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1.
Sensors (Basel) ; 24(17)2024 Aug 29.
Artículo en Inglés | MEDLINE | ID: mdl-39275520

RESUMEN

In the evolving landscape of sixth-generation wireless communication, the integration of visible light communication (VLC) and visible light positioning (VLP), known as visible light positioning and communication (VLPC), emerges as a pivotal technology. This study addresses the challenges of asynchronous code division multiplexing (ACDM) in VLPC networks, focusing on the enhancement of data transmission quality and positioning accuracy. Firstly, we propose an orthogonal pseudo-random code (OPRC) for ACDM-based VLP systems. Leveraging its excellent correlation properties, VLP signals preserve orthogonality even amidst asynchronous transmissions, achieving sub-centimeter average positioning errors. Next, by combining OPRC with successive interference cancellation decoding (SICD), we propose an enhanced ACDM-based VLPC system that utilizes OPRC for improved signal orthogonality and SICD for progressive elimination of multiple access interference (MAI) among VLPC signals. The results show substantial improvements in bit-error rate (BER) and positioning error (PE), approaching the performance levels observed in synchronized VLPC systems. Specifically, the SICD-OPRC scheme reduces average BER to 4.3 × 10-4 and average PE to 2.7 cm, demonstrating its robustness and superiority in complex asynchronous scenarios.

2.
Sensors (Basel) ; 24(7)2024 Apr 05.
Artículo en Inglés | MEDLINE | ID: mdl-38610531

RESUMEN

In this paper, we explore the use of visible light positioning (VLP) technology in vehicles in intelligent transportation systems (ITS), highlighting its potential for maintaining effective line of sight (LOS) and providing high-accuracy positioning between vehicles. The proposed system (V2V-VLP) is based on a position-sensitive detector (PSD) and exploiting car taillights to determine the position and inter-vehicular distance by angle of arrival (AoA) measurements. The integration of the PSD sensor in vehicles promises exceptional positioning accuracy, opening new prospects for navigation and driving safety. The results revealed that the proposed system enables precise measurement of position and distance between vehicles, including lateral distance. We evaluated the impact of different focal lengths on the system performance, achieving cm-level accuracy for distances up to 35 m, with an optimum focal length of 25 mm, and under low signal-to-noise conditions, which meets the standards required for safe and reliable V2V applications. Several experimental tests were carried out to validate the results of the simulations.

3.
Sensors (Basel) ; 24(16)2024 Aug 22.
Artículo en Inglés | MEDLINE | ID: mdl-39205118

RESUMEN

New applications such as augmented reality/virtual reality (AR/VR), Internet-of-Things (IOT), autonomous mobile robot (AMR) services, etc., require high reliability and high accuracy real-time positioning and tracking of persons and devices in indoor areas. Among the different visible-light-positioning (VLP) schemes, such as proximity, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and received-signal-strength (RSS), the RSS scheme is relatively easy to implement. Among these VLP methods, the RSS method is simple and efficient. As the received optical power has an inverse relationship with the distance between the LED transmitter (Tx) and the photodiode (PD) receiver (Rx), position information can be estimated by studying the received optical power from different Txs. In this work, we propose and experimentally demonstrate a real-time VLP system utilizing long short-term memory neural network (LSTM-NN) with principal component analysis (PCA) to mitigate high positioning error, particularly at the positioning unit cell boundaries. Experimental results show that in a positioning unit cell of 100 × 100 × 250 cm3, the average positioning error is 5.912 cm when using LSTM-NN only. By utilizing the PCA, we can observe that the positioning accuracy can be significantly enhanced to 1.806 cm, particularly at the unit cell boundaries and cell corners, showing a positioning error reduction of 69.45%. In the cumulative distribution function (CDF) measurements, when using only the LSTM-NN model, the positioning error of 95% of the experimental data is >15 cm; while using the LSTM-NN with PCA model, the error is reduced to <5 cm. In addition, we also experimentally demonstrate that the proposed real-time VLP system can also be used to predict the direction and the trajectory of the moving Rx.

4.
Sensors (Basel) ; 24(18)2024 Sep 17.
Artículo en Inglés | MEDLINE | ID: mdl-39338751

RESUMEN

Despite the many potential applications of an accurate indoor positioning system (IPS), no universal, readily available system exists. Much of the IPS research to date has been based on the use of radio transmitters as positioning beacons. Visible light positioning (VLP) instead uses LED lights as beacons. Either cameras or photodiodes (PDs) can be used as VLP receivers, and position estimates are usually based on either the angle of arrival (AOA) or the strength of the received signal. Research on the use of AOA with photodiode receivers has so far been limited by the lack of a suitable compact receiver. The quadrature angular diversity aperture receiver (QADA) can fill this gap. In this paper, we describe a new QADA design that uses only three readily available parts: a quadrant photodiode, a 3D-printed aperture, and a programmable system on a chip (PSoC). Extensive experimental results demonstrate that this design provides accurate AOA estimates within a room-sized test chamber. The flexibility and programmability of the PSoC mean that other sensors can be supported by the same PSoC. This has the potential to allow the AOA estimates from the QADA to be combined with information from other sensors to form future powerful sensor-fusion systems requiring only one beacon.

5.
Sensors (Basel) ; 23(14)2023 Jul 12.
Artículo en Inglés | MEDLINE | ID: mdl-37514632

RESUMEN

Visible-light-based transmission application plays an important role in various types of sensor services for the Internet of Things (IoTs). However, in big data scenarios, current visible-light-based systems cannot achieve concurrent high-speed communication, low-speed communication, and positioning. Therefore, in this article, we propose a smart visible-light-based fusion applications system, named Fasys, to solve the above problem for the big data traffic with heterogeneity. Specifically, for low-speed data services, we propose a novel linear block coding and bit interleaving mechanism, which enhances the LED positioning accuracy and recovers the lost data bits in the interframe gap (IFG). For high-speed data services with traffic possessing burstiness, an elegant statistical reliability analysis framework in regard to latency is proposed based on martingale theory. The backlog martingale process is constructed. Leveraging stopping time theory, a tight upper bound of unreliability is obtained. An arrival abstraction and traffic allocation scheme is designed, which contributes to decouple the reliability requirement as the maximum supportable arrival load. Finally, we implement our Fasys system, and extensive experimental results show that our system can achieve consistent high-precision positioning and low-BER data communication for low-speed data services. And the proposed martingale-based traffic allocation scheme can achieve the provisioning of reliability in regard to the latency for high-speed data services.

6.
Sensors (Basel) ; 22(3)2022 Jan 27.
Artículo en Inglés | MEDLINE | ID: mdl-35161749

RESUMEN

Visible light positioning is one of the most popular technologies used for indoor positioning research. Like many other technologies, a calibration procedure is required before the system can be used. More specifically, the location and identity of each light source need to be determined. These parameters are often measured manually, which can be a labour-intensive and error-prone process. Previous work proposed the use of a mobile robot for data collection. However, this robot still needed to be steered by a human operator. In this work, we significantly improve the efficiency of calibration by proposing two novel methods that allow the robot to autonomously collect the required calibration data. In postprocessing, the necessary system parameters can be calculated from these data. The first novel method will be referred to as semi-autonomous calibration, and requires some prior knowledge of the LED locations and a map of the environment. The second, fully-autonomous calibration procedure requires no prior knowledge. Simulation results show that the two novel methods are both more accurate than manual steering. Fully autonomous calibration requires approximately the same amount of time to complete, whereas semi-autonomous calibration is significantly faster.


Asunto(s)
Luz , Calibración , Humanos
7.
Sensors (Basel) ; 22(8)2022 Apr 09.
Artículo en Inglés | MEDLINE | ID: mdl-35458867

RESUMEN

In indoor localization there are applications in which the orientation of the agent to be located is as important as knowing the position. In this paper we present the results of the orientation estimation from a local positioning system based on position-sensitive device (PSD) sensors and the visible light emitted from the illumination of the room in which it is located. The orientation estimation will require that the PSD sensor receives signal from either 2 or 4 light sources simultaneously. As will be shown in the article, the error determining the rotation angle of the agent with the on-board sensor is less than 0.2 degrees for two emitters. On the other hand, by using 4 light sources the three Euler rotation angles are determined, with mean errors in the measurements smaller than 0.35° for the x- and y-axis and 0.16° for the z-axis. The accuracy of the measurement has been evaluated experimentally in a 2.5 m-high ceiling room over an area of 2.2 m2 using geodetic measurement tools to establish the reference ground truth values.

8.
Sensors (Basel) ; 22(15)2022 Aug 05.
Artículo en Inglés | MEDLINE | ID: mdl-35957430

RESUMEN

Nowadays, indoor positioning (IP) is a relevant aspect in several scenarios within the Internet of Things (IoT) framework, e.g., Industry 4.0, Smart City and Smart Factory, in order to track, amongst others, the position of vehicles, people or goods. This paper presents the realization and testing of a low power sensor node equipped with long range wide area network (LoRaWAN) connectivity and providing 2D Visible Light Positioning (VLP) features. Three modulated LED (light emitting diodes) sources, the same as the ones commonly employed in indoor environments, are used. The localization feature is attained from the received light intensities performing optical channel estimation and lateration directly on the target to be localized, equipped with a low-power microcontroller. Moreover, the node exploits a solar cell, both as optical receiver and energy harvester, provisioning energy from the artificial lights used for positioning, thus realizing an innovative solution for self-sufficient indoor localization. The tests performed in a ~1 m2 area reveal accurate positioning results with error lower than 5 cm and energy self-sufficiency even in case of radio transmissions every 10 min, which are compliant with quasi-real time monitoring tasks.


Asunto(s)
Luz Solar , Humanos
9.
Sensors (Basel) ; 22(21)2022 Oct 26.
Artículo en Inglés | MEDLINE | ID: mdl-36365879

RESUMEN

Smart home systems (SHSs) are a modern lifestyle trend, changing daily lives in the most intuitive way. To connect and operate various smart devices under one system, an accurate, convenient, and secure control method is of utmost significance. Nowadays, most smart home control systems are based on radio-frequency (RF) technologies such as Bluetooth, Wi-Fi, and Zigbee. They tend to suffer from poor location accuracy in high-density environments due to the interference and noise in RF signals as well as their penetration through walls, leading to security vulnerabilities and low-precision control. To address these issues, this paper presents a smart home control system based on visible light communication (VLC), with enhanced security and accurate localization for precise and convenient control. The system includes an AC lightbulb, a smartphone running the position and control applications, and a cloud server with location-based access and a database of smart home devices. The design of the AC lightbulb integrates VLC and Bluetooth connectivity in a standard form factor for easy installation and plug-n-play capability. A smartphone camera-based 3D indoor positioning and orientation algorithm that allows precise control by pointing the smartphone the device is also presented. We demonstrate the feasibility of this system through prototype implementation and experimental verification.

10.
Sensors (Basel) ; 22(17)2022 Aug 29.
Artículo en Inglés | MEDLINE | ID: mdl-36080951

RESUMEN

Recently, with the growing interest in indoor location-based services, visible light positioning (VLP) systems have been extensively studied owing to their advantages of low cost, high energy efficiency, and no electromagnetic interference. However, due to structural limitations which lead to the requirement of multiple signal sources, it has been challenging to apply VLP in real-world scenarios. In this study, we propose a single LED, single PD-based tracking system that solves these problems by applying a new Bayesian method that can effectively reduce the computational burden of particle filters. The method of evaluating particle reliability developed in this work adjusts the number of particles on the fly. Using the absolute position of the single LED source, the long-term cumulative error of the inertial measurement unit can be continuously corrected. In this regard, the applicability of the VLP system can be enhanced in places where the multiple luminescent signals are hard to consistently detect. The proposed system was verified through experiments in a classroom and a corridor, and the results show an average error of less than 11 cm at travel distances of 80 to 100 m.

11.
Sensors (Basel) ; 22(19)2022 Sep 21.
Artículo en Inglés | MEDLINE | ID: mdl-36236260

RESUMEN

Visible light positioning (VLP) has attracted intensive attention from both academic and industrial communities thanks to its high accuracy, immunity to electromagnetic interference, and low deployment cost. In general, the receiver in a VLP system determines its own position by exploring the received signal strength (RSS) from the transmitter according to a pre-built RSS attenuation model. In such model-based methods, the LED's emission power and the receiver's height are usually required known and constant parameters to obtain reasonable positioning accuracy. However, the LED's emission power is normally time-varying due to the fact that the LED's optical output power is prone to changing with the LED's temperature, and the receiver's height is random in a realistic application scenario. To this end, we propose a height-independent three-dimensional (3D) VLP scheme based on the RSS ratio (RSSR), rather than only using RSS. Unlike existing RSS-based VLP methods, our method is able to independently find the horizontal coordinate, i.e., two-dimensional (2D) position, without a priori height information of the receiver, and also avoids the negative effect caused by fluctuation of the LED's emission power. Moreover, we can further infer the height of the receiver to achieve three-dimensional (3D) positioning by iterating the 2D results back into positioning equations. To quickly verify the proposed scheme, we conduct theoretical analysis with mathematical proof and experimental results with real data, which confirm that the proposed scheme can achieve high position accuracy without known information of the receiver's height and LED's emission power. We also implement a VLP prototype with five LED transmitters, and experimental results show that the proposed scheme can achieve very low average errors of 2.73 cm in 2D and 7.20 cm in 3D.

12.
Sensors (Basel) ; 22(8)2022 Apr 08.
Artículo en Inglés | MEDLINE | ID: mdl-35458864

RESUMEN

In this paper, we study the design aspects of an indoor visible light positioning (VLP) system that uses an artificial neural network (ANN) for positioning estimation by considering a multipath channel. Previous results usually rely on the simplistic line of sight model with limited validity. The study considers the influence of noise as a performance indicator for the comparison between different design approaches. Three different ANN algorithms are considered, including Levenberg-Marquardt, Bayesian regularization, and scaled conjugate gradient algorithms, to minimize the positioning error (εp) in the VLP system. The ANN design is optimized based on the number of neurons in the hidden layers, the number of training epochs, and the size of the training set. It is shown that, the ANN with Bayesian regularization outperforms the traditional received signal strength (RSS) technique using the non-linear least square estimation for all values of signal to noise ratio (SNR). Furthermore, in the inner region, which includes the area of the receiving plane within the transmitters, the positioning accuracy is improved by 43, 55, and 50% for the SNR of 10, 20, and 30 dB, respectively. In the outer region, which is the remaining area within the room, the positioning accuracy is improved by 57, 32, and 6% for the SNR of 10, 20, and 30 dB, respectively. Moreover, we also analyze the impact of different training dataset sizes in ANN, and we show that it is possible to achieve a minimum εp of 2 cm for 30 dB of SNR using a random selection scheme. Finally, it is observed that εp is low even for lower values of SNR, i.e., εp values are 2, 11, and 44 cm for the SNR of 30, 20, and 10 dB, respectively.


Asunto(s)
Algoritmos , Redes Neurales de la Computación , Teorema de Bayes , Análisis de los Mínimos Cuadrados , Luz
13.
Sensors (Basel) ; 22(22)2022 Nov 15.
Artículo en Inglés | MEDLINE | ID: mdl-36433411

RESUMEN

The high precision three-dimensional (3D) visible light-based indoor positioning (VLIP) systems have gained much attention recently for people or robot navigation, access tracking, etc. In this work, we put forward and present the first demonstration, up to the authors' knowledge, of a 3D VLIP system utilizing a two-stage neural network (TSNN) model. The positioning performance would degrade when the distance between the light emitting diode (LED) plane and the receiver (Rx) plane increases; however, because of the finite LED field-of-view (FOV), light non-overlap zones are created. These light non-overlap zones will produce high positioning error particularly for the 3D VLIP systems. Here, we also propose and demonstrate the Received-Intensity-Selective-Enhancement scheme, known as RISE, to alleviate the light non-overlap zones in the VLIP system. In a practical test-room with dimensions of 200 × 150 × 300 cm3, the experimental results show that the mean errors in the training and testing data sets are reduced by 54.1% and 27.9% when using the TSNN model with RISE in the z-direction, and they are reduced by 39.1% and 37.8% in the xy-direction, respectively, when comparing that with using a one stage NN model only. At the cumulative distribution function (CDF) P90, the TSNN model with RISE can reduce the errors by 36.78% when compared with that in the one stage NN model.


Asunto(s)
Luz , Redes Neurales de la Computación , Humanos
14.
Sensors (Basel) ; 21(7)2021 Mar 30.
Artículo en Inglés | MEDLINE | ID: mdl-33808332

RESUMEN

Most indoor positioning systems require calibration before use. Fingerprinting requires the construction of a signal strength map, while ranging systems need the coordinates of the beacons. Calibration approaches exist for positioning systems that use Wi-Fi, radio frequency identification or ultrawideband. However, few examples are available for the calibration of visible light positioning systems. Most works focused on obtaining the channel model parameters or performed a calibration based on known receiver locations. In this paper, we describe an improved procedure that uses a mobile robot for data collection and is able to obtain a map of the environment with the beacon locations and their identities. Compared to previous work, the error is almost halved. Additionally, this approach does not require prior knowledge of the number of light sources or the receiver location. We demonstrate that the system performs well under a wide range of lighting conditions and investigate the influence of parameters such as the robot trajectory, camera resolution and field of view. Finally, we also close the loop between calibration and positioning and show that our approach has similar or better accuracy than manual calibration.

15.
Sensors (Basel) ; 21(9)2021 Apr 27.
Artículo en Inglés | MEDLINE | ID: mdl-33925300

RESUMEN

This paper present simulation-based results on the impact of transmitter (Tx) position and orientation uncertainty on the accuracy of the visible light positioning (VLP) system based on the received signal strength (RSS). There are several constraining factors for RSS-based algorithms, particularly due to multipath channel characteristics and set-up uncertainties. The impact of Tx uncertainties on positioning error performance is studied, assuming a statistical modelling of the uncertainties. Simulation results show that the Tx uncertainties have a severe impact on the positioning error, which can be leveraged through the usage of more transmitters. Concerning a smaller Tx's position uncertainty of 5 cm, the average positioning errors are 23.3, 15.1, and 13.2 cm with the standard deviation values of 6.4, 4.1, and 2.7 cm for 4-, 9-, and 16-Tx cases, respectively. While for a smaller Tx' orientation uncertainty of 5°, the average positioning errors are 31.9, 20.6, and 17 cm with standard deviation values of 9.2, 6.3, and 3.9 cm for 4-, 9-, and 16-Tx cases, respectively.

16.
Sensors (Basel) ; 21(9)2021 May 08.
Artículo en Inglés | MEDLINE | ID: mdl-34066704

RESUMEN

This paper presents an autonomous method of collecting data for Visible Light Positioning (VLP) and a comprehensive investigation of VLP using a large set of experimental data. Received Signal Strength (RSS) data are efficiently collected using a novel method that utilizes consumer grade Virtual Reality (VR) tracking for accurate ground truth recording. An investigation into the accuracy of the ground truth system showed median and 90th percentile errors of 4.24 and 7.35 mm, respectively. Co-locating a VR tracker with a photodiode-equipped VLP receiver on a mobile robotic platform allows fingerprinting on a scale and accuracy that has not been possible with traditional manual collection methods. RSS data at 7344 locations within a 6.3 × 6.9 m test space fitted with 11 VLP luminaires is collected and has been made available for researchers. The quality and the volume of the data allow for a robust study of Machine Learning (ML)- and channel model-based positioning utilizing visible light. Among the ML-based techniques, ridge regression is found to be the most accurate, outperforming Weighted k Nearest Neighbor, Multilayer Perceptron, and random forest, among others. Model-based positioning is more accurate than ML techniques when a small data set is available for calibration and training. However, if a large data set is available for training, ML-based positioning outperforms its model-based counterparts in terms of localization accuracy.

17.
Sensors (Basel) ; 21(11)2021 Jun 07.
Artículo en Inglés | MEDLINE | ID: mdl-34200221

RESUMEN

Reduced deployment and calibration requirements are key for scalable and cost-effective indoor positioning systems. In this work, we propose a low-complexity, weak calibration procedure for an indoor positioning system based on infrastructure lighting and a positioning-sensitive detector. The proposed calibration relies on genetic algorithms to obtain the relevant system parameters in the real positioning environment without a priori information, and requires a low number of simple measurements. The achievable performance of the proposal was assessed by direct comparison with a formal offline calibration method requiring complex dedicated infrastructure and instruments. The comparative error assessment showed that the maximum accuracy reduction compared to the significantly more costly formal calibration was below 25 mm, and the overall absolute positioning error was smaller than 35 mm with orientation errors of around 0.25°. The performance achieved with the proposed weak calibration procedure is sufficient for many indoor positioning applications and largely reduces the cost and complexity of setting up the positioning system in real environments.

18.
Sensors (Basel) ; 21(3)2021 Jan 29.
Artículo en Inglés | MEDLINE | ID: mdl-33573034

RESUMEN

The accuracy of the received signal strength-based visible light positioning (VLP) system in indoor applications is constrained by the tilt angles of transmitters (Txs) and receivers as well as multipath reflections. In this paper, for the first time, we show that tilting the Tx can be beneficial in VLP systems considering both line of sight (LoS) and non-line of sight transmission paths. With the Txs oriented towards the center of the receiving plane (i.e., the pointing center F), the received power level is maximized due to the LoS components on F. We also show that the proposed scheme offers a significant accuracy improvement of up to ~66% compared with a typical non-tilted Tx VLP at a dedicated location within a room using a low complex linear least square algorithm with polynomial regression. The effect of tilting the Tx on the lighting uniformity is also investigated and results proved that the uniformity achieved complies with the European Standard EN 12464-1. Furthermore, we show that the accuracy of VLP can be further enhanced with a minimum positioning error of 8 mm by changing the height of F.

19.
Sensors (Basel) ; 20(19)2020 Sep 29.
Artículo en Inglés | MEDLINE | ID: mdl-33003578

RESUMEN

Currently, visible light positioning (VLP) enabling an illumination infrastructure requires a costly retrofit. Intensity modulation systems not only necessitate changes to the internal LED driving module, but decrease the LEDs' radiant flux as well. This hinders the infrastructure's ability to meet the maintained illuminance standards. Ideally, the LEDs could be left unmodulated, i.e., unmodulated VLP (uVLP). uVLP systems, inherently low-cost, exploit the characteristics of the light signals of opportunity (LSOOP) to infer a position. In this paper, it is shown that proper signal processing allows using the LED's characteristic frequency (CF) as a discriminative feature in photodiode (PD)-based received signal strength (RSS) uVLP. This manuscript investigates and compares the aptitude of (future) RSS-based uVLP and VLP systems in terms of their feasibility, cost and accuracy. It demonstrates that CF-based uVLP exhibits an acceptable loss of accuracy compared to (regular) VLP. For point source-like LEDs, uVLP only worsens the trilateration-based median p50 and 90th percentile root-mean-square error p90 from 5.3cm to 7.9cm (+50%) and from 9.6cm to 15.6cm (+62%), in the 4m × 4m room under consideration. A large experimental validation shows that employing a robust model-based fingerprinting localisation procedure, instead of trilateration, further boosts uVLP's p50 and p90 accuracy to 5.0cm and 10.6cm. When collating with VLP's p50=3.5cm and p90=6.8cm, uVLP exhibits a comparable positioning performance at a significantly lower cost and at a higher maintained illuminance, all of which underline uVLP's high adoption potential. With this work, a significant step is taken towards the development of an accurate and low-cost tracking system.

20.
Sensors (Basel) ; 20(6)2020 Mar 19.
Artículo en Inglés | MEDLINE | ID: mdl-32204410

RESUMEN

There are several technologies and techniques available when developing indoor positioning systems (IPS). Recently, the development of positioning systems based on optical signals has aroused great interest, mainly those using visible light from the lighting infrastructure. In this work, we analyze which techniques give better results to lay the foundations for the development of a Visible Light Positioning system (VLP). Working only with a receiver, it is analyzed what the result of determining the position of different emitters is when they emit simultaneously and without any synchronism. The results obtained by Frequency Division Multiple Access (FDMA) (with digital bandpass filters, I/Q demodulation, and FFT) and Code Division Multiple Access (CDMA) are compared. The interference between signals when emitted simultaneously from multiple emitters is analyzed as well as the errors they cause and how these effects can be mitigated. As a result of the research, the advantages and disadvantages using different multiple-access determination techniques are determined. In addition, advantages and disadvantages of using FDMA and CDMA techniques as well as hardware requirements that make one more feasible than the other are presented. The system behavior, in terms of errors, is established using FDMA and different configurations such as: I/Q, RMS, or FFT. The work also determines the error rates that can be obtained with the different FDMA and CDMA configurations, considering different error scenarios and integration time. Synthetic emulations and empirical tests were performed, which concluded that IPS systems based on optical signals and PSD sensors can achieve very high measurement accuracies and a high measurement rate. Obtained positioning errors in a room of 3 m height are less than 1 cm when working in noisy environments.

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