zero-baseline analysis of galileo data from multi-gnss experiment
DESCRIPTION
Zero-Baseline Analysis of Galileo Data from Multi-GNSS ExperimentG Katsigianni Thesis TUMTRANSCRIPT
Technische Universität München
Ingenieurfakultät Bau Geo Umwelt
Lehrstuhl für Astronomische und Physikalische Geodäsie
Univ.-Prof. Dr.techn. Mag.rer.nat. Roland Pail
Analysis of GNSS Data from Zero-Baselines for Characterization of the new Satellite Signals and Multi-GNSS Tracking Equipment
Georgia Katsigianni
Master's Thesis
Master’s Course in Earth Oriented Space Science and Technology
Supervisor: Univ.-Prof. Dr.phil.nat Prof. Urs Hugentobler
IAPG-TUM
Date of Submission: April, 2015
1
Declaration
This thesis is a presentation of my original research work. Wherever contributions of
others are involved, every effort is made to indicate this clearly, with due reference to
the literature, and acknowledgement of collaborative research and discussions.
Munich, 15.03.2015 Georgia Katsigianni
2
Acknowledgements
The present master thesis was conducted during the academic semester Oct.
2014-April 2015 in the Institute of Astronomical and Physical Geodesy (IAPG) for
MSc ESPACE program of Technical University of Munich (TUM) under the
supervision of Prof. Hugentobler.
First and foremost, I would like to thank my supervisor Prof. Hugentobler for
his valuable support, guidance and for our perfect cooperation during the whole time
of my studies in TUM.
I would also like to thank all EPACE professors, lecturers, tutors for giving
me valuable knowledge of scientific topics that I am interested in.
Last but not least, I would like to thank my family for their faith, support and
patience and also all my ESPACE friends for their help and guidance.
Thank you all
Georgia Katsigianni
3
Abstract
In the present master thesis, a study is presented about the analysis of GNSS
data with the use of zero-baseline test from the Multi-GNSS Tracking Equipment
(MGEX) network. This study is separated in two parts:
In the first part some explanations are given that are useful for the
understanding of the experiments that follow. A brief description about the four
Galileo In-Orbit-Validation (IOV) satellites is given with their characteristics.
Secondly, the MGEX network is described from which some stations are used for the
experiments. Finally the concepts of differences and linear combinations are
presented with an emphasis on the zero-baseline test that is used extensively for the
experimentation.
The second part describes all the experimentation that is done. It total six
experiments are presented. In each experiment explanations of the goal are followed
by the parameters that are used, the plots that are made, together with an analysis and
the final conclusions.
After the practical part, overall conclusions are given together with some
suggestions of future research.
Key Words
Zero-Baseline Test, GNSS, Galileo, Fourier Transform, Satellite Clock Errors, IOV
satellites
4
Motivation
Conducting differences between observations and forming linear combinations
is a very helpful and commonly used way for satellite positioning, in order to form
new observations and to reduce or eliminate some parameters or error sources.
A common type of differentiation is the so-called zero-baseline test, which is a
form of double difference using the same antenna connected to the two receivers.
Such a difference is very helpful because of its property that range distance between
receivers and satellites and many error sources are cancelled.
The goal of this present master thesis is to study the behavior of some
periodical patterns that are shown when conducting zero-baseline tests. These graphs
are made using measurements from MGEX stations with respect to observations
coming from the four IOV Galileo satellites (E11, E12, E19 and E20). In particular,
the patterns are not expected to be seen in theory and therefore studying the
characteristics and giving possible explanations or hypotheses about the reasons that
are causing it is of particular research interest.
The methodology that is used consists of six experiments. Each experiment
describes the goal, presents the experimentation and/or related graphs and gives ideas
that are used for the following experiment.
In the first experiment a general idea is showed by examining the behavior for
a long time, how and why these patterns are showing. In the second experiment
graphs are created but this time with respect to satellite combinations. The patterns
showed a similar behavior like the one of a beat signal.
In the third experiment the goal is to make comparisons of the results coming
from the previous experiments and the respective ones using a data from files with a
smaller time step.
The fourth experiment deals with the creation of Fourier transformation graphs
for showing the characteristics of the observed beat signal. The tests are made with
respect to satellite combinations and all stations are used.
The fifth experiment deals with conducting tests for one combination and one
station but for a long period of time. The goal in this case is to see the behavior of the
seen pattern with respect to each day.
Finally, in the last experiment a differentiation is performed for one station,
one day and one satellite combination with respect to carrier frequencies.
At the end all important conclusions are presented together with some ideas
and suggestions for future research.
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Table of Contents
Declaration ..................................................................................................................... 1
Acknowledgements ........................................................................................................ 2
Abstract .......................................................................................................................... 3
Motivation ...................................................................................................................... 4
Table of Contents ........................................................................................................... 5
1. Theoretical Part ....................................................................................................... 6
1.1 IOV Galileo Satellites ..................................................................................... 6
1.2 MGEX Network ............................................................................................ 10
1.3 Differences and Linear Combinations ........................................................... 12
2. Practical Part ......................................................................................................... 18
2.1 Experiment Settings ........................................................................................... 19
2.2 Experiment 1: Combinations for all stations for a long time ............................. 22
2.3 Experiment 2: Satellite combinations for each station ...................................... 37
2.4 Experiment 3: Comparison of 1sec and 30sec data file results ......................... 45
2.5 Experiment 4: Fourier Transformations (satellite combinations) ...................... 48
2.6 Experiment 5: Fourier Transformations (for longer time periods) .................... 57
2.7 Experiment 6: E1-E5a (L1-L5) Differentiation ................................................. 66
Conclusions .................................................................................................................. 70
Suggestions .................................................................................................................. 73
References .................................................................................................................... 74
Table of Figures ........................................................................................................... 77
Table of Tables ............................................................................................................ 80
Appendices ................................................................................................................... 81
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1. Theoretical Part
1.1 IOV Galileo Satellites
The European Global Navigation Satellite System Galileo has as goals: the
global provision of a highly accurate and guaranteed positioning service, under civil
control, interoperable with existing operational GPS and GLONASS systems. The
space segment will consist of 27 satellites (plus 3 spares) in three MEO orbital planes
of 56o inclination at 23222km altitude [1] [2]. The Galileo program will be complete
under two main phases:
The In-Orbit-Validation (IOV) phase: The goal of this phase is the verification
of the space, user and ground components, through tests of four operational
experimental satellites and their ground infrastructure. The first two satellites
(Proto Flight Model (PFM) and Flight Model 2 (FM2)) where launched into
the first orbital plane on Oct. 2011 whereas the second two (FM3 and FM4) on
Oct. 2012 respectively. These four satellites form the least number possible for
obtaining a three-dimensional position (Fig. 1.1) [3].
The Full-Operational-Capability (FOC) phase: This is the phase where all 30
satellites are in orbit and all ground infrastructures are deployed. In August
2014 FOC1 and FOC2 where launched to a non-nominal orbit due to injection
anomaly [4]. However in March 2015, those two satellites were successfully
placed in corrected orbits and, furthermore, FOC3 and FOC4 were
successfully launched [5]. By the end of 2015 FOC5, FOC6, FOC 7 and
FOC8 are programmed to be in place [6] (known as FOC1 phase (Fig. 1.3)).
The ground segment will consist of ground stations and up-link stations
worldwide [7].
Satellite Galileo IOV PRN Launched Clocks Status
PFM (GSAT0101) E11 21 Oct. 2011 PHM Operational
FM2 (GSAT0102) E12 21 Oct. 2011 PHM Operational
FM3 (GSAT0103) E19 12 Oct. 2012 PHM Operational
FM4 (GSAT0104) E20 12 Oct. 2012 RAFS Unavailable
Tab. 1.1: IOV satellite characteristics [8]
The table (Tab. 1.1) shows the characteristics of IOV satellites. All four
satellites have a Passive Hydrogen Maser (PHM) clock, an atomic clock that gives
time measurements within 0.45 ns over 12 hours, and a Rubidium Atomic Frequency
Standard (RAFS) that measures respectively 1.8 ns over 12 hours [9]. From March
2014 satellite FM4 is no longer operational due to a sudden loss of power [10].
7
Fig. 1.1: The four IOV satellites in orbit [11]
ESA announced that each of the four satellites has four clocks on board, two
PHM and two RAFS that complete each other in cases of problems. While under
normal circumstances one of the passive hydrogen maser clocks is the master satellite
clock and used as a reference frequency, a rubidium atomic clock is going to be used
in atomic clock failure until the other pair of clocks starts. By this way the Galileo
satellites give high-quality navigation signals continuously [9].
Fig. 1.2: Ground Stations for IOV satellites [11]
8
The IOV phase network of ground stations (Fig. 1.2) will consist of:
Two Ground Control Centers (GCC): The first one in Italy operating the
Ground Mission Segment (GMS), for navigation mission control activities and
the second one in Germany operating the Ground Control Segment (GCS) for
spacecraft housekeeping and constellation maintenance.
A network of Galileo Sensor Stations (GSS) that track the satellites, providing
data to the GCC for their activities [12].
A network of Up-Link Stations (ULS) for the communication of the navigation
data.
Telemetry, Tracking and Command (TT&C) stations for the constellation
control and communication of GCS with each satellite [12].
An In-Orbit Test (IOT) station in Belgium to evaluate the performance of the
satellite’s payloads. The IOT campaign evaluates the performance of
satellite’s clocks and examines the navigation signals [13].
Fig. 1.3: Ground stations for FOC1 phase [11]
In the following table (Tab. 1.2) some technical characteristics about the
Galileo IOV orbit and the spacecraft are given (as for 2013) [14]. The spacecraft has
several sensors and antennas on board. The L-band antenna that transmits the required
navigation signals, the (Search and Rescue) SAR antenna that is used for local rescue
and safety services, the C-band antenna used for communication with the ULS, two S-
band antennas used for TT&C subsystem and also for measuring the satellite’s
altitude (together with a laser retro-reflector), Earth and Sun sensors for the correct
9
orientation of the spacecraft (pointing at the Earth) and lastly space radiators to help
the spacecraft keep the internal heat to acceptable values [9].
Orbit Spacecraft
Inclination 56o Dimensions 2.7x1.1x1.2m
Orbit Circular Solar Array Span 13m
α 29599.8 km Signals 10
Altitude 23222km Mass 700kg
Eccentricity 0.0001 Lifetime > 12 years
Tab. 1.2: IOV satellites technical characteristics (orbit & spacecraft) [9]
The following image (Fig. 1.4) is an artistic impression of how an IOV
satellite looks with its solar arrays deployed. The solar arrays are designed and put in
such a way in order to collect the maximum solar energy while the spacecraft rotates
around the Earth [9].
Fig. 1.4: IOV satellite spacecraft [9]
10
1.2 MGEX Network
The International GNSS Service (IGS) was founded in 1994 with the goal of
providing high-quality of GNSS data, products and services worldwide with open
access. It consists of more than 220 agencies and institutions all over the world that
provide their products using a global network (Fig. 1.5 & Fig. 1.6) of approximately
386 active monitoring stations (as of Jan 2015) [15]. It also provides an archive of
measurements and analyses of previous years. These permanent monitoring stations
are continuously operating providing data of GNSS systems i.e. GPS, GLONASS.
Fig. 1.5: World map of IGS stations [16]
Fig. 1.6: European region of IGS stations [16]
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In addition to IGS network, the Multi-GNSS Experiment (MGEX) has been
established from the IGS to provide all types of GNSS signal data coming from all
GNSS systems including Galileo, QZSS and BeiDou and the modernized GPS and
GLONASS as well as SBAS systems [17].
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1.3 Differences and Linear Combinations
Since GNSS observations are affected by a number of errors (e.g. satellite
clock errors, receiver clock errors, atmospheric delays etc.), a way to eliminate or
mitigate them is by forming other observables, such as differences and linear
combinations. This is feasible due to the fact that all receivers worldwide are
constructed such, that they give their measurements synchronously.
Generally, a GNSS measurement model for code (1.1) and phase (1.2)
measurements are given in the following equations:
𝑃𝑟𝑠 = 𝜌𝑟
𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟𝑠 + 𝐼𝑟
𝑠 + 𝑚𝑟𝑠 + 𝑏𝑟
𝑠 + 𝑒𝑟𝑠 (1.1)
𝐿𝑟𝑠 = 𝜆𝜑𝑟
𝑠 = 𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝜆𝛮𝑟
𝑠 + 𝑇𝑟𝑠 − 𝐼𝑟
𝑠 + 𝜇𝑟𝑠 + 𝛽𝑟
𝑠 + 휀𝑟𝑠 (1.2)
Where 𝜌𝑟𝑠 is the geometrical distance from the satellite to the receiver, 𝛿𝑡𝑟
and 𝛿𝑡𝑠 are the receiver and the satellite clock offsets respectively, 𝑇𝑟𝑠 and 𝐼𝑟
𝑠 are the
tropospheric and the ionospheric delay, 𝑚𝑟𝑠 and 𝜇𝑟
𝑠 are multipath errors, 𝑏𝑟𝑠 and 𝛽𝑟
𝑠
are internal delays (e.g. line biases), 𝑒𝑟𝑠 and 휀𝑟
𝑠 are noise and 𝜆𝛮𝑟𝑠 is the phase
ambiguity.
From the above equations it is possible to form differences in order to
eliminate some common errors or effects. The most common and frequently used are
shown in the table (Tab. 1.3) [18].
When forming single differences from one common satellite (i) and two
stations (A and B) the goal is to eliminate the satellite clock error, since it is the same
for both receivers. In that case the differences for code and phase become as follow:
∆𝑃𝐴𝐵
𝑖 = 𝑃𝐴𝑖 − 𝑃𝐵
𝑖 =
= ∆𝜌𝐴𝐵𝑖 + 𝑐∆𝛿𝑡𝐴𝐵 + ∆𝑇𝐴𝐵
𝑖 + ∆𝐼𝐴𝐵𝑖 + ∆𝑚𝐴𝐵
𝑖 + ∆𝑏𝐴𝐵𝑖 + ∆𝑒𝐴𝐵
𝑖
(1.3)
∆𝐿𝐴𝐵
𝑖 = 𝐿𝐴𝑖 − 𝐿𝐵
𝑖 =
= ∆𝜌𝐴𝐵𝑖 + 𝑐∆𝛿𝑡𝐴𝐵 + ∆𝑇𝐴𝐵
𝑖 − ∆𝐼𝐴𝐵𝑖 + ∆𝜇𝐴𝐵
𝑖 + ∆𝛽𝐴𝐵𝑖 + ∆휀𝐴𝐵
𝑖 + 𝜆∆𝑁𝐴𝐵𝑖
(1.4)
As it can be seen the satellite clock error is eliminated. That is however valid
only in the case of time-synchronous (i.e. same epochs) measurements. The noise of
the differenced measurements in comparison with the original measurements, with the
assumptions that measurements from the two stations are not correlated and there is
the same variance for both signals, is calculated as follow:
𝜎(∆휀𝐴𝐵𝑖 ) = √𝜎2(휀𝐴
𝑖 ) + 𝜎2(휀𝐵𝑖 ) ≅ √2𝜎2(휀𝐴
𝑖 ) = √2𝜎(휀𝐴𝑖 ) (1.5)
13
Single differences using two satellites (i and j) and one station (A) are
calculated in a similar way. In this case the goal is to eliminate the receiver clock
error. The corresponding equations in this case are as follow:
∇𝑃𝐴𝑖𝑗
= 𝑃𝐴𝑖 − 𝑃𝐴
𝑗 =
= ∇𝜌𝐴𝑖𝑗
− 𝑐∇𝛿𝑡𝑖𝑗 + ∇𝑇𝐴𝑖𝑗
+ ∇𝐼𝐴𝑖𝑗
+ ∇𝑚𝐴𝑖𝑗
+ ∇𝑏𝐴𝑖𝑗
+ ∇𝑒𝐴𝑖𝑗
(1.6)
∇𝐿𝐴
𝑖𝑗= 𝐿𝐴
𝑖 − 𝐿𝐴𝑗
=
= ∇𝜌𝐴𝑖𝑗
− 𝑐∇𝛿𝑡𝑖𝑗 + ∇𝑇𝐴𝑖𝑗
− ∇𝐼𝐴𝑖𝑗
+ ∇𝜇𝐴𝑖𝑗
+ ∇𝛽𝐴𝑖𝑗
+ ∇휀𝐴𝑖𝑗
+ 𝜆∇𝑁𝐴𝑖𝑗
(1.7)
Similarly in this case as before, the noise of differenced measurements is also
increased by a factor of √2 .
For the double differences, measurements of two satellites (i and j) and two
receivers (A and B) are used. In this case the goal is to eliminate both satellite and
receiver clock errors. The double difference is simply the difference of two single
differences.
∇∆𝑃𝐴𝐵𝑖𝑗
= ∆𝑃𝐴𝐵𝑖 − ∆𝑃𝐴𝐵
𝑗 =
= ∇∆𝜌𝐴𝐵𝑖𝑗
+ ∇∆𝑇𝐴𝐵𝑖𝑗
+ ∇∆𝐼𝐴𝐵𝑖𝑗
+ ∇∆𝑚𝐴𝐵𝑖𝑗
+ ∇∆𝑏𝐴𝐵𝑖𝑗
+ ∇∆𝑒𝐴𝐵𝑖𝑗
(1.8)
∇∆𝐿𝐴𝐵𝑖𝑗
= ∆𝐿𝐴𝐵𝑖 − ∆𝐿𝐴𝐵
𝑗 =
= ∇∆𝜌𝐴𝐵𝑖𝑗
+ ∇∆𝑇𝐴𝐵𝑖𝑗
− ∇∆𝐼𝐴𝐵𝑖𝑗
+ ∇∆𝜇𝐴𝐵𝑖𝑗
+ ∇∆𝛽𝐴𝐵𝑖𝑗
+ ∇∆휀𝐴𝐵𝑖𝑗
+ 𝜆∇𝑁𝐴𝐵𝑖𝑗
(1.9)
For the calculation of the noise in this case it is assumed that measurements
coming from different satellites to the same receiver are uncorrelated and that all four
original measurement noise values are more or less equal with each other. The noise
in this case is multiplied by a factor of 2:
𝜎(∇∆휀𝐴𝐵
𝑖𝑗) = √𝜎2(휀𝐴
𝑖 ) + 𝜎2(휀𝐵𝑖 ) + 𝜎2(휀𝐴
𝑗) + 𝜎2(휀𝐵
𝑗) ≅ √4𝜎2(휀𝐴
𝑖 ) =
= 2𝜎(휀𝐴𝑖 )
(1.10)
The so-called zero-baseline test is also a type of double difference but in this
case only one station (i.e. common antenna) is used for the two receivers. This is done
by using a splitter and an amplifier to transfer the signal to two receivers. The
characteristic of this test is that measurements coming from the two receivers can be
compared with each other. With differences between satellites and receivers it is
possible to obtain a combination that is constant and independent from satellite
geometry, clock errors, atmospheric effects and other biases. It is a way to determine
14
the noise level of code and phase measurements of the receiver, [19] as well as
validate the data of the software used [20].
For the zero-baseline test the following equations regarding code and phase
measurements for the double difference are as follow:
∇∆𝑃𝐴𝐵𝑖𝑗
= ∆𝑃𝐴𝐵𝑖 − ∆𝑃𝐴𝐵
𝑗 = ∇∆𝑒𝐴𝐵
𝑖𝑗 (1.11)
∇∆𝐿𝐴𝐵𝑖𝑗
= ∆𝐿𝐴𝐵𝑖 − ∆𝐿𝐴𝐵
𝑗 = ∇∆휀𝐴𝐵
𝑖𝑗+ 𝜆∇𝑁𝐴𝐵
𝑖𝑗 (1.12)
It is easily noticed that terms such as∇∆𝜌𝐴𝐵𝑖𝑗
,∇∆𝑇𝐴𝐵𝑖𝑗
,∇∆𝐼𝐴𝐵𝑖𝑗
,∇∆𝑚𝐴𝐵𝑖𝑗
, ∇∆𝜇𝐴𝐵𝑖𝑗
∇∆𝑏𝐴𝐵𝑖𝑗
, ∇∆𝛽𝐴𝐵𝑖𝑗
are zero because of the use of the same station [19]. However, some
errors caused by multipath may remain if the two receivers are not identical because
of the different way it is calculated by them. Also in this case since it is a form of
double difference the noise is multiplied by a factor of 2 (See 1.10).
Another way of reducing and/or eliminating some common errors is through
making the so-called linear combinations by using simultaneous measurements from
different frequencies. The ones that are described in the present thesis are the
Ionosphere-free and the Geometry-free linear combinations.
The general formula of creating such combinations is by using coefficients (𝜅1
and 𝜅2) that are multiplied with the measurements of each frequency [18].
𝐿𝜅 = 𝜅1𝐿1 + 𝜅2𝐿2 (1.13)
With the same assumption as with Eq. 1.5, the noise of the linear combination
is calculated again as [18]:
𝜎(𝐿𝜅) = √(𝜅1𝜎(𝐿1))2 + (𝜅2𝜎(𝐿2))2 = √𝜅1 + 𝜅2 ∙ 𝜎(𝐿) (1.14)
Such linear combinations can be formed by using code and phase
measurements or a combination of both, or even by using single or double
differences. For the second frequency, the following equations for code and phase are
valid:
𝑃2 = 𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 +𝑓1
2
𝑓22 𝐼𝑟
𝑠 + 𝑚𝑟𝑠 + 𝑏𝑟
𝑠 + 𝑒𝑟𝑠 (1.15)
𝐿2 = 𝜆𝜑𝑟
𝑠 =
= 𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝜆2𝛮𝑟
𝑠 + 𝑇𝑟𝑠 −
𝑓12
𝑓22 𝐼𝑟
𝑠 + 𝜇𝑟𝑠 + 𝛽𝑟
𝑠 + 휀𝑟𝑠
(1.16)
15
Single Difference (one satellite)
∆(∙)𝐴𝐵𝑖 = (∙)𝐴
𝑖 − (∙)𝐵𝑖
elimination of satellite clock error
satellite orbit errors, tropospheric and
ionospheric delays are reduced in short
baselines
noise increased by a factor of √2
Single Difference (one receiver)
∇(∙)𝐴𝑖𝑗
= (∙)𝐴𝑖 − (∙)𝐴
𝑗
elimination of receiver clock error
noise increased by a factor of √2
Double Difference
∇∆(∙)𝐴𝐵𝑖𝑗
= ((∙)𝐴𝑖 − (∙)𝐵
𝑖 ) − ((∙)𝐴𝑗
− (∙)𝐵𝑗
)
elimination of satellite, receiver clock
errors and instrumental biases
depends only on relative geometry
noise increased by a factor of 2
Zero - Baseline Difference
∇∆(∙)𝐴𝐵𝑖𝑗
= ((∙)𝐴𝑖 − (∙)𝐵
𝑖 ) − ((∙)𝐴𝑗
− (∙)𝐵𝑗
)
geometrical distance, satellite and
receiver clock errors, tropospheric and
ionospheric delays are eliminated
noise increased by a factor of 2
Tab. 1.3: Types of measurement differences
16
The ionosphere-free linear combination has the attribute that it is independent
from ionospheric effects. Using observation from two frequencies (e.g. f1 = 1575.43
MHz and f2 = 1227.60 MHz) it is possible to eliminate the ionospheric error using the
following coefficients [18]:
𝜅1 =𝑓1
2
𝑓12 − 𝑓2
2 ≅ 2.546 𝜅2 = −𝑓2
2
𝑓12 − 𝑓2
2 ≅ −1.546 (1.17)
The linear combination measurements for phase (𝐿𝐶) and code (𝑃𝐶) are
calculated as [18]:
𝐿𝐶 = 𝜅1𝐿1 + 𝜅2𝐿2 =
= 𝜅1 ∙ ( 𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝜆1𝛮𝑟
𝑠 + 𝑇𝑟𝑠 − 𝐼𝑟
𝑠 + 𝜇𝑟𝑠 + 𝛽𝑟
𝑠 + 휀𝑟𝑠 )
+ 𝜅2 ∙ (𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝜆2𝛮𝑟
𝑠 + 𝑇𝑟𝑠 −
𝑓12
𝑓22 𝐼𝑟
𝑠 + 𝜇𝑟𝑠 + 𝛽𝑟
𝑠 + 휀𝑟𝑠 )
= (𝜅1 + 𝜅2) ∙ (𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 + 𝜇𝑟𝑠 + 𝛽𝑟
𝑠 + 휀𝑟𝑠 ) −
− (𝜅1 + 𝑓1
2
𝑓22 𝜅2 ) ∙ 𝐼𝑟
𝑠 + 𝜅1𝜆1𝛮𝑟𝑠 + 𝜅2𝜆2𝛮𝑟
𝑠 =
= (𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 + 𝜇𝑟𝑠 + 𝛽𝑟
𝑠 + 휀𝑟𝑠 ) +
𝑐
𝑓12−𝑓2
2 (𝑓1𝑁1 − 𝑓2𝑁2)
(1.18)
𝑃𝐶 = 𝜅1𝐿1 + 𝜅2𝐿2 =
= 𝜅1 ∙ ( 𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 + 𝐼𝑟𝑠 + 𝑚𝑟
𝑠 + 𝑏1𝑠 + 𝑒𝑟
𝑠 )
+ 𝜅2 ∙ (𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 +𝑓1
2
𝑓22 𝐼𝑟
𝑠 + 𝑚𝑟𝑠 + 𝑏2
𝑠 + 𝑒𝑟𝑠 )
= (𝜅1 + 𝜅2) ∙ (𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 + 𝑚𝑟𝑠 + 𝑒𝑟
𝑠 ) −
− (𝜅1 + 𝑓1
2
𝑓22 𝜅2 ) ∙ 𝐼𝑟
𝑠 + 𝜅1𝑏1𝑠+𝜅2𝑏2
𝑠 =
= (𝜌𝑟𝑠 + 𝑐𝛿𝑡𝑟 − 𝑐𝛿𝑡𝑠 + 𝑇𝑟
𝑠 + 𝑚𝑟𝑠 + 𝑒𝑟
𝑠 ) + 𝜅1𝑏1𝑠+𝜅2𝑏2
𝑠
(1.19)
The term (𝜅1 + 𝑓1
2
𝑓22 𝜅2 ) ∙ 𝐼𝑟
𝑠 in both phase and code equations are eliminated,
whereas geometry, satellite and receiver clock errors, tropospheric effects, multipath,
biases, noise and phase ambiguities remain. The terms 𝑏1𝑠 and 𝑏2
𝑠 refer to code
biases. For the measurement noise, it is multiplied by a number that depends on the
contributing frequencies in each combination. The formula bellow is valid:
17
𝜎(𝐿𝐶) = √𝑓1
4 + 𝑓24
𝑓12 − 𝑓2
2 ∙ 𝜎(𝐿) = 𝜈 ∙ 𝜎(𝐿) (1.20)
The number 𝜈 depends on the frequencies that are combined. For Galileo
frequencies the values for each combination are given in the following table [18]:
E1 E5a E5b
E1 - 2.588 2.808
E5a - 27.473
E5b -
Tab. 1.4: Values for noise computation
Another useful linear combination is the so-called geometry-free or
ionosphere linear combination. For this one coefficients 𝜅1 and 𝜅2 give [18]:
𝜅1 + 𝜅2 = 0 (1.21)
For the phase and code linear combinations following equations:
𝐿𝐼 = 𝐿1 − 𝐿2 = −𝐼 (1 −𝑓1
2
𝑓22) + 𝜆1𝑁1 − 𝜆2𝑁2 (1.22)
𝑃𝐼 = 𝑃1 − 𝑃2 = 𝐼 (1 −𝑓1
2
𝑓22) + 𝑏1 − 𝑏2 (1.23)
In this type of linear combination, geometry, satellite and receiver clock
errors, tropospheric effects, and non-dispersive error sources are eliminated and only
ionospheric effects and phase ambiguities remain [18]. This linear combination is
used for study the ionospheric effects and/or variations or for calculation of
ionospheric model parameters.
Apart from these two linear combinations there are also other ones like the so-
called Wide lane that is used for detection of cycle slips, Melbourne-Wübbena that is
used for identification of cycle slips on arbitrary long baselines, Multipath to detect
the multipath error, and others. These are not going to be described in the present
thesis since they are not used in the experiments in the practical part.
18
2. Practical Part
In this part of the thesis, the initial settings of the experiments are described as
well as the experiments in detail together with plots diagrams and final results.
Overall five experiments are conducted according to a different purpose. For all of
them measurements from the MGEX stations network were used that allow the
possibility of Zero-Baselines formation. Data processing and results plotting is done
with use of MATLAB software. For receivers clock synchronization BERNESE
GNSS Software developed by Astronomical Institute of the University of Bern [21] is
used.
For the practical part following activities and experiments are made:
Gathering (e.g. downloading) of all data from the stations for a time period
of a year (2014)
Synchronization of receiver’s clocks
Zero-Baselines for all stations for a long period of time (several
combinations)
Zero-Baselines for 3 days for each station with all possible satellite
combinations
Comparison of 30sec and 1sec data results for 3 days
Fourier Transformations with all possible satellite combinations
Fourier Transformations for one station over a long time period
Differences using E1 and E5a frequencies
19
2.1 Experiment Settings
For the experiments done in this thesis MGEX stations are selected that can be
used for Zero-Baseline formations. In order to select such stations the two receivers
have to be connected to the same antenna (e.g. same antenna number). Table in
Appendix A shows the MGEX stations that offer such possibility, their characteristics
(receivers, GNSS systems measured, agencies etc.) and other further details.
Generally, when forming a zero-baseline test, it is high likely that the
compared receivers are asynchronous with each other. In this case the differentiation
is not possible to be done because measurements are referring to different epochs. A
clock synchronization procedure is therefore essential. For example, when comparing
a receiver A (that measures at epoch tA) to a receiver B (that measures at epoch tB)
and forming a range difference (with respect to tB) following equation (2.1) is valid:
∆𝜌𝐴𝐵𝑠 (𝑡𝐵) = 𝜌𝐴
𝑠 (𝑡𝐵) − 𝜌𝐵𝑠 (𝑡𝐵) (2.1)
Where 𝜌𝐴𝑠 (𝑡𝐵) and 𝜌𝐵
𝑠 (𝑡𝐵) are the range measurements at time tB for receiver
A and B respectively. But also, since the receivers are asynchronous, then the range
𝜌𝐴𝑠 (𝑡𝐵) can be further written as:
𝜌𝐴𝑠 (𝑡𝐵) = 𝜌𝐴
𝑠 (𝑡𝐴) + ∆𝜌𝐴𝑠 (𝑡𝐴) (2.2)
It is therefore seen that there is a remaining term ∆𝜌𝐴𝑠 (𝑡𝐴) that refers to the
range difference between the two epochs.
A way to apply a correction to the range (i.e. correcting the asynchronous
receivers) is by forming approximations, using a Taylor expansion.
𝜌(𝑡𝑛+1) = 𝜌(𝑡𝑛+∆𝑡) = 𝜌(𝑡𝑛) + �̇�(𝑡𝑛)∆𝑡 (2.3)
Where 𝜌(𝑡𝑛+1) is the range at epoch tn+1, 𝜌(𝑡𝑛) is the respective range at epoch
tn, �̇�(𝑡𝑛) is the range velocity and ∆𝑡 is the time difference between the two epochs.
As it is been observed from the equation (2.3), the values for radial velocity are
needed for the application of range correction.
These values can be found from RINEX data files. Having measurements for
the Doppler shift it is possible to obtain the required values for range velocity. The
following expressions are valid for Doppler shift ∆𝑓 values [22] :
∆𝑓 = 𝑓𝑟 − 𝑓𝑠 = − 1
𝑐𝑣𝜌𝑓𝑠 = −
1
𝜆𝑠𝑣𝜌 (2.4)
𝑣𝜌 =𝑑𝜌
𝑑𝑡= �̇� (2.5)
20
Where 𝑓𝑠 and 𝑓𝑟 are the satellite and receiver emitted frequencies respectively,
𝑣𝜌 is the radial velocity as seen from the receiver, 𝜆𝑠 is the wavelength emitted from
the receiver and 𝜌 is the distance between the satellite and the receiver. The second
equation (2.5) shows that Doppler shift is a measure of radial velocity, and therefore a
measure of distance change with respect to time. Integrating over time the second
equation the following is valid [22]:
∆𝜌 = ∫ �̇�𝑑𝑡
𝑡
𝑡0
= − 𝜆𝑠 ∫ ∆𝑓𝑑𝑡
𝑡
𝑡0
= − 𝜆𝑠∆𝜑 (2.6)
Where ∆𝜑 is the phase difference that is given by (2.7) when measured in
radians, and by (2.8) in cycles. [22]
𝜑 = 𝜔𝑡 (2.7)
𝜑 = 𝑓𝑡 (2.8)
From the above equations and again Taylor expansions the equations for
corrected code (2.9) and phase measurements (2.10) in meters are computed:
𝑃(𝑡𝑛+1) = 𝑃(𝑡𝑛) + (−𝜆𝑠∆𝑓)∆𝑡 (2.9)
𝐿(𝑡𝑛+1)𝜆𝑠 = 𝐿(𝑡𝑛)𝜆𝑠 + (−𝜆𝑠∆𝑓)∆𝑡 (2.10)
The following table (Tab. 2.1) shows the station pairs that are used in this
thesis and the corresponding observation codes (as given from Rinex 3.02 version
description file (Appendix D)). For each station pair other frequencies apart from E1
and E5a are available but only for one receiver and not both. The files for receivers
USN4 and USN5 of station USN do not give Doppler information but, as seen in
Table (Tab. 2.2), are both connected to an external H-Maser clock (accurate clock)
and therefore they can be considered synchronized. In the second following table
(Tab. 2.2) the corresponding clocks to the receivers are given for each station pair
used.
The very first step that is done is to download Rinex 3 data from MGEX
database. All data files are found from the following website
ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/rinex3. The year 2014 is
chosen for the experiments. For the compression and decompression of Hatanaka
Rinex files a free software is used called CRX2RNX provided from
http://terras.gsi.go.jp/ja/crx2rnx.html webpage. For receiver clock synchronization
some other files are needed (e.g. .CLK_05S, .EPH, .ERP, .DCB etc.) that are found
from ftp://ftp.unibe.ch/aiub/CODE/. The routine for receiver’s clock synchronization
is done using BERNESE software through a Bernese Processing Engine (BPE) for
each station for all files available for the selected year. The individual steps of the
routine can be found in appendices section (Appendix E).
21
Station Pair L1 freq. L5 freq. Other freq. Doppler
GOP6 C1X, L1X C5X, L5X C7X, L7X, C8Q, L8Q D1X
GOP7 C1X, L1X C5X, L5X - -
CONX C1X, L1X C5X, L5X - D1X
CONZ C1C, L1C C5Q, L5Q C7Q, L7Q, C8Q, L8Q D1C
USN4 C1C, L1C C5Q, L5Q C7Q, L7Q, C8Q, L8Q -
USN5 C1C, L1C C5Q, L5Q - -
UNBS C1C, L1C C5Q, L5Q C7Q, L7Q, C8Q, L8Q D1C
UNBD C1X, L1X C5X, L5X - D1X
WTZ2 C1C, L1C C5Q, L5Q C7Q, L7Q, C8Q, L8Q D1C
WTZ3 C1X, L1X C5X, L5X - D1X
SIN0 C1X, L1X C5X, L5X - D1X
SIN1 C1X, L1X C5X, L5X C7X, L7X, C8X, L8X D1X
Tab. 2.1: Observation codes for each station pair
Station
Pair Clocks Receiver
GOP6 External Cesium
LEICA GRX1200+GNSS
GOP7 JAVAD TRE_G3TH DELTA
CONX Internal
JAVAD TRE_G3TH DELTA
CONZ LEICA GRX1200+GNSS
USN4 External
H-Maser
SEPT POLARX4TR
USN5 NOV OEM6
UNBS Internal
SEPT POLARXS
UNBD JAVAD TRE_G2T DELTA
WTZ2 External H-
Maser EFOS 39
LEICA GR25
WTZ3 JAVAD TRE_G3TH DELTA
SIN0 Internal
JAVAD TRE_G3TH DELTA
SIN1 TRIMBLE NETR9
Tab. 2.2: Receivers and clocks for each station [23]
The result files for receiver clock synchronization give values for the Modified
Julian Date (MJD) and the corresponding correction of the receiver clock with respect
to GPS Time for every epoch. After creation of clock synchronization files, all files
that are gathered are corrected respectively for the experimentation.
22
2.2 Experiment 1: Combinations for all stations for a long time
In the first experimentation the goal is to have a general view of the results
coming from zero-baselines both with pseudorange and phase measurements in order
to examine main trends and/or any anomalous cases. A time period of one month
(January 2014) is chosen for all stations. The following table shows the signal and
satellite combinations for each station that is done.
Station Pair L1 freq. L5 freq. Satellites Satellites (PRN)
GOP6 C1X, L1X C5X, L5X 11/12 E11/E12
GOP7 C1X, L1X C5X, L5X
CONX C1X, L1X C5X, L5X 11/12 E11/E12
CONZ C1C, L1C C5Q, L5Q
USN4 C1C, L1C C5Q, L5Q 11/12 E11/E12
USN5 C1C, L1C C5Q, L5Q
UNBS C1C, L1C C5Q, L5Q 11/12 E11/E12
UNBD C1X, L1X C5X, L5X
WTZ2 C1C, L1C C5Q, L5Q 12/19 E12/E19
WTZ3 C1X, L1X C5X, L5X
SIN0 C1X, L1X C5X, L5X 11/12 E11/E12
SIN1 C1X, L1X C5X, L5X
Tab. 2.3: Combinations for experiment 1
Some sample plots are shown below for each station and measurement case
(code or phase). Because of the large number of resulted plots it is not possible for all
of them to be shown in the present document. Some example cases are shown for
individual days. The plots that are shown below correspond to satellite observations
for a specific signal, clock corrections, zero-baselines for phase and code
measurements. In the case of CONX/CONZ stations files are available only for the
first two days of the year 2014; hence no significant work could be done.
For the first station pair that was examined, GOP6/GOP7, it is seen that
satellites 11 and 12 are both visible simultaneously between time period 4.5 to 9 h
(Fig. 2.6). The example plot results that are chosen to be exposed in the present
document represent “good” days where the time frames of the used satellites are as
much coincident as possible (in this example 4.5 hours).
23
Fig. 2.1: Clock correction magnitude plots for GOP6/GOP7, doy: 017
The figure above (Fig. 2.1) shows the clock correction of the receivers of GOP
station pair. It is noticed that the magnitude of correction is not the same, as it is
applied to different types of receivers. For GOP6 receiver (LEICA GRX1200+GNSS)
the mean value of the time correction magnitude is – 602.8 μsec whereas for GOP7
(JAVAD TRE_G3TH DELTA) the respective magnitude is around 20.22 μsec value.
Oscillations of the correction are approximately in the order of 10-3
μsec.
In the plot of pseudorange zero-baseline for E1 frequency (Fig. 2.2), it is
observed that there is an oscillation with the form of noise in the order of 1 to 2 m
level (-0.5m to 0.5m). On the other hand in the respective plot for E5a (Fig. 2.3), it is
also observed a similar noisy behavior in the order of 0.5 to 1 m.
24
Fig. 2.2: Code zero-baseline for GOP6/GOP7 in frequency E1
Fig. 2.3: Code zero-baseline for GOP6/GOP7 in frequency E5a
25
Fig. 2.4: Phase zero-baseline for GOP6/GOP7 in frequency E1
Fig. 2.5: Phase zero-baseline for GOP6/GOP7 in frequency E5a
26
Fig. 2.6: Satellite observations for C1X signal
For the phase plots (Fig. 2.4 and Fig. 2.5) it is seen a pattern that consists of
two periodic oscillations, similar to the wave interference phenomenon. The first
fluctuation has a beat period of about 30 min and the second fluctuation of about 4.2
min. This pattern is not one that would normally be expected since all term in the
zero-baseline equation (1.12) are eliminated except from receiver noise and phase
ambiguities. It is worth mentioning that for all plots the mean value is calculated and
then erased from results to give finally a zero mean that is shown in these plots. This
is done because the interest is focusing on the oscillations of receiver noise and not to
the phase ambiguity term. The oscillations of phase plots have a magnitude of the
order of 1 cm. This behavior of oscillations keeps appearing during the whole period
of the examined one month, giving similar plots. In order to analyze more this
behavior, Fourier transformations are made in following experiments (Experiments 4
and 5).
Similar are the plots of station USN. The pseudorange zero-baseline plot (Fig.
2.7) for E5a frequency shows an oscillation of around 1 meter magnitude and the
phase zero-baseline plot (Fig. 2.8) shows the same periodical pattern of two
fluctuations of 30 min and around 4 min as in the previous station. As for receiver’s
clock correction, the following figures (Fig. 2.9 and Fig. 2.10) show that the
variations of clock correction for both receiver clocks are in the order of 0,004 μsec.
In the second plot it is shown the magnitude of correction: 0.09 μsec for SEPT
POLARX4TR receiver and 0.16 μsec for NOV OEM6 receiver. It is therefore
deduced that those two clocks are very good synchronized with GPS time as they give
values of clock correction in the order of 0.1 μsec. This is due to the use of an external
Active Hydrogen-Maser (AHM) atomic clock that synchronizes them [23].
27
Fig. 2.7: Code zero-baseline for USN4/USN5 in frequency E5a
Fig. 2.8: Phase zero-baseline for USN4/USN5 in frequency E5a
28
Fig. 2.9: Magnitude of clock correction USN4/USN5 (a)
Fig. 2.10: Magnitude of clock correction USN4/USN5 (b)
29
Fig. 2.11: Code zero-baseline for UNBS/UNBD in frequency E5a
Fig. 2.12: Phase zero-baseline for UNBS/UNBD in frequency E1
30
Fig. 2.13: Magnitude of clock correction UNBS/UNBD
For the station UNB plots (Fig. 2.11 and Fig. 2.12) show a similar behavior as
the previous stations. For the code zero-baseline the noise oscillation is in the order of
m, whereas in the phase zero-baseline the same periodic pattern is observed. In the
plot of clock corrections magnitude (Fig. 2.13) it is showed that the two clocks (SEPT
POLARXS for UNBS and JAVAD TRE_G2T DELTA for UNBD) oscillate
periodically with a magnitude of 1 msec (-500 to 500 μsec). For UNBS the oscillation
happens approximately every 38 sec (13 periods within 500 sec) while on the contrary
for UNBD happens a little more than 500 sec (around 550 sec).
The next plots that follow (Fig. 2.14, Fig. 2.15 and Fig. 2.16) are showing the
situation of WTZ2/WTZ3, but with the difference that the measurements coming from
other satellite combination (12, 20) used for the computations of the zero-baselines.
For the pseudorange zero-baseline it is observed a noisy behavior as in the other
station cases with a magnitude of oscillation around 2 m. For the phase zero-baselines
high and low peaks are observed that alternate periodically with a period of about 4.2
min.
For the plots of clock correction it is seen that the one receiver clock (of
WTZ2 receiver LEICA GR25) is quite accurate giving magnitudes of -0.04 μsec for
clock correction. On the other hand the other receiver (JAVAD TRE_G3TH DELTA
in WTZ3) gives much bigger values for the magnitude, around -284.72 μsec. Similar
plots are observed through the whole time period of the examined month.
31
Fig. 2.14: Code zero-baseline for WTZ2/WTZ3 in frequency E1
Fig. 2.15: Phase zero-baseline for WTZ2/WTZ3 in frequency E5a
32
Fig. 2.16: Magnitude of clock correction WTZ2/WTZ3
The last station that was examined was SIN. The combination that was
examined is using satellites 11 and 12. Similar to the previous station cases using the
same satellites, it is seen that the pseudorange keeps again in this case a noisy form
that has a fluctuation magnitude in the order of a meter approximately (Fig. 2.17). For
the phase zero-baseline difference plot the pattern that appeared in the other station
appears here (Fig. 2.18) again, with same periods and order of oscillation magnitude.
For the clock correction plot (Fig. 2.19), it is observed that the one receiver
(TRIMBLE NETR9 of station SIN1) has an accurate clock giving values for clock
correction within -0.02 and -0.06 μsec. The other one (JAVAD TRE_G3TH DELTA
of SIN0) shows fluctuations with a magnitude of 1 msec (-500 to 500 μsec) with a
period of approximately 20 min.
33
Fig. 2.17: Code zero-baseline for SIN0/SIN1 in frequency E5a
Fig. 2.18: Phase zero-baseline for SIN0/SIN1 in frequency E5a
34
Fig. 2.19: Magnitude of clock correction SIN0/SIN1
The main conclusion of the first experiment is that in all station cases similar
plots are seen through the whole one month period that was examined. This means
that the same behavior holds.
In the case of phase plots with satellites 11 and 12, it is not expected to see
such periodical oscillations. This phenomenon appears in both E1 and E5a
frequencies. The behavior resembles to a beat signal.
Fig. 2.20: Representation of beat signal [24]
35
From physics theory, it is known that a beat signal appears when two signals
with similar frequency are combined to one (Fig. 2.20). The equations for
contributing signals Y1 and Y2 (assumed to have same amplitude) to the new signal
Ytotal are the following [24]:
𝑌1 = 𝐴 ∙ cos(2𝜋𝑓1)𝑡 (2.11)
𝑌2 = 𝐴 ∙ cos(2𝜋𝑓2)𝑡 (2.12)
𝑌𝑡𝑜𝑡𝑎𝑙 = 𝑌1 + 𝑌2 = 𝐴{cos(2𝜋𝑓2)𝑡 + cos(2𝜋𝑓2)𝑡} (2.13)
Where f1 and f2 are the frequencies of each signal respectively. Equation (2.13)
can be further written using trigonometrical identity (2.14) and substitutions (2.15) as
[24]:
cos(𝑎 + 𝑏) + cos(𝑎 − 𝑏) = 2cos 𝑎 cos 𝑏 (2.14)
𝑎 + 𝑏 = 2𝜋𝑓1𝑡 , 𝑎 − 𝑏 = 2𝜋𝑓2𝑡 (2.15)
𝑌𝑡𝑜𝑡𝑎𝑙 = 2𝐴{cos (2𝜋(𝑓1 + 𝑓2
2)) 𝑡 ∙ cos (2𝜋(
𝑓1 − 𝑓2
2)) 𝑡} (2.16)
In order to justify if the pattern seen in phase differences (with satellites 11
and 12) resembles to the beat signal, a signal was constructed in Matlab (Fig. 2.21)
using the frequencies that where observed (i.e. 30 min for beat period and 4 min).
Equation (2.16) was used but in a more general form (2.17):
𝑌𝑡𝑜𝑡𝑎𝑙 = 2𝐴{cos(2𝜋(𝛼))𝑡 ∙ cos(2𝜋(𝛽))𝑡} (2.17)
The signal has as input parameters frequencies α=1/(60 min), (2 times 30 min
for a full period) and β=1/(4 min), with amplitude A=1 cm. The following plot (Fig.
2.21) show that indeed the pattern of the constructed beat signal looks like the one
observed in the phase differences. When measuring in the plot the period of the beat it
is indeed noticed that the beat period is 30min and the inside periods are of 4 min.
It is essential that further experiments be done for the calculation of the initial
contributing frequencies f1 and f2, and the causes why in a zero baseline test there are
two signals that are combined. Such pattern is not expected at all with a zero baseline
test. Further details are found in the following experiments about Fourier
transformations.
In order to examine these fluctuations it is also important that another
experiment be done that deals with all satellite combinations to see under which
circumstances they appear.
36
Fig. 2.21: Beat signal constructed in Matlab
37
2.3 Experiment 2: Satellite combinations for each station
Taking into consideration the resulted plots from the first experiment, the idea
of this second experiment is to examine how and under which circumstances these
oscillations appear in phase measurement zero-baselines. The main idea is to check all
possible satellite combinations for both E1 and E5a, for 3 representative “good” days
of each station. The tested days with respect to stations are shown in the following
table:
Station
Pair DOY
GOP6 14, 37, 61
GOP7
USN4 5, 16, 29
USN5
UNBS 5, 9, 12
UNBD
WTZ2 7, 10, 128
WTZ3
Tab. 2.4: Parameters of second experiment
Again in this experiment the plots that are made are too many to be shown all.
For this reason some have been selected to represent each satellite combination
regardless of day and station.
For the combination of satellites 11 and 12 (Fig. 2.22 and Fig. 2.23) it is
observed a behavior seen in the previous experiment with the two fluctuations (beat
signal). These oscillations are observed for both frequencies as well as for all
examined cases. For the GOP6/GOP7 stations the oscillations have a period of
approximately 33 min and 4 min with maximum magnitude of oscillation from -0.8 to
0.8 cm. For the WTZ2/WTZ3 stations the oscillations also have a period of around 34
min and 4 min with a maximum magnitude of oscillation from -0.5 to 0.5 cm. For the
rest of the plots that could not be displayed the same periods are observed with
different magnitudes of oscillation. This gives the conclusion that those periods of
oscillation are stable for this used satellite combination.
For the second pair of satellites combination (11/19) the plots of the results
(Fig. 2.24 and Fig. 2.25) show a noisy behavior resembling to an oscillation that is not
that clearly distinguishable. This was the case for all the days and stations that are
examined. The magnitude interval is changing depending on each case.
38
Fig. 2.22: Phase zero-baseline for GOP6/GOP7 in frequency E5a for 11/12 satellites
Fig. 2.23: Phase zero-baseline for WTZ2/WTZ3 in frequency E1 for 11/12 satellites
39
Fig. 2.24: Phase zero-baseline for UNBS/UNBD in frequency E1 for 11/19 satellites
Fig. 2.25: Phase zero-baseline for USN4/USN5 in frequency E5a for 11/19 satellites
40
Fig. 2.26: Phase zero-baseline for USN4/USN5 in frequency E5a for 11/20 satellites
Fig. 2.27: Phase zero-baseline for WTZ2/WTZ3 in frequency E5a for 11/20 satellites
41
The next combination is done using satellites 11 and 20 (Fig. 2.26 and Fig.
2.27). In this case it is shown an oscillation for stations WTZ2/WTZ3 with a period of
4 min.
For the next two satellite combinations 12 and 19 (Fig. 2.28 and Fig. 2.29) a
similar oscillation is observed like before but not that distinct. The period is again
around 4 min. This behavior is also observed in the other plots that are made.
Same is the case for 12 and 20 satellite combination plots (Fig. 2.30 and Fig.
2.31). It is seen an oscillation but not so clear with a period of 4 to 4.5 min. This
behavior is seen as well in the other cases that were examined.
The last satellite combination is between satellites 19 and 20 (Fig. 2.32 and
Fig. 2.33). All the cases of this combination that are examined do not show any type
of oscillation but a random noisy behavior.
Fig. 2.28: Phase zero-baseline for USN4/USN5 in frequency E1 for 12/19 satellites
42
Fig. 2.29: Phase zero-baseline for UNBS/UNBD in frequency E5a for 12/19 satellites
Fig. 2.30: Phase zero-baseline for UNBS/UNBD in frequency E1 for 12/20 satellites
43
Fig. 2.31: Phase zero-baseline for USN4/USN5 in frequency E5a for 12/20 satellites
Fig. 2.32: Phase zero-baseline for UNBS/UNBD in frequency E5a for 19/20 satellites
44
Fig. 2.33: Phase zero-baseline for USN4/USN5 in frequency E1 for 19/20 satellites
From the plots of this experiment it is deduced that the oscillations appear in
certain satellite combinations and not to all (not for 19/20). Oscillations are observed
in combinations of 11/19, 11/20, 12/19, and 12/20. Furthermore these oscillations are
regardless to signals, days of the year and stations (i.e. receiver types). In the case of
satellite combination 11 and 12 there are two oscillations that appear: one with bigger
beat period of 33 min and one with smaller time period of 4 min.
After completion of this experiment it is shown that more investigation needs
to be done in order to examine the parameters of these oscillations and if possible the
causes of the appearance of the oscillations. From a theoretical point these oscillations
should not appear since by performing a zero-baseline test with phase measurements
only the integer multiple of the carrier wavelength and the doubled noise factor
remain.
In order to check is these oscillations appear not only in 30 sec measurement
files but also 1 sec files, the next experiment is done.
45
2.4 Experiment 3: Comparison of 1sec and 30sec data file results
The following experiment has as a goal to investigate whether files with time
step 30 sec (used in previous experiments) give the same oscillation for satellites 11
and 12 as files with time step 1 sec. The goal is to examine whether these oscillations
appear in both cases and not only in the 30 sec measurement file because of the
sampling time interval. For this experiment GOP6/GOP7 station is considered and
zero-baseline results are compared for days 14, 37, and 61.
The 1 sec files are available as ‘high rate’ from the website:
ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/highrate/rinex3/2014/. The
files are grouped in every hour and give the measurements for every 15 min. There is
a special naming way of the files: each hour has a letter that is representing starting
from ‘a’ for the first hour of the day and then two digits are following representing the
quarter of the hour (e.g. ‘00’, ‘15’, ‘30’ and ‘45’). In order to compare the two file
types with each other it is essential to find the time overlaps of the satellites (i.e. the
time period of interest) and combine the 15 min files to a single one. Some of the
plots made are shown below.
Fig. 2.34: Comparison results of day 14 in E1 frequency
46
Fig. 2.35: Comparison results of day 37 in E5a frequency
Fig. 2.36: Comparison results of day 61 in E5a frequency
47
It is observed that the 1 sec sampling files also show those two oscillations as
the 30 sec files. Therefore the behavior observed is irrelevant from the sampling time
period intervals.
In order to examine more this pattern it is important to analyze the two
frequencies that are contributing and causing it. The following two experiments are
dealing with investigating these frequencies through Fourier Transforms.
48
2.5 Experiment 4: Fourier Transformations (satellite combinations)
In this experiment, the goal is to examine which are the two contributing
frequencies that are causing the pattern shown in phase zero-baseline tests with
satellites 11 and 12. Also it is important to check all possible satellite combinations in
order to observe in which cases the differences are following a periodic oscillation
and with which frequency.
For this experiment the following stations and days where examined as
showed in the table:
Station DOY
USN4/USN5 32, 15
UNBS/UNBD 62, 99
GOP6/GOP7 17, 30
WTZ2/WTZ3 37, 20
SIN0/SIN1 14, 2
Tab. 2.5: Stations and days used for experiment 4
Again it is not possible for all the plots to be shown in this document. Sample
plots are given for each satellite combination. There is a general trend that is observed
for each satellite combination.
For satellite combination 11 and 12 the following graphs show that there are
two frequencies contributing (i.e. two peaks). In the first graph (Fig. 2.37) the highest
peak occurs at 4.211 min period with amplitude of 0.2634 cm, while the second peak
occurs at 3.737 min period with amplitude of 0.1581 cm respectively. In the second
graph (Fig. 2.38) for frequency E5a, the highest peak occurs around 4.25 min with
amplitude of 0.2128 cm and the second peak happens at 3.662 min period with
amplitude 0.1608 cm. Those numbers are changing slightly according to days stations
and frequencies but these two peaks are showing in all cases.
For the second satellite combination (i.e. satellites 11 and 19) it is observed
only one peak (i.e. one main frequency). In the plot Fig. 2.39 of frequency E1 the
peak occurs at 3.657 min period giving amplitude of 0.3057 cm, whereas in Fig. 2.40
for E5a frequency the peak occurs at 3.71 min period giving 0.1585 cm amplitude.
One peak also occurs to the third (i.e. 11 and 20) satellite combination, with
similar period and amplitude. In the plot Fig. 2.41 the peak occurs at 3.746 min with
amplitude of 0.1456 cm, whereas in the plot Fig. 2.42 the peak occurs at 3.711 min
with amplitude of 0.3194 cm.
49
Fig. 2.37: Fourier Transform of satellites 11 and 12 in E1 frequency
Fig. 2.38: Fourier Transform of satellites 11 and 12 in E5a frequency
50
Fig. 2.39: Fourier Transform of satellites 11 and 19 in E1 frequency
Fig. 2.40: Fourier Transform of satellites 11 and 19 in E5a frequency
51
Fig. 2.41: Fourier Transform of satellites 11 and 20 in E1 frequency
Fig. 2.42: Fourier Transform of satellites 11 and 20 in E5a frequency
52
Fig. 2.43: Fourier Transform of satellites 12 and 19 in E1 frequency
Fig. 2.44: Fourier Transform of satellites 12 and 19 in E5a frequency
53
Fig. 2.45: Fourier Transform of satellites 12 and 20 in E1 frequency
Fig. 2.46: Fourier Transform of satellites 12 and 20 in E5a frequency
54
Fig. 2.47: Fourier Transform of satellites 19 and 20 in E1 frequency
Fig. 2.48: Fourier Transform of satellites 19 and 20 in E5a frequency
55
For the combinations of satellite 12 (i.e. combination 12/19 and 12/20), the
resulted plots also show one peak; one occurring frequency. In the plot Fig. 2.43 the
peak is happening at 4.21 min period with 0.4718 cm amplitude, whereas in the plot
Fig. 2.44 the peak occurs at 4.281 min period with 0.4284 cm amplitude.
In the second satellite combination (12/20), in the plot Fig. 2.45 the peak
occurs at 4.186 min with amplitude of 0.1771 cm while on the other hand in Fig. 2.46
the peak occurs at 4.317 min period with amplitude of 0.3319 cm.
For the satellite combination 19/20 plots Fig. 2.47 and Fig. 2.48 show that
there is no peak and therefore no major frequency.
From this experiment and the plots that are shown there is the conclusion that
satellites 11 and 12 are responsible of the frequencies that are observed. In the 11/12
combination there are two peaks observed while in the others of one of the two there
is one peak. In the 19/20 combination no peak is seen.
Generally it can be said that satellites give frequencies with the following
periods and amplitudes:
- E11: Period around 3.7 min with approximately 0.15 – 0.3 cm amplitude
- E12: Period around 4.2 min with approximately 0.2 – 0.5 cm amplitude
- E19: None
- E20: None
Back to the constructed signal of experiment 1, it is now possible to test the
frequencies that were found for E11 and E12 with use of equation (2.16). The signal
has as input parameters frequencies f1=1/(3.7 min), and f2=1/(4.2 min), with amplitude
A=1 cm. The beat signal it shows also the oscillations that were observed in phase
zero baselines and is showing in the following plot (Fig. 2.49).
Performing a Fourier transform (Fig. 2.50) it is also observed that there are
two peaks occurring at the same periods (4.2 and 3.7 min) as found before for
satellites 12 and 11.
It is therefore justified that the oscillations on phase zero baselines are beat
signals created by frequencies f1 and f2. All experiments so far show that this behavior
is caused somehow by satellites 11 and 12, since the beat signal is not related to
receiver types, stations, days of year and carrier frequencies (E1 or E5a). General
hypothesis about what is causing this frequencies are given in the general conclusions
after all the experiments.
56
Fig. 2.49: Beat signal constructed in Matlab (2)
Fig. 2.50: Fourier transform of beat constructed signal
The focus now is to examine the behavior of the amplitude and the time period
of the peaks over a long period of time to examine general trends in order to exclude
some further conclusions. For this reason experiment 5 that is following deals with
this.
57
2.6 Experiment 5: Fourier Transformations (for longer time periods)
In the present experiment the goal is to observe general trends of the two
occurring frequencies for the satellite combination 11/12 over a long time period. For
this case stations USN4/USN5 were chosen for the long time analysis, mainly because
there are not many days of missing data. More specifically there exist data for all days
of year 2014 that are essential for long time processing.
From all the plots of each individual day, the two peaks (period, amplitude)
values are stored in a matrix and at the end of the processing the values for the longer
time series (here 170 days). The longer time plots are shown below.
In plots Fig. 2.51and Fig. 2.52 it is shown the long term behavior of the first
and second peak periods. It is observed that the two peaks interchange with each
other. This means that during Fourier transformation the peaks (i.e. amplitude values)
are interchanged somehow. A probable explanation to this might be the duration of
time overlap (analyzed further). Another remark that is important is that there are
observed slopes of the lines both for 4.2 min period and 3.7 min period. This
observation needs more tests and plots and it is described later on.
Fig. 2.51: Period for 170 days for E1
58
Fig. 2.52: Period for 170 days for E5a
Fig. 2.53: Amplitude [cm] for 170 days for E1
59
Fig. 2.54: Amplitude [cm] for 170 days for E5a
From the amplitude plots (Fig. 2.53 and Fig. 2.54) it is observed that the
values of the amplitudes are not steady over time. A fluctuation (noisy behavior) is
observed, but generally around a mean number. In E1 carrier frequency the mean
values are 0.1821 cm for the 1st peak (satellite 12) and 0.1548 cm for 2
nd peak
(satellite 11). In E5a carrier frequency the mean values are 0.1969 cm for the 1st peak
and 0.1641 cm for 2nd
peak. It is seen that the noisy lines often overlap with each
other. This also shows the interchange of peaks (as seen from period plots Fig. 2.51
and Fig. 2.52).
A hypothesis about the interchange of peaks is the duration of satellite time
overlap. When the duration of time overlap is around 4-6 hours then the Fourier
transform has many data for the calculation if the peaks (and the resulted curve is
smoother), whereas if the duration is short (e.g. 1-2 hours) the Fourier transform does
not have many data (curve is not smooth). An example is given bellow to illustrate
how the duration of time overlap affects the results of the amplitude. In plots Fig. 2.55
and Fig. 2.56 show a day when there was only 1.5 hours of overlap. As it is seen the
Fourier Transformation curve is not that detailed and the peaks (i.e. amplitude valued)
are reversed.
60
Fig. 2.55: Double difference of a day with small time overlaps duration
Fig. 2.56: Fourier Transformation of a day with small time overlaps duration
61
Other plots are made that show the relation between time overlap duration and
values of period (Fig. 2.57). For these plots also the first 170 days are used. The
points are then divided in two groups (limit value is 4 min period) to calculate the
mean period values. In E1 carrier frequency, mean values are 4.3011 min (satellite 12)
and 3.6964 (satellite 11), whereas in E5a values are 4.3013 min and 3.6948 min.
Fig. 2.57: Period values with respect to time overlap duration
In order to prove that the duration of time overlap affects the values of the
amplitude following plots and histograms are made.
In the plot for the 1st peak (blue points) (Fig. 2.58) it is seen that more values
appear (more than 10 points for each half hour bin) in the group of points over 4 min
when duration is more than 4 hours (histogram skewed left). Similarly, the number of
points that are under the 4 min limit (second histogram of this plot) is more or less the
same (less than 5 points regardless the duration in hours). This means that these
points are classified to the 4 min period and that the probability of a point belonging
to the 4 min class gets higher with longer duration of time overlap. Similar are the
conclusions for the corresponding plot for the 2nd
peak (Fig. 2.59).
Another remark that is observed in the first plots (Fig. 2.51 and Fig. 2.52) that
is worth examining is the slope. In order to examine this better other plots are made
(Fig. 2.60, Fig. 2.61, Fig. 2.62, Fig. 2.63) with other satellite combinations (11/19 and
12/19) to avoid these peak interchanges. The plots show the relation of period of the
peaks with respect to days. For all the plots made a time sample of 70 days is showed.
In all the plots a slope is observed, negative for satellite 11 and positive for satellite
12. Also with the help of Least Squares Estimation line approximations are calculated
(Tab. 2.6) that give the values of slope and the y intercept for each case.
62
Fig. 2.58: Histograms for Period values for 1st peak in E5a
Fig. 2.59: Histograms for Period values for 2nd
peak in E5a
63
Fig. 2.60: Period values in E1 for 11/19
Fig. 2.61: Period values in E5a for 11/19
64
Fig. 2.62: Period values in E1 for 12/19
Fig. 2.63: Period values in E5a for 12/19
65
Satellites Frequency Line Equation
y=αx+β σα [10
-6] σβ [min]
11/19 E1 y=-0.0013x+3.7298 2.6530 0.0044
11/19 E5a y=-0.0017x+3.7371 2.5326 0.0040
12/19 E1 y=0.0019x+4.1698 1.2380 0.0020
12/19 E5a y=0.0020x+4.1644 1.2694 0.0021
Tab. 2.6: Results of periods and amplitudes
The main conclusion drawn from this experiment is that there are no standard
values for each station and frequency with respect to time. This is mainly because of
the overlaps time of the satellites examined and because of the slopes that are
observed. The fact that there are slopes in values of period over time for both 11 and
12 satellite shows that the frequencies that are contributing to the beat signal are
changing over the days. For satellite 12 the period values are getting bigger (hence
value of frequency is getting smaller) and for satellite 11 period values are getting
smaller (hence value of frequency is getting bigger).
From plots Fig. 2.60, Fig. 2.61, Fig. 2.62 and Fig. 2.63 it is observed that for
many days the points are the same for the two carrier frequencies. This behavior
brings the need to examine whether the two major peaks are the same for E1 and E5a
frequency for a particular day. For this reason the next experiment deals with
differences between carrier frequencies.
66
2.7 Experiment 6: E1-E5a (L1-L5) Differentiation
From the result from the previous experiments, there is the idea to do E1-E5a
differentiation to see if any conclusion can be drawn. Applying frequency E1-E5a
differentiation results a geometry free linear combination and following equation is
valid:
𝐿1 − 𝐿5 = −I (1 −𝑓1
2
𝑓52) + 𝜆1𝑁1 − 𝜆5𝑁5 (2.18)
As it is seen from the equation geometry term, clock corrections and non-
dispersive errors are removed, while ionosphere and phase ambiguities remain.
The stations that were selected for this experiment are USN4 and USN5, for
day 55 for the satellite combination 11/12. Following differences were conducted:
(𝐿1 − 𝐿5)𝑠𝑎𝑡/𝑟𝑒𝑐 (2.19)
(𝐿1 − 𝐿5)𝑠𝑎𝑡11 − (𝐿1 − 𝐿5)𝑠𝑎𝑡12 (2.20)
(𝐿1 − 𝐿5)𝑟𝑒𝑐1 − (𝐿1 − 𝐿5)𝑟𝑒𝑐2 (2.21)
[(𝐿1 − 𝐿5)𝑠𝑎𝑡11/𝑟𝑒𝑐1 − (𝐿1 − 𝐿5)𝑠𝑎𝑡12/𝑟𝑒𝑐1] −
(𝐿1 − 𝐿5)𝑠𝑎𝑡11/𝑟𝑒𝑐2 − (𝐿1 − 𝐿5)𝑠𝑎𝑡12/𝑟𝑒𝑐2 ] (2.22)
Some of the plots that are made are shown below. Plots Fig. 2.64 and Fig. 2.65
show the curve of the differentiation applying equation (2.19) and (2.20). In the plots
Fig. 2.66 and Fig. 2.67, equation (2.21) is applied for both satellites. In those two
figures the two frequency oscillation pattern is not seen as before. It is observed a
noisy figure curve. This is also the case for the differentiation of all measurements
(plot Fig. 2.68) that is expressed by the equation (2.22). In order to justify whether
there is an occurring periodic phenomenon a Fourier transformation is also done (plot
Fig. 2.69). In the latter plot no peak is observed like the ones from experiment 4 and
5. This leads to the conclusion that the periodic phenomena caused by E1 and E5a
differentiation are cancelled out, i.e. that the periodic phenomena are the same. Hence
there must be the same period for the satellite 11 and 12 for both carrier frequencies.
67
Fig. 2.64: E1-E5a for satellite 11 and USN4
Fig. 2.65: Difference of satellites for USN4
68
Fig. 2.66: Difference of stations for satellite 11
Fig. 2.67: Difference of stations for satellite 12
69
Fig. 2.68: Differentiation of both satellites and both receivers
Fig. 2.69: Fourier transform of the differentiation
70
Conclusions
Finally, in this subchapter the most important conclusions deduced from this
thesis are presented.
From the theoretical part, it is concluded that the European GNSS system,
Galileo has already four satellites (IOV) in orbit that allow performance testing and
analysis of the system. These satellites have on board very accurate passive hydrogen
maser clocks.
Performance testing can be done using the MGEX stations network that
provides users with high-quality of data on a daily basis. MGEX network consists of
nearly 120 stations equally distributed worldwide. Through the MGEX website it is
possible to obtain data from not only Galileo, but also from GPS, GLONASS,
BeiDou, QZSS and SBAS.
Testing can be done by forming differences and linear combinations. One
important case is the so-called zero baseline test. It is a case of a double difference
when using the same antenna connected to the two receivers. This difference has the
identity that it is a geometry-free and ionosphere-free combination. All error sources
are eliminated (i.e. geometry, satellite and receiver clock errors, tropospheric and
ionospheric delays) except from the noise (that is doubled) and the integer multiple of
the carrier wavelength. It is a useful tool while conducting performance experiments.
From the practical part, there are several conclusions corresponding to each
experiment.
From the first and the second experiments, is it concluded that the behavior of
each station case when performing zero-baseline test remains steady over time (days).
A periodic pattern is observed that is characteristic to the combination with 11 and 12
satellites. It is a pattern consisting of two oscillations; the first one has a period of
approximately every 4.2 min and the beat period is nearly every 30 min.
For the other satellite combinations (11/19, 11/20, 12/19, 12/20) also some
periodic oscillations with a period of 4-4.5 min are observed but not that easily
distinguishable. Finally the satellite combination 19/20 is the only one that resulted to
a noisy behavior. This results lead to the idea that it is the satellites that are causing
such periodic phenomena (more specifically a beat signal when 11/12 satellite
combination is examined) and not the stations, receivers, carrier frequencies and
different processing days, since the results show the same curves for all of those cases
examined.
In the third experiment a comparison between 1 sec and 30 sec files is done to
examine whether this pattern is affected or produced by the time sampling interval.
The conducted plots show no differentiation between the files. The same two
oscillation pattern occurs to both types of files.
71
In the experiments 4 and 5, Fourier transformations are made for the better
examination of those occurring periodic phenomena. From all the combinations of
days and satellites it is concluded that it is indeed the satellites that are causing those
oscillations in both E1 and E5a carrier frequency.
From experiment 4, it is deduced that zero baselines when using satellites 11
and 12 show periodic oscillations. When using satellite 11, period is around 3.7 min
with approximately 0.15 – 0.3 cm amplitude. Likewise, when using satellite 12,
period is around 4.2 min with approximately 0.2 – 0.5 cm amplitude. On the contrary
when performing zero baselines with satellites 19 and 20 no periodic oscillations are
occurring.
From experiment 5, it is observed that values for period with respect to days of
year can be approximated with a line that a slope. For values coming from
combinations with satellite 11 the slope is negative around -0.001 and for values
coming from combinations with satellite 12 the slope is positive around 0.002. This
means that the initial signals that contribute to the total beat signal are also changing
over the days (period).
Finally, the last experiment was about forming differences using both carrier
frequencies E1 and E5a (L1 and L5). The difference using 11 and 12 satellites showed
no periodic patterns in this case and no major occurring frequency after Fourier
transformations. Hence values of the peaks for period are the same regardless the
carrier frequency.
Overall, from all the experiments it can be deduced that the first two IOV
satellites (E11 and E12) are the reason of these occurring periodic patterns in zero-
baseline plots. From all the experiments made using different cases of carrier
frequencies, receiver types, observation types, stations and days of year, the
oscillations are seen always when examining those satellite measurements and their
combinations with other ones (with 19 or 20).
A good hypothesis for the reason for this phenomenon could be the satellite
clocks of those satellites. This is quite unexpected since a zero-baseline test by theory
eliminates all satellite clock errors. Conducting a zero baseline is a geometry-free and
ionosphere-free combination that eliminates also all other positioning errors or terms
(i.e. range, ionosphere effects, tropospheric effects, multipath, receiver clock errors
etc.). The fact that there is a periodic pattern shown leads to the conclusion that some
errors-effects that are supposed to be eliminated maybe are not.
From all those positioning terms and errors there are some that are excluded
from the hypothesis. For example, multipath is a type of error that is not periodic and
it should occur to all satellite combinations. Range and ionosphere effects are also
excluded since a zero-baseline is geometry-free and ionosphere-free combination.
Also, the ionospheric and tropospheric effects are not periodic. Receiver clock errors
are also excluded since all receivers are synchronized with respect to the GPS time. In
72
addition if any receiver caused error is the case it should show also for the other
satellite combinations and it would be changing according to stations (because
stations are connected to different receiver types).
From the experiments it is shown that it is the first two satellites that show an
oscillation. Examining all possible satellite errors (e.g. satellite clocks, orbits,
antennas), the only error that can have a periodic behavior are ones related to the
satellite clocks. Furthermore, because the clock corrections are varying with time, the
clock correction is eliminated by forming differences (i.e. single differences) only if
the measurements are acquired at the same epochs. The observed oscillations
however, cannot be caused by the satellite clocks since a zero-baseline test is a
geometry linear combination.
A hypothesis of the oscillations caused might be that the satellite signal is
affected by a type of rapid oscillation of the clock frequency and the receivers cannot
detect it because they are measuring at a different phase if they are not perfectly
synchronized.
73
Suggestions
In the present Master thesis, a number of experiments were conducted giving
results useful for any other type of experimentation. However, research about the
GNSS data analysis does not stop here. Further research can be done for justification
and further investigation. Some ideas are presented below for anyone that is interested
in the present research topic:
Setting of a zero-baseline test with several receivers (of the same type model
or different) on order to examine and compare the results with the MGEX
network measurement data. Using two receivers of the same type means that
the same algorithms for positioning are used (and therefore same algorithms
for computation of the multipath). This is truly interesting to examine whether
there are differences between zero-baselines using the same and/or different
types of receivers.
Performing differences with MGEX stations that are connected to the same
type model. One case is the GOP6/GOP7 and CONX/CONZ stations, because
they are connected to a LEICA GRX1200+GNSS and a JAVAD TRE_G3TH
DELTA receiver. It could also be possible to examine the Fourier transforms
over a time period of one year (as experiment 5) for the calculation of the
mean values of period and amplitude.
Analysis of GNSS data from FOC satellites, in a similar way as in the present
thesis project. This will help to examine and see whether zero-baselines from
measurements from the FOC satellites show the same beat signal behavior as
IOV satellites E11 and E12.
Fourier Transformations for a longer period (e.g. 1-2 years) and from many
stations in order to get a more general view of the attitude of the amplitudes
and periods of the peaks and a more accurate line approximation.
74
References
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Information. [Accessed 03 2015].
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(http://www.esa.int/Our_Activities/Navigation/The_future_-
_Galileo/The_first_four_satellites). [Accessed 03 2015].
[10] A. Cameron and T. Reynolds, "Power Loss Created Trouble Aboard Galileo
Satellite," GPS World: The business and technology of GNSS, 08 07 2014.
[Online]. Available: http://gpsworld.com/trouble-aboard-galileo-satellite/.
[Accessed 03 2015].
[11] J. Hahn, "Galileo IOV - ESA Galileo Project," Dubai, 2013.
75
[12] ESA, "Galileo System," 16 08 2007. [Online]. Available:
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[Accessed 2015].
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www.esa.int/Our_Activities/Navigation/The_future_-
_Galileo/Launching_Galileo/In-orbit_testing2. [Accessed 03 2015].
[14] "Orbital and Technical Parameters," European GNSS Service Centre (GSC), 01
05 2013. [Online]. Available: http://www.gsc-europa.eu/system-status/orbital-
and-technical-parameters. [Accessed 03 2015].
[15] "IGS Stations," IGS, 03 2015. [Online]. Available:
igscb.jpl.nasa.gov/network/list.html. [Accessed 03 2015].
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http://igscb.jpl.nasa.gov/network/netindex.html. [Accessed 03 2015].
[17] "MGEX," IGS, October 2014. [Online]. Available: igs.org/mgex. [Accessed
April 2015].
[18] U. Hugentobler, "ESPACE 2: Satellite Navigation - Lecture Notes of MSc
ESPACE," Munich, IAPG Presentation, 2013.
[19] O. Montenbruck and P. Steigenberger, GPS Lab Exercises - MSc ESPACE,
Munich: Technical University Munich (TUM), 2014.
[20] C. Rizos, S. Ses, M. Kadir, Chia Wee Tong and Teng Chee Boo, "Potential Use
of GPSfor Cadastral Surveys in Malaysia," 2000.
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(AIUB), April 2015. [Online]. Available: http://www.bernese.unibe.ch/.
[Accessed April 2015].
[22] B. Hofmann-Wellenhof, H. Lichtenegger and E. Wasle, GNSS-Global
Navigation Satellite Systems GPS, GLONASS, Galileo and more, Vienna:
Springer-Velag Wien, 2008, p. 59.
[23] "Network," IGS, 2015. [Online]. Available: www.igs.org/network. [Accessed 03
2015].
[24] "PHYSCLIPS-Interference beats and Tartini tones," UNSW-School of Physics
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http://www.animations.physics.unsw.edu.au/jw/beats.htm. [Accessed April
2015].
76
[25] I. G. S. (IGS), "RINEX The Receiver Independent Exchange Format - Version
3.02," April 2013. [Online]. Available:
ftp://igs.org/pub/data/format/rinex302.pdf. [Accessed April 2015].
[26] D. A. Vallado, Fundamentals of Astrodynamics and Applications, 2nd Edition
ed., Space Technology Library (Springer), 2001, p. 163.
77
Table of Figures
Fig. 1.1: The four IOV satellites in orbit [11] ................................................................ 7
Fig. 1.2: Ground Stations for IOV satellites [11]........................................................... 7
Fig. 1.3: Ground stations for FOC1 phase [11] ............................................................. 8
Fig. 1.4: IOV satellite spacecraft [9] .............................................................................. 9
Fig. 1.5: World map of IGS stations [16] .................................................................... 10
Fig. 1.6: European region of IGS stations [16] ............................................................ 10
Fig. 2.1: Clock correction magnitude plots for GOP6/GOP7, doy: 017 ...................... 23
Fig. 2.2: Code zero-baseline for GOP6/GOP7 in frequency E1 .................................. 24
Fig. 2.3: Code zero-baseline for GOP6/GOP7 in frequency E5a ................................ 24
Fig. 2.4: Phase zero-baseline for GOP6/GOP7 in frequency E1 ................................. 25
Fig. 2.5: Phase zero-baseline for GOP6/GOP7 in frequency E5a ............................... 25
Fig. 2.6: Satellite observations for C1X signal ............................................................ 26
Fig. 2.7: Code zero-baseline for USN4/USN5 in frequency E5a ................................ 27
Fig. 2.8: Phase zero-baseline for USN4/USN5 in frequency E5a ............................... 27
Fig. 2.9: Magnitude of clock correction USN4/USN5 (a) ........................................... 28
Fig. 2.10: Magnitude of clock correction USN4/USN5 (b) ......................................... 28
Fig. 2.11: Code zero-baseline for UNBS/UNBD in frequency E5a ............................ 29
Fig. 2.12: Phase zero-baseline for UNBS/UNBD in frequency E1 ............................. 29
Fig. 2.13: Magnitude of clock correction UNBS/UNBD ............................................ 30
Fig. 2.14: Code zero-baseline for WTZ2/WTZ3 in frequency E1 ............................... 31
Fig. 2.15: Phase zero-baseline for WTZ2/WTZ3 in frequency E5a ............................ 31
Fig. 2.16: Magnitude of clock correction WTZ2/WTZ3 ............................................. 32
Fig. 2.17: Code zero-baseline for SIN0/SIN1 in frequency E5a ................................. 33
Fig. 2.18: Phase zero-baseline for SIN0/SIN1 in frequency E5a ................................ 33
Fig. 2.19: Magnitude of clock correction SIN0/SIN1 .................................................. 34
Fig. 2.20: Representation of beat signal [24] ............................................................... 34
Fig. 2.21: Beat signal constructed in Matlab ............................................................... 36
Fig. 2.22: Phase zero-baseline for GOP6/GOP7 in frequency E5a for 11/12 satellites
...................................................................................................................................... 38
Fig. 2.23: Phase zero-baseline for WTZ2/WTZ3 in frequency E1 for 11/12 satellites
...................................................................................................................................... 38
Fig. 2.24: Phase zero-baseline for UNBS/UNBD in frequency E1 for 11/19 satellites
...................................................................................................................................... 39
Fig. 2.25: Phase zero-baseline for USN4/USN5 in frequency E5a for 11/19 satellites
...................................................................................................................................... 39
Fig. 2.26: Phase zero-baseline for USN4/USN5 in frequency E5a for 11/20 satellites
...................................................................................................................................... 40
Fig. 2.27: Phase zero-baseline for WTZ2/WTZ3 in frequency E5a for 11/20 satellites
...................................................................................................................................... 40
Fig. 2.28: Phase zero-baseline for USN4/USN5 in frequency E1 for 12/19 satellites 41
78
Fig. 2.29: Phase zero-baseline for UNBS/UNBD in frequency E5a for 12/19 satellites
...................................................................................................................................... 42
Fig. 2.30: Phase zero-baseline for UNBS/UNBD in frequency E1 for 12/20 satellites
...................................................................................................................................... 42
Fig. 2.31: Phase zero-baseline for USN4/USN5 in frequency E5a for 12/20 satellites
...................................................................................................................................... 43
Fig. 2.32: Phase zero-baseline for UNBS/UNBD in frequency E5a for 19/20 satellites
...................................................................................................................................... 43
Fig. 2.33: Phase zero-baseline for USN4/USN5 in frequency E1 for 19/20 satellites 44
Fig. 2.34: Comparison results of day 14 in E1 frequency ........................................... 45
Fig. 2.35: Comparison results of day 37 in E5a frequency .......................................... 46
Fig. 2.36: Comparison results of day 61 in E5a frequency .......................................... 46
Fig. 2.37: Fourier Transform of satellites 11 and 12 in E1 frequency ......................... 49
Fig. 2.38: Fourier Transform of satellites 11 and 12 in E5a frequency ....................... 49
Fig. 2.39: Fourier Transform of satellites 11 and 19 in E1 frequency ......................... 50
Fig. 2.40: Fourier Transform of satellites 11 and 19 in E5a frequency ....................... 50
Fig. 2.41: Fourier Transform of satellites 11 and 20 in E1 frequency ......................... 51
Fig. 2.42: Fourier Transform of satellites 11 and 20 in E5a frequency ....................... 51
Fig. 2.43: Fourier Transform of satellites 12 and 19 in E1 frequency ......................... 52
Fig. 2.44: Fourier Transform of satellites 12 and 19 in E5a frequency ....................... 52
Fig. 2.45: Fourier Transform of satellites 12 and 20 in E1 frequency ......................... 53
Fig. 2.46: Fourier Transform of satellites 12 and 20 in E5a frequency ....................... 53
Fig. 2.47: Fourier Transform of satellites 19 and 20 in E1 frequency ......................... 54
Fig. 2.48: Fourier Transform of satellites 19 and 20 in E5a frequency ....................... 54
Fig. 2.49: Beat signal constructed in Matlab (2) .......................................................... 56
Fig. 2.50: Fourier transform of beat constructed signal ............................................... 56
Fig. 2.51: Period for 170 days for E1........................................................................... 57
Fig. 2.52: Period for 170 days for E5a ......................................................................... 58
Fig. 2.53: Amplitude [cm] for 170 days for E1 ........................................................... 58
Fig. 2.54: Amplitude [cm] for 170 days for E5a .......................................................... 59
Fig. 2.55: Double difference of a day with small time overlaps duration ................... 60
Fig. 2.56: Fourier Transformation of a day with small time overlaps duration ........... 60
Fig. 2.57: Period values with respect to time overlap duration ................................... 61
Fig. 2.58: Histograms for Period values for 1st peak in E5a ........................................ 62
Fig. 2.59: Histograms for Period values for 2nd
peak in E5a ....................................... 62
Fig. 2.60: Period values in E1 for 11/19 ...................................................................... 63
Fig. 2.61: Period values in E5a for 11/19 .................................................................... 63
Fig. 2.62: Period values in E1 for 12/19 ...................................................................... 64
Fig. 2.63: Period values in E5a for 12/19 .................................................................... 64
Fig. 2.64: E1-E5a for satellite 11 and USN4 ............................................................... 67
Fig. 2.65: Difference of satellites for USN4 ................................................................ 67
Fig. 2.66: Difference of stations for satellite 11 .......................................................... 68
Fig. 2.67: Difference of stations for satellite 12 .......................................................... 68
Fig. 2.68: Differentiation of both satellites and both receivers .................................... 69
79
Fig. 2.69: Fourier transform of the differentiation ....................................................... 69
80
Table of Tables
Tab. 1.1: IOV satellite characteristics [8] ...................................................................... 6
Tab. 1.2: IOV satellites technical characteristics (orbit & spacecraft) [9] ..................... 9
Tab. 1.3: Types of measurement differences ............................................................... 15
Tab. 1.4: Values for noise computation ....................................................................... 17
Tab. 2.1: Observation codes for each station pair ........................................................ 21
Tab. 2.2: Receivers and clocks for each station [23] ................................................... 21
Tab. 2.3: Combinations for experiment 1 .................................................................... 22
Tab. 2.4: Parameters of second experiment ................................................................. 37
Tab. 2.5: Stations and days used for experiment 4 ...................................................... 48
Tab. 2.6: Results of periods and amplitudes ................................................................ 65
81
Appendices
SiteID Country Agency Lat Lon Height Receiver Antenna Satellite System
CONX
Chile
Bundesamt
fuer
Kartographie
und
Geodaesie
-
36.84
-
73.03 00181.2
JAVAD
TRE_G3TH
DELTA
LEIAR25.R3 GPS+GLO+GAL
+SBAS
CONZ -
36.84
-
73.03 00181.2
LEICA
GRX1200
+GNSS
LEIAR25.R3 GPS+GLO+GAL
GOP6
Czech
Republic
Research
Institute of
Geodesy,
Topography
and
Cartography,
p.r.i.
Geodetic
Observatory
Pecny
49.91 14.79 592.62
LEICA
GRX1200
+GNSS
LEIAR25.R4 GPS+GLO+GAL
+SBAS
GOP7 49.91 14.79 592.62
JAVAD
TRE_G3TH
DELTA
LEIAR25.R4 GPS+GLO+GAL
+QZSS+SBAS
SIN0 Republic
of
Singapore
German
Aerospace
Center
1.34 103.6
8 92.54
JAVAD
TRE_G3TH
DELTA
LEIAR25.R3 GPS+GLO+GAL
+QZSS+SBAS
SIN1 1.34 103.6
8 92.54
TRIMBLE
NETR9 LEIAR25.R3
GPS+GLO+GAL
+BDS+QZSS+
SBAS
UNBD
Canada
German
Aerospace
Center
45.95 -
66.64 23.12
JAVAD
TRE_G2T
DELTA
TRM55971.00 GPS+GAL+SBAS
UNBS
University of
New
Brunswick
45.95 -
66.64 23.12 SEPT POLARXS TRM55971.00
GPS+GLO+GAL
+BDS+SBAS
UNX2
Australia
German
Aerospace
Center
-
33.92
151.2
3 87.07
JAVAD
TRE_G3TH
DELTA
LEIAR25.R3 GPS+GLO+GAL
+QZSS+SBAS
UNX3 -
33.92
151.2
3 87.07 SEPT ASTERX3 LEIAR25.R3
GPS+GAL+BDS
+QZSS
USN4
U.S.A. U.S. Naval
Observatory
38.92 -
77.07 57.519
SEPT
POLARX4TR AOAD/M_T
GPS+GLO+GAL
+SBAS
USN5 38.92 -
77.07 57.519 NOV OEM6 AOAD/M_T
GPS+GLO+GAL
+SBAS
WTZ2
Germany
Bundesamt
fuer
Kartographie
und
Geodaesie
Geodetical
Observatory
Wettzell
German
Aerospace
Center
49.14 12.88 663.4 LEICA GR25 LEIAR25.R3 GPS+GLO+GAL
+SBAS
WTZ3 49.14 12.88 663.4
JAVAD
TRE_G3TH
DELTA
LEIAR25.R3 GPS+GLO+GAL
+SBAS
Appendix A: MGEX stations used in this thesis and their details [23]
82
Appendix B: Observation code explanation (as given in Rinex 3.02) [25]
Appendix C: Rinex 3.02 observation codes for GPS [25]
83
Appendix D: Rinex 3.02 observation codes for Galileo [25]
Appendix E: BPE routine for BERNESE software