Effects of Unknown Shadowing and Non-Line-of-Sight on Indoor Tracking Using Visible Light

Transcription

1 Milcom 217 Trac 1 - Waveforms and Signal Processing Effects of Unnown Shadowing and Non-Line-of-Sight on Indoor Tracing Using Visible Light Zafer Vatansever and Maite Brandt-Pearce Charles L. Brown Department of Electrical and Computer Engineering University of Virginia, Charlottesville, VA zv4xv@virginia.edu, mb-p@virginia.edu Abstract Indoor target tracing has garnered interest as communication systems and mobile device capabilities advance. Visible light communication (VLC) is an alternative to RF methods that uses light emitting diodes. In this paper, probabilistic filtering algorithms (particle and extended Kalman filters) are used for indoor tracing. The performance of the filters is compared with an another positioning method: trilateration. Probabilistic filtering methods are shown to be more reliable than trilateration for indoor tracing when non-line-of-sight components are significant. The probabilistic filtering algorithms require a light intensity map that is collected as a fingerprint map prior to tracing. The effect of unpredictable shadowing as the conditions change is examined in a scenario where one of the lamps has been. Our algorithm tracs the user equipment with less error than trilateration. The results also show that the tracing accuracy for our algorithms is on the order of the grid resolution of the fingerprint map for high signal-to-noise ratio environments. Index Terms Visible light communication, indoor positioning, indoor motion tracing, extended Kalman filter, particle filter, trilateration, shadowing I. INTRODUCTION Research on visible light communication (VLC) has made it a strong alternative to other methods used in indoor positioning, such as RF and Wi-Fi [1]. The most distinctive advantages of VLC are: VLC does not create EM interference, visible light is not harmful to living creatures, the capital expenditures for VLC-tracing systems are lower than other methods, and light emitting diodes (LED) provide a larger number of access points than Wi-Fi. LEDs are replacing traditional lamps as standard lighting, require less power, and the requisite LEDs have high life expectancy. VLC systems can be used in shopping malls, museums, warehouses, military and industrial facilities, and hospitals, where RF systems are often disallowed. In this study, we use Bayesian state estimation tools to solve the indoor tracing problem. In [2], we show that the extended Kalman filter (EKF) can be used for indoor target tracing with a diffusing lamp model, and the EKF doesn t require nowledge of the geometry between the transmitter and receiver. Here, we expand our previous study [2] by comparing the performance of the EKF and the particle filter (PF) when non-diffusing lamps are used, and when measurements contain both the line-of-sight (LOS) and the non-line-of-sight (NLOS) parts of the light. We also investigate a scenario where the system experiences unnown shadowing. One of the traditional algorithms used for indoor positioning is received-signal-strength-based trilateration, which relies on the estimated distance between the transmitters and the receiver. The effect of the NLOS light on the performance of trilateration is discussed in [3]. We demonstrate that the Bayesian filtering algorithms used in this study, the EKF and the PF, increase the accuracy compared to the trilateration algorithm, especially when NLOS components are significant. We also show that if one of the LED lamps has unnown shadowing or if there are unpredicted fluctuations in the signalto-noise ratio (SNR), Bayesian tools can still cope with these problems and successfully trac mobile user equipment (UE). VLC-based positioning algorithms are generally divided into three categories: triangulation, fingerprinting and proximity [4]. Triangulation-based methods use the angle of arrival (AOA) or propagation loss of the received signal strength (RSS). The AOA is used to find the position of the mobile user in [5]. The camera on the UE is used to capture the nearby light sources with nown positions and unique IDs. Then, with the help of optimization methods, the location of the user is found. A simpler method is proposed in [6], where the AOA is used to solve the triangulation problem with the least squares approach. The measured RSS can be used to find the distance between the transmitter and the receiver by using the VLC channel model; the distances to multiple transmitters with nown positions are used for solving the trilateration problem [7]. There are also other measurements types, such as time-of-arrival (TOA) and time-difference-of-arrival (TDOA). In TOA, the propagation delay is calculated, as in the Global Positioning System (GPS). However, since the speed of light is high, near-perfect synchronization is required for accurate results. A modification of TOA is TDOA. In TDOA, the LEDs are assumed to be perfectly synchronized, and the location of the UE is found from the propagation delays of the light from the different sources [8]. Proximity is the simplest VLC indoor positioning method. In proximity-based algorithms, the location of the UE is matched to the closest landmar (lamp with nown ID). The accuracy is typically not high; however, increasing the complexity of the system by relying on a dense grid of /17/$ IEEE 51

2 Milcom 217 Trac 1 - Waveforms and Signal Processing Fig. 1: Indoor positioning and navigation algorithm flowchart luminaries with nown IDs may decrease the estimation error [9]. Fingerprinting (or scene analysis), explored in this paper, is a general name that is given to algorithms that use a ind of mapping between a signal feature and the UE location. The mapping method can be landmaring, i.e., choosing RSS indicators in fixed nown positions. The algorithm can then use -Nearest Neighbors (NN) to estimate the location of the mobile user [1] or Bayesian methods that require an apriori fingerprint map of the RSS [2], [4]. In this paper, we first calculate the RSS map throughout the room in an offline phase; this serves as our fingerprint map (P) which is sent to the UE upon entering the room. The UE collects the online RSS measurements (y) from the lamps as it moves in the room using a single photodetector (no camera needed). P is used as a loo-up table for the power received in the predicted position, and y is used as the realtime measurements for Bayesian filtering. The performances of two Bayesian filters, the EKF and PF, are compared with the RSS-trilateration algorithm given in [7]. In addition, to our nowledge, the effects of LOS and NLOS combined and shadowing unbenownst to the system on Bayesian methods have not been examined in the VLC-based literature. Since we use a fingerprint map that consists of both LOS and NLOS, and the user equipment (UE) measures both, the accuracy of the Bayesian filtering methods increases. The results show that variations in the SNR of a particular lamp do not affect the accuracy dramatically, unlie for trilateration. The rest of the paper is organized as follows. Section II describes the VLC model, the SNR analysis, and the collection of the fingerprint map. Section III introduces the tracing algorithms. Numerical results that show how the Bayesian filtering algorithms compare and how their performances differ from the trilateration algorithm under different SNR and shadowing conditions are reported in Section IV. Finally, conclusions are drawn in Section V. II. VISIBLE LIGHT COMMUNICATION MODEL Fig. 1 shows how the offline data collection phase and the online state estimation phase are combined. In the offline phase, P is created prior to tracing and stored in a fingerprint matrix. The P map in this study may be collected manually or automatically according to a predefined resolution [2]. P consists of power levels over a rectangular grid in the room; the size of the grid represents the resolution. The online step starts with the collection of online light intensity measurements, y, by the UE. Filtering is performed based on these measurements. In this section, we discuss the model used to simulate P, how the fingerprint map is constructed, and the noise model we use when we compare the measurements y to elements of P. A. Channel Model In an optical lin, the LEDs are the transmitters, and we assume that the UE has a photodetector acting as a receiver. Each lamp is encoded with an orthogonal code so that the received power from each lamp can be determined by correlating with each code before computing the RSS at the UE. The impulse response of a VLC channel has two parts: the LOS and the NLOS. The NLOS is caused from bouncing of waves from walls or obstacles. In this study, for simplicity, we consider only the first bounce. The LOS DC gain is given as [11]: { Ar(m+1) H LOS = 2πd cos m (φ) cos(ψ), ψ Ψ 2 c, (1), otherwise, where A r is the area of the receiver; m is the Lambertian mode of the transmitted beam, which is related to the semiangle of the LED, d is the distance between the transmitter and the receiver, φ is the radiation angle for the transmitter, ψ is the incident angle at the photodetector, and Ψ c is the field-of-view of the photodetector. The differential NLOS DC gain of the first bounce, i.e., the gain resulting from a differential surface area da, isgivenas [12]: A r(m+1) ρ cos m (φ) cos(α) cos(β) cos(ψ) da, 2π 2 d 2 1 d2 2 dh NLOS = ψ Ψ c,, otherwise, (2) where d 1 is the distance between the LED and the reflection point, d 2 is the distance between the reflection point and the receiver, ρ is the reflectance coefficient, φ is the angle of irradiance from the LED, α is the angle of incidence of the reflective point, β is the angle of irradiance to the receiver, and ψ is the angle of incidence at the photodetector. Fig. 2 (a) shows the geometry used in LOS and NLOS channel models and Fig. 2 (b) illustrates the impulse response of the LOS lin and the first NLOS part. In this wor we collect the RSS from both the LOS and NLOS together into one measurement, as separating them would require a high-bandwidth receiver that would suffer from excessive noise. P t is the transmitted total power from each LED lamp. For each lamp, the received optical power P r from the LOS and NLOS components is found as: P r = P t H LOS + P t dh NLOS. (3) walls In a classical signal-to-noise ratio (SNR) analysis for a VLC system, there are two noise sources: shot and thermal 52

3 Milcom 217 Trac 1 - Waveforms and Signal Processing Normalized Amplitude LOS NLOS Time Delay (ns) Fig. 2: Propagation of the non-line-of-sight lin, (a) the geometry of LOS and NLOS propagation of light, (b) example of the LOS and NLOS parts of the impulse response of the channel [13]. noise [12]. Shot noise depends on the direct and ambient light. Thermal noise results from the electronic noise. Previous wors, lie [7], [14], assume these two are the main noise sources in the system. In a real world scenario, there are other unnowns affecting the system; they are defined as uncertainty noise in this study. This uncertainty noise may be caused from the shadowing of the LOS between the transmitter and the UE, uneven dimming of the lamps, uncertainties during the construction of the fingerprint map, the unnown inclination of the mobile device, etc. The SNR calculation for the system is modified as R 2 Pr 2 SNR = σshot 2 + σ2 thermal + (4) σ2 uncertainty where R is the receiver responsivity, P r is the received power on the photodetector, σshot 2 is the variance of the shot noise, σthermal 2 is the variance of the thermal noise, and σ2 uncertainty is the variance of the uncertainty noise. B. The Fingerprint Map The fingerprint map in this paper is denoted by the matrix P, and it contains the optical RSS received from each of the LED lamps. The fingerprint map is constructed from all the expected received power levels from orthogonally-coded LEDs lamps throughout the room. The room area is divided into an equal-sized rectangular grid. In the calibration step, the received power at each grid point is either calculated using (3) or measured prior to starting the system, and the fingerprint map P is created. The matrix P is sent to each UE as it enters the room. To build the fingerprint map, the physical room floor area is divided into N J equally sized grid points. The average received power on the grid point (i, j) for each LED lamp is denoted as P (i,j), where i =1,...,N and j =1,...,J are the indices in the Cartesian plane. As the power distribution in the room changes, the fingerprint map in the room is re-calibrated and updated according to a pre-defined update frequency. The source of changes in the fingerprint map may be shadowing, power fluctuations, or the movement of users. These changes cause a miss-match between the actual power distribution in the room and the fingerprint map until recalibration occurs. III. POSITIONING/TRACKING METHODS The indoor tracing algorithms proposed in this study use the EKF and the PF. The EKF is nown to be a sub-optimal state estimator when the dynamic models are nonlinear or the noise is non-gaussian. On the other hand, the PF is a better solution for a system that has multi-modal noise or discrete state components; in addition, the PF does not require a linearization step, and uses a numerical method, while the EKF uses an analytical method [15]. State estimation tools need an accurate representation of the dynamic model for the prediction step. The dynamic model is a discretized state-space system that evolves in time, which we assume to be a constant velocity model [16]. The goal of the tracing algorithm is to estimate the state of the UE at each time step, which is given as x =[x, y, ẋ, ẏ] T. The Cartesian coordinates are aligned with the walls of the room and denoted as x and y; ẋ and ẏ are the velocity components. The dynamic model is given by x = Ax 1 + q 1 (5) y = h(x )+r (6) where A is the state transition matrix, x is the hidden state at time. (6) is the state-space model representation of the measurements, where y R m is the vector of RSS measurements, the superscript m is the number of LED light sources, and h( ) is the measurement model function. The process noise is q N(, Q ), a zero mean, Gaussian distributed noise with covariance Q, and r N(, R ) is the measurement noise with covariance R. The measurement noise covariance R has the sum of σshot 2, σ2 thermal and σuncertainty 2 on the diagonal. The RSS measurements, which serve as fingerprints from each LED lamp, are saved in a vector y. Note that we measure the optical power from orthogonally-coded LEDs, and the received RSS from each transmitter is found by convolving with the code at the receiver. The position of the user cannot be observed directly. The channel model equations given in (1) and (2) are highly nonlinear equations of the UE position. Such nonlinear systems can be estimated with the EKF, where a linearization step is used to handle nonlinearities in the system, which relies on Jacobian H( ) of h( ). Model-based linearization of the measurement process requires calculation of derivatives of (1) and (2) with respect to state variables, which is intractable when the geometry is unnown between the transmitter and the receiver. Instead, an alternative method is proposed. Fig. 3 represents the fingerprint map P =[P i,j ].Weuse P to estimate the derivatives of the RSS measurements with respect to distance in both horizontal direction using a finite difference method. ˆx is the predicted state found in the prediction step of the EKF and P (ˆx ) represents the RSS 53

4 Milcom 217 Trac 1 - Waveforms and Signal Processing TABLE I: Simulation Parameters Parameter Value Room dimension (L W H) m 3 Transmitted power from each LED lamp (P t) 2 Watts Lambertian mode (m) 1 LED lamp elevation and azimuth -9 and Positions of the 4 LED lamps in the room(x, y, z) (m) 1.25 m away from the walls, for x and y, and z=3 m Height of the photodetector.75 m Field of view (Ψ c) 7 Physical area of the photodetector (A r) 1cm Receiver elevation and azimuth 9 and Gain of optical filter and refractive index of the lens 1. and 1. at the photodetector Room reflection coefficient (ρ).8 Fig. 3: Power distribution matrix. at the predicted position of the UE, labelled in the figure, ˆP (i±1,j±1) denotes the corresponding expected RSS values in the four adjacent positions. Then, in the update step of the EKF, the Jacobian is estimated as: [ ˆP(i+1,j) H(x ) ˆP (i 1,j) ˆP (i,j+1) ˆP ] (i,j 1) (7) 2Δx 2Δy where i ± 1 and j ± 1 are the indices of the adjacent grid points to P (ˆx ) and (Δx, Δy) is the granularity of the power map grid. The PF also requires nowledge of the fingerprint map P, but this method does not need a linearization step and can handle nonlinearities and non-gaussianity [17]. The PF uses an initial distribution of particles, x (i) p(x ), where superscript (i) is the particle number, and p(x ) is the initial probability density function of particles. Each particle has an associated weight. The weights are equal initially, and are denoted by ω (i). The same dynamic model in (5) is used to propagate the particles. The PF calculates the lielihood of the particle weights ω (i) by looing up the predicted power P (ˆx(i) ) on the predicted positions of the particles from the fingerprint map, and the real-time power measurements y on the UE. At time, the lielihoods are calculated as w (i) = p(y ŷ (i) ), where p( ) is the conditional probability function, y represents the received power on the UE and ŷ (i) = P (ˆx(i) ) is the predicted power vector on the predicted particle position. Recall that we cannot observe the position. Instead, the received power at the UE location is observed, so we first predict the particle positions, ˆx (i), using the dynamic model given in (6) and then find the corresponding power level from P. The lielihoods are normalized by w (i) = w (i) N. =1 w(i) The next step is called resampling, where new particles are drawn based on the posterior probability distribution function obtained after normalization. We use stratified resampling, where the smaller weights are sampled at most once and the higher weights are sampled at least once [18]. The mean of the particle positions become the position estimate. Since we are interested in position tracing here, we only calculate the position estimates. The PF s initial proposed distribution acts lie an initialization algorithm that eliminates the necessity for an initial guess of the state and the initial error covariance that are necessary for the EKF. IV. RESULTS The metric chosen to compare the performance of the proposed algorithms and the trilateration algorithm is the root mean square error (RMSE) of the position estimates. Some of the ey simulation parameters lie the room size and the number of LED lamps are given in Table I. The room is assumed to be empty. The sampling frequency of the photodetector on the UE is 1 Hz. We investigate the relationship between the RMSE and the fingerprint map resolution. We use two different resolutions: Δx =Δy = 1 decimeter (dm) and 1 centimeter (cm). The RMSE results are the mean of the RMSE from 1 random trajectories and 95% confidence intervals are also calculated. The UE is assumed to be moving at a fixed height and the UE orientation is fixed. For trilateration simulations, the positions of the LED lamps are nown. The optical power meets the requirements set by the Illuminating Engineering Society of North America (IESNA). Bayesian filters depend on the choice of a proper dynamic model and nowledge of the noise. The dynamic model is chosen to mimic human wal following an S-shaped trajectory at a sampling interval of 1 ms, which agrees with a constant velocity model [16]. The process noise variance is chosen to be optimal for the EKF and the PF, i.e, the level that minimizes the RMSE for each algorithm. The same process noise level is tested at different SNR levels [2]. The computation time of the PF is proportional to the number of particles used. We found 5 particles to be optimal by trial and error. The EKF requires an initial information of the states. Predefined anchor points, such as doors or windows, are used for estimating the initial state in the room. The choice of initial error covariance matrix is the error introduced due to the initialization. 54

5 Milcom 217 Trac 1 - Waveforms and Signal Processing EKF low res. map LOS+NLOS EKF low res. map LOS EKF high res. map LOS+NLOS EKF high res. map LOS PF low res. map LOS+NLOS PF low res. map LOS PF high res. map LOS+NLOS PF high res. map LOS EKF, low res. map PF, low res. map Trilateration LOS Trilateration LOS+NLOS EKF, high res. map PF, high res. map SNR (db) Fig. 4: Tracing performance of EKF vs. PF for high and low resolution fingerprint maps (LOS+NLOS and LOS) for different SNR values. 95% confidence intervals are also shown. A. Unbiased Fingerprint Map In this section the fingerprint map correctly represents the expected power level from each lamp, i.e, there is no unnown shadowing in the system. Fig. 4 shows the tracing performance and the 95% confidence intervals for two scenarios, when the fingerprint map contains the LOS+NLOS and only the LOS components of light. It shows that the PF outperforms the EKF for both map resolutions and LOS and NLOS conditions. The linearization step in the EKF may sometimes lead to miscalculation and introduce error [15]. The PF does not require the linearization step; instead, it simulates the candidate representations (particles) and loos at the lielihoods between the currently measured power level and the recorded power levels at the positions of the particles. In other words, while the EKF is suboptimal for nonlinear systems, the PF deals better with the nonlinearities than the EKF. Results show that including the NLOS information in the fingerprint map is not crucial EKF, low res. map EKF, high res. map PF, low res. map PF, high res. map SNR (db) Fig. 5: RMSE between the nearest tracing grid point and the nearest true trajectory grid point for high and low resolution fingerprint maps (LOS and NLOS) for different SNR values. 95% confidence intervals are also shown. To isolate the tracing errors due to just noise (without quantization errors due to the power map grid), Fig. 5 shows the RMSE between the quantized positions for both the SNR (db) Fig. 6: Tracing performance of EKF vs. PF vs. trilateration when the fingerprint maps (LOS and NLOS) have different resolutions for the grid for high SNR values. position estimates and the measurements, which correspond to grid points. The results are as expected, i.e, the error decreases as the SNR increases. The PF again outperforms the EKF. Fig. 6 compares the performance of the RSS-trilateration algorithm versus our proposed Bayesian algorithms. We plot the results starting at the lowest SNR values used in [7]. The performance of the trilateration algorithm is highly sensitive to noise. When solving the trilateration problem, an accurate calculation of the distance between the transmitter and the receiver is needed. Noise in the system or even slight shadowing increases the error of the trilateration dramatically. The trilateration solution expects all the measured power to come from the LOS. When this is true, the performance is acceptable, as shown in Fig. 6. When the NLOS is significant, as in the scenario considered in these simulations, the NLOS part of the light will act lie additional noise, thus decreases the accuracy of the RSS-trilateration. At these higher SNR values, our techniques basically measure only quantization error due to the grid. B. Biased Fingerprint Map We compare the performance of the Bayesian filters versus the trilateration algorithm when there is unforeseen shadowing in the system. In this scenario, the fingerprint map is not updated to account for the shadowing and is unaware that there is a change in the illumination conditions. This shadowing introduces a bias to the fingerprint map. The effect of bias can be seen in Figs. 7 and 8. The UE receives lower power from one of the lamps than what is expected. We model the shadowing as an additional path loss factor α on one of the four lamps [13]. In Fig. 7 the performance of the EKF, the PF, and trilateration is shown when there is unforeseen shadowing in the system. The decrease in the received power leads to a decrease in SNR as well. As the SNR loss increases, the accuracy of the three algorithms decreases, but the position error of the trilateration increases the most, as shown in Fig. 7. Fig. 8 shows the effect of unnown shadowing on the tracing accuracy for one realization of a typical trajectory 55

6 Milcom 217 Trac 1 - Waveforms and Signal Processing EKF, low res. map PF, low res. map Trilateration LOS EKF, high res. map PF, high res. map Decreased SNR due to unnown shadowing (db) Fig. 7: Tracing performance when one of the lamps has an unnown shadowing loss, while the others are operating normally. SNR=45 db at α= db LED bulb I is (a) (c) LED bulb III is LED bulb II is LED bulb IV is (b) Fig. 8: The effect of unnown shadowing on the tracing performance for an S-shaped trajectory in the room. (a),(b), (c) and (d) shows the results for each of the four lamps by 3 db. when one of the four lamps has 3 db less SNR than the others. The other three lamps have 45 db SNR. The red square represents the LED lamp that is. From Figs. 8 (a) and (c), we see that as the mobile receiver moves closer to the lamp, the shadowing introduces a bias that moves the estimates away from the lamp. Figs. 8 (b) and (d) show that the effect of the bias is smaller and the estimates are towards the lamp, unlie Figs. 8 (a) and (c). The bias introduced is the effect of the unnown shadowing, and the bias may be negative or positive with reference to the particular lamp. V. CONCLUSION In this paper, an estimated power map is used as a fingerprint map and the performance of tracers based on the (d) EKF and the PF are compared to each other and to the traditional trilateration algorithm. The results for the Bayesian filtering approaches show that the accuracy is dependent on the resolution of the fingerprint map. The results also confirm that the PF is a better filter candidate than the EKF due to its ability to handle strong nonlinearities in the system; furthermore, it does not need an initialization step. Finally, we loo at what happens if one of the lamps is unexpectedly, and see that the Bayesian filters outperform the trilateration methods under such conditions. The future wor of this study will concentrate on an automated process for building and maintaining the fingerprint map. REFERENCES [1] M. Kavehrad and Z. W., Light positioning systems (LPS), in Visible Light Communication, S. Arnon, Ed. Cambridge University Press, 215, pp [2] Z. Vatansever and M. Brandt-Pearce, Visible light positioning with diffusing lamps using an extended Kalman filter, in 217 IEEE Wireless Communications and Networing Conference (WCNC), March 217, pp [3] W. Gu, M. Aminiashani, and M. Kavehrad, Indoor visible light positioning system with multipath reflection analysis, in 216 IEEE International Conference on Consumer Electronics (ICCE), Jan 216, pp [4] T.-H. Do and M. Yoo, An in-depth survey of visible light communication based positioning systems, Sensors, vol. 16, no. 5, p. 678, 216. [5] Y.-S. Kuo, P. Pannuto, K.-J. Hsiao, and P. Dutta, Luxapose: Indoor positioning with mobile phones and visible light, in Proceedings of the 2th Annual International Conference on Mobile Computing and Networing, ser. MobiCom 14, 214, pp [6] H. Liu, H. Darabi, P. Banerjee, and J. Liu, Survey of wireless indoor positioning techniques and systems, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 37, no. 6, pp , Nov 27. [7] W. Zhang, M. I. S. Chowdhury, and M. Kavehrad, Asynchronous indoor positioning system based on visible light communications, Optical Engineering, vol. 53, no. 4, p. 4515, 214. [8] J. Armstrong, Y. A. Seercioglu, and A. Neild, Visible light positioning: a roadmap for international standardization, IEEE Communications Magazine, vol. 51, no. 12, pp , December 213. [9] Y. U. Lee and M. Kavehrad, Two hybrid positioning system design techniques with lighting LEDs and ad-hoc wireless networ, IEEE Transactions on Consumer Electronics, vol. 58, no. 4, pp , November 212. [1] J. Vongulbhisal, B. Chantaramolee, Y. Zhao, and W. S. Mohammed, A fingerprinting-based indoor localization system using intensity modulation of light emitting diodes, Microwave and Optical Technology Letters, vol. 54, no. 5, pp , 212. [11] J. M. Kahn and J. R. Barry, Wireless infrared communications, Proceedings of the IEEE, vol. 85, no. 2, pp , Feb [12] T. Komine and M. Naagawa, Fundamental analysis for visible-light communication system using LED lights, Consumer Electronics, IEEE Transactions on, vol. 5, no. 1, pp. 1 17, Feb 24. [13] J. Lian, Multiuser MIMO indoor visible light communication systems, PhD dissertation, UVA, 217. [14] M. Rahaim, G. Prince, and T. Little, State estimation and motion tracing for spatially diverse VLC networs, in Globecom Worshops (GC Wshps), 212 IEEE, Dec 212, pp [15] S. Sara, Bayesian filtering and smoothing, Institute of Mathematical Statistics Textboos, Cambridge University Press, 213. [16] X. R. Li and V. P. Jilov, Survey of maneuvering target tracing. Part I. Dynamic models, IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 4, pp , 23. [17] M. Arulampalam, S. Masell, N. Gordon, and T. Clapp, A tutorial on particle filters for online nonlinear/non-gaussian Bayesian tracing, IEEE Trans. Sig. Proc., vol. 5, no. 2, pp , Feb. 22. [18] P. Koziersi, M. Lis, and J. Zietiewicz, Resampling in particle filtering-comparison, Poznansie Towarzystwo Przyjaciol Nau,