An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> The use of positioning sensors on automobiles is becoming increasingly common with the desire to facilitate utility and traffic safety by giving the driver information on the automobiles position relative to the surroundings. In this paper we introduce a positioning technique based upon automobile LED lighting — either taillights or headlights — that we believe is cost effective, low complexity, offers the promise of high accuracy while using existing automobile illumination lighting. <s> BIB001 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> We propose an optical wireless indoor localization using light emitting diodes (LEDs) and demonstrate it via simulation. Unique frequency addresses are assigned to each LED lamp, and transmitted through the light radiated by the LED. Using the phase difference, time difference of arrival (TDOA) localization algorithm is employed. Because the proposed localization method used pre-installed LED ceiling lamps, no additional infrastructure for localization is required to install and therefore, inexpensive system can be realized. The performance of the proposed localization method is evaluated by computer simulation, and the indoor location accuracy is less than 1 cm in the space of 5m x 5 m x 3 m. <s> BIB002 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> This paper presents visible light positioning (VLP) techniques based on a traffic light and photodiodes. The position of a vehicle can be determined using both the traffic light position information obtained through a visible light communication (VLC) link and the time difference of arrival (TDOA) of the traffic light signal to two photodiodes mounted in the front of the vehicle. Methods for VLP with one traffic light and two traffic lights are both proposed, and the error due to the non-coplanar effect is studied and the related coplanar rotation methods for both cases are developed. The numerical result shows bias performance of the positioning methods with coplanar rotation is much better than the ones without coplanar rotation, and the effects of the vehicle distance to traffic light and vehicle speed are also discussed. <s> BIB003 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> VLC system transmits data by controlling LED and receives data through photo diode, which is considered as one of strong candidates of next generation wireless communication systems. Especially, VLC shows a better performance than the existing indoor positioning technology using WPAN as it can measure in the unit of cm to mm. In this paper, we proposed an algorithm for estimating the position of mobile station by comparing the received light intensity at the receiver with the pre-calculated light intensity at a given position. The simulation results verified that the proposed estimation algorithm of an indoor VLC system can be providing good position accuracy. <s> BIB004 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In this paper, we propose novel location based service (LBS) technique using visible light communications (VLC) for indoor location service. As an indoor LBS technique, the VLC is employed due to its many advantages for location awareness and its performance is presented through simulations. The performance of location awareness is evaluated in terms of bit error rate and location awareness error. The results of the paper can be applicable to the indoor LBS technique with high accuracy. <s> BIB005 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Energy efficient white LEDs are increasingly being used for indoor lighting but unlike conventional lighting, the intensity of the light emitted by white LEDs can be modulated at high frequencies. Described is a novel positioning technique based on transmitting signals with known sinusoidal components from a number of LEDs. The receiver uses the resultant optical signal at the receiver photodiode to calculate the receiver position. Proof of concept experiments show that white LEDs designed for indoor lighting can be used as the transmitters. The modulation bandwidth of white LEDs is large enough to give a range of localisation that is compatible with typical indoor applications. <s> BIB006 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> It is necessary in visible light communication where different information from adjacent cells is distinguishable without inter-cell interference for indoor localization-based services and positioning systems. In order to mitigate inter-cell interference, a carrier allocation-visible light communication system, adopting various carriers among the system's respective cells, is suggested. The effects of inter-cell interference for a single channel and the proposed systems are investigated by experimentation with simultaneous transmissions of QPSK signals. <s> BIB007 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> This paper proposes a novel indoor positioning algorithm using visible light communications (VLC). The algorithm is implemented by preinstalled light-emitting diode illumination systems. It recovers the VLC channel features from illuminating visible light and estimates receiver locations by analytically solving the Lambertian transmission equation group. According to our research, the algorithm is able to provide position- ing resolution higher than 0.5 mm, in a practical indoor environment. The performance significantly exceeds conventional indoor positioning approaches using microwaves. © 2012 Society of Photo-Optical Instrumentation <s> BIB008 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Improvements in solid-state/LED lighting are driving increased capabilities of lighting systems — offering potential for applications such as Visible Light Communications (VLC) and indoor localization using the lighting medium. In this paper, we motivate the adoption of localization for both the support of handover between arrays of VLC-equipped luminaires as well as for indoor positioning and beam steering. Our approach uses a state estimation model to achieve localization and motion tracking in spatially diverse VLC networks while considering user mobility and dynamic device orientation. Under these conditions, we show simulation results with location and velocity errors of 5cm and 10cm/s, respectively. <s> BIB009 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In this paper, we propose an indoor positioning system in which the visible light radiated from LEDs is used to locate the position of receiver. Compared to current indoor positioning systems using LED light, our system has the advantages of simple implementation, low cost and high accuracy. In our system, a single photo diode (PD) receives pilot signals from LED panels on the ceiling. Then the time differences of arrival (TDOA) of these pilot signals are used to estimate the position of the receiver. Our proposed sytem is simulated in the room measuring 5×5×3m3 with considering effect of noises such as shot noise, thermal noise, and noise caused by the reflected light from the walls. The simulation result shows that our system can achieve a high estimation accuracy of 3.6cm in average. <s> BIB010 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Visible Light Communications (VLC) can be achieved with the use of Light Emitting Diodes (LED). It can be used for indoor positioning of people or smart devices. Previous work considers coherent detection, which uses the amplitude (in-phase (I) component) and phase (quadrature (Q) component) of the optical power signal and achieves an accuracy of less than 1mm, but they did not consider noise. In our work, we utilize a mathematical model for photodetection with Gaussian noise. We employ 3 stages of estimation algorithms on the measurements to minimize the noise affects. The performance is evaluated using MATLAB and we achieve an accuracy of less than 2cm in the room space of 5m × 5m × 3m. <s> BIB011 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> We propose a new indoor positioning system utilizing visible light communication. Intensity modulation/direct detection and carrier allocation methods are utilized in the proposed system. Simultaneous three channel transmissions were applied to calculate the receiver's position. The characteristics of the proposed positioning system were investigated through simulation based on the experimental results, and the feasibility of the proposed system was verified by experimentation. The experimental result shows that the average error of estimated positions is reduced to 2.4 cm using adjustment process by normalizing method, which is compared with 141.1 cm without adjustment process. <s> BIB012 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> A novel concept for integrating visible light communications (VLC) with three-dimensional indoor positioning is presented. A VLC link based on transmitter and receiver characteristics using experimental measurements was modelled. Proposed is a three-dimensional positioning algorithm using received signal strength indication, which changes based on the angle and distance of the location based service. To reduce inter-cell interference, the transmitter's location code was sent using different subcarriers. A demonstration shows that the proposed algorithm can obtain a user's position, including height, accurately and without inter-cell interference. <s> BIB013 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In localization based service based on visible light communication, estimated position can have significant error when receiver is tilted. In this paper, we proposed positioning estimation compensation technique with known tilting angle and verified its feasibility theoretically and experimentally. <s> BIB014 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In a positioning system based on visible light communication, significant error occurs in localisation when the receiver has a tilt angle. The performance of the positioning system, which uses received signal strength and trilateration when Rx is tilted, has been researched and it is demonstrated that the estimated location changes in the same direction that the Rx is tilted and the shape of the estimated position is bent, theoretically and experimentally. The bent shape and error in an estimated position were compensated for by the multiplying weighting factor and by shifting the estimated position, respectively. <s> BIB015 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> An novel concept for integrating visible light produced by LEDs with indoor positioning using multiple optical receivers is presented in this study. We propose an algorithm using the received signal strength indication (RSSI), which changes by on transmission distance and angle. In order to estimate the position, the transmitters location code was received using multiple optical receivers. The validity of the proposed scheme was demonstrated by determining the local position using distances between the transmitter and receivers, and the relative position between receivers. <s> BIB016 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In this paper, we propose a visible light communication (VLC)-based indoor positioning system (IPS) and algorithm using dual-tone multi-frequency (DTMF) technique. Compared with the existing VLC-based IPS algorithms, our algorithm does not need clock synchronization to separate signals from different time slots. With simple procedures, the coarse position or specific position of the mobile can be obtained by analyzing both the time and frequency domain of the received signal. The simulation result shows that the average positioning error is 18 mm at the signal-to-noise ratio (SNR) of 10 dB. <s> BIB017 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Indoor physical analytics calls for high-accuracy localization that existing indoor (e.g., WiFi-based) localization systems may not offer. By exploiting the ever increasingly wider adoption of LED lighting, in this paper, we study the problem of using visible LED lights for accurate localization. We identify the key challenges and tackle them through the design of Pharos. In particular, we establish and experimentally verify an optical channel model suitable for localization. We adopt BFSK and channel hopping to achieve reliable location beaconing from multiple, uncoordinated light sources over shared light medium. Preliminary evaluation shows that Pharos achieves the 90th percentile localization accuracy of 0.4m and 0.7m for two typical indoor environments. We believe visible light based localization holds the potential to significantly improve the position accuracy, despite few potential issues to be conquered in real deployment. <s> BIB018 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Localization, or positioning, is gaining the increasing attention of researchers around the world. The location information, especially the indoor location, is important for navigation systems, heating and air conditioning systems, illumination adjustment, humidity control, robot service, and so on. In this paper, we propose a three-dimensional indoor localization technique using visible light. The main goal of our proposed scheme is to improve the accuracy of VLC-based indoor localization by utilizing multiple VLC transmitters. The simulation results validate the performance of our proposed scheme. <s> BIB019 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> We proposed a two-dimensional positioning system and an algorithm using single transmitter and receiver. The system is using modeled characteristics of device which is based on the experimentally measured. We were able to obtain the estimated position with less than 3 cm of error when polar angle was 15 degrees and the azimuth angles of PD were 45, 315, and 135 degrees. <s> BIB020 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In this paper, a VLC indoor positioning system utilizing optical orthogonal codes (OOCs) is proposed. The use of OOC is to distinguish different transmitted signals at the receiver, the trilateration method then calculate the position of receiver based on these distinguished signals. To expand the scale of system and use efficiently OOC resource, a strategy of reusing/combining codeword is proposed. We also create a combination of simulation and mathematical modeling to investigate the performance of proposed system. Numerical results confirm that the proposed system can achieve a good positioning accuracy level in average. <s> BIB021 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Exploiting the increasingly wide use of Light-emitting Diode (LED) lighting, in this paper, we study the problem of using visible LED lights for accurate localization. The basic idea is to leverage the existing lighting infrastructure and apply trilateration to localize any devices with light sensing capability (e.g., a smartphone), using LED lamps as anchors. Through the design of Epsilon, we identify and tackle several technique challenges. In particular, we establish and experimentally verify the optical channel model for localization. We adopt BFSK and channel hopping to enable reliable location beaconing from multiple, uncoordinated light sources over the shared optical medium. We handle realistic situations towards robust localization, for example, we exploit user involvement to resolve the ambiguity in case of insufficient LED anchors. We have implemented the Epsilon system and evaluated it with a small scale hardware testbed as well as moderate-size simulations. Experimental results confirmed the effectiveness of Epsilon: the 90th percentile accuracies are 0.4m, 0.7m and 0.8m for three typical office environments. Even in the extreme situation with a single light, the 90th percentile accuracy is 1.1m. We believe that visible light based localization is promising to significantly improve the positioning accuracy, despite few open problems in practice. <s> BIB022 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> This paper analyzes an indoor positioning system using white lighting LEDs. The performance of the positioning system is determined by the layout of LEDs, the receiver circuit, incidence angle of light, LED light source, and the photodiode. The Cramer–Rao bound as the theoretical accuracy limitation of received signal strength indicator algorithm is derived. The influences to positioning accuracy of multipath reflections and unparallel optical axis of LEDs and receivers are analyzed in certain scenarios. It is concluded that if the diffuse channel gain is measured previously in a certain environment and the modulation speed is far less than the channel cutoff frequency, the theoretical accuracy limit is not affected by multipath link. Multiple noises of system are analyzed in detail. The influence to positioning accuracy of indoor uniform illumination is also discussed. The result proves that the theoretical estimated accuracy of triangular LEDs array is higher than square LEDs array. With typical parameter values, the simulated theoretical accuracy of system is up to the level of centimeter. <s> BIB023 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> The cross-correlation algorithm is adopted in an indoor optical positioning system using LEDs. After compensating the estimated distance, a max 11-cm positioning error is experimentally achieved with trilateration at 2 m distance. <s> BIB024 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> Visible light communication (VLC) has become a promising research topic in recent years, and finds its wide applications in indoor environments. Particularly, for location based services (LBS), visible light also provides a practical solution for indoor positioning. Multipath-induced dispersion is one of the major concerns for complex indoor environments. It affects not only the communication performance but also the positioning accuracy. In this paper, we investigate the impact of multipath reflections on the positioning accuracy of indoor VLC positioning systems. Combined Deterministic and Modified Monte Carlo (CDMMC) approach is applied to estimate the channel impulse response considering multipath reflections. Since the received signal strength (RSS) information is used for the positioning algorithm, the power distribution from one transmitter in a typical room configuration is first calculated. Then, the positioning accuracy in terms of root mean square error is obtained and analyzed. <s> BIB025 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Time Difference of Arrival-TDOA <s> In this paper, we develop an indoor localization device which embeds localization information into indoor light-emitting-diodes (LED) lighting systems. The key idea of our device is the use of the newly proposed "bit stuffing method". Through the use of stuff bits, our device is able to measure signal strengths even in transient states, which prohibits interference between lighting signals. The stuff bits also scatter the parts of the signal where the LED is turned on, thus provides quality indoor lighting. Additionally, for the indoor localization system based on RSSI and TDM to be practical, we propose methods for the control of LED lamps and compensation of received signals. The effectiveness of the proposed scheme is validated through experiments with a low-cost implementation including an indoor navigation task. <s> BIB026
Suppose that at the same time all of the LED base stations transmit signals to the mobile device. Due to the difference in the distance from the mobile device to the LEDs, the times at which the signals arrive at the mobile device will be different. TDOA algorithms determine the position of the mobile device based on the time difference of arrival of signals from multiple LEDs. For each TDOA with respect to a pair of base stations, the difference in the distances from the mobile device to the pair can be calculated by multiplying the time difference by the speed of light. Therefore, for each TDOA measurements we can determine a hyperbola of possible positions whose distances to the pair of base stations have a constant difference. To enable 2-D positioning, TDOA measurement with respect to at least three base stations must be obtained. As shown in Figure 6 , given two TDOAs with respect to three base station A, B, and C, the two derived distance differences R 2 − R 1 and R 3 − R 1 define two hyperbolas whose intersection is determined to be the position of the mobile device. Let (x, y) denote the coordinates of the mobile device and (x i , y i ) and (x j , y j ) denote the coordinates of the ith and jth LEDs then the distance difference to the ith and jth LEDs, denoted by R ij , defines a hyperbola as follows: The position of the mobile device is determined as the intersection of these hyperbolas. In  BIB005 , a VLC based positioning system used for indoor location based service applications in restaurants, museums, department stores and theaters was proposed. The visible light from four LED panels was modulated using BPSK. After obtaining TDOA information, a nonlinear least square algorithm was used to determine the location. Simulation results showed that the average error was 0.14 m. In BIB010  , a TDOA based indoor positioning system using VLC was proposed. The system consists of a PD receiving signals from multiple LEDs whose positions are known by the receiver. Time division multiplexing was used to separate the signals from different LEDs. Each LED transmits a pilot signal which does not convey any information to the PD. Therefore, the PD has no way to know the ID of the received signal. After receiving a series of anonymous pilot signals from multiple LEDs, a special guessing mechanism was used to find the IDs of the all signals and the position of the mobile device was determined. Simulation results showed that the average error was 3 cm. In  an approach similar to that of BIB010  was applied but a sinusoidal pilot signal was used instead of a square pulse. A simulation was conducted that included consideration of the rising and falling times of the LED. The result showed that the average error distance was 68.2 cm. With the TDOA algorithm, the important part is estimating the time difference or the distance difference of arrival. There are many methods for extracting the TDOA from the received signal. In BIB010   , since time division multiplexing was used, the signals from different base stations were separated and thus the TDOA can be obtained easily. In BIB001 BIB002 BIB011 BIB006 , frequency division multiplexing was used, with which the signals from different base stations were mixed together, and TDOA was estimated based on phase difference of arrival. In BIB001 a VLC based positioning system for automobiles was presented. The two taillights in the vehicle ahead transmit an intensity modulated sinusoidal light signal to two receivers in the vehicle behind. The light signals from the different taillights were modulated at different frequencies. Bandpass filtering was applied to separate the two signals from the mixed signal at each receiver. After that, the phase difference of arrival of signals at each receiver was determined. The distance difference then can be calculated easily based on the phase difference, the known modulated frequency and the speed of light. The system was tested with a simplistic hardware at the range of 1 m and an accuracy of 1 cm was achieved. The indoor positioning system proposed in BIB002 also used the same mechanism of modulation and multiplexing as in BIB001 . In the first step, the sinusoid light signals from three LED base stations located in the ceiling were modulated at different frequencies. At the receiver, a bandpass filter whose pass band was adjusted to the frequency of each base station was used to extract signals from the different base stations. A Hilbert transform was used to extract the in-phase and quadrature components of each signal, to calculate the phase differences of each pair of signals. In the second step, the modulated frequencies were switched between base stations. After the same process, the phase differences were calculated again. Based on the calculated phase differences, the distances from the receiver to the three base stations were calculated and the position was determined easily using trilateration. Without any noise assumed, the simulation reported a very high accuracy of less than 1 cm achieved by this system. The authors of BIB011 extended the work in BIB002 by adding additive white Gaussian noise to the simulation and applying statistical methods to minimize the estimation error after the positioning stage. The simulation showed that the proposed statistical method can reduce the estimation error from 15.3 cm to less than 2 cm in a room space of 5 m × 5 m × 3 m. In BIB006 , light signals from multiple base stations were modulated to transmit in sinusoidal form. Based on measuring the peak-to-peak amplitude of the received sinusoid light signals, the phase differences were calculated. Then, based on the phase differences, the known modulation frequency and the speed of light, the TDOA were obtained to determine the position. Usually TDOA based methods require at least three base stations or three receivers to estimate the position. In BIB003 , a clever method was proposed to enable the 2-D positioning with only one traffic light transmitting signal containing its position information to the two PDs mounted in the front of the vehicle. The proposed method is described in Figure 7 . At time t 1 , the signal transmit from a traffic light is received by the two PDs and the TDOA ∆t 1 along with the corresponding hyperbola H 1 are obtained. At time t 2 when the vehicle is closer to the traffic light, the second hyperbola H 2 corresponding to the TDOA ∆t 2 is obtained. Assuming that the displacement of the vehicle from t 1 to t 2 is known, the position of the traffic light relative to the vehicle is determined as the intersection of the two hyperbolas. Finally the absolute position of the vehicle is calculated based on the relative and absolute position of the traffic light. The simulation results showed that the accuracy of this system greatly depends on the distance between the vehicle and the traffic light, as well as the speed of the vehicle. More specifically, the accuracy increased when the distance increased. For example, the positioning error was very high when the distance was shorter than 5 m, but when the distance was 50 m, the positioning error was only 0.5 m. Regarding the speed of vehicle, as one might expect, the positioning error increased when the speed increased. However when the distance was greater than 20 m, the speed of vehicle had a very small effect on the accuracy. The light path from the LED to the receiver is illustrated in Figure 8 . Suppose that LED has a Lambertian radiation pattern, the received power can be calculated as BIB025 : where P t is the transmitted power, A is the physical area of the detector in the PD, m is the order of Lambertian emission, φ is the irradiance angle, ψ is the incidence angle, T s (ψ) is the gain of the optical filter, g(ψ) is the gain of the optical concentrator, Ψ c is the field of view at the PD, and d is the distance between the LED and receiver. In theory, given that all other parameters are known, the distance can be derived from the received power using Equation  . Then trilateration is used to determine the location similarly to the TOA technique. In practice, however, the light propagation suffers from multipath, reflection, obstruction, and many other factors which make the result obtained from Equation (13) unreliable. For example BIB025 examined the effect of the reflected light on the accuracy of a VLC based positioning system using RSS. In that system, the distance from the mobile device to the LED base stations were derived from the received power using Equation (13) directly. The simulation results showed that the root mean square error increased from 4 cm, which was the result with no reflected light, to 80 cm when the reflected light was considered. Therefore, the main challenge when applying RSS is to find an appropriate path loss model to estimate the distance. A VLC based positioning system using RSS was proposed in  BIB007 BIB012 BIB013 . The visible light from three LED base stations installed in the ceiling was modulated in Quadrature Phase Shift Keying (QPSK) at different frequencies. After receiving the mixed signal, the signals from the different LEDs were extracted and the distances to each LED was calculated in two steps. In the first step, since the system did not use any type of inertial sensor (e.g., acceleration sensor, gyroscope) to obtain the information about the orientation of mobile device, the rough distance was calculated without considering the effect of irradiance angle and incidence angle on the received power. Because the light signal was attenuated by the effect of these two angles, the roughly-estimated distance was longer than the real distance. In the second step, the maximum possible distance was calculated based on the known height of the ceiling and the illuminating coverage of the LED. Then a compensated distance was calculated based on the maximum possible distance and the roughly estimated distance. The final estimated distance was calculated by subtracting the compensated distance from the roughly estimated distance. The location then is determined using trilateration and the linear least square method. The experiment was conducted in a space of 60 cm×60 cm×85 cm and an error of 6 cm was reported. In BIB014 BIB015 a gyroscope was used to obtain the orientation information of the mobile device. They found that the estimated position given by RSS positioning tend to move toward the direction of a tilting receiver. A compensation mechanism for the error caused by the tilt angle of the receiver was proposed. The experiment showed that by applying the proposed compensation, the average distance error was reduced from 40 cm to 1.5 cm. While systems in  BIB007 BIB012 BIB013 BIB014 BIB015 used multiple base stations transmitting signals to a single receiver, in BIB016 BIB020 , three PD receivers installed on a disk of radius 20 cm on top of the mobile device were used to receive a signal from a single LED base station. The distances from the LED to the receivers were estimated from the received signal strengths at each receiver. The position of the mobile device was determined based on the known coordinates of the LED, the arrangement of multiple PDs (i.e., their relative position to each other), and the distances from the LED to multiple PDs. The simulation showed that a distance error of less than 1.5 cm in a 2 × 2 × 2 m 3 environment was achieved. Note that the system aimed to autonomous machine control application such as cleaning robots. Therefore, the size of 40 cm in diameter of the receiver is acceptable. However, for applications in which the sizes of the mobile devices are limited, this technique is almost impractical. In BIB021 , optical orthogonal code (OOC) was used to distinguish multiple signals. Then the distances to different base stations were calculated based on RSS, and trilateration was used to determine the position. The simulation showed that the average error distance was 8 cm in an area of 12 m × 35 m. A creative technique using dual-tone multi-frequency (DTMF), which is widely used in telephone dialing, voice mail, and electronic banking systems to separate the light signal from different LED base stations was proposed in BIB017 . The paper also developed a new algorithm for calculating the path loss based on the RSS corresponding to different frequencies. The coordinates of LED base stations were assumed to be known to the mobile device. A simulation in an area of 2 m × 2 m reported an average error distance of 18 mm. In BIB018 , beacon light modulated in Binary Frequency Shift Keying (BFSK) transmitted a signal containing coordinates of LED base stations to the mobile device. The duty cycle remained the same at different frequencies to prevent flickering. Random channel hoping was used to avoid persistent collision among light sources. Each LED base station transmitted beacon signals at a random channel for a certain period, and then hopped to other channels. The RSS was translated to distance using a simple model which assumed that all LEDs were facing downward and that the receiver was facing squarely upward toward the ceiling. Then, the least mean square (LMS) method was used to determine the position. An experiment was conducted in an empty conference room of 5 m × 8 m and a cubicle area of 3.5 m × 6.5 m. The accuracy reported was 0.3 m and 0.7 m for the conference room and the cubicle area, respectively. The work in BIB018 was extended in BIB022 by addressing more practical challenges including enabling reliable communication and robust localization in case of insufficient light sources or imperfect orientation. The simulation results showed that an accuracy of 0.4 m in a space 20 m × 20 m × 3 m was achieved. In BIB004 , the receiver calculated the light intensity at each position based on its knowledge about the system. Upon receiving the light from the LED, the received light intensity was compared to the pre-calculated light to find the position of the mobile device. The simulation showed that depending on the angle of the mobile device, distance errors of 3 to 35 cm were achieved. A positioning system for moving robot using RSS was demonstrated BIB026 . Multiple LED base stations transmitted their IDs to the PD mounted on the robot. TDM was used to separate different light signals. A method called bit stuffing was proposed to prevent interferences between ID pulses and thus allowed a simple function to be used for determining the position. The experiment was conducted in a space 120 cm × 120 cm × 170 cm. The maximum and mean error distances were reported to be 10.3 cm and 3.2 cm, respectively. The system in BIB008 also used RSS and TDM. The light was modulated in On-Off Keying (OOK) to transmit the coordinates of LED base stations. A frame structure was designed to keep the transmission power stable while different bits were transmitted. Based on this frame structure, an algorithm was developed to calculate the path loss. The simulation results showed that depending on the noise level, the average error distance ranged from 0.5 mm to 7.3 mm in a space of 3 m × 3 m × 3 m. A state estimation model which was inspired by Kalman Filter recursive estimation to achieve localization and motion tracking was proposed in BIB009 . There were two scenarios in the estimation process. In the first scenario, the RSS was measured when the receiver was directed perpendicular to the ceiling and the state (i.e., the position) was estimated. In the second scenario, RSS was measured and the effect of the rotation of the receiver was added to the state model. Then the state was updated corresponding to the changes in the state model. Simulation results showed that position and velocity errors of 5 cm and 10 cm/s were achieved in a space of 6 m × 6 m × 4 m. A Cramer-Rao bound was used in BIB023 to analyze the theoretical accuracy of an indoor VLC based positioning system using RSS. Signals from different base stations were separated by frequency. The cases where LEDs and PD are not parallel were discussed. The positioning accuracy corresponding to two types of LED array layouts: square and triangle were analyzed. The results showed that the theoretical accuracy corresponding to the triangle LED layout was higher than that of the square LED layout. In addition, the accuracy of 4.78 cm was shown to be achievable with specific parameter values. An idea of measuring RSS by calculating the cross correlation between received signal and transmitted signal was proposed in BIB024 . The effects of the irradiance and incidence angle of the light on the RSS were compensated for by multiplying the RSS calculated by cross correlation with a weighting factor. Trilateration and the linear least square method were used to determine the position. The experiment was conducted with three LED base stations transmitting orthogonal codes modulated in OOK to a PD moving in a plane parallel to that of the LEDs at a distance of 2 m. The average error distance reported was 6 cm. In BIB019 a VLC based three dimensional indoor positioning using RSS was proposed. To reduce the error of the RSS-to-distance calculation, a compensated distance was included in the path loss model. Using the proposed scheme, multiple LED base stations were utilized to obtain higher positioning accuracy. Simulation results showed that the accuracy was increased when the number of LED base stations was increased.