Nghiên cứu giải pháp nâng cao khả năng chống nhiễu cho các bộ thu định vị GNSS tiên tiến

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


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

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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

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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

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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

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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

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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

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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

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

Integration ................................................................................................................ 103

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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

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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.

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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

19


operational constellation is made up of 30 satellites. GPS signal frequencies are allocated in
three bands: L1 (1575.42 MHz), L2 (1227.6 MHz), and L5(1176.45 MHz) [3].
Also in 1970s, Russia developed its own navigation satellite system called GLObal’naya
NAvigatsionnaya Sputnikovaya Sistema (GLONASS). It was designed to have 24 satellites
in 3 orbit planes. At the time of writing, there were 29 satellites but only 24 satellites were

operational. The GLONASS signals are transmitted on G1 (1598.0625 – 1605.375 MHz),
G2 (1242.9375 – 1248.625 MHz), and G3 (1201.5 MHz) bands [4].
With the objective of being the first civilian GNSS, Galileo project was approved by
European Space Agency in 2002. When fully deployed, the system will consist of 27
operational and 3 spares satellites in 3 circular Medium Earth Orbit (MEO). Galileo signals
are transmitted in 4 frequency bands: E1 (1575.42MHz), E5 (1191.795 MHz), E5a (1176.45
MHz), E5b (1207.14 MHz) and E6 (1276.75 MHz) [32].
In 2000, China launched the first satellite of Chinese satellite navigation system (Beidou-1).
The coverage of the system was limited to China and neighboring regions. The second
generation Beidou system became operational in 2011 with 10 satellites in orbit. It is
designed to have 5 geostationary Earth Orbit (GEO) satellites, 27 Medium Earth Orbit
(MEO) satellites, and 3 inclined geosynchronous satellite orbit (IGSO) satellites. The Beidou
signals are transmitted in three bands: B1 (1559.052 – 1591.788 MHz), B2 (1166.22 –
1217.37 MHz), and B3 (1250.618 – 1286.423 MHz) [4].

1.3. GNSS Threats
To operate GNSS services in a reliable way, understanding the growing threats to satellite
navigation signals is essential. Since the signal power is extremely weak, GNSS signals can
easily be disrupted by emerging threats which can be divided into 2 categories: natural (i.e.,
multipath and atmosphere) and man-made threats (interference, spoofing, GNSS segment
errors, and cyber-attacks) [33] (see Figure 1.2).

Figure 1.2: Typical GNSS Threats

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1.3.1. Multipath
The error is well-known and is source of problems not only in GNSS but also in the radio
telecommunication field. It is caused by reflection: the GNSS signals are reflected by high

building or objects and cause large error if the receiver tracks the reflected signal instead of
the line-of-sight signal. Multipath is one of the most significant challenges amongst natural
threats and can cause errors of several to hundreds of meters in positioning performance.
1.3.2. Atmosphere
Before reaching GNSS receivers, GNSS signals must pass through the atmosphere with all
its variations. While the troposphere layer only causes small changes in signal phase and
amplitude, the ionosphere causes more serious errors, particularly during periods of intense
solar activity. Perturbation in the ionosphere around the equator and the two poles, which is
the so-called scintillation - can cause GNSS signal disruptions or very rapid changes in phase
and amplitude of the signal. Thus, a GNSS receiver will be loss of lock if it has not a robust
engine.
1.3.3. Interference
The simplest form of jamming consists in transmitting a specific signal or noise to cause
GNSS receiver overload or loss of lock. The attack is sometimes unintentional. High power
harmonics from radar systems, TV radios, VHFs, mobile satellite services and personal
electronics can inadvertently interfere with the GNSS signal.
Recently, with the advent of hand-held GNSS jammers, GNSS signals within a radius of a
some tens of meters are completely disrupted. The operating principle of these devices is to
use a chirp signal to intervene in the operating frequency range of the GNSS signal. There
are currently no effective methods to minimize the impact of this type of attack
1.3.4. Spoofing
GNSS spoofing is a kind of attack that deceives a GNSS receiver by transmitting a fake
GNSS signal with false information or by transmitting the genuine signal grabbed elsewhere
or at another time. These counterfeit signals modify the navigation message and code phase
in such a way that the receiver estimates its position somewhere else than in its actual
position, or in the correct position but at another time. A common form of GNSS spoofing
attacks begins broadcasting signals synchronized with the genuine signals. The power of the
counterfeit signal is then gradually increased to dominate the genuine signal. As a result, the
GNSS receiver cannot realize the change and completely tracks the counterfeit signals.
1.3.5. GNSS Segment errors

The GNSS system can fail even without human intervention. The satellite onboard atomic
clocks sometimes generates cumulative errors before informing users. On 1st January 2004,
the error on GPS SVN-23 satellite caused a range error of up to 300 km.

21


An error in signal modulation or generating process can also lead to errors in positioning
performance of the receiver. In 1993, the evil waveform from GPS PRN 9 caused 8 meters
in pseudorange error.
1.3.6. Cyber Attacks
Unlike other forms of attacks, this attack is related to manipulation of the software layer in
devices to change the position information. There is evidence that the attack is used in the
maritime segment with Automatic Identification System (AIS) data manipulation.

1.4. GNSS Receiver Architecture
1.4.1. Signal Conditioning and Sampling
The architecture of the signal conditioning and sampling is illustrated as in Figure 1.3
In this stage, the received signal is conditioned to meet the requirement of the sampling
process. For simplicity, consider the GPS L1 signal from a satellite:
𝑠(𝑡) = √2𝑃𝑠 𝐶(𝑡 − 𝜏)𝐷(𝑡 − 𝜏)cos(2𝜋𝑓𝑠 𝑡 + 𝛷)

(1.7)

where 𝑃𝑠 is the received power of the GPS L1 signal. 𝐶(𝑡) and 𝐷(𝑡) denotes the code and
data of the consdired satellite.
After the mixer, the received signal is separated into I and Q component. Without loss of
generality, from now on, we will use the complex signal to represent the signal on I and Q
channel. The signal after mixer is:
̂ ))

𝑠̂ (𝑡) = √𝑃̂𝑠 𝐶(𝑡 − 𝜏)𝐷(𝑡 − 𝜏)𝑒𝑥𝑝 (𝑗(2𝜋𝑓𝐼𝐹 𝑡 + 𝛷
̂ ))
+ √𝑃̂𝑠 𝐶(𝑡 − 𝜏)𝐷(𝑡 − 𝜏)𝑒𝑥𝑝 (𝑗(2𝜋(2𝑓𝐿1 + 𝑓𝐼𝐹 )𝑡 + 𝛷

Figure 1.3: Signal conditioning and sampling stage

22

(1.8)


1.4.2.

Acquisition

The acquisition stage is aimed to roughly estimate the code phase and Doppler shift of visible
GNSS satellites. In fact, the stage performs correlation with every Doppler frequency and
code phase bin in the search space (Figure 1.4). A satellite is considered as visible if there is
the value of a cell in the search space higher than a specified threshold. The code and
frequency corresponding to the cell is the output of the acquisition. The selected threshold
must be considered carefully because it is related to the number of satellite in use that is
proportional to the accuracy of the solution.

x[n]

FFT

IFFT

|.|2

(.)

*j
()*

90

FFT
Carrier
NCO

Code NCO
FFT-based Acquisition

Noncoherent
Integration

Figure 1.4: Acquisition Architecture

1.4.3. Tracking and Data Demodulation
After the acquisition, the receiver has roughly code phase and Doppler frequency of every
satellite in view. However, those parameters are changing over time due to the change of the
relative position between the satellite and receiver. The tracking stage is aimed to keep track
the replica local code and carrier and the received signal with the Delay Lock Loop (DLL)
and Phase Lock Loop (PLL)

Figure 1.5: Tracking Architecture

23

Similar to acquisition stage it performs mixing the received signal with the replica code and
carrier. The PLL wipes off the carrier [31] and the DLL align the local and incoming PRN
codes. The signal after the direct digital frequency synthesizer (DDFS) is down-converted
to baseband and is ideally contained in only the in-phase (I) channel. The DLL tracks the
time delay of the incoming PRN. The baseband signal is correlated with 3 local replica codetaps: Early (E), Prompt (P), and Late (L), through multiplication and integration, usually
over an integer PRN code period (T0). Discriminator feedbacks adjust the Code NCO, which
fluctuates the local replica code rate to synchronize with the incoming code [34]
1.4.4. Positioning Computation
Positioning computation is performed with the assumption that the received signal is
acquired and tracked successfully from a minimum of four satellites in view. After
navigation message demodulation, the receiver can determine the received time and the
position of all satellites in view. To apply (1.1), the receiver needs to measure the distance
from the receiver to all satellites. In GNSS receivers, the quantity cannot be directly
calculated but it is derived through the transmission time. It is worthy to note that the
convergence solution of (1.6) will not change if a constant value is added to all pseudoranges.
Therefore, the receiver will calculate the difference between transmission time instead of the
absolute value. The differences are computed by counting the number of sample intervals
since the receiver started to the preamble bits in the same subframe for all satellites (Figure
1.6).

Figure 1.6: Transmission time estimation in GNSS receivers

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1.5. Countermeasures to GNSS Threats
This section presents the state of the art of antenna array processing techniques, frontend
and digital signal conditioning-based techniques, and correlator/tracking and PVT based

techniques (see Figure 1.7). The implementation of antenna array and snapshot positioning
are more emphasized because they are main focuses of the dissertation.

Figure 1.7: Interference mitigation techniques in GNSS receivers

1.5.1.

Antenna array processing techniques

With the spatial diversity setting by multiple elements, antenna array processing techniques
are considered as a powerful tool for interference mitigation in GNSS applications [35] [36]
[37] [38]. From an application point of view, the antenna array processing techniques can be
used to either suppress interference effect or localize the interference source.
Regarding interference mitigation, although the specific implementation varies between
techniques, the existing methods in this group can be classified based on the optimization
criteria for calculating optimal weights.
Minimum Mean Square Error Criterion: The technique was first proposed by [39] and aims
to minimize the mean square error between the output of the array 𝒙(𝑡) and the interested
signal 𝑑(𝑡)
Problem

min 𝐸{[𝑑(𝑡) − 𝒘𝑇 𝒙(𝑡)]}

(1.9)

Solution

𝑤𝑀𝑀𝑆𝐸 = 𝑹−1
𝑥𝑥 𝒓𝑥𝑑

(1.10)

𝒘

where 𝒘 is the weighting coefficients vector, 𝒙(𝑡) is the vector of the received array signals.
It is straightforward to derive the solution to the problem in (1.9)

25


In the implementation the referent signal is actually the local code and the navigation bits in
the tracking stage [30]. However, the navigation bits are not available under strong
interference. Hence, this technique is suitable for weak interference environment.
Signal to Interference plus Noise Ratio Criterion:
Problem

𝒘𝑇 𝑹𝑠𝑠 𝒘∗
max 𝑇
𝒘 𝒘 𝑹𝑖𝑖 𝒘∗ + 𝒘𝑇 𝑹𝑛𝑛 𝒘∗

(1.11)

Solution

𝒘𝑆𝐼𝑁𝑅 = (𝑹𝑖𝑖 + 𝑹𝑛𝑛 )−1 𝒂∗𝑠

(1.12)

Power Inversion Criterion:
With the assumption that the received signal is weaker than the interference, this technique

is proposed to null the stronger signal [40]
Problem

min 𝐸{[𝒘𝑇 𝒙(𝑡)]} subject to 𝒘𝑇 𝒇 = 1

(1.13)

Solution

𝒘𝑃𝐼 = 𝜇𝑹−1
𝑥𝑥 𝒇

(1.14)

𝒘

Beam Steering Criterion:
This technique merely maximizes the array gain following the direction of the interested
signals.
Problem

𝒘𝑇 𝒂𝑠 = 𝐾

(1.15)

Solution

𝒘𝐵𝑆 = 𝒂𝑠∗

(1.16)

Null Steering Criterion:
Similarly, the null steering will minimize the gain in the direction of interference. In [41],
this technique can be used to suppress GNSS interference effectively. The optimal criterion
and weight vector is given as follows:
Problem

𝒘𝑇 𝒂𝒊 = 1

(1.17)

Solution

𝒘𝑁𝑆 = 𝒂∗𝑖 .∗ 𝒃

(1.18)

where 𝒂𝑖 is the vector of interference direction consisting of [1, exp(𝑗𝜙1𝑖 ) , … , exp(𝑗Φ𝐾𝑖 )]

𝑇

Although the effect of this technique is undeniable, the most challenge in the implementation
of this technique is the antenna array frontend. Recently, thanks to the commercial
availability of chipset for GNSS specialized applications, there are several efforts for
implementing low-cost antenna arrays for GNSS signal [42] [29].

26