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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

Zero-Baseline Analysis of Galileo Data from Multi-GNSS Experiment

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Page 1: Zero-Baseline Analysis of Galileo Data from Multi-GNSS Experiment

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

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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

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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

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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

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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].

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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]

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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

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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]

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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)

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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

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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)

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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

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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:

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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.

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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

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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)

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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).

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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.

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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).

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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.

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Fig. 2.2: Code zero-baseline for GOP6/GOP7 in frequency E1

Fig. 2.3: Code zero-baseline for GOP6/GOP7 in frequency E5a

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Fig. 2.4: Phase zero-baseline for GOP6/GOP7 in frequency E1

Fig. 2.5: Phase zero-baseline for GOP6/GOP7 in frequency E5a

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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].

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Fig. 2.7: Code zero-baseline for USN4/USN5 in frequency E5a

Fig. 2.8: Phase zero-baseline for USN4/USN5 in frequency E5a

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Fig. 2.9: Magnitude of clock correction USN4/USN5 (a)

Fig. 2.10: Magnitude of clock correction USN4/USN5 (b)

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Fig. 2.11: Code zero-baseline for UNBS/UNBD in frequency E5a

Fig. 2.12: Phase zero-baseline for UNBS/UNBD in frequency E1

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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.

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Fig. 2.14: Code zero-baseline for WTZ2/WTZ3 in frequency E1

Fig. 2.15: Phase zero-baseline for WTZ2/WTZ3 in frequency E5a

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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.

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Fig. 2.17: Code zero-baseline for SIN0/SIN1 in frequency E5a

Fig. 2.18: Phase zero-baseline for SIN0/SIN1 in frequency E5a

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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]

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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.

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Fig. 2.21: Beat signal constructed in Matlab

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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.

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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

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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

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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

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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

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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

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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

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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.

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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

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Fig. 2.35: Comparison results of day 37 in E5a frequency

Fig. 2.36: Comparison results of day 61 in E5a frequency

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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.

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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.

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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

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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

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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

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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

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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

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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

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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.

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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.

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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

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Fig. 2.52: Period for 170 days for E5a

Fig. 2.53: Amplitude [cm] for 170 days for E1

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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.

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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

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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.

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Fig. 2.58: Histograms for Period values for 1st peak in E5a

Fig. 2.59: Histograms for Period values for 2nd

peak in E5a

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Fig. 2.60: Period values in E1 for 11/19

Fig. 2.61: Period values in E5a for 11/19

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Fig. 2.62: Period values in E1 for 12/19

Fig. 2.63: Period values in E5a for 12/19

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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.

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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.

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Fig. 2.64: E1-E5a for satellite 11 and USN4

Fig. 2.65: Difference of satellites for USN4

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Fig. 2.66: Difference of stations for satellite 11

Fig. 2.67: Difference of stations for satellite 12

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Fig. 2.68: Differentiation of both satellites and both receivers

Fig. 2.69: Fourier transform of the differentiation

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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.

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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

Page 73: Zero-Baseline Analysis of Galileo Data from Multi-GNSS Experiment

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.

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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.

Page 75: Zero-Baseline Analysis of Galileo Data from Multi-GNSS Experiment

74

References

[1] "What is Galileo," ESA, 2014. [Online]. Available:

http://www.esa.int/Our_Activities/Navigation/The_future_-

_Galileo/What_is_Galileo. [Accessed 2015].

[2] "IOV Satellites Facts and Figures," ESA, [Online]. Available:

http://www.esa.int/Our_Activities/Navigation/Facts_and_figures. [Accessed

2015].

[3] D. Odijk, P. J. G. Teunissen and A. Knodabandeh, "Galileo IOV RTK

positioning: standalone and combined with GPS," Survey Review, pp. 1-2, 2013.

[4] "Update on Galileo Launch Injection Anomaly," ESA, 26 August 2014. [Online].

Available: http://www.esa.int/Our_Activities/Navigation/The_future_-

_Galileo/Launching_Galileo/Update_on_Galileo_launch_injection_anomaly.

[Accessed April 2015].

[5] "Two new satellites join the Galileo constellation," ESA, 28 March 2015.

[Online]. Available: http://www.esa.int/Our_Activities/Navigation/The_future_-

_Galileo/Launching_Galileo/Two_new_satellites_join_the_Galileo_constellation.

[Accessed April 2015].

[6] "Launch Schedule," Spaceflight Now, 2015. [Online]. Available:

http://spaceflightnow.com/launch-schedule/. [Accessed 2015].

[7] "Galileo Fact Sheet," ESA, 15 02 2013. [Online]. Available:

http://download.esa.int/docs/Galileo_IOV_Launch/Galileo_factsheet_2012.pdf.

[Accessed 03 2015].

[8] "Constellation Information," European GNSS Service Centre (GSC), 26 02 2015.

[Online]. Available: www.gsc-europa.eu/system-status/Constellation-

Information. [Accessed 03 2015].

[9] "The First Four Satellites," ESA, [Online]. Available:

(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.

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75

[12] ESA, "Galileo System," 16 08 2007. [Online]. Available:

www.esa.int/Our_Activities/Navigation/The_future_-_Galileo/Galileo_system.

[Accessed 2015].

[13] ESA, "In-Orbit-Testing," 18 07 2014. [Online]. Available:

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].

[16] "IGS Tracking Network," IGS, 05 2010. [Online]. Available:

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.

[21] "Bernese GNSS Sofware," Astronomical Institute of the University of Bern

(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

Sydney, Australia, [Online]. Available:

http://www.animations.physics.unsw.edu.au/jw/beats.htm. [Accessed April

2015].

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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.

Page 78: Zero-Baseline Analysis of Galileo Data from Multi-GNSS Experiment

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

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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

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79

Fig. 2.69: Fourier transform of the differentiation ....................................................... 69

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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

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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]

Page 83: Zero-Baseline Analysis of Galileo Data from Multi-GNSS Experiment

82

Appendix B: Observation code explanation (as given in Rinex 3.02) [25]

Appendix C: Rinex 3.02 observation codes for GPS [25]

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83

Appendix D: Rinex 3.02 observation codes for Galileo [25]

Appendix E: BPE routine for BERNESE software