Efficient Closed-Form Solutions for Visible Light Positioning in Low-Cost IoT Devices

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how “optimality” is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.

This thesis implements a state-of-the-art solution separation advanced RAIM (ARAIM) algorithm as it is written as reported in the literature. Specifically, a GNSS fault detection and exclusion algorithm for a multi-constellation GNSS was implemented in software and tested against simulated data. RAIM algorithms have been created in many forms over the last couple of decades and are still in development today. The position solution results produced by this ARAIM algorithm were compared to that of a snapshot weighted least squares (WLS) solution in which failed satellites are removed before processing and an WLS solution with no corrections applied. In addition, the difference in position solution between ARAIM and the simulation truth was compared to the ARAIM reported horizontal and vertical protection limits, as well as, the position performance criteria. This thesis also investigates the performance of the exclusion method and how it affects the performance of the overall ARAIM algorithm. The algorithm implemented and tested in this thesis will be used as a basis of comparison for on-going research into robust GNSS processing techniques.

Asymptotically efficient GNSS trilateration

In this paper, we propose a novel visible light positioning (VLP) scheme under multi-path propagation, which is a practical scenario that has not been well studied for VLP. The new scheme exploits the so-called dual-mode light-emitting diode (DM-LED) of different radiation lobe mode numbers at the transmitter and a photodiode at the receiver. Specifically, we devise a method that utilizes a radiation angle measurement approach for DM-LED, derive the Cramér-Rao lower bound (CRLB) of the estimated distance and analyze the characteristics of key parameters. In addition, two localization algorithms based on linear and nonlinear least squares methods are developed. Simulation results show that under the ideal light-of-sight scenario, the CRLB of the proposed VLP scheme can be close to that of the conventional received signal strength (RSS) aided VLP scheme. Furthermore, we implement the first ever prototype DM-LED lamp to validate the new DM-LED aided VLP system model. Both simulation and experiment results demonstrate that the proposed system outperforms its RSS-aided VLP counterpart in terms of positioning accuracy in the more realistic, and thus more challenging multi-path scenario, even with a tilting receiver.

Noise resilient solution and its analysis for multistatic localization using differential arrival times

Visible light positioning (VLP) is an emerging positioning technique that utilizes indoor light sources to broadcast archer locations through visible light communication (VLC). Benefited by the densely deployed light lamps, VLP holds the promise for more accurate positioning accuracy than RF based approaches, and thus enables interesting applications such as retail navigation and shelf-level advertising in supermarkets and shopping malls. However, we observe that in existing VLP systems, receiving devices are heavily burdened in handling light flickering for VLC. In order to prevent human from being disturbed, the VLC transmitter lamps have to transmit pulses in a high rate (over 1kHz). Since the pulse rate far exceeds the cameras' sampling capability (30fps), receiver design either requires customized light sensor with cumbersome calibration on receiving signal strength [2] or processing high resolution images to leverage rolling shutter effect of the CMOS camera to decode message [1]. The heavy burden on receiving devices motivated us to try getting rid of light flickers. Since human eyes normally can not perceive changes in polarization, the idea is to modulate polarization instead of intensity for communication. In this demo, we demonstrate the VLC system in our VLP design [3] which realizes this idea. It enables lightweight VLC that is even affordable in wearables (Google Glass), without incurring hardware modification or computation off-loading. Moreover, it also makes other types of illuminating light beyond LED light (even sun light) possible to construct communication, therefore eliminates the barrier for deploying future VLC-based applications. As detailed in the full paper [3], our design was inspired by the liquid crystal display (LCD), from which we borrowed polarizer and liquid crystal. Liquid crystal has the property to change the polarization of bypassing polarized light according to the applied voltage. We use polarizer to polarize illuminating light and leverage liquid crystal to modulate bits through changing the light's polarization. The receiver can thus detect changes in polarization with a polarizing film, through which different polarizations result in different intensities. Since the SNR of such communication channel may significantly vary with the mobility of receiving device, we propose to add a dispersion filter to the transmitter. The dispersion filter can cast different frequency of lights into different polarization directions so that SNR in different receiving directions are evened. With the above techniques, VLC transmitter generates signal in low baud rate and mobile devices can perform VLC through camera directly. The communication is long in distance and lightweight enough for resource-constrained devices since the information is carried in intensity changes rather than certain image patterns in rolling shutter approaches. In this demo, we will illustrate the prototype implementation of the VLC communication system. We use incandescent lamps as illuminating light sources. The transmitter consists of a polarizing film, a liquid crystal layer, a dispersor and a control board. The receiver is demonstrated in Android smartphone with polarizing film in front of the camera.

This paper investigates the error bounds for position estimation in downlink visible light communication (VLC) systems. More precisely, we use Cramér-Rao lower bounds (CRLBs) to study the effect of signal-dependent shot noise (SDSN) on the error performance in visible light positioning. We consider synchronous, quasi-synchronous, and asynchronous visible light positioning (VLP) systems. The system performance is assessed based on the position estimation, and uses information from parameters relating to the time of arrival (TOA), time difference of arrival (TDOA), and received signal strength (RSS). The results demonstrate that SDSN has a negative impact on the error bounds in all considered scenarios. Moreover, the level of degradation observed is not uniform among all cases at higher SDSN levels.

Visible light positioning (VLP) has become a promising indoor localization approach as it can provide sub-meter localization. VLP usually requires no less than three LED lamps for angle-of-arrival (AoA) or received-signal-strength (RSS) based localization. However, it is hard to identify multiple LED lamps in some indoor environments, such as a long corridor or tunnel, which makes existing VLP useless. To address this problem, we propose a VLP approach using only a single LED lamp. In this approach, we utilize the inertial measurements to infer rotation angles and exploit visual projection geometry to calibrate rotation angles. The experiment results demonstrate the proposed VLP approach can achieve sub-meter positioning accuracy by using only one LED lamp.

The accuracy of the visible light positioning (VLP) system is improved by using regression-based and interpolation-based approaches. These approaches are mixed with the received signal strength in both linear and nonlinear least squares techniques. The simplicity of the model is the key point, where a highly accurate VLP system with only one equation “interpolation” is used instead of many complex equations. Gaussian noise and reflections up to three bounces with high reflectivity are the source of noise. In addition, the strength of the methods is studied by changing some affecting parameters. In a previous work, we introduced the regression-based approach in VLP-based systems with one reflection. Here, we extend the work with three reflections, leading to an increase in noise to examine system robustness. The approaches are compared to the traditional ones, and show a remarkable enhancement, e.g., the average error has been improved by 67%.

This paper tackles indoor receiver localization as a regression task using visible light positioning (VLP). This technology has gained prominence as an alternative to conventional indoor positioning. Traditional systems such as WiFi and ZigBee face notable drawbacks: electromagnetic interference, added infrastructure, limited accuracy, and high deployment costs. In general, classical positioning approaches—lateration, triangulation, proximity, and least squares—typically infer location from measurements like received signal strength (RSS), time of arrival (TOA), time difference of arrival (TDOA), or angle of arrival (AOA). However, in real-world VLP scenarios, these methods face difficulties since they depend on ideal signals, which means unaffected by physical obstacles and perfectly aligned between transmitters and receiver. Our work proposes the application of the extreme learning machine (ELM) algorithm, its regularized version (R-ELM) and the Levenberg-Marquardt algorithm (LMA), to predict the receiver’s position based simply on the light signals emitted by light-emitting diodes (LEDs) and captured by a photodiode (PD). To evaluate the overall performance of these models, two experimental datasets were used: one in a 2D environment with 7344 RSS samples and another novel in a 3D environment with 27000 training records and 18000 testing samples by analyzing power spectral densities. To assess performance and analyze parameter optimization of ELM, R-ELM, and LMA, metrics such as root mean square error (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</i>), correlation coefficient (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>), training and testing times were used. By considering the state of the art, the LMA model proved to be the most accurate in the 2D environment (RMSE less than 10 cm), although its training time was excessive (over one hour), incompatible with for real-time applications (time variant channels). In contrast, the R-ELM achieved an accuracy of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</i> = 12.4806 cm and completed its training in 31.2 ms (real-time learning), positioning it as a much more efficient alternative compared to LMA. For the 3D dataset, the R-ELM also showed the best overall performance, with an average RMSE close to 22.4784 cm and a training time of 1.0250 s. Incorporating both the dominant frequency and power as inputs into the ELM enhanced the model’s accuracy compared to using each input separately. Lastly, RMSE was evaluated as a function of the distance from the center of the room of each data set, concluding that the R-ELM is more stable in areas with weak signals or missing data, which is particularly valuable in real environments where the signal is not always homogeneous. Finally, the results demonstrate that it is possible to achieve a precise and fast positioning system based on VLP using the R-ELM, as this model generally achieves higher accuracy and computational efficiency.

It has been demonstrated by several authors that the well-known weighted least squares (WLS) approximation can be equiripple if a suitable weighting function is applied. In the pre- sent paper, the WLS algorithm is generalized to SAW filter syn- thesis with prescribed magnitude and phase specifications. Several weighting techniques producing quasi-equiripple designs are pre- sented. The frequency sampling technique is used for SAW filter frequency response approximation to reduce the number of the optimized variables. The WLS algorithm rapidly converges both for linear and non-linear phase SAW filters. Typically, no more than 5-10 iterations are required to obtain the WLS solution to accuracy better than 0.5-1 dB in the stopband when compared with the optimum Chebyshev approximation. Moreover, it is shown that the WLS technique can be effectively applied for sec- ond-order effect compensation.

Indoor positioning systems based on visible light communication (VLC) using white light-emitting diodes (WLEDs) have been widely studied in the literature. In this paper, we present an indoor visible-light positioning (VLP) system based on red–green–blue (RGB) LEDs and a frequency division multiplexing (FDM) scheme. This system combines the functions of an FDM scheme at the transmitters (RGB LEDs) and a received signal strength (RSS) technique to estimate the receiver position. The contribution of this work is two-fold. First, a new VLP system with RGB LEDs is proposed for a multi-cell network. Here, the RGB LEDs allow the exploitation of the chromatic space to transmit the VLP information. In addition, the VLC receiver leverages the responsivity of a single photodiode for estimating the FDM signals in RGB lighting channels. A second contribution is the derivation of an expression to calculate the optical power received by the photodiode for each incident RGB light. To this end, we consider a VLC channel model that includes both line-of-sight (LOS) and non-line-of-sight (NLOS) components. The fast Fourier transform (FFT) estimates the powers and frequencies of the received FDM signal. The receiver uses these optical signal powers in the RSS-based localization application to calculate the Euclidean distances and the frequencies for the RGB LED position. Subsequently, the receiver’s location is estimated using the Euclidean distances and RGB LED positions via a trilateration algorithm. Finally, Monte Carlo simulations are performed to evaluate the error performance of the proposed VLP system in a multi-cell scenario. The results show a high positioning accuracy performance for different color points. The average positioning error for all chromatic points was less than 2.2 cm. These results suggest that the analyzed VLP system could be used in application scenarios where white light balance or luminaire color planning are also the goals.

Constrained Power System State Estimation

This article reports a novel visible light positioning (VLP) system and the associated experimental results. The developed VLP system is completely passive as it does not require a tracked object to carry any active device or tag. At the same time, it does not require any modification to the existing lighting infrastructure. The positioning system, termed Watchers on the Wall (WoW), localizes a target based on measuring the change it creates in the received signal strength (RSS) of the ambient light recorded at an array of light-sensors embedded in the wall. A prototype system has been implemented and tested to investigate the performance of the proposed approach with regard to localization and tracking. The experimental results show that the median and 90-percentile localization errors of 7 and 21 cm, respectively, can be achieved for a 2 m × 3.6 m testbed. The effect of various parameters like the height of placement and the number of light-sensors, as well as the size of the fingerprint database, has also been studied. The impact of various distance metrics on the localization performance of the weighted K-nearest neighbor (WKNN) classifier has been investigated. It has been found that two distance metrics outperform the commonly employed Euclidean metric. The experimental results also demonstrated that the developed system could track a mobile target along multiple routes with a median error of 12 cm.

To address three-dimensional (3D) localization problems in the wireless sensor networks (WSNs) of mobile communications, a closed-form algorithm by utilizing hybrid information extracted from the received-signal-strength (RSS) with unknown signal powers and the angle-of-arrival (AOA) is proposed in this paper. Firstly, the distance of the target is expressed as the linear equation with respect to coordinates of target and trigonometric functions of angles. Then, the RSS measurement is rewritten as the ratios of distances between the target and different receiving sensors. Furthermore, the set of pseudo-linear equations for the location of target is derived with respect to the AOA and nonlinear RSS measurements. Under the condition of the small variance of measurements, the first-order Taylor expansion around the value of measurement is taken to the set of pseudo-linear equations and the first-order perturbation errors is also obtained. Finally, the solution of the target localization is derived utilizing the weighted least square (WLS). Theoretical analysis and simulation results show that the performance of proposed algorithm converge to the CRLB in the situation of the moderate measurement errors.