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# Robust Visible Light Positioning: a Comparative Study of Machine Learning Estimators in Spatial Segmentation and Transmitter Failure Scenarios

Kevin Acuna-Condori, Hongyu Guan, Bastien Béchadergue, Luc Chassagne

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## To cite this version:

Kevin Acuna-Condori, Hongyu Guan, Bastien Béchadergue, Luc Chassagne. Robust Visible Light Positioning: a Comparative Study of Machine Learning Estimators in Spatial Segmentation and Transmitter Failure Scenarios. ICC 2025 - IEEE International Conference on Communications, Jun 2025, Montreal, Canada. pp.3845-3851, 10.1109/ICC52391.2025.11160859. hal-05327822

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https://hal.science/hal-05327822v1

Submitted on 23 Oct 2025

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# Robust Visible Light Positioning: A Comparative Study of Machine Learning Estimators in Spatial Segmentation and Transmitter Failure Scenarios

Kevin Acuna-Condori*, Hongyu Guan*, Bastien Béchadergue* and Luc Chassagne*

*Laboratoire d'Ingénierie des Systèmes de Versailles

Université Paris-Saclay, UVSQ, 78140 Vélizy-Villacoublay, France

Email: {kevin-jose.acuna-condori, hongyu.guan, bastien.bechadergue, luc.chassagne}@uvsq.fr

***Abstract***—Visible Light Positioning (VLP) systems present a promising alternative for indoor positioning by leveraging existing Light-Emitting Diode (LED) lighting infrastructure to achieve high accuracy. However, challenges such as uneven error distribution and vulnerability to transmitter failures can compromise system robustness. This study conducts a comprehensive comparative analysis of machine learning estimators for VLP, emphasizing spatial segmentation and transmitter failure scenarios.

An experimental setup with four LED transmitters was utilized to collect a dataset of received signal strengths across various positions within a 1.2 × 1.2 m testbed. Polynomial interpolation was applied to augment the dataset, expanding the number of samples from 169 to 625. The workspace was divided into center and edge regions based on cumulative angles of emission, and classification models were employed to validate this segmentation.

Several machine learning estimators were evaluated for position estimation. Gaussian Process (GP) regressor achieved the lowest overall Root Mean Square Error (RMSE) of 1.973 cm, particularly excelling in the center region. All models exhibited lower errors in the center compared to the edge, highlighting significant regional disparities.

Robustness under transmitter failure was assessed by simulating the failure of one transmitter. GP regressor demonstrated resilience, maintaining low RMSE and experiencing moderate performance degradation (28.1%). These findings underscore the importance of spatial segmentation in VLP systems and the effectiveness of GP and Support Vector Machine estimators in achieving robust and accurate positioning. The study suggests that accounting for regional differences and potential transmitter failures can lead to more resilient and precise VLP solutions.

***Keywords***—Visible Light Positioning, Machine Learning, Spatial Segmentation, Transmitter Failure, Received Signal Strength, Data Interpolation, Gaussian Process Regression

## I. INTRODUCTION

Visible Light Positioning (VLP) technology has emerged as a promising alternative for Indoor Positioning Systems (IPS) in recent years. Unlike other technologies such as Wi-Fi, Bluetooth Low Energy, and Radio Frequency Identification, VLP utilizes the existing Light-Emitting Diode (LED) lighting infrastructure, which provides a cost-effective and easily deployable solution [1]. VLP systems are particularly attractive in environments where precision and reliability are important, such as museums, theaters, offices, schools, shopping centers, and critical areas like hospitals and military zones. However,

the robustness evaluation of these systems is not extensively studied [2].

To develop a VLP system, various techniques are employed, including Received Signal Strength (RSS), Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Angle of Arrival (AOA). RSS-based methods are the most widely studied due to their practical implementation advantages [3]. RSS methods require only the measurement of signal strength at a photodiode (PD) receiver, making them versatile, embeddable, and low-cost. The RSS from multiple LED transmitters is used by position estimation algorithms to determine the receiver's location, as extensively studied in [2].

However, existing studies often overlook critical scenarios such as transmitter failures (i.e. situations where an LED transmitter becomes non-functional due to issues such as burnout, power loss, or physical damage, leading to a loss of signal) and the impact of environmental factors on estimator performance [4]. Additionally, the Lambertian radiation pattern of LEDs results in signal degradation as the angle of emission increases, particularly at the edges of the transmitter array. This leads

<figure><img src="image_4.png" /><figcaption>Fig. 1. Setup of VLP system.</figcaption></figure>
to decreased signal-to-noise ratio (SNR), affecting positioning accuracy [5]. Consequently, error distribution is often uneven across the workspace, but this important phenomenon is frequently neglected in comparative analyses of estimation models.

This study contributes to the field by providing a comprehensive evaluation of several machine learning-based position estimation models in VLP systems, proposes incorporating spatial segmentation to analyze error distribution. Classification models are trained to validate the segmentation into center and edge regions, which can be utilized in future region-focused estimation architectures. Furthermore, various interpolation methods suitable for VLP systems are evaluated to enhance the dataset for training. Finally, the study assesses estimator robustness in scenarios involving transmitter failures.

This paper is organized as follows: Section II presents the system overview, Section III details the methodology, including data interpolation, region segmentation, and machine learning estimators. Section IV discusses the results. Finally, Section V concludes with main finding of this work.

## II. SYSTEM OVERVIEW

### A. Visible Light Positioning System

The experimental setup for the positioning system is introduced in Shi et al. [6]. Four infrared LED transmitters ($T_1-T_4$) with 940 nm wavelength are arranged in a square configuration at 2.16 m height (Fig. 1), each employing commercial optical antennas (LiFiMAX) containing three parallel silicon PD in the receiver chain. The LED arrays operate with a bias current of 350 mA, maintaining linearity in the electro-optical response through controlled ±250 mA drive current variations, amplified via a Mini-Circuits ZHL-6A-S+ power amplifier with 13 dB gain.

Each transmitter features a semi-angle at half power of $\phi_{1/2} = 45^\circ$ and downward orientation ($\eta_{t,i} = [0, 0, -1]$). The receiver contains three PDs with total photosensitive area 79.2 mm$^2$ and 0.62 A/W responsivity at 940 nm, vertically oriented ($\eta_r = [0, 0, 1]$) at 0.2 m height. A transimpedance amplifier with 30 MHz bandwidth and RC equalization compensates for PD capacitance effects in the receiver chain.

Multi-band carrierless amplitude and phase signals are generated in MATLAB and transmitted through an Ettus Universal Software Radio Peripheral (USRP) X300 with Ettus BasicTX daughterboard. A single transmitter unit was sequentially positioned at each predefined location ($T_1-T_4$), with RSS measurements collected at all receiver grid positions before relocating to the next transmitter site. The 1.2 × 1.2 m test area features blackout curtains to isolate it from any external light signals as well as reflected light, maintaining a constant vertical separation $h = 1.96$ m between transmitters and receiver.

### B. Enhanced Dataset Collection

The original dataset (ODB) contains 169 samples from a 13×13 grid (10 cm spacing) in the xy plane. Each sample's feature vector $P_i = [P_{i,1}, ..., P_{i,4}]$ derives from RSS measurements. For each transmitter position, the USRP X300 recorded baseband signals through its Ettus BasicRX daughterboard during receiver grid sweeps, with post-processing in MATLAB extracting RSS values.

To ensure measurement consistency, the receiver maintains fixed orientation during data collection. Additionally, a split of 75% of the data is used for training and 25% of unseen data for testing, applied to both classification and regression tasks. Time-stamped position labels $X_i = (x_i, y_i)$ are registered using a laser-guided positioning system.

## III. METHODOLOGY

### A. Data Interpolation

In VLP systems, acquiring in-situ experimental samples is time-consuming, and practical constraints often limit the number of samples that can be collected. To address this challenge, interpolation techniques can be employed to augment the dataset, thereby enhancing the training of machine learning algorithms. In this study, the dataset is expanded from an ODB of 169 samples on a 13 × 13 grid to an extended database (EDB) of 625 samples on a denser 25 × 25 grid with 5 cm spacing between each point.

The data augmentation process involves two main steps: the validation of the interpolation methods; and the generation of the extended database.

1) **Validation of Interpolation Methods:** A subset of the ODB, comprising points at 20 cm intervals, is employed to interpolate the values for the intermediate points. This step serves as a benchmark, allowing for the evaluation of the accuracy and feasibility of various interpolation techniques against known measurements.

The following interpolation methods are assessed, implemented using the SciPy library in Python:

a) **Linear Interpolation:** Linear interpolation estimates unknown values by linearly interpolating between adjacent known data points.

b) **Nearest Neighbor:** This method assigns to each unknown point the value of its nearest measured data point.

c) **Radial Basis Function (RBF) Interpolation:** RBF interpolation employs radial basis functions, which are powerful for handling multidimensional and irregularly spaced data. The method uses a weighted sum of radial basis functions centered at known data points to estimate unknown values.

d) **Cubic Spline Interpolation:** This technique fits a cubic spline—consisting of piecewise third-degree polynomials—to the data points. It ensures continuity not only of the function but also of its first and second derivatives across data points.

e) **Polynomial Interpolation:** Polynomial interpolation fits a single polynomial curve of degree $n$ (where $n$ is typically one less than the number of data points) over the entire dataset.

2) **Generation of the Extended Database:** Using the full ODB, the EDB is generated by applying the interpolation method that exhibited the most robust performance during the validation phase.
## B. Region Segmentation and Classification

Distinct behaviors are exhibited by edge points compared to central points due to the spatial distribution of transmitters within the workspace. Points at the center of this distribution show a balanced spread of the angle $\phi_i$, whereas edge points demonstrate smaller angles for some transmitters and larger angles for others. Additionally, edge points, where power decreases with distance, have smaller SNR and are more susceptible to reflections, which are not considered in this study. Consequently, they necessitate distinct analytical approaches.

Figure 2 presents a normalized distribution of the cumulative angles of emission ($\sum_{i=1}^4 \phi_i$) for each point in the xy plane of the testbed. This distribution forms the basis for proposing the use of two distinct regions—the center and the edge (delineated based on a geometric criterion)—for studying and analyzing the robustness of position estimators in VLP systems. It is posited that this differentiation provides crucial insights for evaluating the effectiveness of these estimators.

To confirm the appropriateness of this delineation and to demonstrate differing behaviors across these regions, several machine learning algorithms are employed to perform regional classification tasks, utilizing received power ($P_r$) from the EDB as inputs. The classifiers to be evaluated for this task are listed in Table II and are described in greater detail in the next subsection.

## C. Machine Learning Estimators

This work includes a comparative analysis of several machine learning methods used for position estimation. Descriptions of the models used as position estimators (as regressor) and region segmentation (as classifier) are presented below:

1) **K-Nearest Neighbor (KNN):** This algorithm assigns a class based on the majority vote of the nearest neighbors,

categorizing an object with the class most common among its k nearest neighbors:

$$y = \arg \max_j \sum_{i=1}^{k} I(y_i = j) \quad (1)$$

where I is the indicator function, and $y_i$ are the labels of the k nearest training examples to the query point [2].

2) **Weighted K-Nearest Neighbor (WKNN):** This variant of KNN weights neighbors by the inverse of their distance to the query point, enhancing the influence of closer neighbors:

$$y = \arg \max_j \sum_{i=1}^{k} \frac{I(y_i = j)}{d(x, x_i)} \quad (2)$$

where $d(x, x_i)$ is the distance between the query point x and its i-th nearest neighbor [7].

3) **Improved Weighted K-Nearest Neighbor (IWKNN):** Enhancing WKNN, this method adjusts weights based on both the distance and the density of points, refining the influence of each neighbor:

$$y = \arg \max_j \sum_{i=1}^{k} \frac{I(y_i = j)}{d(x, x_i) \cdot a(x_i)} \quad (3)$$

where $a(x_i)$ denotes the angle between the query point x and its i-th nearest neighbor [8].

4) **Random Forest (RF):** Random Forests build multiple decision trees and output the class that is the mode of the classes output by the individual trees:

$$y = \text{mode}\{y^{(1)}, y^{(2)}, \dots, y^{(T)}\} \quad (4)$$

where T is the number of trees in the forest [9].

5) **Extreme Decision Trees (EDT):** EDTs are similar to RF but introduce more randomness by selecting cut-points at random for each feature, which helps in reducing variance[10].

6) **Gradient Boosting (GB):** GB builds an ensemble of weak prediction models, typically decision trees, in a stage-wise fashion by optimizing a loss function [11].

7) **Support Vector Machine (SVM):** SVMs create a hyper-plane that optimally separates the classes in the feature space, maximizing the margin between them:

$$\min_{\mathbf{w},b} \frac{1}{2} \|\mathbf{w}\|^2 + C \sum_{i=1}^{n} \xi_i \quad (5)$$

subject to $y_i(\mathbf{w} \cdot \mathbf{x}_i + b) \ge 1 - \xi_i$ for each i [12].

8) **Multi-Layer Perceptron (MLP):** MLPs are feedforward neural networks for classification, operating through layers of neurons with nonlinear activation functions:

$$\mathbf{y} = \sigma(\mathbf{W}_2\sigma(\mathbf{W}_1\mathbf{x} + \mathbf{b}_1) + \mathbf{b}_2) \quad (6)$$

where $\sigma$ is the activation function [13].

<figure><img src="image_5.png" /><figcaption>Fig. 2. Normalized cumulative angle of emission.</figcaption></figure>
9) Gaussian Process (GP): GP models offer a probabilistic approach to regression and classification, using a collection of random variables, any finite number of which have a joint Gaussian distribution:

$$y(x) = \mathcal{N}(\mu(x), \sigma^2(x)) \qquad (7)$$

where $\mu(x)$ and $\sigma^2(x)$ are the mean and variance of the Gaussian process at point $x$ [14].

10) Voting (VO): The Voting method combines different algorithms, using majority voting for classification decisions:

$$y = \text{majority}\{y^{(1)}, y^{(2)}, \dots, y^{(M)}\} \qquad (8)$$

where $M$ is the number of models involved in the vote [2].

## D. Sensitivity Analysis to Transmitter Failures

Certain environments where VLP systems are deployed, such as hospitals and military applications, may exhibit higher sensitivity to positioning errors. Therefore, it is imperative to investigate the impact of critical conditions on position estimation to assess the robustness of the estimators and to gain new insights and decision-making criteria.

A scenario is proposed in which one of the transmitters fails. The estimation error for each of the evaluated models is assessed by utilizing only three out of the four transmitters as inputs. This evaluation process is repeated four times, each time simulating the independent failure of a different transmitter. The average estimation error across these simulations is then reported.

# IV. RESULTS AND DISCUSSION

## A. Analysis of Data Interpolation Techniques

Table I compares the results of interpolating received power measurements from each of the four transmitters using different interpolation methods. As observed, the RBF interpolation

<figure><img src="image_6.png" /><figcaption>Fig. 3. Inference of receptor region using a GP classifier.</figcaption></figure>

with a cubic kernel presents the lowest error rates in the interpolation of $T_1$ and $T_4$; however, it does not perform well for the estimation of $T_2$. In contrast, the polynomial interpolation method (degree $n = 3$) stands out by accurately estimating $T_2$ and achieving the lowest average Mean Squared Error (MSE = 0.046), calculated by averaging the MSEs of all $T$s, suggesting greater versatility in fitting curves that capture the general trend of the data and approximating new power measurements at unseen positions. Conversely, the Nearest Neighbor method exhibits the highest MSE (MSE = 0.526) and is not recommended for interpolation in VLP systems.

Considering the lowest MSE obtained, the polynomial interpolation method was selected for generating the mesh grid ($25 \times 25$) of the EDB. This choice is coherent since the relationships in VLP systems tend to follow polynomial trends.

## B. Evaluation of Region Segmentation and Classification

To confirm that the two proposed regions in Fig. 2 (center and edge) exhibit distinct characteristics and behaviors, various classification models were trained using the EDB to infer the region to which each sample belongs. The results obtained are detailed in Table II. The GP based model stands out, achieving the highest precision, recall, and F1-score, with 99.36% in each metric and a processing time of 0.0134 ms, indicating not only high effectiveness but also efficiency in region classification. In contrast, methods such as WKNN, despite being slightly faster (0.0106 ms), show lower effectiveness compared to more complex techniques like GB and MLP, both achieving performance over 98.70% in all evaluated metrics. Overall, these results confirm the existence of distinct characteristics and behaviors in both regions, evidenced by the high classification accuracy achieved by the models (mean accuracy = 97.88%). Figure 3 shows the inference of the model with the highest accuracy (GP), where samples classified as belonging to the center region are depicted in green and those classified as edge region are in blue.

This analysis suggests that the distinction between the center and edge regions is statistically significant and can be effectively exploited by classification models. These findings support the proposal to consider the estimation behavior in the center and edge regions within the robustness evaluation. Moreover, these regional differences suggest the potential development of future position estimation techniques in VLP systems. The ability to accurately classify these differences may enable the application of specific signal preprocessing and equalization methods for each region, as well as region-specific estimators.

## C. Comparative Analysis of Machine Learning Estimators

The performance of various machine learning estimators for position estimation in VLP systems was analyzed, considering overall accuracy, performance in center and edge regions, and robustness under transmitter failure conditions. Table III presents a comparison of different estimators, including metrics such as Root Mean Square Error (RMSE) in centimeters, the 90th percentile of the Cumulative Distribution Function
<figure><img src="image_7.png" /><figcaption>Fig. 4. Reference Position (blue point) versus Estimated Position (red points) for each model and the visual distribution of error in Center and Edge regions</figcaption></figure>

<table><caption>TABLE I
COMPARISON OF MSE PER INTERPOLATION METHODS</caption><thead><tr><th>Method</th><th>T<sub>1</sub></th><th>T<sub>2</sub></th><th>T<sub>3</sub></th><th>T<sub>4</sub></th><th>Mean</th></tr></thead><tbody><tr><td>Linear</td><td>0.03666</td><td>0.10191</td><td>0.08357</td><td>0.02539</td><td>0.06188</td></tr><tr><td>Nearest Neighbor</td><td>0.37301</td><td>0.63804</td><td>0.48534</td><td>0.60780</td><td>0.52605</td></tr><tr><td>Cubic Spline</td><td>0.02358</td><td>0.12543</td><td>0.07408</td><td>0.01621</td><td>0.05982</td></tr><tr><td>RBF (Linear)</td><td>0.02911</td><td>0.06975</td><td>0.08143</td><td>0.01841</td><td>0.04967</td></tr><tr><td>RBF (Cubic)</td><td>0.02096</td><td>0.10439</td><td>0.08160</td><td>0.01511</td><td>0.05552</td></tr><tr><td><strong>Polynomial</strong></td><td><strong>0.02980</strong></td><td><strong>0.05309</strong></td><td><strong>0.07787</strong></td><td><strong>0.02370</strong></td><td><strong>0.04611</strong></td></tr></tbody></table>

<table><caption>TABLE II
COMPARISON OF CLASSIFIERS</caption><thead><tr><th>Method</th><th>Accuracy</th><th>Precision</th><th>Recall</th><th>F1 Score</th><th>Time (ms)</th></tr></thead><tbody><tr><td>KNN</td><td>96.82%</td><td>97.06%</td><td>96.75%</td><td>96.81%</td><td>0.0527</td></tr><tr><td>WKNN</td><td>96.18%</td><td>96.18%</td><td>96.18%</td><td>96.18%</td><td>0.0106</td></tr><tr><td>RF</td><td>97.45%</td><td>97.45%</td><td>97.45%</td><td>97.45%</td><td>0.0266</td></tr><tr><td>ET</td><td>98.09%</td><td>98.19%</td><td>98.05%</td><td>98.09%</td><td>0.0294</td></tr><tr><td>GB</td><td>98.73%</td><td>98.78%</td><td>98.70%</td><td>98.72%</td><td>0.0077</td></tr><tr><td>MLP</td><td>98.73%</td><td>98.78%</td><td>98.70%</td><td>98.72%</td><td>0.0020</td></tr><tr><td>SVM</td><td>97.45%</td><td>97.62%</td><td>97.40%</td><td>97.45%</td><td>0.0083</td></tr><tr><td><strong>GP</strong></td><td><strong>99.36%</strong></td><td><strong>99.38%</strong></td><td><strong>99.35%</strong></td><td><strong>99.36%</strong></td><td><strong>0.0134</strong></td></tr><tr><td>VO</td><td>98.09%</td><td>98.19%</td><td>98.05%</td><td>98.09%</td><td>0.0638</td></tr><tr><td><strong>Mean</strong></td><td><strong>97.88%</strong></td><td><strong>97.96%</strong></td><td><strong>97.85%</strong></td><td><strong>97.87%</strong></td><td><strong>0.0238</strong></td></tr></tbody></table>

(CDF), mean inference time, RMSE under transmitter failure, and the impact percentage due to failure. To assess robustness under transmitter failure, a simulation of one transmitter failure was conducted, and the performance degradation was evaluated.

SVM and GP regressors achieved the lowest overall RMSE values, with 1.855 cm and 1.973 cm, respectively. Specifically, the GP regressor exhibited superior performance in the center region (RMSE = 1.074 cm) and maintained competitive accuracy in the edge region (RMSE = 2.555 cm). Similarly,

the SVM performed well in both regions. In all cases, the models presented a lower error in the center region than at the edge, reaffirming the proposition that these are distinct zones. This observation invites the exploration of methods that better distribute the error or focus on increasing the precision in the edge region. The differentiation of segments is thus of significant importance.

MLP showed good performance, with an overall RMSE of 2.581 cm, and demonstrated a relatively low impact under transmitter failure (26.3%). This indicates that MLPs can maintain reasonable accuracy even when one transmitter fails, showcasing robustness.

KNN based methods, including WKNN and IWKNN, achieved moderate RMSE values and demonstrated relatively lower impact percentages under failure conditions (around 34%). These methods benefit from simplicity and fast inference times (approximately 0.009 ms), although their accuracy is slightly lower than that of VO and SVM.

Ensemble methods such as RF and GB Regressor presented higher RMSE values and greater impact percentages under transmitter failure (over 50%), suggesting that they may be less suitable for scenarios with potential transmitter malfunctions. The EDT showed good RMSE in the center region (1.493 cm) but experienced significant performance degradation under failure (impact of 59.3%).

In terms of inference time, most estimators demonstrated acceptable computational efficiency. The GP regressor achieved a good balance between accuracy and computational efficiency (mean inference time = 0.0155 ms). Although the EDT had a longer inference time (2.9005 ms), the processing times of all estimators are suitable for practical applications.

The GP regressor exhibited a moderate impact (28.1%), maintaining relatively low RMSE under failure (2.527 cm). In contrast, methods like RF and EDT showed significant
<table><caption>TABLE III
COMPARISON OF DIFFERENT ESTIMATOR METHODS</caption><thead><tr><th rowspan="2">Method</th><th colspan="3">RMSE (cm)</th><th rowspan="2">CDF (90%)</th><th rowspan="2">Mean Inference Time (ms)</th><th colspan="3">Failure Analysis</th></tr><tr><th>General</th><th>Center</th><th>Edge</th><th>RMSE (cm)</th><th>Δ RMSE (cm)</th><th>Impact (%)</th></tr></thead><tbody><tr><td>K-Nearest Neighbor</td><td>3.0755</td><td>2.4941</td><td>3.5461</td><td>5.0396</td><td>0.0086</td><td>4.1185</td><td>1.0430</td><td>33.9%</td></tr><tr><td>Weighted K-Nearest Neighbor</td><td>2.8854</td><td>2.3876</td><td>3.2942</td><td>4.6050</td><td>0.0090</td><td>3.8765</td><td>0.9911</td><td>34.4%</td></tr><tr><td>Improved Weighted K-Nearest Neighbor</td><td>2.8721</td><td>2.3983</td><td>3.2638</td><td>4.5003</td><td>0.3598</td><td>4.0512</td><td>1.1790</td><td>41.1%</td></tr><tr><td>Random Forest</td><td>3.4570</td><td>2.6425</td><td>4.0905</td><td>5.7267</td><td>0.2914</td><td>5.4421</td><td>1.9851</td><td>57.4%</td></tr><tr><td>Extreme Decision Trees</td><td>2.2647</td><td>1.4929</td><td>2.8143</td><td>3.4659</td><td>2.9005</td><td>3.6088</td><td>1.3441</td><td>59.3%</td></tr><tr><td>Gradient Boosting Regressor</td><td>3.3459</td><td>2.9963</td><td>3.6508</td><td>4.8115</td><td>0.0332</td><td>5.0810</td><td>1.7351</td><td>51.9%</td></tr><tr><td>Multi-Layer Perceptron</td><td>2.5807</td><td>1.9586</td><td>3.0624</td><td>3.5250</td><td>0.0120</td><td>3.2594</td><td>0.6787</td><td>26.3%</td></tr><tr><td>Support Vector Machine</td><td>1.8553</td><td>1.1582</td><td>2.3375</td><td>2.4757</td><td>0.0238</td><td>2.6787</td><td>0.8234</td><td>44.4%</td></tr><tr><td><strong>Gaussian Process</strong></td><td><strong>1.9731</strong></td><td><strong>1.0738</strong></td><td><strong>2.5554</strong></td><td><strong>2.3753</strong></td><td><strong>0.0155</strong></td><td><strong>2.5267</strong></td><td><strong>0.5536</strong></td><td><strong>28.1%</strong></td></tr><tr><td>Voting Estimator</td><td>2.2004</td><td>1.5630</td><td>2.6740</td><td>3.1190</td><td>0.1686</td><td>3.4323</td><td>1.2319</td><td>56.0%</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Comparison of cumulative distribution function.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Estimation with regular $4T$ vs. $3T$</figcaption></figure>

performance degradation, with impact percentages over 57%.

Figure 4 shows the estimated positions (in red) versus the reference positions (in blue) for each model, highlighting the two regions (center and edge). It is visually apparent that the edge region is more susceptible to errors in all models, reinforcing the importance of addressing the specific challenges in this region. Figure 5 illustrates the CDFs of positioning errors for all estimators, emphasizing that the GP and SVM regressors display the steepest curves, indicating higher accuracy. Finally, Figure 6 presents the position estimation comparison between using four transmitters versus simulating the failure of one transmitter, employing the GP estimator, allowing visual comparison of the estimator's robustness.

V. CONCLUSIONS

This paper presented a comprehensive comparative study of machine learning estimators for position estimation in VLP systems, with a focus on spatial segmentation and transmitter failure scenarios. The use of polynomial interpolation was validated as an effective method for augmenting the dataset, enhancing the training process of the estimators.

The segmentation of the workspace into center and edge regions was confirmed to be statistically significant through high classification accuracies achieved by various models, particularly the GP classifier. This regional differentiation allowed for a detailed analysis of the estimators' performance across different spatial zones.

The comparative analysis revealed that the GP and SVM regressors exhibited superior performance, achieving the lowest overall RMSE values and CDFs. Notably, all models demonstrated lower errors in the center region compared to the edge region, highlighting the importance of addressing the specific challenges associated with edge areas. The GP regressor also demonstrated robustness under transmitter failure conditions, keeping low RMSE and moderate performance degradation.

These findings underscore the significance of considering spatial segmentation in the evaluation and design of VLP systems. By acknowledging the distinct characteristics of different regions within the workspace, more effective and robust positioning solutions can be developed. Future work may focus on developing specialized estimators or preprocessing
techniques for edge regions to achieve a more uniform error
distribution across the entire area.

ACKNOWLEDGMENT

This work was supported in part by the French National
Research Agency (ANR) through the Project SAFELiFi under
Grant ANR-21-CE25-0001-01, in part by the French Agence
de l'innovation de défense (AID) through the project SO-
LERIS under Grant 2022 29 0951, and in part by the European
Union's Smart Networks and Services Joint Undertaking (SNS
JU) under grant agreement No. 101139292.

REFERENCES

[1] Z. Zhu et al., "A survey on indoor visible light positioning systems: Fundamentals, applications, and challenges," *IEEE Communications Surveys & Tutorials*, pp. 1–1, 2024.

[2] V. P. Rekkas et al., "Artificial intelligence in visible light positioning for indoor iot: A methodological review," *IEEE Open Journal of the Communications Society*, vol. 4, p. 2838 – 2869, 2023.

[3] R. Wang et al., "A survey of visible-light-communication-based indoor positioning systems," *Sensors*, vol. 24, no. 16, 2024.

[4] W. Sun, J. Chen, and C. Yu, "Indoor receiving signal strength based visible light positioning enabled with equivalent virtual lamps," *Applied Optics*, vol. 62, no. 17, p. 4583 – 4590, 2023.

[5] J. De Bruycker et al., "Evaluation of machine learning models for received signal strength based visible light positioning with obstacles," in *2024 14th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)*, 2024, pp. 318–323.

[6] L. Shi et al., "Experimental demonstration of integrated optical wireless sensing and communication," *Journal of Lightwave Technology*, vol. 42, no. 20, p. 7070 – 7084, 2024.

[7] A. H. A. Bakar et al., "Accurate visible light positioning using multiple-photodiode receiver and machine learning," *IEEE Transactions on Instrumentation and Measurement*, vol. 70, pp. 1–12, 2021.

[8] R. Liu et al., "Accuracy enhancement of indoor visible light positioning using improved wknn algorithm," in *2023 IEEE 11th International Conference on Information, Communication and Networks (ICICN)*, 2023, pp. 109–114.

[9] R. Liu, Z. Liang, K. Yang, and W. Li, "Machine learning based visible light indoor positioning with single-led and single rotatable photo detector," *IEEE Photonics Journal*, vol. 14, no. 3, pp. 1–11, 2022.

[10] P. Geurts, D. Ernst, and L. Wehenkel, "Extremely randomized trees," *Machine Learning*, vol. 63, no. 1, pp. 3–42, 2006.

[11] J. H. Friedman, "Greedy function approximation: A gradient boosting machine," *Annals of Statistics*, vol. 29, no. 5, pp. 1189–1232, 2001.

[12] K. V. Menu, C. A. Leke, and A. R. Ndjiongue, "Machine learning assisted indoor visible light communication system," in *2023 International Telecommunications Conference (ITC-Egypt)*, 2023, pp. 440–445.

[13] H. Ramchoun et al., "Multilayer perceptron: Architecture optimization and training," *International Journal of Interactive Multimedia and Artificial Intelligence*, vol. 4, pp. 26–30, 01 2016.

[14] N. Knudde et al., "Data-efficient gaussian process regression for accurate visible light positioning," *IEEE Communications Letters*, vol. 24, no. 8, pp. 1705-1709, 2020.