Main parameters in VLC.

## Abstract

This chapter aims at improving the accuracy of estimation the localization by using the RSS method to estimate the positions and take into account the effects of both LOS propagation. The proposed system is depending on developing a mathematical model for the noisy VLC positioning system. For improving the results, adopting the KF is combined with the proposed system, which is considered an optimal estimator. The performance of the proposed technique is determined by evaluating the positioning errors in a typical room. Also this chapter develops the accuracy of the positioning system by using different ideas with average techniques. The discussion of the results for averaging technique is displayed.

### Keywords

- RSS
- KF
- VLC
- localization

## 1. Introduction

This chapter aims at improving the accuracy of estimation the localization by using the Received Signal Strength (RSS) method to estimate the positions and take into account the effects of both line of sight (LOS) and non-line of sight (NLoS) propagations. The proposed system is depending on developing a mathematical model for the noisy Visible light communication (VLC) positioning system. For improving the results, adopting the Kalman filter (KF) is combined with the proposed system, which is considered an optimal estimator. The performance of the proposed technique is determined by evaluating the positioning errors in a typical room. Also, this chapter develops the accuracy of the positioning system by using different ideas with average techniques.

The remaining of this chapter is organized as follows: Section 2 discusses the optical channel in indoor systems. Section 3 is devoted to explaining the methodology of localization using RSS techniques. A mathematical derivation for performance evaluation is developed in the same section as well. In Section 4, The proposed KF algorithm is presented with explaining its algorithm for estimation correction. There is an average technique aiming to use the average method as shown in Section 5. Using both effects of LOS and the first reflection of NLoS propagation is done in the average proposed system. Adopting KF with averaging is shown in Section 6. The discussion of the results for averaging technique is displayed in Section 7. Section 8 shows the comparison between the results with some recent references. Finally, the concluding remarks are given in Section 9.

## 2. Optical channel model

The characteristics of the channel modeling have been analyzed with the effects of the channel distortions in [1]. The power associated with the channel is separated into two factors, these being optical path loss (PL) and multipath dispersion. The PL is calculated from the knowledge of the receiver size, the transmitter beam divergence, and separation distance. However, a NLoS configuration (diffuse systems) mainly used in the indoor environment, uses reflections of the room surfaces and furniture. These reflections could be seen as unwanted signals or multi-path distortions which predict the PL more complex. The OW channel transfer function is defined by

According to Figure 1, it describes

The received power therefore becomes

where

where

The total NLoS channel gain for

where

The determination of the parameters for the previous equation is as follows:

where

The simulation of the power distribution is done for two cases, first case is using four transmitters which are distributed in different positions (1.25, 1.25, 3) m, (1.25, 3.75,3) m, (3.75, 1.25, 3) m, (3.75, 3.75, 3) m in room with size (5,5,3) m, as shown in Figure 2. Second case is using only one transmitter that is located in the center of the ceiling. This power distribution is shown in Figure 3. The simulation is done with using some parameters where

## 3. RSS mathematical analysis

The proposed technique depends on estimating the receiver position using RSS method, then further improving the acquired estimation by adopting the Kalman filtering algorithm. In the initial estimation, RSS technique is used taking into account the effect of LoS. Specifically, A mathematical model is developed for the noisy VLC positioning system and estimate both the angular and horizontal-distance errors. Because of the dependence of horizontal-distance error on the irradiance angle error. The performance of the proposed technique is determined by evaluating the positioning errors in a typical room. Also, the results are compared to that of the traditional RSS system. Depending on Figure 1; the analysis assumes that

If the transmitter and receiver are aligned together, then

In the general case (

The last equation expresses the ideal system case, which means there is no noise affecting the system. From which:

where

where

From Figure 1, the horizontal distance without any noises is given by

In the case of a noisy channel, the horizontal-distance error

The value of the horizontal-distance error

According to the RSS method, the positioning error is simply obtained from the distance errors. The positioning algorithm uses three maximum power levels to determine the location of the user [3]. Here, RSS algorithm is used to estimate

where

for any

## 4. Proposed KF algorithm

In this section, a KF algorithm is proposed to further improve the previous estimation (introduced in the last section) of the receiver position. Specifically, the estimation of the irradiance angle developed in the last section is further improved by adopting a KF algorithm.

The proposed system with KF is shown in Figure 5 where the PD collects the received power and inserts it into the proposed system. The process of the proposed system is analyzing the mathematical equations to calculate the irradiance angle

### 4.1 Predict step

We denote the state vector by

where

where

### 4.2 Measurement step

The updated state variable

respectively, where

Here

where

Finally, after getting the estimated angle then recalculate the positioning error using equations developed in Section 3.

## 5. Proposed localization methodology using an averaging RSS technique

Second technique contains the averaging localization method and Kalman filtering with averaging schemes. For the averaging technique, the position of the receiver has been estimated by RSSI technique for multiple times (e.g.,

To enhance the results of improving the localization, The algorithm of Kalman filtering has been adopted for estimation the received power over

Typical room is considered for evaluating the positioning performances for proposed techniques and the results of them are compared with the traditional RSS system.

For determining the receiver location, the trilateration method is used with the RSS from three LEDs transmitters having the maximum received levels [3]. Our techniques depend on the average of estimated receiver position over a certain number of measurements to decrease the localization error. This decreasing in error gets at the cost of exceeding the system mathematical complexity. Figure 6 shows a simple block diagram that demonstrates this approach.

### 5.1 RSS technique

Using (2), the received LoS power from transmitter

where

where

If consider the effect of NLOS as well, the total power collected at the receiver is obtained by modifying (24) to:

### 5.2 Linear LS method

To estimate the receiver location, the linear LS estimation is commonly used. Let

where

where

Here for any

The solution of (29) is:

### 5.3 Complexity analysis

The complexity of proposed averaging RSS technique can be analyzed by counting the number of mathematical operations required to solve the LS method once and then multiplying the resulting by the number of samples. Specifically, the total number of floating-point operations is

## 6. Kalman filtering with averaging

KF estimates the states of a linear system from the noisy measurements then produces the estimation of unknown variables that aim to get more accurate than those which based on a single measurement value.

At this section, a KF algorithm is adapted to enhance the estimation performance of the receiver positioning system. In the first, KF estimates several samples of measured received powers. Then, the average of these estimated power values is evaluated. Using the output of KF which is the estimated average power, the position of the receiver can be calculated by using RSS technique. The block diagram of the proposed Kalman filtering with averaging technique is shown in Figure 7.

KF algorithm is shown in the previous chapter in Section 4 recursively estimates the state of variables in the system in two phases; prediction and measurement [4, 5]. We denote the state vector by

## 7. Simulation and discussion for averaging technique

In this section, The simulation results are presented and compared them to that of traditional systems. Table 1 shows the main parameters used in the simulation.

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

Room dimensions | |

Number of transmitters | 4 |

Transmitted power | 30 W |

Locations of LEDs | |

FoV of photodetector | |

The active area of the photodetector | 1 cm |

In case of demonstrating the relation between the SNR and the average positioning error, Figure 8 shows that using five different positions of the receiver and the average positioning error in a meter. This figure shows that the proposed system outperform the traditional RSS method by nearly 1 cm at SNR=10 dB while adopting KF decreases the error by 11.5 cm that means improvement by 52.27%.

Figures 9 and 10, plot the true path with three different methods. The simulation is done at a FoV of

The pedestrian is moving in random directions inside the room. In Figure 11, compare between three techniques: Traditional RSS, proposed RSS, and proposed RSS with Kalman filtering. The comparison is done at a FoV of

In the second technique, simulation results for the proposed system are presented and compared with that of traditional systems. The main parameters used in the simulations for the VLC link are listed in Table 2.

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

Room dimensions | |

Number of transmitters | 4 |

Total transmitted power | 30 W |

Locations of LEDs | |

FOV of photodetector | |

SNR | 20 |

Active area of photodetector | 1 cm |

Wall reflectivity | 0.8 |

Number of samples | 50 |

Range of receiver in room | (1–3.5) m over both |

### 7.1 Positioning error

In the simulation, the performance measure is determined by the positioning error:

where

### 7.2 Averaging RSS and traditional RSS techniques

The RSS variations of the positioning error at every sample are shown in Figure 13 for receiver position

The positioning error using the proposed averaging RSS technique (with 100 samples) is plotted in same figure as well. The improvement using proposed technique is clear from the figure. The traditional RSS errors are more than 0.6 m (42.4%), where the error when employing the proposed averaging RSS is only 0.217 m (15.3%). That is, an improvement of about 27.1% is getting when adapting the proposed system. Both LoS and NLoS effects are studied for position of the receiver

## 8. Kalman filtering, averaging RSS, and traditional RSS techniques

In this section, different comparisons are shown between the performance of three methods; The traditional RSS technique, proposed averaging RSS technique, and the proposed Kalman filtering with averaging. We use same values which given for the VLC link of Table 2.

### 8.1 LoS propagation

The effects of LoS only on two tracks’ estimations for both

From the figures, both tracksâ€™ estimations are the nearest to the real one when employing the proposed techniques. Also, The results show that adopting KF estimation reduces the positioning error and improve the estimation. Table 3 for three techniques summarizes the error and improving percentages.

Localization method | Average positioning error | Percentage improvement |
---|---|---|

Traditional RSS | 18 cm | — |

Averaging RSS | 12 cm | 33.3% |

Kalman filtering | 5 cm | 72.2% |

### 8.2 Both LoS and NLoS propagations

The effect of both LOS and NLOS on Kalman filtering tracks’ estimations for both

### 8.3 Kalman filtering response

The response for a random position estimation for the KF is shown in Figure 18. The filter input is a measured value of received power, while the filter output is the corresponding estimated value at different number of samples. The filter response (estimated value) is near to the actual value where the samples are greater than 11.

### 8.4 Position estimation accuracy comparison

As mentioned in the introduction, several techniques have been proposed for indoor localization based on VLC technology. In this section, a comparison is provided between the position estimation accuracy and that of previous works for same simulation parameters. The results of this comparison are summarized in Table 4.

Reference | Sys. parameters | Ref. acc. | Present work | Present work |
---|---|---|---|---|

AVG sys. Acc. | KF acc. | |||

[6] | LoS, FoV | 5 cm | 3.7 cm | 3.1 cm |

[7] | LoS/NLoS, FoV | 13.95 cm | 9.1 cm | 4.8 cm |

[8] | LoS, FoV | 10 cm | 6.17 cm | 1.75 cm |

[9] | LoS, FoV | 14.5 cm | 17.4 cm | 3.5 cm |

[10] | LoS, FoV | 5 cm | 11 cm | 2.3 cm |

It is clear from the Table 3 that both proposed averaging RSS and Kalman filtering with averaging techniques achieve better accuracy than that proposed in [6, 7, 8]. Since the authors in [9, 10] have adopted Kalman filtering, they have better accuracy than the proposed averaging method. However, employing Kalman filtering with averaging gives a better accuracy.

## 9. Concluding remarks

First, the proposed techniques have been analyzed mathematically, taking into account the effects of LoS propagation. The positioning estimation accuracy of proposed techniques has been evaluated in a typical room. The results reveal that an improvement of about 52% in the average positioning error is achievable using the proposed technique with KF, when compared to that of the traditional RSS.

Secondly, both averaging and Kalman filtering by averaging schemes are adapted to improve the positioning system. Specifically, in the averaging technique, the receiver position has been determined by using the average of the samples of RSS estimations. The position is determined by RSS estimation of a Kalman filtered averaged multiple received power samples in the second proposed system, Kalman filtering with averaging algorithm.

Simulation results reveal that an improvement of about 33.3% in estimation accuracy is achievable when using the averaging scheme as compared to that of traditional RSS scheme. This improvement increases to 72.2% when adopting proposed Kalman filtering with averaging scheme.

## References

- 1.
Ghassemlooy, Z. Popoola, and W. Rajbhandari. Optical wireless communications system and channel modelling with MATLAB. Boca Raton, 2nd Edition, 2013. - 2.
C. Huang and X. Zhang. LOS-NLOS identification algorithm for indoor visible light positioning system. pages 575–578, Bali, Indonesia, Dec. 17–20, 2017. - 3.
Maxim Shchekotov. Indoor localization method based on wi-fi trilateration technique. In Proc. 16th Conference of Fruct Association (ACP 2018), Pages 177–179, Oulu, Finland, Oct. 27–31, 2014. - 4.
Greg Welch and Gary Bishop. An introduction to the Kalman filter. Technical Report 95-041, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA, July 24, 2006. - 5.
Yuta Teruyama and Takashi Watanabe. Effectiveness of variable-gain kalman filter based on angle error calculated from acceleration signals in lower limb angle measurement with inertial sensors. Computational and Mathematical Methods in Medicine, 10(1155):398042(1–12), 2013. - 6.
F. Mousa, N. Almaadeed, K. Busawon, A. Bouridane, R. Binns, and I. Elliot. Indoor visible light communication localization system utilizing received signal strength indication technique and trilateration method. Optical Engineering, 57(1):016107(1–10), Jan. 2018. - 7.
G. B. Prince and T. D. C. Little. A two phase hybrid RSS/AoA algorithm for indoor device localization using visible light. In IEEE Global Communications Conference (GLOBECOM 2012), Pages 3347–3352, Anaheim, CA, Dec. 3–7, 2012. - 8.
A. Şahin, Y. S. Eroğlu, İ Güvenç, N. Pala, and M. Yüksel. Hybrid 3-D localization for visible light communication systems. Journal of Lightwave Technology, 33(22):4589–4599, Nov. 2015. - 9.
Lihui Feng Zhitian Li and Aiying Yang. Fusion based on visible light positioning and inertial navigation using extended kalman filters. IEEE SENSORS, 17(1093):093â€“1103, JUNE 2017. - 10.
Fatih Erden Yusuf Said Eroglu and Ismail Guvenc. Adaptive kalman tracking for indoor visible light positioning. Eess.SP, 1, Sep 2019.