MINISTRY OF EDUCATION AND TRAINING
HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY
NGUYEN DINH THUAN
ROBUST SIGNAL PROCESSING TECHNIQUES FOR MODERN
GNSS RECEIVERS
Major: Computer Engineering
Code No.: 9480106
COMPUTER ENGINEERING DISSERTATION
SUPERVISORS:
1. Assoc. Prof. Ta Hai Tung
2. Prof. Letizia Lo Presti
Hanoi - 2019
STATEMENT OF ORIGINALITY AND AUTHENTICITY
I confirm that my dissertation is an original and authentic piece of work written by
myself. The data, results in the thesis is reliable and has never been published by
others. I further confirm that I have fully referenced and acknowledged all material
incorporated as secondary resources in accordance with the regulations
Hanoi,
SUPERVISORS
PHD STUDENT
PGS.TS. Tạ Hải Tùng
Nguyễn Đình Thuận
Prof. Letizia Lo Presti
1
ACKNOWLEDGEMENTS
I would like to express my gratitude to Hanoi University of Technology, Graduate
School, School of Information and Communication Technology, Department of
Computer Engineering and Politecnico di Torino, NavSaS group for creating
favorable conditions for me to work and study.
I would like to express my special thanks to my supervisors, Assoc. Ta Hai Tung and
Prof. Letizia Lo Presti. The supervisors have always been helpful, giving great advice,
scientific orientations so that I can develop and complete my research.
Sincerely thank the lecturers, colleagues in the Department of Computer Engineering,
School of Information and Communication Technology, Hanoi University of Science
and Technology where I work, study and carry out research projects for the
enthusiastic in helping and encouraging me during the research.
With gratitude to teachers, scientists, colleagues and close friends for encouraging
and supporting me in the research process.
Finally, I would like to express my deep gratitude to my family for encouraging me
to overcome all obstacles to complete this thesis.
Nguyen Dinh Thuan
2
TABLE OF CONTENTS
STATEMENT OF ORIGINALITY AND AUTHENTICITY ......................................... 1
ACKNOWLEDGEMENTS ................................................................................................ 2
TABLE OF CONTENTS .................................................................................................... 3
LIST OF ACRONYMS ....................................................................................................... 6
LIST OF TABLES ............................................................................................................... 8
LIST OF FIGURES ............................................................................................................. 9
INTRODUCTION ............................................................................................................. 13
1.
FUNDAMENTAL BACKGROUND ....................................................................... 18
1.1.
GNSS positioning principle .................................................................................. 18
1.2.
History and development of GNSS ...................................................................... 19
1.3.
GNSS Threats ....................................................................................................... 20
1.3.1.
Multipath ....................................................................................................... 21
1.3.2.
Atmosphere.................................................................................................... 21
1.3.3.
Interference .................................................................................................... 21
1.3.4.
Spoofing ........................................................................................................ 21
1.3.5.
GNSS Segment errors .................................................................................... 21
1.3.6.
Cyber Attacks ................................................................................................ 22
1.4.
1.4.1.
Signal Conditioning and Sampling ................................................................ 22
1.4.2.
Acquisition .................................................................................................... 23
1.4.3.
Tracking and Data Demodulation ................................................................. 23
1.4.4.
Positioning Computation ............................................................................... 24
1.5.
Countermeasures to GNSS Threats ...................................................................... 25
1.5.1.
Antenna array processing techniques ............................................................ 25
1.5.2.
Frontend and Digital Signal Conditioning based techniques ........................ 28
1.5.3.
Correlator/Tracking and PVT based techniques ............................................ 29
1.6.
2.
GNSS Receiver Architecture ................................................................................ 22
GNSS Simulator and effect of sampling frequency .............................................. 30
GNSS SIGNAL SIMULATOR DESIGN AND IMPLEMENTATION ............... 32
2.1.
Modeling methodology ......................................................................................... 32
3
2.2.
Overview of the modeling of antenna array signals in GNSS receivers .............. 32
2.2.1.
General model of the received signal in GNSS receivers ............................. 33
2.2.2.
Interference .................................................................................................... 37
2.2.3.
Multipath ....................................................................................................... 38
2.2.4.
Noise .............................................................................................................. 39
2.3.
Effect of sampling frequency on the positioning performance ............................. 39
2.3.1.
Residual code phase estimation ..................................................................... 40
2.3.2.
Correlation output calculation ....................................................................... 40
2.3.3. Effect of sampling frequency on correlation shape and DLL discriminator
function 42
2.3.4.
Effect of the sampling frequency and the integration period selection ......... 42
2.3.5.
Effect on the presence of Doppler and local oscillator (LO) clock drift. ...... 45
2.3.6.
Theoretical code tracking loop error estimate ............................................... 46
2.3.7.
Theoretical results evaluation by simulated, and numerical models ............. 49
2.3.8.
Effect of Doppler and coherent integration period ........................................ 50
2.4.
Sampling Frequency Effect Mitigation Technique ............................................... 53
2.4.1.
2.5.
Performance verification ....................................................................................... 57
2.5.1.
Verification of the simulated antenna array signals ...................................... 58
2.5.2.
Antenna distortion simulation ....................................................................... 64
2.5.3.
Verification of multipath simulation ............................................................. 66
2.6.
3.
Receiver implementation ............................................................................... 55
Conclusion ............................................................................................................ 67
ANTENNA ARRAY PROCESSINGS FOR GNSS RECEIVERS ....................... 69
3.1.
The proposed solution for synchronizing separated antenna array element ......... 69
3.1.1.
Determining the samples difference .............................................................. 70
3.1.2.
Determining the clock phase shift ................................................................. 71
3.2.
Implementation a low-cost antenna array ............................................................. 75
3.3.
Antenna array frontend verification ...................................................................... 76
3.3.1.
Phase difference between frontends .............................................................. 76
3.3.2.
Carrier to noise ration improvement .............................................................. 77
4
3.4.
4.
Conclusion ............................................................................................................ 78
GNSS SNAPSHOT PROCESSING TECHNIQUE FOR GNSS RECEIVERS .. 80
4.1.
Proposed Design of GNSS Snapshot Receiver ..................................................... 80
4.1.1.
GNSS Grabber ............................................................................................... 80
Implementation of GNSS Grabber ............................................................................ 80
Firmware Architecture .............................................................................................. 81
4.2.
Server Software..................................................................................................... 81
4.2.1.
GNSS signal acquisition ............................................................................... 81
4.2.2.
Combined Doppler and Snapshot Algorithm ............................................. 84
4.3.
Loosely coupled Snapshot GNSS/INS ................................................................. 89
4.4.
Tightly coupled Snapshot GNSS/INS ................................................................... 96
4.5.
Results ................................................................................................................... 97
4.5.1.
Standalone Snapshot GNSS Receiver ........................................................... 97
4.5.2.
Snapshot GNSS/INS Integration ................................................................. 102
4.6.
Conclusion .......................................................................................................... 104
CONCLUSIONS AND FUTURE WORKS .................................................................. 105
PUBLICATIONS ............................................................................................................. 107
REFERENCES ................................................................................................................ 109
APPENDIX ...................................................................................................................... 116
A.
Correlation output calculation ............................................................................ 116
B.
Error analysis for coherent early minus late DLL .............................................. 117
5
LIST OF ACRONYMS
Acronym
Meaning
ADC
Analog to Digital Converter
AGC
Automatic Gain Control
AWGN
Additive White Gaussian Noise
BB
BaseBand
BOC
Binary Offset Carrier
BPSK
Binary Phase Shift Keying
C/A
Coarse/Acquisition
C/N0
Carrier-to-Noise-Density Ratio
CDC
Conventional Differential Combination
CDMA
Code Division Multiple Access
CRC
Cyclic Redundancy Check
CS
Commercial Service
DLL
Delay Lock Loop
DFT
Discrete Fourier Transform
DSP
Digital Signal Processor
EGNOS
European Geostationary Navigation
Overlay Service
EU
European Union
FEC
Forward Error Correction
FFT
Fast Fourier Transform
FPGA
Field Programmable Gate Array
6
FOC
Full Operational Capability
GLONASS
Global Orbiting Navigation Satellite
System
I
Inphase
IF
Intermediate Frequency
Q
Quadrature
PVT
Position Velocity Time
SDR
Software Defined Radio
7
LIST OF TABLES
Table 2.1: GNSS Simulator Features .................................................................................. 57
Table 2.2: The coordinate of 4 elements ............................................................................. 58
Table 2.3: The direction of 6 visible satellites..................................................................... 59
Table 2.4: The carrier phase relative to the first element of each satellite at the four elements
of the array. ................................................................................................................ 59
Table 2.5: The simulation scenario...................................................................................... 60
Table 2.6: Estimated carrier phase using the post-correlator beamforming tracking loop.. 62
Table 4.1: Configuration of the GPS grabber .................................................................... 97
Table 4.2: Information of acquired satellites ...................................................................... 99
8
LIST OF FIGURES
Figure 1.1: Satellite navigation principle ............................................................................ 18
Figure 1.2: Typical GNSS Threats ...................................................................................... 20
Figure 1.3: Signal conditioning and sampling stage........................................................... 22
Figure 1.4: Acquisition Architecture ................................................................................... 23
Figure 1.5: Tracking Architecture ....................................................................................... 23
Figure 1.6: Transmission time estimation in GNSS receivers............................................. 24
Figure 1.7: Interference mitigation techniques in GNSS receivers ..................................... 25
Figure 1.8: The traditional low-cost architecture of antenna array for GNSS applications 27
Figure 1.9: The correlation between 2 GPS signal grabbed by antenna array .................... 28
Figure 1.10: Spectrum and histogram of GNSS signal in the absence of interference ....... 28
Figure 1.11: Snapshot positioning architecture ............................................................... 29
Figure 2.1: Geometry of antenna array................................................................................ 33
Figure 2.2: The model of the received signal for a single antenna ...................................... 33
Figure 2.3: GPS multi-antenna frontend.............................................................................. 34
Figure 2.4: Flowchart of the simulator ................................................................................ 35
Figure 2.5: Bandlimited Gaussian interference model ........................................................ 38
Figure 2.6: Multipath model ................................................................................................ 38
Figure 2.7: Effect of sampling frequency on the positioning performance ......................... 39
Figure 2.8: Residual code phases versus the number of samples per code chip with 4fc < fs <
5fc ............................................................................................................................... 40
Figure 2.9: Normalised correlator and EML discriminator functions for different sampling
frequencies. Results are obtained by correlating the incoming signal with various local
generated replica signals that have the time delay from−Tc to Tc with step = 10-2Tc. 42
Figure 2.10: Correlation shapes for 1 ms integration with various sampling frequencies .. 43
Figure 2.11: Ambiguous synchronization between a local PRN code and two different
incoming analog signals of the same PRN sequence, but with slightly differing code
phase offset................................................................................................................. 43
Figure 2.12: Correlation shapes and their errors with respect to the ideal correlation at a
sampling frequency fs =16.3676 MHz using various coherent integration periods ... 44
Figure 2.13: Representation of code tracking loop [54] ...................................................... 46
9
Figure 2.14: DLL jitter versus different sampling frequencies (step= fc) for a GPS L1 C/A
with C/N0=40 dB-Hz, BL=0.5 Hz, T=1 ms, and fixed BW βr = 2fc. .......................... 48
Figure 2.15: Upper bound and lower bound of the DLL jitter versus different sampling
frequencies (step = 5∗10-2 fc) for a GPS L1 C/A with C/N0=45 dB-Hz, BL=0.5 Hz, T=1
ms, and βr = fs ............................................................................................................. 49
Figure 2.16: Mean values of two error bounds σs1 and σs2 versus different sampling
frequencies (step = 10-1 fc) for a GPS L1 C/A with C/N0=45 dB-Hz, BL=0.5 Hz, T=1
ms, and βr = fs ............................................................................................................. 49
Figure 2.17: DLL tracking error comparison among the simulated, numerical and theoretical
models (step = 10-1 fc) for a GPS L1 C/A with T=1 ms, and βr = fs. .......................... 50
Figure 2.18: DLL tracking error versus Doppler frequencies fD for different integration
periods T when the sampling frequency is an integer multiple of the nominal code rate
(ns=4), in which the blue dotted lines indicate the typical Doppler range. ................ 51
Figure 2.19: DLL tracking error versus integration periods T. GPS L1 C/A is used with fs =
4.092 MHz (ns=4), C/N0=40 dB-Hz, BL=0.5 Hz, T=1 ms, and βr = fs ....................... 52
Figure 2.20: DLL tracking error versus Doppler frequencies fD for different integration
periods T when the sampling frequency is a non-integer multiple of the nominal code
rate. ............................................................................................................................. 52
Figure 2.21: Code chip selection versus jitter values with M=4, where Triangle, circle, and
diamond dots indicate samples belonging to (k−1)th, kth , and (k+1)th chips,
respectively. ............................................................................................................... 54
Figure 2.22: Correlator shapes versus different jitter techniques for GPS L1 C/A signal,
where τ runs in the range [−Tc,Tc] with step interval =10−3Tc, fs=4.092 MHz, fD = 0
Hz, βr = fs and θNCO(0) = 0.125. .................................................................................. 55
Figure 2.23: Pseudo-code algorithm that can be used to implement jittering solution on SDR
receiver ....................................................................................................................... 56
Figure 2.24: The results after applying the mitigation technique ........................................ 57
Figure 2.25: Antenna array configuration ........................................................................... 59
Figure 2.26: Post-correlator beamforming receiver architecture [30] ................................. 61
Figure 2.27: Scatter diagram of the tracking output of the satellite PRN01 at 4 elements . 62
Figure 2.28: Estimated position of elements (East-North) .................................................. 64
Figure 2.29: Estimated position of elements (Up) ............................................................... 64
Figure 2.30: Element patterns utilized for simulation (East-North) .................................... 65
Figure 2.31: The C/N0 of the satellite PRN 1 ..................................................................... 65
10
Figure 2.32: Multipath error ................................................................................................ 67
Figure 3.1: The architecture of antenna array based GNSS receiver .................................. 69
Figure 3.2: Time difference between 2 elements ................................................................ 71
Figure 3.3: Navigation message .......................................................................................... 71
Figure 3.4: The architecture of the system to determine the phase offset ........................... 72
Figure 3.5: The impact of clock phase shift ........................................................................ 73
Figure 3.6: The loop filter using for estimating the clock drift ........................................... 74
Figure 3.7: The estimated frequency shift using the loop filter. ......................................... 74
Figure 3.8: The scatter plot of the signal after mitigating clock phase shift ....................... 75
Figure 3.9: The 3-elements antenna array frontend modified from turner RTL2832Us ..... 76
Figure 3.10: The setup of the verification of the frontend using a GPS simulator .............. 77
Figure 3.11: Tracking output of satellites in view ............................................................... 77
Figure 3.12: 𝑪/𝑵𝟎 of the satellite PRN 09 for the received signal at every element and
beamed signal ............................................................................................................. 78
Figure 4.1: The architecture of the GNSS grabber ........................................................... 80
Figure 4.2: The flowchart of the grabber firmware ......................................................... 81
Figure 4.3: Acquisition search space................................................................................. 82
Figure 4.4: Probability of Detection w.r.t 𝑪/𝑵𝟎 with 𝑷𝒇𝒂 = 𝟏𝟎 − 𝟑 ............................ 84
Figure 4.5: FFT-based acquisition ..................................................................................... 84
Figure 4.6: Snapshot solution diagram ............................................................................. 88
Figure 4.7: Traditional loosely-coupled GPS/INS integration ............................................ 90
Figure 4.8: INS mechanization [3]. ..................................................................................... 94
Figure 4.9: Tightly-coupled integration scheme ................................................................. 96
Figure 4.10: The prototype of GNSS grabber.................................................................... 98
Figure 4.11: Acquisition result of the grabbed signal ......................................................... 98
Figure 4.12: The position converged after 7 iterations ................................................. 100
Figure 4.13: The positioning accuracy of the proposed solution ................................. 101
Figure 4.14: Power consumption comparison of our proposed solution and Ublox LEA 6T
.................................................................................................................................. 102
Figure 4.15: The experiment setup .................................................................................... 102
11
Figure 4.16: GNSS Snapshot/INS integration result ......................................................... 103
Figure 4.17: Positioning performance between GNSS Snapshot and GNSS Snapshot/INS
Integration ................................................................................................................ 103
12
INTRODUCTION
Nowadays, GNSS receivers have become core components in many applications ranging
from vehicle navigation to unmanned vehicle guidance, from location-based services to
environment monitoring. Besides providing position information for many applications,
GNSS services also provide a highly precise timescale for synchronizing systems such as
telecommunication and network. Hence, the performance of GNSS which have considerable
influence on the operation of these services must be guaranteed. In [1] a list of four
parameters of GNSS performance is reported: accuracy, availability, continuity, and
integrity. Recently, the accuracy of GNSS has been significantly improved with the
development of new navigation systems (Galileo-European system and BEIDOU-Chinese
system) and the modernization of the existing navigation systems GPS and GLONASS.
However, GNSS services are seriously being threatened by the emergence of jamming and
spoofing threats.
Because GNSS signals are buried under ambient noise, the signals and services of GNSS
systems are highly sensitive to interference such as radio frequency interference, jamming
and spoofing; meanwhile, the quality of such services is not guaranteed to the conventional
users. Technically, the GNSS signal is transmitted from satellites away from Earth (about
20.000 km), so when it comes to receivers, the signal power is smaller than the background
noise about 1024 times (26dB) [2]. Therefore, any source of interference (jammer, digital
terrestrial communication systems, ionosphere scintillation) may reduce the quality of the
received signal, which in turn can disable the operation of the receiver. In addition, because
the GNSS systems are often under the management of military based organizations [3] [4]
[5], the open services (e.g., GPS L1 C/A, Beidou B1, GLONASS L1OF) are provided to
users without any guarantee of their reliability and continuity. However, ensuring reliable
and continuous position and time information is essential in modern GNSS receivers. To
meet these requirements, receivers must make use of advanced techniques to detect and
mitigate interferences so that they can provide the requested continuous position and time
information. These techniques are called “interference mitigation techniques”.
In recent studies [6] [7] reflecting the state of the art, interference mitigation techniques can
be classified according to the position of the algorithm within the processing stages of GNSS
receiver chain. In short, they are classified into three groups namely antenna array
processing techniques, frontend and digital signal conditioning-based techniques, and
correlator/tracking and PVT based techniques
Antenna array signal processing technique: A popular method for robust GNSS receiver
performance consists in using multiple physical antenna elements which constitute a socalled antenna array. This technique has been studied since the 1940’s and has been widely
used in radar and telecommunications applications [8] [9] [10] [11]. Recent studies exploited
this technique for GNSS applications considering it as an effective method to mitigate
13
interference. However, conventional antenna array-based processing leads to complicated
and expensive systems, and it is not suitable for mobile receivers [12] [13] [14]. Although
there are several efforts to design low-cost antenna array for GNSS applications [9] [10],
issues involved to the implementation in a GNSS receiver still exist. While 2 bits of
quantization in ADC, have been proved to be enough for GNSS receivers [15], however it
makes the GNSS receivers less robust to threats due to the saturation of the ADC against the
high power of the interference. Also, expanding the number of antenna elements is a
challenge due to the limited interface bandwidth. To overcome those limitations, the signal
from elements can be independently grabbed first and then their signals are synchronized. In
this approach, synchronization becomes the vital process to be performed before combining
the signals from the array. Thus, the design of robust calibration algorithms that corrects for
the time, phase and frequency mismatch among array data becomes a necessity. To estimate
the phase difference between elements, we can use least squares and maximum likelihood
such as [16] [17]. Phase calibration of antenna arrays can also use the live-sky GNSS
signal [18] [11]. Regarding time offset estimation, there are some studies in
telecommunication field which address the issue using the correlation technique [41] [42].
However, those studies assume that the power of the interested signal is much higher than
ambient noise. Therefore, the assumption may not hold true when GNSS signals are
involved.
Frontend and Digital Signal Conditioning based techniques: In this second group of
interference mitigation techniques, some unusual properties of interference signals such as
high power, spectrum shape, raw sample distributions are used for interference detection.
While [19] proposed the use of AGC to detect jamming signal, [15] uses this information to
detect a spoofing repeater. Although this is considered as a promising technique in detecting
jamming and simplistic spoofing, the information needed for its implementation is not
always available in commercial frontends. On top of this, for what concerns the application
to spoofing detection, since this technique observes the sudden change in the receiver power,
it is useful only if it monitors the signal before the occurrence of a spoofing attack. In more
complicated spoofing scenarios, the technique cannot differentiate the spoofed signal from
the real signals because the spoofed signals are mimicking the properties of the authentic
signals. While the frontend-based techniques are only for interference detection, the digital
signal conditioning-based techniques are useful in minimizing the effect of interference.
Among the techniques of this second group, pulse blanker and notch filter have shown that
they can improve several dB after jamming mitigation [20] [21]. However, as mentioned
above, this technique cannot apply to spoofing mitigation because spoofing signal properties
are analogous to those of authentic signals.
Correlator/Tracking and PVT based techniques: Like the second group of interference
mitigation techniques, these techniques rely on the detection of abnormal outputs in
correlator or PVT in order to identify the presence of interference. Take C/N0 monitoring
14
technique as an example. This technique is based on the abnormal power of the interference.
However, it uses the carrier to noise ratio information instead of absolute received signal
power using in the second group of interference mitigation techniques. In PVT based
techniques, the consistent check or cross check will guarantee the reliable information in
PVT stages (i.e., pseudorange, ephemeris data). A typical technique in this group is Receiver
Autonomous Integrity Monitoring (RAIM). Although it is proved to be effective to detect
failures in pseudorange measurement [22] [23], the measurement is available only if the
tracking stage is without loss of lock. The requirement cannot be guaranteed under powerful
jamming attack which aims to cause the receiver complete loss of lock. Therefore, to
guarantee the availability of a PVT solution, recent studies have suggested to adopt a coarse
time positioning solution for coping with environments affected by interference. It is
considered as an efficient method that can be applied to an area where the continuous GNSS
signal tracking is not guaranteed due to interference [24] [25]. Compared to traditional
receiver, the positioning performance of this technique is less precise. Recent studies have
been improving its positioning performance on the GPS L1 snapshot receiver [26] [27] [28]
but the use of multi-constellation and INS integration in snapshot receiver has not been
explored sufficiently in previous works.
Another difficulty during the design and implementation of interference mitigation
techniques is the performance evaluation and verification process. Currently, these processes
can be done using either live-sky GNSS signal [29] or GNSS simulator signal [30]. The first
approach is straightforward to implement, but it is difficult to control the environments along
with GNSS signals. Therefore, the latter is the method being used favorite now. However,
there are existing limitations with the use of GNSS simulators available in the market for
SDR based study. Because the input data of the study is the digitalized IF signal, in order to
grab such kind of data we need to use a grabber frontend which may include unavoidable
errors, moreover, the performance of the SDR based receiver are strongly affected by the
sampling frequency so the chosen value should be considered carefully during simulation.
Motivation
From the above analysis, advanced processing techniques for resilient positioning and timing
are essential in modern GNSS receivers. Therefore, goal of this work is to propose
techniques to overcome the existing limitations in antenna array processing and snapshot
processing for modern GNSS receivers. The proposed techniques not only reduce the
implementation cost but also leverage the distributed data processing ability.
Scope of Research
The work mainly focusses on antenna array processing technique and snapshot technique for
modern multi-GNSS receivers. While the first technique enables designing and
implementing a low-cost antenna array for GNSS applications, the second technique can
provide reliable position and time information in strongly interfered environment. Remark
15
also that all the simulations through the dissertation are performed with the data generated
from a software-based GNSS simulator. The design and implementation of this simulator
are also part of this thesis. The approach to these techniques is based on SDR technology
where the signal processing chains are implemented by means of software on a personal
computer before deploying to the FPGA.
Methodology
For this study, the following approach is adopted. First, relevant literature and studies are
reviewed to get in-depth knowledge of interference mitigation techniques. Also, the
processing chains in GNSS receivers (i.e., acquisition, tracking and PVT computation) are
reviewed. Second, solutions are proposed to address the existing issues in the
implementation of modern GNSS receivers. Finally, the obtained result is analyzed,
processed and checked against information obtained from literature and previous studies.
Contribution
As mentioned above, the study focuses on proposing solutions to address the two main
issues: the use of low-cost antenna array to detect GNSS threats and the use of multi-GNSS
snapshot positioning technique for discontinuous GNSS signal environment.
Regarding antenna array signal processing technique, the work has proposed the
synchronization mechanism that enables the use of low-cost antenna array processing in
GNSS field. Theoretical and empirical results show that this is a promising solution that will
not only reduce deployment costs but also be a flexible solution for expanding the number
of antenna elements.
As for the second issue addressed, the thesis proposes an integrated model of a multi-system
snapshot receiver with an inertial positioning system (INS). Theoretical and experimental
results have shown the superiority of performance of this solution over the use of solutions
exploiting only single GNSS systems. This integrated model is particularly suitable for
environments where GNSS signals are intermittent.
The results presented in this thesis have been published in 6 conferences and 5 journals as
listed in the attachment. The works have been carried on at Hanoi University of Science and
Technology (Vietnam) and at Politecnico di Torino (Italy).
Thesis outline
The thesis is organized in 4 chapters as follows:
Chapter 1 – Fundamental Background: In this chapter, the background knowledge related to
the stages of GNSS receiver architecture including acquisition, tracking and data
demodulation, and position computation are revised. Also, this chapter show state of the art
of the interference mitigation techniques. The limitations of existing works in the
16
implementation of antenna array frontend and snapshot positioning technique are also
carefully considered.
Chapter 2 - GNSS Signal Simulator Design and Implementation: In this chapter, the design,
and implementation of a GNSS software-based simulator are carefully considered. As one
of the most critical parameters related to the speed of signal generation, the effect of
sampling frequency is also generalized theoretically in both simulator and receiver sides.
Chapter 3 – Antenna Array Signal Processing for GNSS Receivers: This chapter focuses on
a solution enabling the extension of the number of elements and the quantization bits. It is
applied in a low-cost antenna array for detecting the source of spoofing and interference.
Chapter 4 – Snapshot Signal Processing for GNSS Receivers: This chapter shows how the
multi-constellation snapshot technique can be effectively implemented. In addition, to
improve positioning performance, the snapshot GNSS/INS integration is proposed.
17
CHAPTER 1
1. FUNDAMENTAL BACKGROUND
This chapter provides the overview of relevant theory for the thesis. As pointed out in the
previous sections, the thesis mainly focuses on the array processing and Snapshot positioning
for modern GNSS receivers under threats. Therefore, this chapter first provides the principle
of GNSS positioning and history and development of existing GNSSes. Then, the brief
introduction of emerging threats is provided. Finally, the processing chains in GNSS
receivers are fully described.
1.1. GNSS positioning principle
This section will explain the general principle of GNSS navigation. Basically, GNSS
positioning is based on trilateration techniques. In this technique, the receiver firstly
determines the distance from its position to at least three known points. After that, the
receiver’s position is determined by the intersection of 3 spheres (Figure 1.1)
Figure 1.1: Satellite navigation principle
Let 𝐮 = [𝑥𝑢
𝑦𝑢
𝑧𝑢 ] and 𝐱 𝑖 = [𝑥 𝑖
𝑦𝑖
𝑧 𝑖 ] be the position of the receiver and of the
satellite i. The geometry distance from the receiver to satellite is defined as 𝑟 𝑖 = ||𝐮 − 𝐱 𝑖 ||.
Clearly, the vector 𝐮 can be determined if we know the satellite position 𝐱 𝐢 and the distance
𝑟 𝑖 with i=1,2,3.
In GNSS receivers, the distance cannot be measured directly but it uses the transmission
time from satellite to receiver. Unfortunately, the receiver clock is not synchronized with
the atomic clocks onboard of GNSS satellites. As a result, we have one more unknown
variable 𝛿𝑡𝑢 besides 3 unknown elements of 𝒖. With 4 satellites, the equations in these four
unknowns are as follows:
18
ρ1 = √(𝑥𝑢 − 𝑥1 )2 + (𝑦𝑢 − 𝑦1 )2 + (𝑧𝑢 − 𝑧1 )2 + 𝑐δ𝑡𝑢
ρ2 = √(𝑥𝑢 − 𝑥 2 )2 + (𝑦𝑢 − 𝑦 2 )2 + (𝑧𝑢 − 𝑧 2 )2 + 𝑐δ𝑡𝑢
3
ρ = √(𝑥𝑢 −
𝑥 3 )2
+ (𝑦𝑢 −
𝑦 3 )2
+ (𝑧𝑢 −
𝑧 3 )2
(1.1)
+ 𝑐δ𝑡𝑢
{ρ4 = √(𝑥𝑢 − 𝑥 4 )2 + (𝑦𝑢 − 𝑦 4 )2 + (𝑧𝑢 − 𝑧 4 )2 + 𝑐δ𝑡𝑢
where c is the speed of light.
When considering the other errors (e.g., ionospheric, tropospheric), we have the complete
form of the equations [31]
Denote vector solution 𝒙 = [𝒙𝒖 𝒚𝒖 𝒛𝒖 𝜹𝒕𝒖 ] and using the first order of Taylor
expansion as an approximate for every equation as follows:
Δ𝜌1
Δ𝜌
{ 2
Δ𝜌3
Δ𝜌4
ℎ(𝑥) ≈ ℎ(𝑥0 ) + ℎ′ (𝑥0 )(𝑥 − 𝑥0 )
(1.2)
= 𝑎𝑥1 Δ𝑥1 + ax2 Δ𝑦𝑢 + 𝑎𝑧1 Δ𝑧𝑢 + 𝑐Δ𝑡𝑢
= 𝑎𝑥1 Δ𝑥1 + ax2 Δ𝑦𝑢 + 𝑎𝑧1 Δ𝑧𝑢 + 𝑐Δ𝑡𝑢
= 𝑎𝑥1 Δ𝑥1 + ax2 Δ𝑦𝑢 + 𝑎𝑧1 Δ𝑧𝑢 + 𝑐Δ𝑡𝑢
= 𝑎𝑥1 Δ𝑥1 + ax2 Δ𝑦𝑢 + 𝑎𝑧1 Δ𝑧𝑢 + 𝑐Δ𝑡𝑢
(1.3)
Δ𝜌1
Δ𝜌
Let us denote Δ𝜌 = { 2 , H =
Δ𝜌3
Δ𝜌4
ax1
ax2
ax3
{ax4
ay1
ay2
ay3
ay4
az1
az2
az3
az4
1
Δ𝑥1
1
Δ𝑥
, and Δ𝑥 = { 2 ,
Δ𝑥3
1
Δ𝑡𝑢
1
then
Δ𝜌 = HΔx
(1.4)
Δ𝑥 = 𝐻 −1 Δ𝜌
(1.5)
or
If there are more than 4 satellites in view, (1.5) becomes:
Δ𝑥 = (𝐻 𝑇 𝐻)−1 𝐻 𝑇 Δ𝜌
(1.6)
1.2. History and development of GNSS
The first GNSS is the Global Positioning System (GPS). The project was approved by the
United States Department of Defense in 1973. When the system was fully operational in
1995, its constellation consisted of 24 satellites spreading in 6 orbit planes. The current
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