The Usage of ANN for Regression Analysis in Visible Light Positioning Systems
<p>A VLP system with system configuration.</p> "> Figure 2
<p>Block diagram of the proposed system.</p> "> Figure 3
<p>The received power distributions for the proposed system for: (<b>a</b>) LoS; (<b>b</b>) NLoS; and (<b>c</b>) LoS and NLoS links.</p> "> Figure 4
<p>The artificial neural network with: (<b>a</b>) a basic structure; and (<b>b</b>) a structure of <span class="html-italic">k</span><sup>th</sup> neuron with <span class="html-italic">N</span> inputs in the layer <span class="html-italic">m</span>.</p> "> Figure 5
<p>The layout of the neural network used with four layers.</p> "> Figure 6
<p>The measured 95% quantile function for different ANN algorithms for: (<b>a</b>) the inner; and (<b>b</b>) the outer regions.</p> "> Figure 7
<p>The <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mi>p</mi> </msub> </mrow> </semantics></math> for the inner region for different training methods of ANN: (<b>a</b>) LM, and (<b>b</b>) BR.</p> "> Figure 8
<p>The measured 95% quantile function for a various number of epochs for BR in the: (<b>a</b>) inner, and (<b>b</b>) outer regions.</p> "> Figure 9
<p>The measured 95% quantile function for NLLS and BR.</p> "> Figure 10
<p>Different error distribution plots using BR algorithm for SNR value: (<b>a</b>) 5 dB; (<b>b</b>) 10 dB; (<b>c</b>) 15 dB; (<b>d</b>) 20 dB; (<b>e</b>) 25 dB; and (<b>f</b>) 30 dB.</p> "> Figure 11
<p>The measured 95% quantile function for a different number of samples in the input with: (<b>a</b>) RS; and (<b>b</b>) US.</p> ">
Abstract
:1. Introduction
2. VLP System Modelling
2.1. System Model
2.2. Estimation Algorithms
3. The Concept of Neural Network
3.1. Use of ANN for Regression
3.2. ANN Training Methods
3.2.1. Levenberg–Marquardt Algorithm
3.2.2. Bayesian Regularization Algorithm
3.2.3. Scaled Conjugate Gradient Algorithm
4. Results and Discussion
4.1. VLP Error Performance
4.2. Selection of the Training Algorithm and Number of Neurons in the HL
4.3. Impact of Epochs and Noise Performance on the VLP System
4.4. Impact of Different Training Dataset Sizes on the VLP System
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Abbreviations
Short Form | Description |
---|---|
ANN | Artificial neural network |
AOA | Angle of arrival |
BR | Bayesian regularization |
FOV | Field of view |
HLs | Hidden layers |
HPA | Half-power angle |
LEDs | Light-emitting diodes |
LLS | Linear least square |
LM | Levenberg-Marquardt |
LoS | Line of sight |
NLLS | Nonlinear least square |
NLoS | Non-line of sight |
OOK | On-off keying |
PD | Photodiode |
RF | Radio frequency |
RSS | Received signal strength |
Rx | Receiver |
SCG | Scaled conjugate gradient |
SNR | Signal to noise ratio |
TOA | Time of arrival |
Txs | Transmitters |
VLC | Visible light communication |
VLP | Visible light positioning |
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Notation | Definition |
---|---|
Positioning error | |
ht | Height of the Tx |
hr | Height of the Rx |
m | Lambertian mode |
Total received power from the ith Tx | |
Received power from the ith Tx due to the path loss | |
Received power from ith Tx due to NLoS path | |
Additive white Gaussian noise | |
Distance between the ith Tx and the Rx | |
The irradiance angle from the ith Tx to the Rx | |
φ | Incident angle |
Photodiode responsivity | |
Transmitted power from the ith Tx | |
Ts | Transmittance function |
g | Concentrator gain of the Rx |
Area of the photodetector | |
The horizontal distance from the ith Tx to the Rx | |
h | The difference in height between the Tx and Rx, i.e., (ht− hr) |
The distances, receiving incident angle, and the irradiance angle between the ith Tx and the reflective area, respectively | |
The distances, receiving incident angle, and the irradiance angle between the reflective area and the Rx, respectively | |
ρ | The reflectance factor depending on the material of the reflective surface |
Reflectance area | |
Coefficients of the polynomial model for the order polynomial | |
The estimated position of the Rx | |
Averaged squared error | |
The estimated position of the Rx. | |
Weight | |
The vector containing all the network weights and biases for the neuron i.e., | |
The network output for the kth neuron | |
The target output of the network for the kth neuron | |
Learning rate | |
Maximum number of layers | |
Bias vector | |
m | Number of layers |
k | Number of neurons |
Input vector, | |
N | Total number of inputs |
Number of inputs | |
Error matrix | |
Sensitivity matrix | |
Least mean square error function | |
F | Mean square error |
Jacobian matrix | |
A scalar | |
I | Identity matrix |
Squared error | |
Sum of squared weights | |
Regularization parameters | |
Effective number of parameters | |
Hessian matrix | |
Total number of parameters (weights and biases) of the network | |
The trace of the inverse of Hessian matrix | |
Quadratic approximation of the error function, | |
The set of non-zero weight vectors | |
Second-order information | |
A Scalar | |
Comparison parameter | |
Percentage of the confidence interval | |
Quantile function | |
Minimum positioning error | |
Step size |
Dataset A | Dataset B | |
---|---|---|
Grid size | 60 × 60 | 100 × 100 |
Total number of sample | 18,000 | 50,000 |
Parameter | Value |
---|---|
Room size | 6 × 6 × 3 m3 |
Locations of the Txs | |
, , , | (−1.7, −1.7, 3), |
, , , | (−1.7, 1.7, 3), |
, , , | (1.7, −1.7, 3), |
, , ) | (1.7, 1.7, 3) |
Area of PD | 10−4 m2 |
Half-power angle (HPA) | 70° |
Responsivity of PD | 0.5 A/W |
Field of view (FOV) | 75° |
Transmitted power | 1 W |
Reflection coefficient | 0.7 |
Activation function | Sigmoid, linear |
Number of neurons in the input layer | 4 |
Number of neurons in the hidden layer | 2–36 |
Number of neurons in the output layer | 2 |
Number of hidden layers | 2 |
Percentage of train to test | 0.8 |
Algorithms | Neurons in HL 1 | Neurons in HL 2 | |
---|---|---|---|
LM | 0.11 | 36 | 36 |
BR | 0.06 | 32 | 28 |
BR | RSS with NLLS | |
---|---|---|
Max. PR (µW) | 6.7 × 104 | 6.7 × 104 |
Min. PR (µW) | 3.6 × 104 | 3.6 × 104 |
Max. at 20 dB (m) | 0.89 | 1.29 |
Min. at 20 dB (m) | 16 × 10−4 | 18 × 10−4 |
Max. at 25 dB (m) | 0.71 | 0.72 |
Min. at 25 dB (m) | 6.1 × 10−4 | 15 × 10−4 |
Max. at 30 dB (m) | 0.54 | 0.67 |
Min. at 30 dB (m) | 5.4 × 10−4 | 4.6 × 10−4 |
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Chaudhary, N.; Younus, O.I.; Alves, L.N.; Ghassemlooy, Z.; Zvanovec, S. The Usage of ANN for Regression Analysis in Visible Light Positioning Systems. Sensors 2022, 22, 2879. https://doi.org/10.3390/s22082879
Chaudhary N, Younus OI, Alves LN, Ghassemlooy Z, Zvanovec S. The Usage of ANN for Regression Analysis in Visible Light Positioning Systems. Sensors. 2022; 22(8):2879. https://doi.org/10.3390/s22082879
Chicago/Turabian StyleChaudhary, Neha, Othman Isam Younus, Luis Nero Alves, Zabih Ghassemlooy, and Stanislav Zvanovec. 2022. "The Usage of ANN for Regression Analysis in Visible Light Positioning Systems" Sensors 22, no. 8: 2879. https://doi.org/10.3390/s22082879
APA StyleChaudhary, N., Younus, O. I., Alves, L. N., Ghassemlooy, Z., & Zvanovec, S. (2022). The Usage of ANN for Regression Analysis in Visible Light Positioning Systems. Sensors, 22(8), 2879. https://doi.org/10.3390/s22082879