Research of An Improved Satellite-based Quantum Positioning
System
Wei Fan
1, a
1
Universty of Rochester, Rochester, U.S
Keywords: Quantum Positioning System, GNSS, TDOA, Acquisition Tracking and pointing.
Abstract: The accuracy of traditional GPS system is limited, and it is liable to be deceived and jammed. The problem
of its application has become increasingly prominent. Based on quantum physics, quantum navigation
technology has the potential to achieve high-precision navigation and positioning services. At present, the
implementation scheme of baseline interferometric satellite-based quantum positioning system proposed by
the United States requires six satellites to achieve positioning, and the cost of the system is high. This paper
presents an improved satellite-based QPS system and describes it systematically. The whole QPS system
includes the establishment of satellite-ground optical link, the acquisition of TDOA by entangled light, the
process of ranging and positioning. Compared with the traditional baseline interferometric satellite-based
QPS system, the number of satellites needed is reduced effectively.
1 INTRODUCTION
Global Navigation Satellite System (GNSS),
represented by GPS, has been widely used, but its
accuracy and security problems are becoming
prominent in current applications. The accuracy of
GPS can only reach meter level, and the GPS signal
is easy to be rewritten and deceived. With the
increasing demand for navigation and positioning
services, the accuracy and security of traditional
navigation systems such as GPS have become one of
the bottleneck of future applications. With the
development of quantum technology, the navigation
system based on quantum technology may become
an important solution. Quantum Positioning System
(QPS) was first proposed by Dr. Giovannetti of
Massachusetts Institute of Technology (MIT) in
2001 in Nature. It is proved that the quantum
entanglement and compression properties can further
improve the positioning accuracy. QPS can not only
break through the limit of traditional positioning
accuracy, but also provide good security in
confidentiality and anti-jamming ability. It may
fundamentally solve the security problem of
transmission and it also breaks the stereotype of
people's thinking in information transmission and
coding. (Giovannetti, V, et.al, 2001; Marks, & Paul,
2014)
QPS can be divided into two categories: passive
quantum positioning system and active quantum
positioning system. Active QPS locates by sending
and receiving quantum signals, and passive QPS
locates by quantum sensor devices. Passive QPS
based on inertial navigation obtains high-precision
magnetic field and gravity field data through cold
atom interference technology. Combining with
traditional geomagnetic navigation and gravity
navigation technology, it achieves high-precision
navigation. The research group of Stanford
University demonstrated the working principle of
atomic interferometric gyroscope based on Sagnac
effect. The British Defense Science and Technology
Laboratory (DSTL), the Landragin Group of the
French Observatory and the Rasel Group of
Germany also carried out relevant research. China
University of Science and Technology, Wuhan
Institute of Physics and Mathematics of Chinese
Academy of Sciences, Tsinghua University and
China Academy of Aerospace Sciences and
Technology, have studied quantum interference
gyroscope, atomic spin gyroscope and nuclear
magnetic resonance gyroscope based on quantum
technology.
In addition to the passive QPS based on inertial
navigation, the active QPS is also an important
development direction. Active QPS uses entangled
light with quantum entanglement to replace
456
Fan, W.
Research of An Improved Satellite-based Quantum Positioning System.
DOI: 10.5220/0008873104560460
In Proceedings of 5th International Conference on Vehicle, Mechanical and Electrical Engineering (ICVMEE 2019), pages 456-460
ISBN: 978-989-758-412-1
Copyright
c
2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
electromagnetic wave on the basis of GPS. By
measuring the time difference of arrival (TDOA) of
two interrelated entangled light beams, the distance
between satellite and user and the spatial coordinates
of user are calculated according to the acquired
TDOA. The satellite-based interferometric QPS
proposed by the US Army Research Laboratory,
combined with the traditional satellite positioning
idea and the optical quantum entanglement pulse
interferometric ranging technology, is the first to put
forward the design scheme of the satellite-based
QPS to achieve positioning. It uses satellite to
broadcast quantum signals. The basic structure of
QPS is composed of three baselines which are
composed of two groups of satellites with six known
positions. The satellites are located in two focal
points of a hyperboloid, and the user is at the
intersection point of a hyperboloid consisting of a
hyperboloid. But the disadvantage is that six
satellites with three baselines are needed to
participate in positioning, which is costly.
(Giovannetti, & V, 2004)
Based on the existing active QPS, this paper
improves the implementation scheme of baseline
interferometric quantum positioning system
proposed by Dr. Thomas B. Bahder, U. S. Army
Research Laboratory. An improved QPS based on
three satellites is proposed to locate users. The
number of satellites needed and the complexity of
the system is reduced. The whole process of ranging
and positioning of the improved satellite-based QPS
is analyzed and the system structure is designed.
Firstly, a satellite-ground optical link is established
between the satellite and the ground. The quantum
entangled light emitted by the user equipment and
transmits to the satellite along the satellite-ground
optical link, and then returns to the user through the
reflection of the satellite along the original path. The
TDOA of signal light and reference light is obtained
by pulse matching counting and data fitting with
least square method. Finally, the distance and user
space coordinates are calculated according to the
TDOA simultaneous equations obtained from
entangled light of three satellites. Through the
Acquisition Tracking and Pointing (ATP) system to
achieve the uninterrupted positioning of the user.
The structure of this paper is as follows: Firstly, the
flow of the whole system is explained, including the
establishment of satellite-ground optical link, the
acquisition of TDOA by entangled light, and then
ranging and location solution by simultaneous
equations. (Bahder, T. B, 2004)
2 BASIC PRINCIPLE OF
IMPROVED SATELLITE-
BASED QPS LOCATION
The ranging and positioning process of improved
satellite-based QPS can be divided into three parts:
Firstly, a stable optical link is established between
satellites and the earth, and the positioning are
carried out by using quantum entangled optical
dynamic communication. The establishment of
satellite-to-ground optical link is to provide accurate
optical links for quantum entangled optical signals to
propagate between satellites and users, including
beacon light emission, acquisition, tracking and
aiming. These four sub-processes are realized by
ATP system. Then, based on the quantum entangled
light ranging, according to the established satellite-
ground optical link, the quantum entangled light
dynamic communication is used for ranging and
positioning. Its working process is divided into the
emission and reception of quantum entangled light
and the acquisition of TDOA. Finally, the position is
calculated based on the equations obtained by
TDOA quantum ranging. (Yang, C, et.al, 2010)
Geometric positioning principle is used in
positioning calculation. Two entangled beams of
light emitted by the entangled photon pairs generator
at the user end, one of which arrives at the satellite
along the satellite-ground optical link and reflects
back to the ground from the satellite, then received
by a single photon detector on the user side; the
other light is directly emitted to another single
photon detector on the user side to complete the
emission and reception of entangled photon pairs.
The distance is calculated by using TDOA of two
entangled beams. The user's spatial coordinates are
calculated by three TDOAs obtained from three
satellites.
When the difference of arrival time
between
satellite n (n=1, 2, 3) and user is obtained, the
distance between satellite and user can be calculated
as
. Let the space coordinates of
three quantum satellites be
and
respectively. The formula of
the relationship between the distance between each
satellite and the user and the coordinates of the
ground user can be obtained:
. By measuring
the arrival time difference of entangled light from
the user to three satellites, three formulas of parallel
equations are obtained:
Research of An Improved Satellite-based Quantum Positioning System
457
The space coordinates (x, y, z) of the ground user
are obtained. The improved QPS maintains the
satellite-ground optical link between the moving
satellite and the user through the advanced aiming
module, realizes the uninterrupted positioning of the
user.
3 DESIGN OF IMPROVED
SATELLITE-BASED QPS
The establishment of satellite-ground optical link is
realized by ATP system, as shown in Figure 1. The
yellow line represents the path of light propagation
and the red line represents the electrical signal. ATP
system consists of beacon light module, coarse
tracking module, meticulous tracking module and
advanced aiming module. The coarse tracking
module consists of an optical antenna, a turntable, a
coarse tracking detector and a coarse tracking
controller. The meticulous tracking module consists
of a fast reflector, a meticulous tracking detector and
a meticulous tracking controller. (Giovannetti, V,
et.al, 2003)
Figure 1. ATP system schematic diagram.
Satellite terminal and ground terminal transmit
beacon light to each other through their beacon light
module, and use ATP system to capture, track and
aim beacon signal, establish a two-way aiming
satellite-ground light link. Firstly, the satellite end
acts as the emitter of beacon light and the ground
end acts as the capturer. Based on ephemeris
information, the orbit and time period of the satellite
passing over the ground are calculated at the ground
end, and then the turntable in the coarse tracking
module is rotated to point its line of sight to the
uncertain region of the satellite passing over the
user. Subsequently, the optical antenna at the
satellite scans the uncertain area where the user is
located, searches for the beacon light emitted by the
user, realizes rough tracking, and acquisition process.
In the precise tracking stage, FSM first reflects the
up-going beacon light which is output by an optical
antenna and processed by a collimating lens, then
enters the precise tracking detector through the
precise tracking lens of the detector, and forms a
spot on the detector. The precise tracking controller
calculates the output control signal through a certain
control algorithm and controls the FSM to deflect at
a certain angle, so that the beacon light can
accurately track the detector center and achieve the
precise alignment of the incident optical axis and the
optical axis of the main optical antenna. At this
point, the satellite terminal and the ground terminal
are in the tracking state. When two-way tracking is
completed at both ends of the satellite and the user,
the establishment and maintenance of the satellite-
ground optical link can be realized, and the emission
and reception of quantum entangled light can be
carried out in the next step. (Cahill, R. T, 2003)
On the established precisely aligned satellite-
ground optical link, ranging based on quantum
entangled light is the key to the whole QPS. The
TDOA acquisition process for a set of improved
QPS is shown in Figure 2. The yellow line
represents quantum entangled beam, and the red line
represents electrical signal. The process is mainly
completed by four parts: entangled photon pair
generator, ATP system, single photon detector and
data processing unit. (Liao, S. K, et.al, 2017)
Figure 2. The TDOA acquisition process of the improved
QPS.
After the satellite-ground optical link is
established, the user end begins to transmit and
receive quantum entangled light. The entangled
ICVMEE 2019 - 5th International Conference on Vehicle, Mechanical and Electrical Engineering
458
photon pair generator produces correlated signal
light and reference light, in which the signal light is
incident to the advanced sighting mirror. The
advanced sighting module drives the advanced
sighting mirror to adjust an angle by calculating the
instantaneous angle deviation caused by the relative
motion of the satellite and the ground, so as to
compensate the angle deviation of the signal light.
Then the signal light enters the FSM of the precise
tracking module, and reflects it to the mirror of the
coarse tracking module, and then to the optical
antenna, which transmits the signal light to the cone
reflector at the satellite end. The signal light of
entangled photon pair passes through the ground
corner cone reflector and returns to the ground-end
ATP system along the original path. First, through
the optical antenna to enters the mirror of the coarse
tracking module and reflects to the FSM of the
meticulous tracking module, and then incident to the
single photon detector 1. After emitted by the
entangled photon pair generator, the reference light
reflected by the mirror, and be directly received into
the single photon detector 2. (Thon, S. M, et.al, 2009)
4 POSITIONING SOLUTION AND
SIMULATION OF IMPROVED
STAR-BASED QPS
The time difference between the time1 when the
signal light reaches the detector 1 and the time2
when the reference light reaches the detector 2 is
called the arrival time difference Δt. And
multiplying it by the speed of light to obtain the
optical path difference between the signal light and
the reference light, and calculating the distance
between the satellite and the ground user. This paper
proposes a pulse matching count and data fitting
process to obtain the arrival time difference. The
whole process is shown in Figure 3:
Figure 3. Pulse matching measurement process.
A pulse matching count is performed with flow1
by adding different delay values ΔT to the signal of
flow2. When the delay value of flow2 is equal to
, all the pulses on flow1 and flow2 can be matched,
and the matched pulse value reaches the maximum.
Since the second-order correlation function of the
entangled light corresponds to the relationship
between the counting value and the time delay, the
delay corresponding to its maximum value is the
delayed value of the entangled light. According to
the corresponding matching counts obtained by
given different delays , the matching counts are
normalized, and then drawn the discrete point curve.
By fitting the value of the second-order correlation
function of the discrete entangled light obtained by
normalization, it is found that the corresponding ΔT
of the maximum value of the function is the actual
arrival time difference of the entangled light.
Figure 4 is a second-order correlation function
curve of the entangled light obtained by pulse
matching counting at delay time ΔT, where the red
point is a normalized discrete sample point, green
line is the fitted second-order correlation function
curve, and the blue line corresponds to the peak
point coordinate of the fitted curve. The entangled
light Δt obtained by the curve is
.
(Takenaka, H, et.al, 2017)
5 FIGURE 4 SECOND-ORDER
CORRELATION FUCTION
CURVE
Figure 4. Second-order correlation function curve of
entangled light at different ΔT.
6 CONCLUSION
In this paper, an improved star-based QPS system is
proposed and systematically described. The whole
Research of An Improved Satellite-based Quantum Positioning System
459
QPS system includes: the establishment of the star-
ground optical link, the acquisition of TDOA of the
entangled light, the ranging and positioning solution
process. Compared to the traditional 3-baseline star-
based QPS system, the number of satellites required
is effectively reduced.
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