1. Accuracy of AOA-Based and RSS-Based 3D Localization for
5/8/2018
Accuracy of AOA-Based and RSS-Based 3D Localization for
Visible Light Communications
2015
Presenter: Yusuf Said Eroglu
Authors: Alphan Sahin, Yusuf Said Eroglu, Ismail Guvenc, Murat Yuksel, and Nezih Pala

2. Outline Background System model
Proposed localization methods for visible light communications
Angle-of-arrival (AoA) based localization
Received signal strength (RSS) based localization
CRLB for RSS based localization
Numerical results
Concluding remarks

3. Beam pattern: Lambertian
Background
Visible light communications (VLC) delivers high accuracy for 3D indoor localization due to the following reasons:
Highly directed beam with light emitting diodes (LEDs)
Averaged-out multipath fading
No RF interference
Beam pattern: Lambertian
LED direction
Photodetector
𝜆/2 ≫𝜆
Photocurrent
VLC Signal

4. Background
Angle of arrival (AOA) based localization takes the direction information of LED transmitters.
2D Scenario (For illustration)
For 3D scenario, Least Squares Method is used for estimation

5. 5/8/2018
Background
Received signal strength (RSS) based localization considers the captured power from LED transmitters.
Highly accurate compared to AoA, but highly non-linear and challenging to analyze.
The authors in [2] explicitly emphasize the complexity of obtaining the Cramer-Rao lower bound (CRLB) in 3D.
VAP
VAP
Lambertian
Pattern [3]
VLC receiver
Lambertian
Pattern [3]
[2] X. Zhang, J. Duan, Y. Fu, and A. Shi, “Theoretical accuracy analysis of indoor visible light communication positioning system based on received signal strength indicator,” IEEE J. Lightw. Technol., vol. 32, no. 21, pp. 4180–4186, Nov

6. (𝑘−1)th VLC access point
System Model
3D scenario
Multiple VAPs with multiple LEDs
(𝑘−1)th VLC access point
𝑧-axis .
LED Transmitters
𝑘th VLC access point
𝐧 mk
𝐫 𝑚𝑘
𝐧 2k
𝐧 1k O
LED Transmitters
𝑦-axis
𝑥-axis

7. (𝑘−1)th VLC access point
System Model
Assumption 1: VLC Receiver knows the positions and orientations of LED transmitters.
(𝑘−1)th VLC access point
𝑧-axis .
LED Transmitters
𝑘th VLC access point
𝐧 mk
𝐫 𝑚𝑘
𝐧 2k
𝐧 1k O
𝐯 𝑚𝑘
𝐫 R
𝐧 R
𝑦-axis
𝑥-axis
VLC Receiver

8. (𝑘−1)th VLC access point
System Model
Assumption 2: VLC receiver is able to measure RSS associated with each LED transmitter.
RSS associated with each LED transmitter is modeled based on Lambertian pattern [3].
(𝑘−1)th VLC access point
𝑧-axis
𝑥-axis
𝑦-axis
𝐫 R
𝐧 R
𝐫 𝑚𝑘
VLC Receiver
𝐧 1k
𝐧 mk .
𝐯 𝑚𝑘
𝜙 𝑚𝑘
𝜃 𝑚𝑘
𝜃 FOV
Lambertian
pattern
Field of
view
𝑘th VAP
𝐧 2k O
𝑘th VLC access point

9. System Model Received Signal Strength (RSS):
𝑃 𝑚𝑘 = 𝑛+1 2𝜋 cos 𝑛 𝜙 𝑚𝑘 × 1 𝑅 𝑚𝑘 2 × 𝐴 𝑅 cos 𝜃 𝑚𝑘 × rect 𝜃 𝑚𝑘 𝜃 FOV × rect 𝜙 𝑚𝑘 90 ∘
Lambertian
Pattern
Propagation
Effective
Area of photodetector
Receiver’s FOV
Transmitter’s FOV
𝜙 𝑚𝑘
𝐧 R
𝜃 𝑚𝑘
𝜃 FOV
𝐧 mk
Lambertian
pattern
Field of
view
𝐯 𝑚𝑘
VLC Receiver
𝑘th VAP

10. System Model Received Signal Strength (RSS): where Lambertian pattern
𝜙 𝑚𝑘
𝐧 R
𝜃 𝑚𝑘
𝜃 FOV
𝐧 mk
Lambertian
pattern
Field of
view
𝐯 𝑚𝑘
VLC Receiver
𝑘th VAP

11. Proposed Method 1: AoA Based Localization
5/8/2018
Proposed Method 1: AoA Based Localization
Idea: Select one of the LED transmitters as an anchor node for each VAP and find the location which minimizes the sum squared distances
𝑑 1
𝑑 2
𝑑 3
𝐿 2 :Line
𝐿 3
𝐿 1
VLC Receiver
𝑧-axis
𝑥-axis
𝑦-axis
The objective function is expressed as
𝐫 = arg min 𝛉 𝑘 𝛽 𝑚𝑘 𝑑 𝑚𝑘 2 𝛉
𝛽 𝑚𝑘 : Weights

12. Proposed Method 1: AoA Based Localization
How to find the weights?
How to find the distance between a point and a line?
The closed-form solution is obtained with least squares (LS) method as
𝑧-axis
𝑥-axis
𝑦-axis
𝑑 1
𝑑 2
𝑑 3
Bad
Very good
Good
Heuristic: The receiver is more likely to be on the directions of LED transmitters with high RSSs.
𝛽 𝑚𝑘 = 𝑃 𝑚𝑘
𝛉: An arbitrary point
𝐫 𝑚𝑘 : LED transmitter location
𝐧 𝑚𝑘 :LED transmitter direction
𝑑 𝑚𝑘 (𝛉)= 𝐀 𝑚𝑘 𝐫 𝑚𝑘 − 𝐀 𝑚𝑘 𝛉 𝟐
𝐀 𝑚𝑘 =𝐈− 𝐧 𝑚𝑘 𝐧 𝑚𝑘 T
𝐫 = 𝐀 † 𝐛
𝐀= 𝑘 𝑃 𝑚𝑘 𝐀 𝑚𝑘
𝐛= 𝑘 𝑃 𝑚𝑘 𝐀 𝑚𝑘 𝐫 𝑚𝑘

13. Proposed Method 2: RSS Based Localization
Noise disturbs the received signal strength as
In AWGN, maximum likelihood (ML) estimation of 𝛉 corresponds to non-linear least squares (NLS) problem:
𝐬=𝐩 𝛉 +𝐧= 𝑃 11 ⋮ 𝑃 𝑚𝑘 ⋮ 𝑃 𝑀𝐾 +𝐧
Noisy
observations
Additive white
Gaussian noise vector
Receive signal strength expression related
to each LED transmitter
VAP
VLC receiver
Lambertian
pattern
𝛉 ML = 𝛉 NLS = arg min 𝛉 𝐬−𝐩 𝛉 2 2
𝐬−𝐩 𝛉 =𝟎
System of nonlinear equations
(due to Lambertian pattern)
Idea: Find the intersection of RSS contours.

14. Proposed Method 2: RSS Based Localization
How to solve the system of nonlinear equations?
As 𝐇 is analytically available, CRLB which capture any deployment scenario in 3D is obtained as
Multivariate Newton-Raphson method
𝛉 (𝑖+1) = 𝛉 (𝑖) − 𝐇 † 𝐬−𝐩 𝛉 (𝑖)
𝑖:iteration index
𝐇= 𝜕 𝒑 1 𝛉 𝜕𝑥 𝜕 𝐩 1 𝛉 𝜕𝑦 𝜕 𝐩 1 𝛉 𝜕𝑧 𝜕 𝐩 2 𝛉 𝜕𝑥 𝜕 𝐩 2 𝛉 𝜕𝑦 𝜕 𝐩 2 𝛉 𝜕𝑧 ⋮ ⋮ ⋮ 𝜕 𝐩 1 𝛉 𝜕𝑥 𝜕 𝐩 1 𝛉 𝜕𝑦 𝜕 𝐩 1 𝛉 𝜕𝑧
(We derive 𝐇 analytically in the paper.)
Jacobian matrix of 𝐩 𝛉
𝐉= 1 𝜎 𝑛 2 𝐇 T 𝐇
RMSE 𝛉 ≥ tr 𝐉 −1 𝛉
where

15. Numerical Results Simulation Setup: An 8 m×8 m×3 m empty room
36 VAPs with 4 LED Transmitters (𝑛=30, i.e., highly directive LEDs).
VLC receiver with FOV of 85 ° and photodetector area is 1 c m 2 facing toward the ceiling
𝜃 polar is a parameter to investigate impact of different configurations

16. Numerical Results AOA-based localization RSS-based localization
5/8/2018
Numerical Results
AOA-based localization
RSS-based localization
AOA based localization: The accuracy is within the range of 0 and 1 m. It is good when VLC receiver is on the intersection of the directions of LED transmitters.
RSS based localization: The accuracy is within the range of 0 and 0.1 m. It attains the CRLB at some points.
(50 iterations are considered for the learning rule, Initial point is obtained from AoA-based localization)
Positioning accuracy of the AOA-based localization approach is within the range of 0 and 1 m. In particular, it provides high positioning accuracy when the position of the VLC receiver is on the intersection of the directions of LED transmitters. However, its performance degrades at the locations close to the edges of the room since the setup does not provide sufficient numbers of LED transmitters where their directions homogeneously span the room, especially on z-axis.
For the RSS-based localization method, the initial point of the learning rule is set to the result of AOA-based algorithm. For each realization, 10 LED transmitters with highest RSSs are taken into account. It converges to the optimal point with 1 mm tolerance in less than 50 iterations. As shown in second figure, RSS-based approach offers superior positioning accuracy compared to the AOA-based approach since it exploits the Lambertian pattern. It can achieve better than 10 cm positioning error when the initial point is close to the global optimum.
In third figure, CRLB is also given for the same setup. Based on CRLB, RSS based localization achieves acceptable performance with the learning rule.
CRLB

17. 5/8/2018
Numerical Results
CDF of CRLB for a given 𝜃 polar (The receiver’s height is fixed to 0:5 m)
When the receiver is located at a low altitude, the lower 𝜃 polar offers better positioning accuracy

18. Concluding Remarks and Future Work
5/8/2018
Concluding Remarks and Future Work
AOA-based localization can be solved with an LS estimator
Low positioning accuracy
RSS-based localization method introduces high positioning accuracy
Nonlinear equations  learning rule based on Newton-Raphson method
CRLB is derived for RSS based localization method
Journal Paper (IEEE Journal of Lightwave Technology)
Future Work
The optimization of physical configurations of LED transmitters is one of the study items.
In this study, we investigate the positioning accuracy of two different localization methods for VLC systems: AOA-based localization and RSS-based localization.
We show that AOA based localization can be solved with an LS estimator which tends to yield low positioning accuracy.
On the other hand, RSS-based localization method introduces high positioning accuracy at the expense of a system of nonlinear equations.
In order to solve system of nonlinear equations, we derive an analytical learning rule and achieve up to 10 cm localization error when it is incorporated with AOA-based localization.
In addition, we derive CRLB based on RSS information for an arbitrary configuration in 3D geometry. The numerical results indicate that there exists a trade-off between high positioning accuracy and seamless localization for RSS-based method, due to the directivity of LEDs.
As a result, even distribution of the light in the room may be one of the factors for obtaining not only acceptable positioning error but also seamless localization.

19. References
[1] Y. S. Eroglu, I. Guvenc, N. Pala, and M. Yuksel, “AOA-based localization and tracking in multi-element VLC systems,” in Proc. IEEE Wireless and Microwave Technology Conference (WAMICON), Apr
[2] X. Zhang, J. Duan, Y. Fu, and A. Shi, “Theoretical accuracy analysis of indoor visible light communication positioning system based on received signal strength indicator,” IEEE J. Lightw. Technol., vol. 32, no. 21, pp. 4180–4186, Nov
[3] J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Select. Areas Commun. (JSAC), vol. 11, no. 3, pp. 367–379, Apr

20. Q&A