Visible light positioning (VLP) based on an image sensor uses light sources to emit ID (Identity Document) signals containing the position of the light sources and uses a mobile phone as the receiver. The stripes images carrying ID information are acquired by the rolling shutter efect of the Complementary Metal Oxide Semiconductor (CMOS) image sensor. And then using the geometric relationship between the object point and the image point of the light sources to complete the positioning. Quantization error is inevitable when obtaining the imaging coordinates of fringe images. Based on this, we design an easily identifiable light source signal mechanism, which consists of two parts: the information sequence and the all-bright sequence. We use diferent methods to get the imaging coordinates of the light source and fit the deviation between the ideal imaging coordinates and the identified imaging coordinates, the fitting results show that the imaging deviations obey Gaussian distribution. And this paper simulates positionings on the basis of considering the imaging deviation, the positioning results show that the positioning error can be controlled within 1.3cm efectively under the signal mechanism and identification method we proposed.
The VLP positioning system is mainly composed of a receiver and a transmitter. The transmitter is generally light source, and the receiver is distinguished by a Photo-Diode (PD) or an Image-Sensor (IS)[11]. PD is sensitive to the beam direction, so it greatly limits the mobility of the positioning terminal. And PD-based positioning requires extremely high angle measurement and received signal strength measurement, which will lead to large positioning errors[12]. In contrast, IS is more widely incorporated into various mobile devices. Thus it’s can complete high-accuracy positioning without additional equipment just using a mobile phone camera[13].
In VLP based on IS, we encode the actual position of the light sources and load them onto the light sources to emit in the form of high-frequency flashing The flicker frequency of the modulated light sources reaches kHz, CMOS image sensor can detect the change and image them as light and dark stripes images[14]. Identifying the images, decoding the ID information of light sources, and then calculating the imaging coordinates of the light sources (′ , ′ ). By querying the pre-established ID database, matching the three-dimensional(3-D) position coordinates of the light sources (, , )[15]. The position of the IS can be calculated through the geometric relationship between the object point coordinates and the image point coordinates, that is, positioning is achieved. While calculating the coordinates of the light sources on the imaging plane, there will be inevitable quantization errors which will lead to positioning deviations due to the variety of stripes images. Therefore, this paper proposes an easily identifiable signaling mechanism as the emission signal of light sources and proposes two identification algorithms based on this signal mechanism. By fitting the imaging deviation of the light sources obtained by actual measurement, it can be found that the imaging deviations conform to the Gaussian distribution. After taking the imaging deviation into account, we test positionings using the obtained data and the results show that the positioning accuracy of the algorithm proposed in this paper is better than the positioning accuracy of direct identification. 2. Single camera positioning algorithm The VLP based on IS is to get the position and attitude information of IS. To simplify the experiments, we only discuss the case where IS is fixed at the same height. Fig. 1 shows a typical indoor positioning system. We installed 4 LEDs on the ceiling of the room and the LEDs were not in a straight line. Each LED transmits its unique ID signal representing its own 3-D coordinate information to the optical channel through OOK modulation. We use the mobile phone as the receiver to capture images of light sources. Then detecting the ID and image coordinates of the LEDs. After obtaining the above information, we use the following algorithm to complete the position calculation of the receiver = ( , , ).
Let the 3-D positions of LEDs be (, , ), = 1, 2, 3, 4, where are the numbers of the
light sources. The height of the mobile phone from the ceiling is and the distance from each
LED to the lens( ) is denoted as 1, 2, 3, 4. They can be expressed as (
After imaging by the IS, we can get the position coordinates (′ , ′ ), ′ = 1, 2, 3, 4 of each LED on the imaging plane, where ′ are the numbers of the imaging light sources. Then we can
R1
R3 R4
R2 LED3 P f
Q d1' (u1', v1') Z
Y
X
calculate the distance (′ and ′ ) from each image point to the image center = (0, 0) and
to the optical axis of the lens, as shown in (
According to the triangle similarity principle, the distance from each LED to the lens can be
calculated as shown in (
( − )2 + ( − )2 = 2 · ( 22′ − 1)
Therefore, the receiver’s coordinate of that is (
[ ; ] = ( )− 1
⎡2 − 1 2 − 1⎤
= 2 ⎣3 − 1 3 − 1⎦ ,
4 − 1 4 − 1
(
12′ (22 − 12) + (22 − 12) + 2 · ( 2 − 1) ⎢⎢ 22′ ⎥⎥ = ⎢⎢(32 − 12) + (32 − 12) + 2 · ( 2 − 1)⎥⎥ ⎢⎣ ⎥⎦
32′
(42 − 12) + (42 − 12) + 2 · ( 2 − 1)
⎤
(
To obtain the coordinates of the light sources image point in the positioning algorithm proposed in section 2, we need to identify the captured light source image. When obtaining the imaging coordinates of the light source, the imaged stripes images are not all complete circular contours due to the high scanning frequency of the camera, as shown in Fig. 2, which causes inevitable quantization errors and afects subsequent positioning. Therefore, we propose a design method for light source emission signal which is easy to identify.
(a) (c) (b) (d)
Under the premise of satisfying indoor lighting, we choose every 4 light sources as a set of positioning light source groups. The positions of those 4 light sources are not on the same straight line. The emission data of each light source consists of two parts: the information sequence and the all-bright sequence . The information sequence is the ID information that matches the actual 3-D position of the light source. Due to the great autocorrelation characteristics of the pseudo-random code, we might as well choose the pseudo-code as the ID of the light source. The all-bright sequence , as the name implies, is used to identify the image point of the light source and the ID demodulation. The transmitter uses OOK modulation to load the 3-D position of the light sources to the light sources at a frequency of 3kHz. Due to the high flicker frequency, the human eye cannot perceive this flickering. This not only ensures the lighting function of the light source but also completes the work of the positioning transmitting
To verify the superiority of the signal proposed in this paper, we discuss the situation of 4 indoor light sources that the requirements for the number of IDs are not high. Therefore, a Pseudo-noise Sequence = [ 1, 2, ..., 1 ], = 1, 2, 3, 4 (including but not limited to shift) with a code length of 1 = 7 and duration of 4 is selected to be assigned to each light source. To ensure that the receiving step can identify the light source quickly and accurately, adding two all-bright sequence = [1 , 2, ...2 ] of time 4 and code length 2 = 7 for each light
source. Since the light source is grounded at the cathode, here the 2 represents the binary all
“1” symbol. To collect the imaging of the light source information emission sequence and the
all-bright sequence simultaneously within , the all-bright sequence needs to be shifted, that
is, there is always a 4 delay between the all-bright sequences of the light source, as shown in
Fig. 3. Therefore, the total emission sequence of the light source groups in are shown as (
LED1 LED2 LED3 LED4
T 4
T 4
T 4
T
4
1 = ([︀ 0 0 1 1 ⊗ [︀ 11, 12, ... 11 ]︀ ) ⊕ (︀[ 1 1 0 0 ⊗ [︀ 1, 2, ... 2 ]︀ )
︀]
︀]
1 1 1
2 = ([︀ 1 0 0 1 ⊗ [︀ 21, 22, ... 21 ]︀ ) ⊕ (︀[ 0 1 1 0 ⊗ [︀ 1, 2, ... 2 ]︀ )
︀]
︀]
2 2 2
3 = ([︀ 1 1 0 0 ⊗ [︀ 31, 32, ... 31 ]︀ ) ⊕ (︀[ 0 0 1 1 ⊗ [︀ 1, 2, ... 2 ]︀ )
︀]
︀]
3 3 3
4 = ([︀ 0 1 1 0 ⊗ [︀ 41, 42, ... 41 ]︀ ) ⊕ (︀[ 1 0 0 1 ⊗ [︀ 1, 2, ... 2 ]︀ )
︀]
︀]
4 4 4
In addition, the number of light sources is more than 4 or even more in the actual environment,
so 1 and 2 can change the sequence length according to the number of light sources in the
(
Selecting the IS mounted on the mobile phone as the receiver, and aligning the light source array within time to obtain 4 photos , = 1, 2, 3, 4 continuously, where are the numbers of the photos. In this step, the acquired color images are transformed into grayscale images and binary images at first. Then we segment the binary images to process each light source in the captured images. Finally, we obtain the processed image ′ and pixel matrices (, )× , , = 1, 2, 3, 4, where (, ) is image coordinates of pixels, N is the number of pixels in row (ie horizontally), M is the number of pixels in column (ie vertical). After completing the above steps, using the identification algorithm to extract the centroid coordinates of the light sources.
The traditional identification algorithm is to find the upper, lower, left, and right edges of the
light source fringe image respectively, and take the midpoint as the imaging coordinate, or use
the fitting method to fit the circular edge of the light source and take the center of the circle as
the imaging coordinate. The above identification methods all have errors as shown in Fig. 2.
Based on the description in section 3.1, we propose two identification methods here as shown
in Table 1 and Table 2: (
Detecting the area of each light source in the image ′ and calculating its two-dimensional pixel coordinates. Taking light LED1 as an example, the main processes of these two methods are described in algorithm 1 and algorithm 2. And some identification results are shown in Fig. 4. 1. Traverse the column pixels of any one 1(, )× , = 1, 2, 3, 4 2. Record the column 1 whose pixel value is not 0 for the first time and the column 2 whose pixel value is 0 again; 3. Traverse the rows pixels of 1(, )× , = 1, 2, 3, 4 selected in step 1; 4. Record the row 1 whose pixel value is not 0 for the first time and the row 2 whose pixel value is 0 again; 5. Calculate the pixel value:
2
= ∑︁ 1(, )|= 1+2
=1 2
(
Considering the strictness of synchronization and to simplify the experiment, we use the smartphone to capture video images at a frame rate of 24fps and convert the video images into frame images. Then use Matlab to process these images. All the key system parameters adopted are provided in Table 3.
To verify our proposed methods, we use the camera of a smartphone(iphone12) to capture
the light source video carrying the information sequence described in section 3.2 at the test
point (
= @()( − (
In order to see the errors of diferent identification methods more clearly, our paper chooses the Root Mean Square Error (RMSE) to calculate the identification error: = √︁ (′ − ′ )2 + (′ − ′ )2 (13) where, (′ , ′ ) is the imaging coordinates of LEDi measured by the above 4 methods at the test point, (′ , ′ ) is the ideal imaging coordinates of the test point.
Cumulative distribution function (CDF) is the integral of the probability density function, which can describe the probability distribution of identification error. Taking LED1 as an example, the error cumulative distribution function of diferent identification methods are shown in Fig. 6 and Fig. 7. Fig. 6 is the deviation diagram of the centroid coordinates fringe 900 800 700 l) 600 e x i (ep 500 u l a lev 400 x i np 300 m u loC 200 100 0
images identified directly and the ideal imaging coordinates. Fig. 7 is the deviation diagram of the centroid coordinates using the algorithms proposed in 3.2 and the ideal imaging coordinates. 0.9 0.8
It can be seen that the coordinate error of the light source identified by fitting the stripes image directly is 0pix-50pix, and there is a 57% chance that the error exceeds 10pix. The error of the image method is 0pix-60pix, and the probability of exceeding 10pix is 68%. They all have large errors. The error of using the signal mechanisms proposed by 3.1 to identify the full bright spot are all about 0-3pix. Among them, algorithm 2 is to calculate the pixels of images, and the pixel coordinates are integers, so there are many repetitions of error values.
Fitting the coordinate deviation distribution obtained by the above four methods. Fig. 8 is the abscissa deviation distribution fitted according to the histogram of deviation coordinate diference using 4 methods, and Fig. 9 is the ordinate deviation distribution fitted according to the histogram of deviation coordinate diference using 4 methods. It can be seen that the deviation of the actual imaging coordinates of the light source is in line with the Gaussian distribution as shown in (14). The parameters are shown in Table 4. = 0 + 0− (− )2
22 ︂( ′ )︂ ′ = ︂( ′ )︂ ′ + ︂(
︂) 0 −2 −1 0
1 (c) 2 3 −1
0 (d) 1
In our positioning system, the source of the positioning error is mainly the quantization error caused by the image identification of the LED described in section 4.1, so the ideal imaging coordinates of the light source need to be rewritten as (15). where (, 2) and (, 2) are Gaussian white noises that are independent of each other on the horizontal and vertical axes of the light source on the imaging plane, the means and standard deviations are shown in Table 4.
Considering the identification error, we do positioning tests on the data obtained by each method at the test point. Then we calculated the positioning error which is the RMSE of the estimated position results and test point. The statistical result is shown in Fig. 10.
It can be seen that algorithm 1 and algorithm 2 perform better than the direct solution. More than 90% of the positioning error is within 1.69cm when using the fitted stripes images directly. More than 90% of the positioning error is within 1.77 cm when using the stripes coordinates identified by the image method directly. While more than 90 % of the positioning error is within (14) (15) 1.26cm when using algorithm 1, and the positioning error of algorithm 2 is within 1.25cm. So the two algorithms proposed in the paper all have high accuracy.
1
Indoor visible light position based on a single camera will be a large error when calculating fringe coordinates directly as the imaging centroid coordinates of light sources. In this paper, we proposed a light source emission signal mechanism combining information sequence and allbright sequence, we compared and fitted the imaging deviations of diferent methods. The results show that the imaging deviations obey the Gaussian distribution. We simulated positionings after taking the identification error into account. The results show that the two identification methods based on this signal mechanism can reduce the positioning error to within 1.3cm. The positioning accuracy is greatly improved compared with the positioning method of identifying the light source directly.
This paper tests multiple positioning at the test point, and the statistical results show the superiority of the signal proposed in this paper in positioning accuracy. In future work, we consider transplanting the positioning system into the real environment and consider the influence of some non-positioning light sources (such as sunlight) in the real environment to complete random and dynamic positioning.
This research was supported by The National Natural Science Foundation of China (62171075). Conference on Automation, Electronics and Electrical Engineering (AUTEEE), 2018, pp. 202–208. doi:10.1109/AUTEEE.2018.8720798. [13] H. Li, H. Huang, Y. Xu, Z. Wei, S. Yuan, P. Lin, H. Wu, W. Lei, J. Fang, Z. Chen, A fast and high-accuracy real-time visible light positioning system based on single led lamp with a beacon, IEEE Photonics Journal 12 (2020) 1–12. doi:10.1109/JPHOT.2020.3032448. [14] W. Guan, L. Huang, B. Hussain, C. P. Yue, Robust robotic localization using visible light positioning and inertial fusion, IEEE Sensors Journal 22 (2022) 4882–4892. doi:10.1109/ JSEN.2021.3053342. [15] Y. Wu, X. Liu, W. Guan, B. Chen, X. Chen, C. Xie, High-speed 3d indoor localization system based on visible light communication using diferential evolution algorithm, Optics Communications 424 (2018) 177–189. doi:https://doi.org/10.1016/j.optcom. 2018.04.062.