Nghiên cứu giải pháp nâng cao khả năng chống nhiễu cho các bộ thu định vị GNSS tiên tiến robust signal processing techniques for modern GNSS receivers

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
2

Tc. 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

9


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

1
0


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
-1
theoretical models (step = 10 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
10


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

11


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: �/�� 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 �/�� with ���� = �� − �
............................ 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
11


Figure 4.14: Power consumption comparison of our proposed solution and Ublox LEA 6T

.................................................................................................................................. 102
Figure 4.15: The experiment setup .................................................................................... 102

12


Figure 4.16: GNSS Snapshot/INS integration result ......................................................... 103
Figure 4.17: Positioning performance between GNSS Snapshot and GNSS Snapshot/INS
Integration ................................................................................................................ 103

13


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
14


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
15


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
16


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 multisystem 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

17


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.

18


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

�� �� ] and ��� = [� �
Let � = [��
��
� � ] be the position of the
receiver
and
of
the
satellite
i.
The
geometry
distance
from
the
receiver
to satellite is defined
as � � = �||� − �� � ||. Clearly, the vector � can be determined if we know the satellite
position �� and the distance
��
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 ��� besides 3 unknown elements of �. With 4 satellites, the equations in these
four
unknowns are as follows:
19

1 2 + (�
√(�� − �21 )2 +
(�� − �
ρ11 )2= +
2 ))2 +
√(�
(��� 3−
�
�δ�
ρ
=
−
�
−
� 2 2
�
3
2
2
) + (� − � ) + �δ��3ρ 2 = √(�� − � )
�
2 + (� −�� 3 )2 + (� − �
) + ��
�
�
4
4
2
{ρ = √(�� − � ) + (�� − � 4 )2 + (�� −

� 4 )2 + ��

20

(1.1)


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

� = [��

��

��

��� ] and using the first order

of Taylor
expansion as an approximate for every equation as follows:
ℎ(�) ≈ ℎ(�0 ) + ℎ′ (�0 )(� − �0 )
(1.2)

�1 = ��1�1 + ax2 �� +
(1.3)

��1 �� + ���
�2 = ��1 �1 + ax2 �� +

{
��1 �� + ���
�3 = ��1�1 + ax2 �� +
��1 �� + ���
�4 =���1
Δ�1++�Δ�
ax2 �� +
Δ�
�1

Δ�1
Δ�2
Let us denote Δ� = {
,
H=
Δ�
then
Δ�
3
4

�

ax1
ax2

�

ay1
ay2

az1
1
Δ�1
az2
1
, and Δ� =
,
{

ax3

ay3
az3
{ax4 1 ay4
az4
1

Δ� = HΔx
(1.4)

or
Δ� = � −1 Δ�
(1.5)
If there are more than 4 satellites in view, (1.5) becomes:
21

Δ�2
Δ�
Δ� 3

�


Δ� = (� � �)−1 � � Δ�

(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

22