial coefficients and R

^{2}values for S2 with and without the tilted Txs.

#### 4.3. Impact of the Tx Tilting and the Altitude of F on VLP

_{p}for different values of D

_{r}to realize the impact of tilted Txs near the center of the receiving plane, and further analyze the impact of changing the height of z

_{F}on the positioning accuracy. Figure 6 illustrates Inv(90%) as a function of D

_{r}for S1 and S2 with the LLS algorithm, which is applied for the case with LoS and NLoS paths to estimate the Rx’s position, as described in Section 3. The quantile function Inv($\chi $) is used as a performance metric to observe the confidence interval of ε

_{p}, which is given by:

_{p}.

_{p}to include the majority of the measured points. Note that, the Txs’ tilting angle is fixed at the point F for all values of D

_{r}. Moreover, the error can be reduced significantly depending on S1 or S2. For instance, for S1, ε

_{p}values of 1.7 and 3.6 cm are obtained for both tilting and non-tilting scenarios, respectively for D

_{r}of 40 cm. In addition, we have achieved the accuracy improvement of 44, 24, 60, and 64% for D

_{r}of 1, 2, 3, and 4 m, respectively with the maximum accuracy improvement of 66% for D

_{r}of 3.6 m. In addition, for S2, ε

_{p}of 1.3 cm is obtained for the observation area with D

_{r}of 40 cm with the tilted Tx. Hence, the Tx’s tilting (LED tilting angle) can improve the positioning accuracy in both S1 and S2 with the same detection area of 5 × 5 m

^{2}(up to D

_{r}of 5 m) as compared with the case with non-tilting Tx. This could be explained by the fact that, for large observation areas (i.e., large D

_{r}), the CDF of the error becomes affected by the walls and corners of the room, with no improvement in the accuracy. Hence, the NLoS paths become dominant for regions far away from the point F, which degrades the positioning accuracy. Therefore, the proposed VLP system with the tilted Txs outperforms the system with no tilting Txs for almost the entire room i.e., an area of 5 × 5 m

^{2}.

_{F}) on the positioning accuracy, which is eventually the variation in the Tx’s tilting. Figure 7 depict the Inv(90%) as a function of D

_{r}for a range z

_{F}(i.e., −2 to 2 m) with and without the tilting Txs for S1 and S2. Note that, a high negative value of z

_{F}implies that the Tx is pointing vertically downwards towards the Rx. For instance, −∞ for z

_{F}corresponds to the standard non-tilted case and it does not imply reception under the floor. From the Figure 7, it is observed that, (i) ε

_{p}increases and decreases s with the positive and negative values of z

_{F}(i.e., z

_{F}> 0, < 0), respectively for both S1 and S2; (ii) the minimum ε

_{p}of 1.3 cm is at z

_{F}of −0.5 m compared with 1.7 cm for z

_{F}of 0 m for S1 with D

_{r}of 40 cm, see Figure 7a; and (iii) the lowest ε

_{p}is achieved at −2 < z

_{F}< 0 m depending on the value of D

_{r}. The proposed VLP system can be further improved for the regions with D

_{r}of up to 5.5 m by adjusting the negative value of z

_{F}. For S2, the minimum ε

_{p}of 0.8 cm is observed at z

_{F}of −2 m and D

_{r}of 40 cm compared with 1.3 cm at F (i.e., z

_{F}= 0 m), see Figure 7b. However, the case with tilting Txs offers the lowest ε

_{p}for D

_{r}up to 4.36 m.

_{r}without and with the tilting Tx and a range of z

_{F}. The dashed line represents the EN 12464-1 European standard of lighting in an indoor environment [37], which defines the minimum acceptable ranges of uniformity of the light distribution. We have shown that the proposed VLP system with the tilting Txs is capable of providing higher uniformity for the entire room for z

_{F}≤ −1 m. The uniformity of the VLP system with tilted Tx increases with the decreased value of z

_{F}.

## 5. Conclusions

_{F}of 0 m. The results also showed that, the uniformity of the proposed VLP system in line with European Standard EN 12464-1, therefore meeting the uniformity requirement of the visible illumination regions. Furthermore, we improved the accuracy of the proposed VLP system by controlling the height of F by achieving the lowest ε

_{p}of 1.3 and 0.8 cm for S1 and S2, respectively. Ultimately, it was concluded that the proposed VLP system with the tilting Tx outperforms the non-tilted Tx scenario. Likewise, we could gain lower ε

_{p}when considering S2, whereas ε

_{p}will increase with D

_{r}as indicated for S1.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Short Form | Description |

ADT | Angle diversity transmitter |

ANN | Artificial neural network |

CDF | Cumulative distribution function |

IS | Image sensor |

LEDs | Light-emitting diodes |

LLS | Linear least square |

LoS | Line of sight |

NLLS | Nonlinear least square |

NLoS | Non-line of sight |

OOK | On-off keying |

PA | Positioning accuracy |

PDs | Photodiodes |

PR | Polynomial regression |

RF | Radio frequency |

RMS | Root mean square |

RSS | Received signal strength |

RSSI | Received signal strength indicator |

Rx | Receiver |

TOF | Time of flight |

Tx | Transmitter |

VLC | Visible light communication |

VLP | Visible light positioning |

WCS | World coordinate system |

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**Figure 1.**An example of a reflected light ray in case of light-emitting diode (LED) tilt: (

**a**) near-wall reflections case, and (

**b**) far wall reflections case.

**Figure 2.**The proposed indoor visible light positioning (VLP) system with the tilted transmitter (Tx).

**Figure 4.**The received power distributions for the proposed system for the Txs with: (

**a**) no tilting, and (

**b**) tilting.

**Figure 5.**The distance estimation for Tx-k using the polynomial regression (PR) method employed in S2 for the Txs with: (

**a**) no tilting, and (

**b**) tilting.

**Figure 6.**The measured quantile function at $\chi $ of 90% for various D

_{r}for linear least square (LLS) with and without the tilted Txs.

**Figure 7.**The measured quantile function at $\chi $ of 90% for various z

_{F}values for: (

**a**) S1, and (

**b**) S2.

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

Room size | (l, b, h) | 6 × 6 × 3 m^{3} |

The coordinates of | ||

Tx-1 | (x_{1}, y_{1}, z_{1}) | (−1.7 m, −1.7 m, 3 m) |

Tx-2 | (x_{2}, y_{2}, z_{2}) | (1.7 m, −1.7 m, 3 m) |

Tx-3 | (x_{3}, y_{3}, z_{3}) | (−1.7 m, 1.7 m, 3 m) |

Tx-4 | (x_{4}, y_{4}, z_{4}) | (1.7 m, 1.7 m, 3 m) |

Transmit power of each Tx | ${P}_{t}$ | 1 W |

Receiver’s field of view | FoV | 75° |

Reflection coefficient | $\rho $ | 0.7 |

Half power angle | HPA | 60° |

Photodiode area | ${A}_{r}$ | 10^{−4} m^{2} |

Responsivity | $\mathcal{R}$ | 1 A/W |

Reflection coefficient | $\rho $ | 0.7 |

Tx Number | $\mathbf{Tilted}\text{}\mathbf{LED}\text{}\mathbf{Normal},\text{}{\widehat{\mathit{t}}}_{\mathit{k}}$ |
---|---|

Tx-1 | [0.4, 0.4, −0.8] |

Tx-2 | [−0.4, 0.4, −0.8] |

Tx-3 | [0.4, −0.4, −0.8] |

Tx-4 | [−0.4, −0.4, −0.8] |

Cases | Estimated Polynomial Coefficients (No Units) | R^{2} | ||||
---|---|---|---|---|---|---|

${\mathit{a}}_{0}$ | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{a}}_{3}$ | ${\mathit{a}}_{4}$ | ||

With tilted Tx | 7.38 × 10^{4} | −3.60 × 10^{5} | 2.37 × 10^{4} | −6.26 × 10^{2} | 8.10 | 0.98 |

Without tilted Tx | 8.86 × 10^{6} | 9.93 × 10^{5} | 3.96 × 10^{4} | 7.35 × 10^{2} | 7.44 | 0.96 |

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Chaudhary, N.; Younus, O.I.; Alves, L.N.; Ghassemlooy, Z.; Zvanovec, S.; Le-Minh, H.
An Indoor Visible Light Positioning System Using Tilted LEDs with High Accuracy. *Sensors* **2021**, *21*, 920.
https://doi.org/10.3390/s21030920

**AMA Style**

Chaudhary N, Younus OI, Alves LN, Ghassemlooy Z, Zvanovec S, Le-Minh H.
An Indoor Visible Light Positioning System Using Tilted LEDs with High Accuracy. *Sensors*. 2021; 21(3):920.
https://doi.org/10.3390/s21030920

**Chicago/Turabian Style**

Chaudhary, Neha, Othman Isam Younus, Luis Nero Alves, Zabih Ghassemlooy, Stanislav Zvanovec, and Hoa Le-Minh.
2021. "An Indoor Visible Light Positioning System Using Tilted LEDs with High Accuracy" *Sensors* 21, no. 3: 920.
https://doi.org/10.3390/s21030920