Content uploaded by Yirong Chen
Author content
All content in this area was uploaded by Yirong Chen on Jul 10, 2019
Content may be subject to copyright.
Performance comparison and analysis
on different optimization models for
high-precision three-dimensional
visible light positioning
Bangdong Chen
Jiajia Jiang
Weipeng Guan
Shangsheng Wen
Jingyi Li
Yirong Chen
Bangdong Chen, Jiajia Jiang, Weipeng Guan, Shangsheng Wen, Jingyi Li, Yirong Chen, “Performance
comparison and analysis on different optimization models for high-precision three-dimensional
visible light positioning,”Opt. Eng. 57(12), 125101 (2018), doi: 10.1117/1.OE.57.12.125101.
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
Performance comparison and analysis on different
optimization models for high-precision
three-dimensional visible light positioning
Bangdong Chen,aJiajia Jiang,aWeipeng Guan,b,*Shangsheng Wen,cJingyi Li,band Yirong Chena
aSouth China University of Technology, School of Electronic and Information Engineering, Guangzhou, Guangdong, China
bSouth China University of Technology, School of Automation Science and Engineering, Guangzhou, Guangdong, China
cSouth China University of Technology, School of Materials Science and Engineering, Guangzhou, Guangdong, China
Abstract. With the development of visible light communication, indoor visible light positioning (VLP) becomes
popular for researchers in the communication industry. However, most existing VLP algorithms only provide
solutions for positioning on a two-dimensional plane, and those focusing on three-dimensional (3-D) positioning
usually contain various sensors or hybrid algorithms. To solve these problems, first we transform the 3-D location
model in VLP into an optimization model and adopt distance based optimization model (DBOM) for positioning
based on the measured distances from the positioning terminal to multiple LEDs base stations. Second, we
further come up with an area-based optimization model (ABOM) for localization by the intersection of three
circles based on the received signal strength trilateration algorithm. The proposed ABOM converts the 3-D
optimization problem into a one-dimensional searching problem, thereby ensuring the real-time positioning per-
formance. Third, an effective 3-D optimization algorithm is adopted to judge the positioning performances of two
proposed models. Last but not least, we also set up an extended simulation, analyzing the nonlinearity of the
Lambert model and the positioning unit size’s effect on the maximum positioning height, which has never been
considered by existing works. Our simulation shows that the average positioning error is 0.96 cm for ABOM and
3.21 cm for DBOM. Besides, the experimental results of the actual scene also confirm that the mentioned system
can achieve an average 3-D positioning error of 4.34 cm. ©2018 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI:
10.1117/1.OE.57.12.125101]
Keywords: visible light positioning; distance-based optimization model; area-based optimization model; real-time performance.
Paper 181300 received Sep. 10, 2018; accepted for publication Nov. 9, 2018; published online Dec. 5, 2018.
1 Introduction
Indoor positioning has become a research hotspot to satisfy
life needs and business demands, for it is fundamental for
the tracking for mobile intelligent devices and navigation
service. Conventional indoor positioning systems include
a wireless local area network, Zig Bee, ultrawideband
(UWB), Bluetooth, radio-frequency identification (RFID),
infrared ray, and ultrasonic wave. However, UWB and
RFID require additional infrastructure and new hardware
components, and other RF-based systems can only deliver
positioning accuracies from tens of centimeters to a few
meters, while taking at least a few seconds for per position-
ing process. Different from the traditional indoor positioning
technologies mentioned above, the visible light positioning
(VLP) technology is a kind of indoor positioning technology
based on visible light communication (VLC) technology.1,2
Compared with the previous indoor positioning techniques,
it has the following advantages: first, the VLP system utilizes
the existing lighting facilities to realize positioning simulta-
neously, which is cost-saving and environmentally friendly.
Second, light wave with a shorter wave length is less vulner-
able to multipath fading in indoor environments, thus achiev-
ing a higher positioning accuracy. Third, no RF interference
will be generated by LED, so it can be applied in environ-
ments such as hospitals and airplanes, where RF is hazardous
or even forbidden. At present, VLP systems are mainly
divided into two categories: photodiode-based [photoelectric
detector (PD)-based] and image-sensor-based.3Since an
image-sensor-based positioning system needs complicated
image processing techniques,4it sets high demands on sys-
tem performance, simplicity, and reliability. On the contrary,
the PD-based positioning system offers a better solution
with lower cost for VLP. For a PD-based positioning system,
triangulation is used to determine the absolute position of
the terminal using the geometric properties of triangles,
which involves the time of arrival, the time difference of
arrival (TDOA), the received signal strength (RSS), the angle
of arrival (AOA),5,6and the phase difference of arrival.7
Among the above techniques, RSS-based positioning is pre-
ferred due to its low cost and high accuracy, which works out
the distance between LED and terminal based on the strength
of received signals. However, the problem of intercell inter-
ference must be solved when measuring received light signal
strength of different LEDs. So in our previous works,8–10 to
reduce intercell interference, we have modulated the visible
light from LEDs with code division multiple access (CDMA)
technology to separate the overlapping signals in time
domain and frequency domain. For the readers that are inter-
ested in the CDMA, refer to our previous reports.
So far, many schemes for VLP systems have been
raised; however, the vast majority of them can only realize
two-dimensional (2-D) positioning,11–13 thereby failing to
provide the height information that is needed on many
*Address author correspondence to: Weipeng Guan, E-mail: gwpscut@163
.com 0091-3286/2018/$25.00 © 2018 SPIE
Optical Engineering 125101-1 December 2018 •Vol. 57(12)
Optical Engineering 57(12), 125101 (December 2018)
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
occasions. Thus, researchers of VLP have gradually turned to
work on three-dimensional (3-D) positioning. For example,
in Ref. 14, Keskin et al. investigated direct and two-step
positioning approaches for both synchronous and asynchro-
nous VLP systems, as well as provided various numerical
examples to illustrate the improved performance of the pro-
posed estimators with respect to the current state-of-the-art
and to investigate their robustness against model uncertain-
ties in VLP systems. In Ref. 15, Du et al. proposed a
low-complexity TDOA-based indoor VLP system using
an enhanced practical localization scheme based on cross-
correlation and achieved an average positioning accuracy
of 9.2 cm. In Ref. 16, Li et al. used a 2-D plane structure
with height change for positioning, where the height value
and the 2-D plane value are determined, respectively.
In Ref. 17, Kim et al. proposed a 3-D indoor positioning
system using AOA and RSS with a single transmitter and
multiple optical receivers and achieve a positioning accuracy
of less than 6 cm. However, an assumed height is set in
advance and different presumed heights are needed for dif-
ferent positioning situations, which has a low practicality in
actual scene. Besides, since the range of height estimation is
limited, these methods are just small range approximation
and not 3-D positioning actually. In Ref. 18, Wang et al.
used the front camera of mobile phone and a collinear equa-
tion model to realize a level of decimeter 3-D positioning
error. Due to the limitation of the algorithms, some methods
can achieve relatively satisfying positioning accuracy only in
a small space. In Ref. 19, Zheng et al. determined the receiv-
er’s coordinates in a space of 100 ×118.5 ×128.7 cm using
the original 2-D positioning algorithm improved by an error
correcting algorithm for the corners, which is developed into
a 3-D positioning algorithm. In Ref. 20, Lim proposed
a maximum likelihood approach for indoor positioning sys-
tems based on RSS method to estimate the position of object,
in which the Newton–Raphson iterative method is used for
the estimation process. Since the initial predictions have
a high impact on the accuracy of this iterative approach,
this system performs well only when a good initial value
in the estimation process is set. Moreover, some methods
use multiple sensors, PDs, or receivers,21,22 which increase
algorithm complexity, positioning errors, and performance
instability. What is worse, these methods fail to achieve
time synchronization, thus cannot to judge whether the
data come from the same anchor point. According to the
discussion above, existing VLP methods still have many
deficiencies, such as long computing time, low accuracy,
high complexity, poor robustness, and disability to achieve
synchronization.
Aiming to solve the above problems in traditional VLP, in
our prior works,23–26 we had built a positioning system, trans-
forming the 3-D location model in VLP into an optimization
model. And many works had been made to improve the posi-
tioning accuracy. In Ref. 24, we proposed an indoor high
precision 3-D positioning system using the artificial neural
networks and modified genetic algorithms, and the position-
ing error is less than 1.02 cm on average. In order to improve
the robustness of the VLC-based system, in Ref. 26,we
proposed to use the particle swarm optimization to realize
the 3-D positioning process, and results showed the mean
error is 0.96 cm which indicated good positioning accuracy.
Furthermore, we keep studying the practicality of the VLP
system and schemes, finding most PD-based work only
focuses on the localization accuracy while ignoring the
real-time ability that is essential for positioning.
In this paper, first we transform 3-D location model in
VLP into optimization model and adopt distance-based
optimization model (DBOM) for positioning based on the
measured distances from the positioning terminal to multiple
LEDs base stations. Second, we further come up with area-
based optimization model (ABOM) for localization by the
intersection of three circles based on the RSS trilateration
algorithm. Third, an effective 3-D optimization algorithm
is adopted to realize the positioning process and judge the
positioning performance of two proposed models. It is worth
mentioning that the proposed ABOM ingeniously turns
the 3-D positioning problem into a one-dimensional (1-D)
search problem, thereby ensuring the real-time performance
in positioning. Last but not least, we also setup an extended
simulation, analyzing the nonlinearity of the Lambert model
and discussing the positioning unit size’s effect on the maxi-
mum positioning height, which has never been considered by
the existing works.
The remainder of this paper is organized as follows.
Section 2describes the indoor optical wireless channel
model, two proposed optimization models of 3-D VLP sys-
tem and provides details of the proposed ant colony algo-
rithm (ACO). Sections 3and 4describe the simulation
results, experiment results, and contrastive analysis to verify
the proposed approach. Section 5gives the conclusion of the
article.
2 System Principle and Optimization Models
2.1 Channel Model of Indoor Optical Wireless
As shown in Fig. 1, the proposed positioning system can be
divided into transmitting part and receiving part. The trans-
mitting part includes four LEDs installed on the four corners
of the ceiling in order to meet the needs of lighting, and the
PD at the receiving part can detect the intensity of light from
four LEDs by converting the light signal into electrical
signal. In this article, all of the LEDs are considered to be
Lambertian sources for their large beam divergence. In
Fig. 1, angle θis the angle between the Z-axis and the normal
direction of the PD and if we place the receiver horizontally
on a certain 2-D plane, which makes the angle θ¼0,
the channel gain HLOSð0Þof a line-of-sight (LOS) wireless
channel can be given as
Fig. 1 Indoor optical wireless positioning system.
Optical Engineering 125101-2 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
EQ-TARGET;temp:intralink-;e001;63;752HLOSð0Þ
¼mtþ1
2πd2A·TsðΨÞ·GðΨÞ·cosmtðΦÞ·cosðΨÞ;0≤Ψ≤Ψc
0;Ψ>Ψc
;
(1)
where dis the physical distance between the LED and the
positioning terminal; Ais the physical area of the PD;
TsðΨÞis the gain of an optical filter; GðΨÞis the gain of
an optical concentrator; Ψis the angle of incidence; Φis
the angle of irradiance; Ψcis the field-of-view of the
receiver; mtis the Lambertian parameters and can defined
as mt¼−ln 2
lnðcos Φ1∕2Þ, where Φ1∕2is the half-power angles
of the transmitter (LED) and the receiver (PD), respectively.
When the emitted optical power ptis received by the
receiver, the incident optical power from LOS path pLOS
can be given by pLOS ¼pt·HLOSð0Þ. In the VLP system
with no optical filter and concentrator, the power of the direct
channel prreceived at the PD can be calculated in the con-
dition of 0≤Ψ≤Ψcby the following as
EQ-TARGET;temp:intralink-;e002;63;527
pr¼R·λ·pLOS
¼R·λ·ðmtþ1Þ·A
2πd2·pt·cosmtðΦÞ·cosðΨÞ;(2)
where Ris the equivalent impedance of the receiver, and
λis the responsivity of the optical detector.
In practical application system, the total optical power
ptotal received at the PD consists of the ambient light
power pam, the power of the reflection channel pNLOS ,
and the power of the direct channel pLOS. In general, only
pLOS is utilized for positioning, while pam and pNLOS are
both viewed as noise power.27,28 In this paper, we mainly
adopt thermal and shot noise components with normal dis-
tribution, and the total noise variance can be expressed as
EQ-TARGET;temp:intralink-;e003;63;358σ2
noise ¼σ2
shot þσ2
thermal þðR·λ·pNLOSÞ2;(3)
where σ2
shot is caused by the optical power including the
effective signal strength and that from the lighting environ-
ment, while σ2
thermal is caused by the random motion of
electrons. σ2
shot,σ2
thermal, and pNLOS are all described in detail
in Ref. 29.
2.2 Two Proposed Optimization Models of
Three-Dimensional VLP System
The position of any point in a positioning space is related to
the receiving light strength, which depends on the optical
channel gain. In order to get a clearer relationship between
the optical channel gain and the position of any point in the
positioning space, we simplify the optical channel gain
model and further summarize two optimization models for
3-D VLP system. The former is DBOM and the latter is
ABOM. Indeed, we have already studied DBOM before,
but we just focused on the optimization of algorithms and
never analyzed it in depth. After exploring different optimi-
zation algorithms, we find that DBOM can be concluded
essentially and applied to various kinds of algorithms.
Meanwhile, we also put forward ABOM, which transforms
the 3-D search problem into a 1-D search problem, thereby
remarkably promoting the real-time ability of positioning
system. In addition, ABOM can realize a higher positioning
accuracy than DBOM.
In the VLP system, the coordinates of the four LEDs are
ðXi;Yi;Z
iÞ,i¼1;2;3;4and the coordinate of the position-
ing terminal is ðXt;Yt;Z
tÞ, which can use 3-D coordinates of
the four LEDs to determine its own location. The physical
distance between the LEDs and the positioning terminal
dican be given as
EQ-TARGET;temp:intralink-;e004;326;664di¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðXi−XtÞ2þðYi−YtÞ2þðZi−ZtÞ2
q:(4)
Therefore, the irradiant angle Φcan be represented as
EQ-TARGET;temp:intralink-;e005;326;614 cosðΦÞ¼Zi−Zt
di
:(5)
Since it is assumed that the surface of receiver is parallel
to the ceiling, the incident angle Ψis equal to the irradiant
angle Φ, then we can get the following equation: cosðΨÞ¼
cosðΦÞ. Then, Eq. (2) can be converted into the following
form:
EQ-TARGET;temp:intralink-;e006;326;516pr¼C·1
d2
i
·cosmtþ1ðΦÞ¼C·ðZi−ZtÞmtþ1
dmtþ3
i
;(6)
where Cis a constant acquired in the indoor optical wireless
positioning system, which can be calculated as
EQ-TARGET;temp:intralink-;e007;326;447C¼R·λ·ðmtþ1Þ·A·pt
2π:(7)
Therefore, dican be represented as
EQ-TARGET;temp:intralink-;e008;326;394di¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C·ðZi−ZtÞmtþ1
pr
mtþ3
s:(8)
At this point, Eq. (8) is the key formula of DBOM and as
for ABOM, further exploration is needed.
As Fig. 2shows, according to the Pythagorean theorem,
the estimated horizontal distances dxiyifrom the receiving
terminal to each LED can be calculated as
EQ-TARGET;temp:intralink-;e009;326;287d2
xiyi¼d2
i−ðH−hÞ2;(9)
where H¼Ziand h¼Zt. After getting three dxiyi, we can
use triangulation algorithm to calculate the terminal’s coor-
dinate and the equations can be expressed as follows:
EQ-TARGET;temp:intralink-;e010;326;222
8
<
:
ðxe−x1Þ2þðye−y1Þ2¼d2
x1y1
ðxe−x2Þ2þðye−y2Þ2¼d2
x2y2
ðxe−x3Þ2þðye−y3Þ2¼d2
x3y3
;(10)
where ðx1;y
1Þ,ðx2;y
2Þ, and ðx3;y
3Þare the X-coordinates
and Y-coordinates of the LEDi,i¼1;2;3in Fig. 2, respec-
tively. The estimated terminal’s position coordinate in X- and
Y-axes ðxe;y
eÞcan be calculated by two linear equations,
which can be simply obtained through subtracting the first
and second equations from the third in Eq. (10). In order
to get the estimation for the positioning terminal, the follow-
ing equation set should be solved:
Optical Engineering 125101-3 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
EQ-TARGET;temp:intralink-;e011;63;564
2xeðx1−x3Þþx2
3−x2
1þ2yeðy1−y3Þþy2
3−y2
1¼d2
x3y3−d2
x1y1
2xeðx2−x3Þþx2
3−x2
2þ2yeðy2−y3Þþy2
3−y2
2¼d2
x3y3−d2
x2y2
:
(11)
The two linear equations can be expressed as matrix as
following:
EQ-TARGET;temp:intralink-;e012;63;493MX ¼N; (12)
where
EQ-TARGET;temp:intralink-;e013;63;451M¼x1−x3y1−y3
x2−x3y2−y3;(13)
EQ-TARGET;temp:intralink-;e014;63;412X¼xe
ye;(14)
EQ-TARGET;temp:intralink-;e015;63;373N¼ðd2
x3y3−d2
x1y1þx2
1þy2
1−x2
3−y2
3Þ∕2
ðd2
x3y3−d2
x2y2þx2
2þy2
2−x2
3−y2
3Þ∕2:(15)
Each positioning unit has four LEDs, but we only need
three LEDs for positioning, so we can divide the entire
space into four parts. As shown in Fig. 3, we divide the
space into four cubes, each with β1,β2,β3,β4as the
bottom. In positioning, the terminal can receive power
from four LEDs. If the minimal light power is pj, where
j¼1;2;3;4, that means the terminal locates in the cube
with βjas the bottom. This shows that we use the received
light power value as the basis for selecting the nearest three
lights as the LEDs required for positioning.
As analyzed above, in order to calculate the terminal posi-
tion, dishould be estimated. RSS was measured to determine
di.However,asdiand Ztare both unavailable in Eq. (8)in
the 3-D positioning system, the coordinates on the horizontal
plane cannot be calculated. So, it is necessary to find the
Z-coordinate first. In this paper, we think of the positioning
problem as an optimization problem and employ ACO to
solve the optimization problem. In this section, the position-
ing system is converted into an optimization model.
The estimated distance dican be obtained by pr, and then
through the following equation we can get three radii of three
projection circles:
EQ-TARGET;temp:intralink-;e016;326;532ri¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d2
i−ðH−hÞ2
q:(16)
As Fig. 4shows, we can use riand ðxi;y
iÞto draw three
circles in the plane with height h. At different heights, the
total area within overlapped circles is different. A larger
overlapped area means a less accurate estimated position,
which means the probability of positioning terminal’s exist-
ence is low at the given height. Thus, position of the terminal
can be estimated by both height and the numerical mean
of cross points of circles when the overlapped area is the
minimum. There are several circles at six different heights
in Fig. 4, and it shows a scene that realizes position by get-
ting three circles. The crossing point of three circles is the
estimated point, which changes with the radius of three
circles.
For the convenience of observation, Fig. 5shows the over-
lap of three circles at each height. We set the Z-coordinate
Fig. 2 Geometric principle block diagram of spatial 3-D RSS trilater-
ation algorithm.
Fig. 3 Three-lamp positioning based on the division of positioning
unit. Fig. 4 Geometric model of 3-D coordinate optimization search.
Optical Engineering 125101-4 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
of the test point to 0.5 m and let the terminal move from 3.0
to 0.5 m. As mentioned before, the optimal height is the
situation of minimum overlap area. From the figure, we can
know when the height of the terminal is 0.5 m, the overlap
area is zero. Therefore, 0.5 m is the optimal height.
Under the previous analysis, a specific h0can be found
when the overlapped area is a minimum value. That can
be expressed as
EQ-TARGET;temp:intralink-;e017;63;395S¼minZ
X23
X13
ðC3−C1ÞdxþZ
X12
X23
ðC2−C1Þdx;(17)
where Sis the overlapped area of the three circles, which is
also the decision factor of this positioning algorithm, Xij
ði; j ¼1;2;3Þis the horizontal coordinate of i’th and j’th
LED intersection points of the circles. According to the
equation of the projection circle as follows:
EQ-TARGET;temp:intralink-;e018;63;280ðx−xiÞ2þðy−yiÞ2¼r2
i. (18)
Ciði¼1;2;3Þcan be expressed as
EQ-TARGET;temp:intralink-;e019;63;227Ci∶y¼yiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r2
i−ðx−xiÞ2
q:(19)
It is worth mentioning that, we have integrated dimen-
sion reduction ideas into ABOM model, for we transform
3-D search problems for 3-D positioning into 1-D search
problems. In most existing literature, they must search all
the X-, Y-, and Z-coordinates in the positioning process.
However in ABOM, we first search the Z-coordinate of
the receiving terminal and then get the X- and Y-coordinates
of the terminal through solving the equation set shown in
Eq. (11). Due to the reduction of searching dimensions,
the algorithm can achieve better real-time performance. In
order to verify real-time performance of the proposed algo-
rithm, related simulation experiments will be setup in Sec. 3
using a PC computer (Acer T5000-59E4, Windows 10, 8G
RAM, Intel(R) Core(TM) i5-6300HQ CPU @ 2.30 GHz,
GPU(0) Intel(R) HD Graphics 530, GPU(1) NVIDIA
GeForce GTX 950M). Through simulation, we can get
the average positioning time of each point during positioning
process is 1 ms. At the same time, because the search range is
greatly reduced, it can reach a quite high positioning accu-
racy. With regard to accuracy, we analyze it in detail in
Sec. 3.2.
2.3 Ant Colony Algorithm for VLP
As ACO can automatically acquire and search relevant spa-
tial information, it can be used to find the nonlinear global
optimal solution self-adaptively. According to two proposed
models of DBOM and ABOM above, the VLC positioning
problem can be transformed into a global optimization prob-
lem, which can be solved by ACO efficiently. Therefore, we
propose an approach for indoor 3-D localization by adopting
ACO to realize the estimation of anchor points.
The mentioned positioning algorithm includes two main
steps: (1) initialize parameters and randomly distribute ants
and (2) ant colony optimization iteration. The flow diagram
for the proposed ACO-based 3-D localization is shown in
Fig. 6and more details of the algorithm are given as follows:
Step 1. Initialize parameters and randomly distribute ants.
The first iteration ants of ACO algorithm are randomly set
in the room. So, we first set the ant group size (antnum), the
max iteration number (iter_max), pheromone concentration
(τ), the optimal τ(τ_best), pheromone volatilization coeffi-
cient (ρ), transfer probability constant ðp0Þ, the total phero-
mone release amount ðQÞ, and transfer probability(p).
Besides, each ant is given a random coordinate
ðXe;Ye;Z
eÞas an initial estimated position of the terminal
and a current best location ðXb;Yb;Z
bÞin VLP system.
Absolutely, the search space is surely limited by the
room’s size. And the search space limits of the ants are
Fig. 5 The overlap of three circles at each height.
Optical Engineering 125101-5 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
0≤X0≤4m,0≤Y0≤4m, and 0≤Z0≤6m. Then, we
calculate the fitness of every ant using the fitness function
given below, which is the basis for determining the optimal
solution.
(1) According to DBOM given above, the fitness func-
tion can be calculated as follows:
After Eq. (8), we learn that the physical distance between
the LEDðjÞ(j¼1;2;3;4) and the positioning terminal can
be expressed as
EQ-TARGET;temp:intralink-;e020;63;243dðjÞ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C·ðzr−ZeÞmtþ1
pðjÞ
LOS
mtþ3
s;(20)
where zris the height of the LEDs as well as the height of
the room, pðjÞ
LOS is the received optical power from LEDðjÞ
detected by PD according to their unique ID information.
And the distance between the current estimated location
and LEDðjÞis
EQ-TARGET;temp:intralink-;e021;63;142dðjÞ
e¼½ðxðjÞ
r−XeÞ2þðyðjÞ
r−YeÞ2þðzr−ZeÞ21
2;(21)
where the coordinate of LEDðjÞis ðxðjÞ
r;y
ðjÞ
r;z
rÞ. Therefore,
the fitness for DBOM can be defined as
EQ-TARGET;temp:intralink-;e022;326;360fitDBOM ¼X
4
j¼1
½dðjÞ
e−dðjÞ2:(22)
(2) According to ABOM given above, the fitness func-
tion can be calculated as follows:
EQ-TARGET;temp:intralink-;e023;326;288fitABOM ¼Z
X23
X13
ðC3−C1ÞdxþZ
X12
X23
ðC2−C1Þdx: (23)
If the individual ant is close enough to the ideal location,
the value of the fitness function will be close to zero. So, the
individual with the minimum fitness value is selected as the
best individual. Then, its height is regarded as the optimum
solution for ABOM, while its 3-D position coordinates is
regarded as the optimum solution for DBOM.
Step 2. Ant colony optimization iteration.
(1) Compute transfer probability (p) and update each
ant’s positions.
In ACO iteration progress, we first compute ants’transfer
probability according to
Fig. 6 ACO algorithm flow diagram.
Optical Engineering 125101-6 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
EQ-TARGET;temp:intralink-;e024;63;752pn¼τn−τ_best
τ_best (24)
where pnis the nth ant’s transfer prability, τnis the nth ant’s
pheromone concentration. We choose to update an ant’s
position if this ant’snewfitDBOM is smaller than its previous
one. Further, we also update each ant’s position according to
the following equations:
If pn<p0, we give a slight adjustment
EQ-TARGET;temp:intralink-;e025;63;653
8
<
:
Xeðmþ1Þ¼XeðmÞþð2·rand −1Þ·λ
Yeðmþ1Þ¼YeðmÞþð2·rand −1Þ·λ
Zeðmþ1Þ¼ZeðmÞþð2·rand −1Þ·λ
;(25)
where mis the times of iteration, λis the step coefficient
given by λ¼1
m, and rand indicates a random number in
range of 0 and 1.
If pn≥p0, we give a relatively large adjustment
EQ-TARGET;temp:intralink-;e026;63;549
8
<
:
Xeðmþ1Þ¼XeðmÞþLx·ðrand −0.5Þ
Yeðmþ1Þ¼YeðmÞþLy·ðrand −0.5Þ
Zeðmþ1Þ¼ZeðmÞþLz·ðrand −0.5Þ
;(26)
where Lx,Ly, and Lzare the length, width, and height of the
room, respectively. Moreover, we also make some improve-
ment for the algorithm: If an ant crawls out of the room, we
move it randomly to the neighborhood of ðXb;Yb;Z
bÞ.
(2) Update pheromone content τand keep the current
optimal solution.
Pheromone content τcan be updated by the following
equation:
EQ-TARGET;temp:intralink-;e027;63;383τmþ1¼ð1−ρÞ·τmþQ
fitDBOM
:(27)
Meanwhile, in each iteration, we keep tracking every
ant’s pheromone content τto find the global best position
in the mth iteration (G_Bestm), which are also recorded.
Finally, we get the optimal solution from the records of
G_Bestms.
3 Simulation and Analysis
3.1 Simulation Model for Indoor Three-Dimensional
Positioning
In this section, simulation is set up to test the 3-D positioning
performance of the proposed system. There are four LEDs
installed on the top of a positioning unit with a size of
4×4×6m. The location of receiver is estimated by
ACO algorithm based on both DBOM and ABOM for fur-
ther comparison. The parameters of indoor 3-D positioning
system are illustrated in Table 1.
3.2 Result and Analysis
3.2.1 Multipoint testing
To assess and compare the performances of two different
optimization models, multipoint at different heights is tested
by our proposed algorithm. There are 100 test points in each
plane and 600 points totally within the positioning unit.
The positioning results of DBOM and ABOM are shown
in Figs. 7and 8, respectively, where the blue sign “o”rep-
resents the estimated position and the red sign “x”represents
the real position of the tested node. The overall result of
DBOM is inferior to the result of ABOM, for some devia-
tions between estimated position and real position based on
DBOM model are relatively large. However, the result of
ABOM indicates that the performance of the 3-D static posi-
tioning is good, and the estimated position is located close to
the real position. The total positioning error etotal is defined
as follows:
EQ-TARGET;temp:intralink-;e028;326;165etotal ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðXt−xeÞ2þðYt−yeÞ2þðZt−zeÞ2
q;(28)
where ðXt;Yt;Z
tÞare the real position coordinate of every
detection node, while ðxe;y
e;z
eÞare the estimated position
coordinate calculated by the mentioned algorithm. The pre-
cision curve (CDF curve of positioning error) is shown in
Fig. 9.
Table 1 Parameters of the indoor three-dimensional positioning
system.
Parameter Value
Every positioning unit size
ðL×W×HÞ∕m3
4×4×6
Positions of four LEDs ðx;y; zÞ(m) LED1 (0,0,6) LED2 (0,4,6)
LED3 (4,4,6) LED4 (4,0,6)
Height of the receiver (m) 0.4 to 2.9 (resolution: 0.5)
Plane range of the receiver (m) (0.2,0.2) to (3.8,3.8)
(resolution: 0.4)
Power of each LED (W) 10
The half-power angles of
LED (deg) (φ1∕2)
60
The half-power angles of
receiver (deg) (θ1∕2)
60
The FOV of the receiver (deg) 90
The FOV of the LED (deg) 60
The effective area of PD (cm2) 1.0
The order of Lambert’s luminous
intensity (mt)
1
The photoelectric conversion
efficiency (A · W−1)(r)
0.35
The gain of optical filter [TsðϕÞ 1.0
The gain of optical
concentrator [GðϕÞ]
1.0
Ant colony size 100 for DBOM
40 for ABOM
Maximum iteration times 20
Optical Engineering 125101-7 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
As indicated by the curves in Fig. 9(a),if90%is
assumed as an acceptable service coverage rate, the pro-
posed algorithm will be able to deliver an accuracy of
less than 4.71 cm in the 3-D space. As for the positioning
error of the horizontal view and vertical view, about 90%
CDF are less than 3.05 and 4.39 cm, respectively. The
average error of 600 detection nodes in DBOM is 3.21 cm
with a maximum error of 10.12 cm and a minimum error
of 0.48 cm. As shown in Fig. 9(b) for ABOM, if 95% is
assumed as an acceptable service coverage rate, the
Fig. 7 The distribution of the real position and its estimated 3-D position based on DBOM: (a)–(f) the 3-D
positioning results in 0.4, 0.9, 1.4, 1.9, 2.4, and 2.9 m high position points, respectively.
Fig. 8 The distribution of the real position and its estimated 3-D position based on ABOM: (a)–(f) the 3-D
positioning results in 0.4, 0.9, 1.4, 1.9, 2.4, and 2.9 m high position points, respectively.
Optical Engineering 125101-8 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
proposed algorithm will be able to deliver an accuracy of
less than 2.95 cm in the same room. In the positioning error
of the horizontal view and vertical view, about 90% CDF is
less than 2.29 and 0.8 cm, respectively. The average error of
600 detection nodes is 0.96 cm while the maximum error is
7.13 cm and the minimum error is 0 cm. Comparing the
results of ABOM with that of DBOM, it can be concluded
that using ABOM-based ACO indoor 3-D positioning sys-
tem can reach a quite high positioning accuracy.
3.2.2 Iteration times comparison and analysis
Both of the real-time ability and positioning accuracy are
crucial for the performance of indoor positioning system.
The real-time ability is determined by the calculating time
of the positioning algorithm, while the calculation time is
mainly determined by the complexity of the algorithm ignor-
ing the hardware performance of the computer. In addition,
the complexity of this algorithm is measured by iterative
algebra. Since ABOM is a 1-D search model and DBOM
is a 3-D one, algebra of ABOM is absolutely less than
that of DBOM, thereby behaving better in real-time perfor-
mance. At the same time, the amount of calculation in per
generation of 1-D searching is less than that of 3-D search-
ing. Therefore, ABOM has better real-time performance
than DBOM.
In order to compare the real-time ability of the proposed
positioning system based on DBOM and ABOM, the
velocity curves (CDF curve of iterations) of the positioning
process for two systems based on DBOM and ABOM are
shown in Fig. 10. From curve (b) for ABOM, we can
know that 91.15% of the detection nodes can reach a
quite small error within 11 generations, while from curve
(a) for DBOM, it can be found that only about 10% can
achieve the same convergence velocity, which is far from
satisfying for a real-time system requiring high real-time
ability. Therefore, the results indicate that the proposed
ABOM-based ACO system is not only better in positioning
accuracy but also superior in real-time performance.
Fig. 9 The CDF curves of positioning error in 3-D: (a) the results of DBOM and (b) the results of ABOM.
Fig. 10 The CDF curves of the number of iterations in 3-D VLP: (a) the results of DBOM and (b) the
results of ABOM.
Optical Engineering 125101-9 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
3.2.3 Positioning in motion scene
Comparing the two optimization models, it can be concluded
that ABOM is better than DBOM in terms of positioning
accuracy and real-time ability. Therefore, in order to get
a better positioning effect in real-time positioning, only
ABOM is considered in this part. Since about 91.5% of
the ants can reach a quite small error within 11 generations,
we set the maximum algebra to 15 in the motion simulation.
To verify the real-time performance of ABOM, another sim-
ulation of motion positioning is carried out. In this simula-
tion, a circle path is given by assuming a moving target in the
positioning unit at a speed of 1m∕s. There are 191 samples
tested totally in Fig. 11. The pink track is the circle path and
the blue points are the estimated location that tracks the
path. Figure 11 shows that the ACO algorithm performs
well in motion scene. In order to better present the result,
Figs. 12(a) and 12(b) show the horizontal view and the ver-
tical view of the positioning results. As shown in Fig. 13,
about 90% of 3-D errors are less than 3.612 cm in motion
positioning scene in the 3-D positioning unit. That means
using ABOM-based ACO indoor 3-D positioning system
can reach a quite high positioning accuracy even in motion
scene.
3.3 Extended Simulation and Result Analysis
3.3.1 Analysis of the nonlinearity of Lambert model
As shown in Figs. 7,8, and 11, the maximum height of the
positioning unit is 6 m, while the maximum positioning
height is only 3 m both in static positioning and motion
positioning, for the Lambert model is not a linear model.
In Eq. (1), the angle Ψin Lambert model makes the PD-
based VLC direct channel become a nonlinear model, so
we cannot use ACO to realize positioning from floor to
the ceiling of the positioning unit. And software simulations
are set up to demonstrate this phenomenon.
In the positioning unit of 4×4×6m, we set five test
points, the horizontal coordinates of which are (0.5, 0.8),
(0.9, 3.2), (2.0, 2.0), (2.7, 3.2), and (3.1, 3.5). When they
move from 0 to 6 m, four attenuation factors HLOSð0Þiði¼
1;2;3;4Þof the LEDs at different heights are calculated.
In Fig. 14, the abscissa represents the height of different
positioning points while the Y-axis represents the sum of
four attenuation factors from the terminal to four LEDs.
As the height increases, all the curves in the figure rise
first and then decrease. However, the peak heights of the
curves for different test points are different. As shown in the
figure, the curves of the five test points turn at Z¼5m,
Z¼4.64 m,Z¼3.18 m,Z¼4.14 m, and Z¼4.9 m,
respectively, corresponding to the coordinates of (0.5, 0.8),
(0.9, 3.2), (2.0, 2.0), (2.7, 3.2), and (3.1, 3.5). That means
the closer the receiving terminal is to one of the four LEDs,
the higher the turning point of the curve will be. What is
more, if the terminal is right under one of the four LEDs,
there is no doubt that the curve will always rise until the
terminal meets with the LED.
As mentioned above, we realize positioning by measuring
the attenuation factor. But the positioning in the whole 3-D
space can be used only when the change of the sum of four
Fig. 11 3-D positioning result under motion scene.
Fig. 12 (a) The horizontal view and (b) vertical view of motion positioning result, respectively.
Optical Engineering 125101-10 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
attenuation factors as the height is linear. Otherwise, a certain
sum of four attenuation factors will correspond to two correct
solutions of height, which leads to the failure to location.
That means, if we do a global positioning directly, we
may find two optimal solutions, one is more than the height
of the turning point and another is less than it. Because the
two optimal solutions will appear randomly, it will cause a
great deal of error. In fact, we can only realize the positioning
within the linear part of the Lambert model, which reflects in
the attenuation factor curve. Therefore, if we want to achieve
positioning for all points on every 4×4mplane, the maxi-
mum height should be no less than the heights of all
positioning points. So, as shown and analyzed in Fig. 14,
the maximum positioning height of the 4×4×6mposition-
ing unit is 3.18 m, which can ensure that all the positioning
points can achieve high-precision positioning.
Figure 15 shows the convergence process of positioning
in the entire space. In this figure, the blue circle represents a
test point (2, 2, 2) while the red dots represent the ant colony.
There are totally 100 ants and the ants of first generation are
set randomly in the whole room. They move to the optimum
solution quickly generation by generation. Finally in gener-
ation 24, the ants gather in two areas, which are the two opti-
mal solutions. One of the optimal solutions is the test point,
and another is (1.938, 2.042, and 4.083). That means the two
optimal solutions are on both sides of the Z¼3.18 m as
described previously.
However, the maximum positioning height is not always
3.18 m, but is related to the distribution of the four LEDs and
the total height of the positioning unit. In Fig. 16, the
curves represent the sum of four attenuation factors in the
positioning unit whose size are 3×3×6m,4×4×6m,
5×5×6m, and 6×6×6m, respectively. From the figure,
we can know that when the positioning unit size is
3×3×6m, the maximum positioning height can reach to
3.9 m; when the space size of the positioning unit is
4×4×6m, the maximum positioning height is 3.18 m;
when the positioning unit size is 5×5×6m, the maximum
positioning height is 2.48 m; when the space size of the posi-
tioning unit is 6×6×6m, the maximum positioning height
is only 1.78 m. That means the more compactly the four
LEDs gather, the higher the maximum positioning height
will be. However, it is obvious that the denser the distribution
of the four LEDs is, the more LEDs we need to set in
the same positioning unit, which means more costs and
a waste of resources.
As shown in the following Fig. 17, the horizontal coor-
dinate of the test point is (1.5, 1.5), which is the middle
point of every plane and the curves represent the sum of
four attenuation factors in different positioning units
whose size are 3×3×6m,3×3×5m,3×3×4m and
3×3×3m, respectively. There we use relative height
rate to measure the maximum positioning height of different
units, which can be defined as the maximum height divided
by total space height and expressed as λ¼Hmax ∕Htotal.
From Fig. 17, we can know that when the size of the posi-
tioning unit is 3×3×6m, the maximum positioning height
is 3.9 m and the relative height rate can reach to 0.65; when
the positioning unit size is 3×3×5m, the maximum posi-
tioning height reaches 2.88 m, and the relative height rate
λreduces to 0.576; when the space size of the unit is
3×3×4m, the maximum height is 1.88 m and the relative
height rate is 0.47; when the space size of the unit is
3×3×3m, the maximum height is only 0.86 m and the
relative height rate is only 0.287. That means the higher
the total height of the positioning unit is, the higher the rel-
ative height rate as well as the maximum positioning height
will be. However in practice, it is obvious that buildings with
high spatial height are relatively rare or even nonexistent.
Besides, when the total height of the positioning unit is
too high, the terminal may probably receive a very weak
visible light signal or even no signal. What is more, the
higher the LEDs locate, the stronger the luminous intensity
is needed to meet people’s daily lighting needs, which means
the more money we need to spend.
Through the above analyses, we come to a conclusion that
we can control the maximum positioning height through
controlling the distribution of the four LEDs and the total
height of the positioning unit. At the same time, we should
balance them with the actual situation. In order to stay con-
sistent with reality and prove our conclusion, in Sec. 3.3.2,
we setup a simulation in another positioning unit, whose
Fig. 13 The CDF curves of motion positioning error.
Fig. 14 Attenuation factor curve with increasing height at different test
points.
Optical Engineering 125101-11 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
space size is 3×3×6m, which is different from those in
Sec. 3.2.3.
On the other hand, because the angle Ψexists in the
Lambert model. When we increase the height of the PD,
the angle of incidence Ψwill increase too. Therefore, if
we want to avoid the curve dropping at a low height, we
can reduce Ψ. For this, the single PD can be replaced by
multiple PDs, and each PD is arranged at a certain angle,
therefore the angle of incidence will be reduced accordingly
and correspondingly the maximum positioning height will
increase.
3.3.2 Set up simulation to increase the maximum
positioning height
In the next simulation, we increase the maximum positioning
height by changing the size of the positioning unit and prove
it with motion positioning. As shown in Figs. 18 and 19,we
can see the maximum positioning height has been increased
to 3.9 m, nearly 1 m more than the previous simulation in
Sec. 3.2.3. Figure 20 shows the histogram of 3-D, horizontal
Fig. 15 Convergence process of positioning in the entire space.
Fig. 16 Attenuation factor curves at different concentrations.
Optical Engineering 125101-12 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
and vertical positioning errors, respectively. As we can see,
the error distributions are similar to the simulation in
Sec. 3.2.2. It proves that the proposed algorithm also per-
forms very well in a positioning unit with different size.
4 Experiment Setup and Result
4.1 Experiment Setup
The experiment shown in Fig. 21 is established to verify the
practicability of the proposed system and prove our theoreti-
cal analysis. Four LEDs are mounted in a cube frame with a
size of 1.0 m ×1.0 m ×1.8 m, the frequencies of whose sig-
nals are modulated at 400, 800, 1600, and 3200 Hz, respec-
tively. The experiment imitates real VLC scenes, satisfying
the needs of positioning and lighting simultaneously. Current
driving circuit passes the resulting waveform to the LEDs
and PD detects the modulated light signals. Then, they
successively pass an amplifier circuit, a voltage comparator
circuit, and a filter circuit. Meanwhile, the signals are also
delivered to MCU, where we use ABOM-based ACO algo-
rithm for positioning. LCD attached to the receiver can dis-
play the result of positioning synchronously. The parameters
of the experiment are shown in Table 2.
Fig. 17 Attenuation factor curves at different heights of positioning
unit.
Fig. 18 3-D positioning result under motion scene.
Fig. 19 (a) The horizontal view and (b) vertical view of motion positioning result, respectively.
Fig. 20 Histogram of motion positioning error.
Optical Engineering 125101-13 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
In a practical situation, signals emitted by LEDs will be
influenced by various factors in propagation, such as back-
ground noise, shot noise, thermal noise, and other uncertain
signal interferences. Therefore, the received signal is proc-
essed by Kalman filter.26
4.2 Result and Analysis
In the experiment, 36 positions evenly distributing at the
height of 0.3, 0.6, and 0.9 m respectively, are tested totally.
At each test point, the proposed modified ABOM-based
ACO algorithm is applied to calculate the position. Each
position estimation is repeated for six times and the 3-D aver-
age positioning error for each location is also calculated. The
position results are shown in Figs. 22–24 and the average
errors are written in the figures strictly as the experiment
results show. The experiment results suggest that the average
Fig. 21 Experimental platform of VLC system based on DBOM-based
ACO.
Table 2 Experiment parameters.
Parameter Reference
Indoor space unit size
ðL×W×HÞ(m3)
1.0m×1.0m×1.8m
Positions of four LEDs
ðx;y;zÞ(m)
LED1 (0,0,1.8) LED2 (1,0,1.8)
LED3 (1,1,1.8) LED4 (0,1,1.8)
Height of the receiver (m) 0.3, 0.6, 0.9
X,Yplane range of
the receiver (m)
X: 0.2 to 0.8 (resolution: 0.2)
Y: 0.25 to 0.75 (resolution: 0.25)
The effective area of
PD (cm2)
1.0
Frequency of the light
signals (Hz)
400, 800, 1600, 3200
Fig. 22 Estimated position and 3-D positioning error of the experi-
ment with the height of 0.3 m.
Fig. 23 Estimated position and 3-D positioning error of the experi-
ment with the height of 0.6 m.
Fig. 24 Estimated position and 3-D positioning error of the experi-
ment with the height of 0.9 m.
Optical Engineering 125101-14 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
3-D error is 4.342 cm and the maximum error is 7.90 cm. In
Fig. 25, over 90% of the errors are within 6 cm. The results
indicate that our proposed system based on ABOM-based
ACO algorithm performs well.
The error may result from the following reasons. First,
though we have used Kalman filter to improve the position-
ing accuracy, error caused by noise still cannot be totally
avoided. Second, measurement error also causes accidental
error. For example, there exists coordinate deviation of the
receiver between the reality and the ideal location. Finally,
systematic error is resulted from calculation and equipment.
But it still proves that the system satisfies the requirement of
cm-level indoor positioning. In addition, compared with the
known VLC positioning system that we mentioned in Sec. 1,
this system has higher precision, better real-time perfor-
mance, and lower complexity.
5 Conclusion
After transforming the 3-D VLP model into the optimization
model, this paper selects the distance based optimization
model for positioning and adopts an effective 3-D optimiza-
tion algorithm to judge its performance. Moreover, we also
utilize an area-based optimization model for location, which
converts the 3-D optimization problem into a 1-D searching
problem and ensures the real-time positioning performance.
Last but not least, we also set up an extended simulation,
analyzing the nonlinearity of the Lambert model, and discus-
sing positioning unit size’s effect on the maximum position-
ing height, which has never been considered by the
existing works.
By an all-round comparison on simulation results, we
prove that the proposed ABOM positioning system has better
real-time performance and higher accuracy than DBOM,
which reflects that ABOM has greater prospects in practical
scenes. The simulation results show the average error of
ABOM is 0.96 cm and the proposed system can also achieve
a good positioning effect in the motion positioning. Our
experiments for real scene confirm that the proposed system
can achieve an average indoor positioning accuracy of
4.34 cm. To sum up, both the results of simulation and
experiment show that the proposed positioning ABOM
system has good accuracy, indicating that it can become
a promising solution for indoor positioning applications.
Acknowledgments
This work supported by the National Undergraduate
Innovative and Entrepreneurial Training Program (Grant
Nos. 201710561006, 201710561054, 201710561057,
201710561058, 201710561199, 201710561202,
201810561217, 201810561195, 201810561218, and
201810561219), Special Funds for the Cultivation of
Guangdong College Students’Scientific and Technological
Innovation (“Climbing Program”Special Funds)
(pdjh2017b0040, pdjha0028), Guangdong Science and
Technology Project (2017B010114001).
References
1. M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor positioning system
using visible light and accelerometer,”J. Lightwave Technol. 32(19),
3306–3316 (2014).
2. W. Zhang, M. I. S. Chowdhury, and M. Kavehrad, “Asynchronous
indoor positioning system based on visible light communications,”
Opt. Eng. 53(4), 045105 (2014).
3. C. Xie et al., “The LED-ID detection and recognition method based on
visible light positioning using proximity method,”IEEE Photonics J.
10(2), 1–16 (2018).
4. W. Guan et al., “Performance analysis and enhancement for visible light
communication using CMOS sensors,”Opt. Commun. 410, 531–551
(2018).
5. T. H. Do and M. Yoo, “An in-depth survey of visible light communi-
cation based positioning systems,”Sensors 16(5), 678 (2016).
6. H. Steendam, “A 3-D positioning algorithm for AOA-based VLP with
an aperture-based receiver,”IEEE J. Sel. Areas Commun. 36(1), 23–33
(2018).
7. S. Zhang et al., “Experimental demonstration of indoor sub-decimetre
accuracy VLP system using differential PDOA,”IEEE Photonics
Technol. Lett. 30(19), 1703–1706 (2018).
8. W. Guan et al., “High precision three-dimensional iterative indoor
localization algorithm using code division multiple access modulation
based on visible light communication,”Opt. Eng. 55(10), 106105
(2016).
9. W. Guan et al., “Indoor positioning technology of visible light commu-
nication based on CDMA modulation,”Acta Opt. Sin. 36(11), 1106006
(2016).
10. H. Chen et al., “Indoor high precision three-dimensional positioning
system based on visible light communication using modified genetic
algorithm,”Opt. Commun. 413, 103–120 (2018).
11. W. Zhang and M. Kavehrad, “
A 2-D indoor localization system based
on visible light LED,”in IEEE Photonics Society Summer Topical
Meeting Series, pp. 80–81 (2012).
12. H. Lv et al., “High accuracy VLC indoor positioning system with differ-
ential detection,”IEEE Photonics J. 9(3), 1–13 (2017).
13. Z. Zheng, L. Liu, and W. Hu, “Accuracy of ranging based on DMT
visible light communication for indoor positioning,”IEEE Photonics
Technol. Lett. 29(8), 679–682 (2017).
14. M. F. Keskin, S. Gezici, and O. Arikan, “Direct and two-step position-
ing in visible light systems,”IEEE Trans. Commun. 66(1), 239–254
(2018).
15. P. Du et al., “Demonstration of a low-complexity indoor visible light
positioning system using an enhanced TDOA scheme,”IEEE
Photonics J. 10(4), 1–10 (2018).
16. Q. L. Li et al., “Three-dimensional indoor visible light positioning sys-
tem with a single transmitter and a single tilted receiver,”Opt. Eng.
55(10), 106103 (2016).
17. H. S. Kim et al., “Three-dimensional visible light indoor localization
using AOA and RSS with multiple optical receivers,”J. Lightwave
Technol. 32(14), 2480–2485 (2014).
18. Y. Wang et al., “Research on the collinear equation model of visual
positioning based on visible light communication,”in MATEC Web of
Conf.(2015), Int. Conf. on Engineering Technology and Application,
ICETA (2015).
19. H. Zheng et al., “A 3-D high accuracy positioning system based on
visible light communication with novel positioning algorithm,”Opt.
Commun. 396, 160–168 (2017).
20. J. Lim, “Ubiquitous 3-D positioning systems by led-based visible light
communications,”IEEE Wireless Commun. 22(2), 80–85 (2015).
21. Y. Xu et al., “Reversed three-dimensional visible light indoor position-
ing utilizing annular receivers with multi-photodiodes,”Sensors 16(8),
1254 (2016).
Fig. 25 The CDF curves of positioning error for experiment.
Optical Engineering 125101-15 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
22. W. Xu et al., “Indoor positioning for multiphotodiode device using
visible-light communications,”IEEE Photonics J. 8(1), 1–11 (2017).
23. W. Guan et al., “A novel three-dimensional indoor positioning algorithm
design based on visible light communication,”Opt. Commun. 392, 282–
293 (2017).
24. W. Guan et al., “High-precision approach to localization scheme of
visible light communication based on artificial neural networks and
modified genetic algorithms,”Opt. Eng. 56(10), 106103 (2017).
25. Q. Peng et al., “Three-dimensional high-precision indoor positioning
strategy using Tabu search based on visible light communication,”
Opt. Eng. 57(1), 016101 (2018).
26. Y. Cai et al., “Indoor high precision three-dimensional positioning
system based on visible light communication using particle swarm
optimization,”IEEE Photonics J. 9(6), 1–20 (2017).
27. W. P. Guan et al., “Research on visible light communication system
based on hybrid modulation technique,”J. Optoelectron.·Laser 26,
2125–2132 (2015).
28. W. Guan et al., “Research on visible light communication receiving
system based on artificial neural networks,”Chin. J. Lasers 42(11),
1105002 (2015).
29. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light
communication system using LED lights,”IEEE Trans. Consum.
Electron. 50(1), 100–107 (2004).
Bangdong Chen is currently pursuing his BE degree in the
Information Engineering Department at South China University of
Technology. His research interests are in wireless optical communi-
cation technology and visible light positioning technology.
Jiajia Jiang is currently pursuing her BE degree in the Information
Engineering Department at South China University of Technology.
Her research is currently focused on visible light wireless communi-
cation technology.
Weipeng Guan received his BE degree in the Electronic Science
and Technology Department (Electronic Materials and Components
Department) from South China University of Technology, Guangzhou,
China, in 2016. He is now working toward his ME degree in the
Control Theory and Control Engineering Department at South China
University of Technology. His research is currently focused on visible
light wireless communication technology and visible light positioning
technology.
Shangsheng Wen received his BE degree from Wuhan University of
Science and Technology in 1984, his ME degree in Anhui Institute of
Optics and Fine Mechanics, Chinese Academy of Sciences, in 1993,
and his PhD degree from South China Normal University in 2001. He
is a professor of the State Key Laboratory of Luminescent Materials
and Devices. He has undertaken more than 20 scientific research
projects and published hundreds of papers. His research focus on
visible light communication.
Jingyi Li is currently pursuing his BE degree in the Automation
Science and Engineering Department at South China University of
Technology. His research is focused on visible light wireless commu-
nication technology and indoor positioning technology.
Yirong Chen is currently pursuing his BE degree in the Electrical
Science and Technology Department at South China University of
Technology. His research interests are in wireless optical communi-
cation technology and visible light-positioning technology.
Optical Engineering 125101-16 December 2018 •Vol. 57(12)
Chen et al.: Performance comparison and analysis on different optimization models. . .
Downloaded From: https://www.spiedigitallibrary.org/journals/Optical-Engineering on 1/23/2019
Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
