Crustal motion at the permanent GPS station SVEA, Antarctica
Walyeldeen Hassan Edres
Master’s of Science Thesis in Geodesy No. 3119 TRITA-GIT EX 09-017
Division of Geodesy
Royal Institute of Technology (KTH) 100 44 Stockholm, Sweden
August 2009
Crustal motion at the permanent GPS station SVEA, Antarctica
Author: W. Hassan
Supervisor: Dr. M. Horemuž
Examiner: professor. L. E. Sjöberg
Acknowledgements
First and foremost, I would like to take this opportunity to present my sincere gratitude and all kinds of respect to my Supervisor Dr. Milan Horemuž for his advice and guidance during this thesis work. I wish also to give my sincere thankfulness to Professor Lars Sjöberg for his guidance during the master courses as well as for his researches to help us to understand and solve many problems in Geodesy field. I would like to thank Mr. Erick Asenjo for his information about the SVEA station. My deepest gratitude also to Dr. Huaan Fan.
I would like to express my deepest appreciation and my respect to Sweden's country and especially to The Royal Institute of Technology for giving me the opportunity to study this master program.
I wish to express my gratitude to University of Khartoum for the scholarship, and also the teacher’s encouragement during my studies.
Many thanks with respect and love to my friends Faisal .A, Abdalla .A, Mokashfi .S, Abdalmajed .Y, khatim .S, Sedahmed .A, and his wife for all helps and the greatest time during my study. I would like to express my gratitude and all respect to Elbasher Mohammed and Osama Adam for their greatly supports, advises and helps.
I would like to thank my colleagues at the Geodesy and Geoinformatics master program for their kind friendship during my study.
I would like to express my sincere gratitude to my parents and my brother Anwar and my sisters for their encouragement and support in my whole life.
Finally, I also wish to thank everybody who has given me any kind of help to be successful in my life.
WalyEldeen Hassan Stockholm, May, 2009
I
Abstract
Since the last two decades, the Global Positioning System (GPS) has played a special role in Antarctica in the study of crustal motion. The permanent GPS station SVEA was installed in Antarctica by the division of geodesy at KTH. In November 14, 2004 the station became operational and provides continuous GPS data.
The objective of this study is to estimate the crustal motion at SVEA. The GPS data of the first five days of January, years 2005, 2006, 2007 and 2008 of station SVEA and six IGS reference stations have been processed using the Bernese GPS Software 0.5.
Two methods (regression analysis and the Bernese software) were used to estimate the velocity at SVEA. In addition, horizontal velocities have been calculated from the plate motion calculator. A student’s t‐test has been used to judge whether the estimated motions are significant or not at risk level 5%.
The estimated velocity components (in mm/year) are 8.0±1.9 North, 1.0 ± 0.5 East and 0.1 ± 0.9 Up in linear regression analysis and 8.4 ±1.9 North, 1.1 ± 0.5 East and 0.2 ± 0.9 Up in the Bernese GPS Software. From the statistical test, the estimated velocity in the North component is significant in the Bernese GPS Software at risk level 5%. For the rest of the components, the estimated velocities are not significant for any method. The estimated horizontal velocities are mostly consistent with plate motion models. In order to estimate reliable and accurate crustal motion in the Up component, the time span should be longer than four years.
Keywords: Antarctica, Campaign, GPS, IGS, processing, session, SVEA, velocity.
II
Abbreviation
CODE Center for Orbit Determination in Europe CIO Conventional International Origin
DoD Department of Defense
GNSS Global Navigation Satellite System GPS Global Positioning System
LEO Low Earth Orbit
ICRF International Celestial Reference Frame ICRS International Celestial Reference System IGS International GNSS Service
IRM IERS Reference Meridian IRP IERS Reference Pole
ITRF International Terrestrial Reference Frame ITRS International Terrestrial Reference System NAVSTAR Navigation System with Time and Ranging NNR No Net Rotation
NNSS Navy Navigation Satellite System QIF Quasi Ionosphere‐Free
RINEX Receiver Independent Exchange Format RMS Root Mean Square
RTK Real Time Kinematic
SCAR Scientific Committee on Antarctic Research SLR Satellite Laser Ranging
VLBI Very Long Baseline Interferomety WGS World Geodetic System
III
Contents
Acknowledgements ………...………... I Abstract ………...………..………... II Abbreviation………...………... III List of Figures………...………….………... IV List of Tables ………...………….………... IIV
1 Introduction ... 1
1.1 Background ... 1
1.2 Thesis Motivation and Objectives ... 2
1.3 Thesis Outline ... 5
2 Concepts of the global positioning system (GPS) ... 7
2.1 Geodetic Reference System ... 7
2.1.1 International Celestial Reference System. ... 7
2.1.2 International Terrestrial Reference System. ... 7
2.2 GPS Overview ... 9
2.3 GPS observables ... 10
2.4 The code observation ... 10
2.4.1 The phase observation ... 10
2.5 GPS differencing ... 11
2.5.1 The single difference ... 11
2.5.2 The double difference ... 11
2.5.3 The triple difference... 12
2.6 The error sources in GPS... 12
2.6.1 Satellite and Receiver clock error ... 12
2.6.2 The Ephemeris error ... 12
2.6.3 The atmosphere effect’s ... 13
2.6.4 Multipath ... 14
2.6.5 Antenna phase center ... 14
3 Data Processing ... 15
3.1 GPS Data ... 15
3.2 Overview of the Bernese GPS Software Version 0.5 ... 16
3.3 The Processing Steps ... 17
3.3.1 Orbit Generation ... 17
3.3.2 Receiver Clock Synchronization ... 18
3.3.3 Baselines ... 18
3.3.4 Preprocessing Phase Observations ... 19
3.3.5 Screening of Post‐Fit Residuals ... 19
3.3.6 First Network Solution ... 20
3.3.7 Ambiguity Resolution ... 20
3.3.8 Final network Solution... 20
3.3.9 Flow Diagram for the Processing Steps ... 21
4 The SVEA GPS Station Coordinates ... 23
4.1 Combination of Solutions ... 23
4.2 Stability of the Session Solution ... 28
5 Velocity Estimation and Analysis ... 31
5.1 Velocity estimation using Linear Regression Analysis ... 31
5.2 Velocity Estimation using the Bernese GPS software ... 33
5.3 The horizontal displacement of station SVEA ... 34
5.4 Analysis of the Estimated Velocity ... 36
5.5 The Horizontal Velocity from the Plate Motion Calculator ... 37
6 Conclusions and Recommendations ... 39
References ... 41
Appendix ... 43
List of Figures
Figure 1.1: The permanent GPS station SVEA ….………..………..………. 4 Figure 1.2: The Antarctica Map, the location of the reference IGS stations and station SVEA………..………. 4 Figure 3.1: The baselines between SVEA station and the IGS stations ……… ..…..18 Figure 3.2: The flow diagram shows a summery of the processing strategy (for each session) by using Bernese GPS software……….……….…… 21 Figure 4.1 The temporal coordinate change of station SVEA in the X coordinate …24 Figure 4.2: The temporal coordinate change of station SVEA in the Y coordinate …25 Figure 4.3: The temporal coordinate change of station SVEA in the Z coordinate …25 Figure 4.4: The temporal coordinate change of station SVEA in the North component ………..…27 Figure 4.5: The temporal coordinate change of station SVEA in the East component………. 27
Figure 4.6: The temporal coordinate change of station SVEA in the UP component ……… 28
Figure 5.1: The estimated horizontal velocity (mm/yr) using Linear Regression Analysis (black) is 8.1 ± 1.9 at azimuth 7.46 0.06 ° , and Bernese software (red) is 8.5 ± 1.9 at azimuth 7.12 0.06 ° …….……… 35 Figure 5.2: The estimated velocity using Bernese GPS software and Linear Regression versus the calculated velocity from plate motion models in the North component ……… 38 Figure 5.3: The estimated velocity using Bernese GPS software and Linear Regression versus the calculated velocity from plate motion models in the East component ……… 38
IV
Lis
Tab SYO Tab stat Tab cros stat all I Tab solu
Tab solu Tab solu
Tab solu
Tab the Tab pre
Tab the
Tab pre Tab usin
Tab
st of Tabl
ble 1.1: Th OG, MAW1, ble 1.2: Th
tions ………
ble 3.1: Th ss mark (X tions while IGS stations ble 4.1: The ution and th ble 4.2: The ution and th ble 4.3: The ution and th ble 4.4: The ution and th ble 5.1: The Bernese G ble 5.2: The
dicted coor ble 5.3: The Bernese G ble 5.4: The
dicted coor ble 5.5: The ng the Line ble 5.6: The
es
he general MCM4 and he approxi
………
e campaig X) refers to
the right m s………
e residuals he RMS in ( e residuals he RMS in ( e residuals he RMS in ( e residuals he RMS in ( e estimated PS softwar e residual
rdinates, us e estimated
PS softwar e residual
rdinates, us e results of ear Regress e calculated
informatio d VESL) as imate dist
………
gns and ses o the obser mark ( ) re
………
s in (mm) b (mm) camp s in (mm) b
(mm) camp s in (mm) b
(mm) camp s in (mm) b
(mm) camp d velocity re………
errors in (m sing Linear d velocity re ………..……
errors in (m sing the Be f the statis sion Analys d horizonta
on of the well as SV tance from
………
ssions that rvation dat efers to the
………
between th paign 2005
between th paign 2006
between th paign 2007
between th paign 2008
(mm⁄yr) a
….. ………
(mm) betwe r Regressio
(mm⁄yr) an
………
(mm) betwe ernese GPS stical stude is and the B al velocity fr
IIV
reference EA GPS sta m station S
………
t have bee ta that are e observatio
………
he combine
….………
he combine
………
he combine
…..………
he combine
………
and its stan
………
een the com on Analysis
nd its stan
………
een the com software … ent’s t‐ test
Bernese GP from the Pla
IGS statio ation…………
SVEA to th
………
en used for e not availa on data tha
………
ed solution
………
ed solution
………
ed solution
………
ed solution
………
ndard error
………
mputed coo ...
dard error
………
mputed coo
………
t of the est PS software
ate Motion
ons (DAV1,
………
he referen
………
r processin able for so at are availa
………
n and the
………
n and the
………
n and the
………
n and the
………
r (± mm)
……….
ordinates a ...…..
r (± mm)
……….
ordinates a
….………
timated vel e ………
Calculator
, OHI2,
………. 3 nce IGS
……… 3 ng. The ome IGS able for
…16 session
……… 28 session
… 29 session
… 29 session
… 29 m), using
….. 32 and the
. 32 m), using
. 33 and the
…. 33 locities,
….. 36
r….. 37
Chapter 1
1 Introduction
1.1 Background
In many applications of engineering, deformation measurement is a very important field, especially in geodesy to study the crustal motion and other geodynamic phenomena. In general there are two reasons for deformation studies: practical reasons and scientific reasons. Practical reasons include checking the stability of a structure and detecting the precursors of earthquakes; scientific reasons include understanding the mechanism of deformation [CHEN, 1983].
The methods for deformation monitoring can be divided into geodetic and non‐
geodetic methods [Horemuž, 2004]. In geodetic methods, the geodetic concepts and precise geodetic instruments were used to detect the deformation. This method has a wide application in global deformation such as landslides, tectonic and continental motion by using the geodetic space technique such as the global positioning system (GPS), Very Long Baseline Interferometry (VLBI) and satellite laser ranging (SLR).
The geodetic methods were used in local deformation studies such as in dams, mining and structures (VASA ship) by using highly accurate instruments such as Precise Level, Precise Theodolite, and Precise Total Station.
Usually, the geodetic deformation methods make use of the deformation network.
The deformation network can be either a reference (absolute) network or a relative network. In absolute deformation networks, some of the network points (stations) are regarded as fixed points, which are placed outside the deformable body so that the deformation can be explained as absolute displacement of the object points. In the relative deformation network, all points (stations) are regarded as a subject of deformation, or in other words, all points are located inside the deformable body.
The relative deformation networks are more complicated than the absolute ones due to the relative deformation (rotation and displacement) between the deformation network points [Caspary, 1988].
1. Introduction
1.2 Thesis Motivation and Objectives
Since the mid 19th century, several researches in the geodesy field have been conducted in Antarctica using the photogrammetrical and astronomical techniques.
In the last couple of decades, the Global Positioning System (GPS) has become a very important geodetic technique for monitoring deformation networks due to its high accuracy to detect the crustal motion and realize the Terrestrial Reference System in Antarctica [Dietrich, et al., 1998; Reinhard, et al., 2008].
In this thesis, we are going to use the permanent GPS station SVEA. It is installed in a rock area in Heimefrontfjella, Antarctica by the division of geodesy at the Royal Institute of Technology, Stockholm, Sweden, under the supervision of Professor Lars Sjöberg and Mr. Erick Asenjo. This station is equipped with a Trimble R7 GPS receiver with consumption 1.8‐2.3 W, antenna type ASHTECH with Radome code SNOW (ASH701945E_M SNOW) and steel tripod (see figure.1.1). The R7 GPS receiver is a dual frequency system with L C capability and the operating temperature of this receiver goes down to 40 ° C.
Data are logged in a 1 GB Compact Flash memory; this memory can work down to 40 ° C. The data are collected annually by manually changing the memory card during the summer expeditions. At this time, the automatic transfer of data via satellite communication is not possible.
The receiver is powered from six 12 V batteries, with a capacity of 600 Ah. The batteries are charged through solar panels until the sun is above the horizon and by wind generators during the period of winter darkness.
This station has been in operation since the 1
stof December 2004 and provides daily observation and navigation data of continuous measurements with a recording dual frequency (phase and code observations) in an interval sampling rate of 15 seconds.
In addition, Real Time Kinematic (RTK) service will be available when station SVEA is open [Sjöberg, et al., 2006].
The main objectives of this thesis are to process the GPS data of the first five days of January, years (2005, 2006, 2007 and 2008) of the SVEA station using the Bernese GPS software 0.5 with International GNSS Service (IGS) reference stations in Antarctica as a reference (absolute) network, in order to estimate the possible crustal motions and plate motions at station SVEA.
1.2 Thesis motivation and objectives
Table 1.1 shows the general information about the reference IGS stations (DAV1, OHI2, SYOG, MAW1, MCM4 and VESL) and station SVEA, these IGS reference stations have been chosen depending on the approximate shortest distance from station SVEA as in Table 1.2. The map of Antarctica and the location of the IGS reference stations, as well as the location of station SVEA, is given in Figure 1.2.
Table 3.1: The general information of the reference IGS stations (DAV1, OHI2, SYOG, MAW1, MCM4 and VESL) as well as SVEA GPS station.
STATION NAME RECEIVER TYPE ANTENNA TYPE Location dav1 66010M001 ASHTECH UZ‐12 AOAD/M_T AUST Davis, Antarctica mcm4 66001M003 ASHTECH Z‐XII3 AOAD/M_T JPLA Ross Island, Antarctica ohi2 66008M005 AOA SNR‐8000 AOAD/M_T DOME O'Higgins, Antarctica maw1 66004M001 LEICA GRX1200 AOAD/M_T AUST Mawson, Antarctica syog 66006S002 TRIMBLE 4000SSI AOAD/M_T DOME East Ongle Island, Antarctica vesl 66009M001 TRIMBLE 4000SSI TRM29659.00 TCWD Vesleskarvet, Antarctica
SVEA TRIMBLE R7 ASH701945E_M SNOW Heimefrontfjella, Antarctica
Table 1.4: The approximate distance from station SVEA to the reference IGS stations.
Base line Distance in km
SVEA ⎯ DAV1 2879.1
SVEA ⎯ MAW1 2574.2
SVEA ⎯ MCM4 3050.7
SVEA ⎯ OHI2 2153.9
SVEA ⎯ SYOG 1804.8
SVEA ⎯ VESL 422
1. Introduction
Figure 1.1: The permanent GPS station SVEA.
Figure 1.2: The Antarctica Map, the location of the reference IGS stations and station
SVEA.
1.3 Thesis Outline
1.3 Thesis Outline
The thesis consists of six chapters. The first chapter is an introduction which describes the background of the deformation and the thesis motivation and objectives. Chapter two is oriented to give overview of the most important theory behind the GPS. Chapter three describes the processing strategy in the Bernese GPS software that has been used in this thesis. Chapter four contains the temporal change of SVEA coordinates and the daily repeatability results. Chapter five describes the estimation of the velocity by using two methods and then the statistical analysis of the estimated velocity as well as the calculated horizontal velocity from the plate tectonic motion calculator. The last chapter contains the conclusion of this study and some recommendations for the next work.
Chapter 2
2 Concepts of the global positioning system (GPS)
In order to understand the GPS positioning it is important to understand the basic theories and concepts behind the global positioning system (GPS). This chapter gives an overview and the most important concepts of the GPS System.
2.1 Geodetic Reference System
2.1.1 International Celestial Reference System.
The space fixed inertial system is usually related to extraterrestrial objects like stars, quasars (extragalactic radio sources), planets, or the Moon. They are therefore, also is called the International Celestial Reference System (ICRS) [Seeber .G, 2003].
This system is a very important to describe the dynamic motion of the GPS satellite according to the principles of Newton’s mechanics .The ICRS was defined as the system with origin at the gravity center of earth and the Z axis toward the mean position of the celestial pole that has been defined by the Conventional International Origin (CIO) at epoch J2000.0 (The time epoch, 12 January 1 of year 2000) and the X‐axis is toward the vernal equinox, which is defined by a set of fundamental stars at epoch J2000.0 [Fan, 2007]. In January 1998 the International Earth Rotation Service (IERS) was established the International Celestial Reference Frame ICRF (The realization of ICRS) by using a set of 608 radio star observed by VLBI.
2.1.2 International Terrestrial Reference System.
The position of the points on (or close to) the Earth surface can be defined by the International Terrestrial Reference system (ITRS). This system was defined as the system with origin at the gravity center of Earth and the Z axis toward the mean position of the pole that has been defined by IERS Reference Pole (IRP). The Xaxis is toward the intersection of the Greenwich meridian plane which was defined by IERS Reference Meridian (IRM) in the equatorial plane and Yaxis is perpendicular with the Xaxis in the same equatorial plane [Fan, 2007].
The ITRS was realized by a number of terrestrial sites where the temporal effects (plate tectonic motion, tidal effects) were used to improve the ITRS [Hofmann‐
Wellenhof , et al, 2002], and the result of this realization is the terrestrial reference
frame such as the World Global System 1984 (WGS 84) and the International
Terrestrial Reference Frame .
2. Concepts of the global positioning System (GPS)
• World Geodetic System 1984 (WGS84) :
The World Geodetic System 1984 (WGS84) is a Conventional Terrestrial Frame, realized by modifying the Navy Navigation Satellite System (NNSS), or TRANSIT.
Associated to this frame is a geocentric ellipsoid of which is defined by the semi major axis a, the flattening of the ellipsoid f, the angular velocity of earth rotation and the geocentric gravitational constant μ (Mass of earth include the atmosphere) .This frame has been used for GPS satellite system since 1987, and the origin and axes of WGS84 defined as [Fan, 2007]:
− The origin at Earth’s centre of mass including the oceans and the atmosphere.
− The Z‐Axis from the origin toward the IERS Reference Pole (IRP) which is consistent with the CIO within precision of the realization (0.03 sec).
− The X‐Axis at the Intersection of the Greenwich meridian plane with the equatorial plane.
− The Y‐Axis is inside the equatorial plane and completes a right‐handed coordinate system (O-XYZ).
− International Terrestrial Reference Frame ITRF :
The International Terrestrial Reference Frame (ITRF) is a Conventional Terrestrial System, realized by a set of control ground points most of them equipped by Satellite Laser Ranging (SLR) or Very Long Base Line Interferometry (VLBI). This frame has been updated and designated by ITRF , where is the last year in which data were used for the realization, and the origin and axes of (ITRF) defined as [Fan, 2007]:
− The origin at Earth’s centre of mass includes the oceans and the atmosphere.
− The Z‐Axis from the origin toward the IERS Reference Pole (IRP) which is consistent with the CIO within precision of the realization (0.03 sec).
− The X‐Axis at the Intersection of the Greenwich meridian plane with the equatorial plane.
− The Y‐Axis is inside the equatorial plane and completes a right‐handed coordinate system (O-XYZ).
Example of ITRF : ITRF designates the frame of coordinate and velocities constructed in 1998 using all the IERS data available through 1997, the last ITRF is designated ITRF which is coincided with WGS 84 at 10cm level [Fan, 2007].
2. 2 GPS Overview
2.2 GPS Overview
In 1973, the US Department of Defense (DoD) commenced the development of NAVSTAR (Navigation System with Time and Ranging) Global Positioning System (GPS), and the first satellites were launched in 1978. The GPS system was controlled and oriented by the DoD but is partially available for civilian and foreign users.
In general GPS satellite system consists of three segments (space segment;
Control/monitoring segment and the User segment).
− The space segment consists of 28 satellites including spares. The satellites are in 6 orbits, at a height of 20200 km above the Earth. The six orbital planes are equally spaced, and are inclined at 55 degree to the equator. The system has been designed so that at least four to eight satellites will always be available in view at least 15 degree above the horizon, each GPS satellite broadcast L Band carrier frequencies, both frequencies are derived from the fundamental frequency (f =10.23 MHZ) . L1 = 1575.42 MHz (10.23 × 154) and L2 = 1227.6 MHz (10.23 × 120), wave length 19 cm and 24.4 cm respectively. The carriers are phase modulated to carry two codes, known as the P code (precise code) and the C/A code (Course/Acquisition code). In addition the GPS satellite broadcast continues information about the satellite clock, the satellite orbit, the satellite health status, and various other data, which are called GPS navigation message.
− The Control/monitoring segment consists of a master control station located near Colorado Springs, five monitor stations around the equator and three ground control stations. The main task of control/monitoring segment is to update the satellite orbit, satellite clock and the satellite states (health) by tracking the navigation signals by the monitor stations and sends their data back to the master control station, and then the calculated orbit, clock parameters and other parameters are uploaded to the satellite via one of the three ground control stations.
− The User segment consists of the user community and GPS receivers. In general the user community can be divided into two groups’ military users and civilian users. The GPS receiver types can be classified into four groups depends on the used code as the following [Sjöberg L E, 2007]:
i. C/A –code pseudorange receiver.
ii. C/A –code carrier phase receiver.
iii. P –code carrier phase receiver.
iv. Y –code carrier phase receiver.
2. Concepts of the global positioning System (GPS)
2.3 GPS observables 2.4 The code observation
The code observation is observing the signal traveling time from the satellite to receiver (the difference ∆ between the time of emission on the satellite ( ) and the reception time on the receiver t R )) as the following [Sjöberg, 2007]:
∆ ∆ ̃ ∆ 2.1
, are the receiver and satellite clock readings.
, are the receiver and satellite clock biases.
When the traveling time is known the pseudorange can be calculated by multiplying the traveling time by the light speed ( ), as the following:
∆ ∆ ̃ ∆ ∆ 2.2 Where is the true distance between the position of the satellite at epoch and
receiver position at epoch ( , , ∆ ∆ ),
which is difference from the geometric distance by the time derivation of p or the radial velocity of the satellite relative to the receiver antenna [Sjöberg, 2007].
2.4.1 The phase observation
The phase observation is the difference between two phases that has been measured by the GPS receiver, the basic equation of the phase observation can be written as [Sjöberg, 2007]:
1 ∆ 2.3
is the phase measurement (in cycles) at epoch t.
is the random observation error.
is the omitted phase from the satellite at time t.
is the phase generated by the receiver at signal reception time t.
2.4 GPS differencing
, are the signal frequency and signal speed respectively.
is the satellite to receiver distance.
is an unknown integer number of cycles (the initial phase ambiguity).
∆ is the clock (receiver and satellite ) bias difference . 2.5 GPS differencing
The basic observable of GPS is the phase measurement, and in order to compute high accurate position it is necessary to use a linear combination of the observables for further processing. These combinations are in the form of single differences, double differences and triple differences .These differences are used to correct the clock errors, cycle slips and the integer ambiguities. Bellow the main concept of the GPS phase differencing.
2.5.1 The single difference
A single difference is the difference in phase of simultaneous measurement between one satellite and two receivers , [Sjöberg, 2007; seeber, 2003]; the single deference formula can be written as :
∆ ∆
1 1 2.4 The main advantage of the single difference is the effects of the satellite clock errors can be eliminated.
2.5.2 The double difference
A double difference is the difference of two single differences observed at the same receivers , but with respect to two different satellites , at the same time [Sjöberg, 2007; seeber, 2003]; the double difference formula can be written as:
∆ ∆ ∆ ∆ ∆
1 2.5 The main advantage of the double differencing is the effect of the receiver clock error can be eliminated, but the phase integer 1 are still remaining.
2. Concepts of the global positioning System (GPS)
2.5.3 The triple difference
A triple difference is the difference of two double differences related to the same receivers , and satellites , but at different epochs ( , ) [Sjöberg, 2007;
seeber, 2003], the triple difference equation can be written as:
, ∆ ∆ ∆ ∆
(2.6) The main advantage of the triple differencing is that the phase ambiguity can be eliminated if there is no cycle slips between epoch and epoch , so that the triple difference can be used to detect the cycle slips [Sjöberg, 2007].
2.6 The error sources in GPS
The GPS position of the ground station is influenced by many errors; those errors should be eliminated or reduced in order to compute accurate position. Bellow is given an overview of the most important sources of the GPS position error and how to eliminate or reduce those errors.
2.6.1 Satellite and Receiver clock error
The crux of the GPS satellite is four atomic clocks (two Cesium and two Rubidium) and all GPS receivers are equipped with a quartz clock for time measuring and signal synchronization. And all those clocks contain some biases, which are denoted by the satellite clock error and receiver clock error. Usually the best way to eliminate those errors is by forming GPS differencing.
2.6.2 The Ephemeris error
There are three sets of data available to determine the satellite position and velocity vectors in the terrestrial reference frame at very instant: almanac data, broadcast ephemerides, and precise ephemeris [Hofmann‐Wellenohof, et al., 2002].
The ephemeris data were processed at the Master Control Station and updated to be as part of the satellite navigation message for each individual satellite. The ephemeris error is the disagreement between the true position and velocity of the satellite and the interpolated satellite position and velocity [Mohinder, et al., 2007].
Nowadays, there is precise position of the satellite (precise orbit) available with an
error about 0.05 to 0.2 m, which is leads in general about a part of millimeter in the
final ground position.
2.5 The Error sources in GPS
2.6.3 The atmosphere effect’s
The Earth’s atmosphere is usually distinguished by two layers, the ionosphere layer and the troposphere layer, since the GPS satellite signals crossing those layers it will be affected by the components of those layers (signal delay and signal bending).
− The ionosphere is the upper part of Earth’s atmosphere between approximately 70 and 1000 km. Signal propagation is mainly affected by free charged particles [Seeber, 2003].The ionosphere effect can be eliminated by combine the GPS observable simultaneously for range, pseudorange, phase and Doppler observables. The following equations 2.7 to 2.11 describes the elimination of the ionosphere effect for phase observable, which is so called Ionosphere ‐ Free Linear combination[Rolf, et al.,2007,p39‐40]:
Ionosphere ‐ Free Linear combination can be written as:
2.7 Ionosphere ‐ Free Linear combination in double difference equation can be written as:
2.8 Or in term :
, 2.9
Where
is called the Narrow–Lane ambiguity and ( is called Wide–
Lane ambiguity.
Wide ‐ Lane Linear combination can be written a s:
2.10 Wide‐Lane Linear combination in double difference equation can be written as:
, 2.11
2 . Concepts of the global positioning System (GPS)
The ionosphere effect can be eliminated by using Ionosphere ‐ Free Linear combination L , but the integer ambiguity cannot be integer due to the multiplication with non‐integer coefficients [Sjöberg, 2007].
− The troposphere is the lower part of Earth’s atmosphere, which extends from the surface to about 40 km. Signal propagation depends mainly on the water vapor content and on temperature [Seeber, 2003]. The troposphere can be divided into two parts: dry part is about 90% of the total troposphere effect and wet part is about 10% of the troposphere effect. Usually the way to eliminate the troposphere effect is by estimating the local troposphere model as in the practical solution (at least in GPS positioning) is to extend the network solution software with some extra unknown parameters for the so‐called zenith troposphere delay [Sjöberg, 2007], or by using the global troposphere models such as the troposphere models from the International GNSS service (IGS).
2.6.4 Multipath
The multipath effect is an error due to the reflection of the transmitted GPS satellite signal by the environment (buildings, water, trees and other reflecting bodies) around the GPS receiver which is meaning the receiver will receive the omitted signal from the GPS satellite through more than one path. There are many methods to reduce or to estimate the multipath effects, these methods were classified by Ray et al. (1999) as (1) antenna –based mitigation (such as choke ring antenna) , (2) improved receiver technology (such as Delay Lock Loop), and (3) signal and data processing. However, multi path effects cannot be eliminated totally because the multi path environment is specific to each site [Hofmann‐Wellenhof, et al, 2002].
2.6.5 Antenna phase center
The antenna phase center is the point to which the radio signal measurement is referred and generally is not identical with the geometrical antenna center due to the offsets are different for the satellite signals ( ) as well as the offsets are function of the azimuth and the zenith angle [Hofmann‐Wellenhof, et al, 2002].
There are two effects of the antenna phase center (offset and variation), and general there are two calibration methods for modeling the antenna phase center (absolute and relative). Nowadays, the antenna phase center models are developed by many calibration agencies (such as IGS, National Geodetic Survey and other agencies) for most of GPS antenna types.
Chapter 3
3 Data Processing
In order to compute highly accurate positions by GPS, the GPS data should be processed in the correct way and should use the appropriate GPS software. This chapter will begin by providing some basic information on the GPS data that have been used in this thesis, the second part is an overview of the Bernese GPS software and the last part describes the processing strategy.
3.1 GPS Data
The GPS data can be divided into two groups. The first group is the GPS observation data in Receiver Independent Exchange Format (Rinex) see [Werner, 2007] for details. The observation data of station SVEA is available daily with the 15 second recording rate since 14 November 2004 until 21 January 2008 in the division of geodesy at KTH (see section 1.2), and for the rest of IGS reference stations the observation data is available daily with the 30 second recording rate (except some IGS station) in all IGS analysis centers. The second group is the product data. This data is available daily in all IGS analysis centers and contains the following files:
− Precise ephemeris: This file describes the precise position of the satellites on the orbit.
− Pole information: This file describes the Earth’s rotation parameters.
− Ionosphere model: This file contains the ionosphere correction.
− Absolute Antenna model: This file contains the antenna correction.
In this thesis, from the continuous GPS data of SVEA, a very small sample observation data has been chosen. Only the observation data of the first five days of January, years (2005, 2006, 2007 and 2008) were used for processing. The years are denoted as campaigns and the days are denoted as sessions of these campaigns.
Table 3.1 shows the campaigns and sessions that have been used for the processing.
The observation data for some IGS stations at some sessions were not available, so each session with uncompleted observation data was neglected to avoid the changes on the network geometry from session to a session.
3. Da
Tab cros stat for
Campa
Campa (20 Campa
(20 Campa
(20 Campa
(20
3.2 The Soft cele GPS GPS curr resp new file Pro The cod the
ata processi
ble 3.1: Th ss mark (X tions while
all IGS stat
aigns (1 aign05 005)
aign06 006)
aign07 007)
aign08 008)
Overv e Astronom
tware as a estial mech S/GLONAS S software rently reali pect to the w, user‐frie name usi ocessing En e source of de in about nearly 100
ing
e campaig X) refers to e the right tions.
session 1
1
stof January)
view of the mical Institu a compreh hanics to
receivers.
version 3, ized as ver older vers endly, and o
ing sessio ngine (BPE) f the Berne 1200 mod 0 programs
gns and ses o the obser mark ( )
)
sessio
(2nd of Ja
e Bernese ute Univer hensive an analyze d Since 198 in 1996, ve rsion 5. The sions (versi
oriented fo n is varia ), etc.
ese GPS Sof dules. The m
s such as:
ssions that rvation dat refers to t
on 2 anuary) (3
re GPS Soft sity of Ber d scientifi data collec 88, the dev ersion 4 an e most imp ion 3 and 4) or Window able, the P
ftware 5.0 menu progr
t have bee ta that are the observ
session 3
rd
of January)
tware Ver rne (AIUB)
c tool in cted by hi velopment w nd in 2004,
portant enh ) are: The ws 2000 an
Perl script
consists of ram acts as
en used for e not availa ation data
)
sessio
(4
thof Jan
X X X
rsion 0.5 developed geodesy, g igh accura was starte the Bernes hancements user inter d XP opera t language
f more tha s a user int
r processin able for so
that are av
on 4 nuary) s
(5th
d the Berne geodynami acy, geodet ed by the B se GPS soft s of version face is com ation syste e as the B
n 300000 terface for
ng. The ome IGS vailable
session 5 hof January)
X X
ese GPS cs, and tic‐type Bernese tware is n 5with mpletely ms, the Bernese
lines of most of
3.2 Overview of the Bernese GPS software version 5
• Transfer part: to import Rinex to Bernese and to export Rinex from Bernese.
• Orbit and earth rotation part: to generate the precise orbit by using the planetary ephemeris file, to generate orbit in the Bernese format (standard orbit), to update orbits, etc.
• Processing part: For processing the GNSS data.
• Service part: This part contains a set of useful tools to edit/browse/manipulate binary data files, compare the coordinate sets, display residuals, etc.
• Conversation part: Programs to extract external information necessary for the processing.
• The Bernese Processing Engine (BPE): is an integrated part of the Bernese GPS Software Version 5 menu system. The Bernese Processing Engine (BPE) is a tool operating on top of these parts (programs) and is ideally suited to set up automated processing procedures. The processing strategy is set up once and for all from the RINEX files to the final results with all necessary programs. It is even possible to set up a parallel processing on different machines.
These programs (parts) are activated through pull‐down menus that reflect the main parts of the software in a logical way.
The Bernese GPS software has been used in many applications such as precise point positioning (with sub-cm accuracy), estimating the atmosphere parameters, precise and LEO orbit determination and estimating of Earth rotation parameters, combined processing of GPS and GLONASS observations, automatic processing of permanent networks and Ambiguity resolution on long baselines (2000 km and longer).The Bernese GPS software has been used in the CODE Analysis Centre to analyze the data of a global network of about 200 GPS receivers every day since 1992. The developments in the Bernese GPS Software is for the future GALILEO navigation system [Rolf, et al., 2007, p.1‐4].
3.3 The Processing Steps 3.3.1 Orbit Generation
The precise ephemeris and pole information models from Center for Orbit
Determination in Europe (CODE) were used to generate the tabular orbit and the
satellite clock information. The tabular orbit is the precise orbit in the Bernese
format, which represents the satellite geocentric position in the inertial space every
15 minutes. The standard orbit has been computed for each session by using the
tabular orbit and the pole information model [Rolf, et al., 2007, p. 83‐100]. This step
has been achieved in high accuracy (the RMS is in level 2 to 3 cm).
3. Da
3.3 Befo coo the syn com rece obs 3.3.
The dep and In t inte bas figu
ata Processi
.2 Receiv fore startin rdinates of
coordinat chronizatio mbination L
eiver clock servation fil .3 Baselin
ere are fo pending on d the distan this thesis, erested just
e lines fro ure.3.1).
Figure
ing
ver Clock S ng the proc f the refere tes from e on was don L3 to estim k correctio
les [ Rolf, et nes
our metho n the comm
nce betwee , the basel t in station om the inte
e 3.1: The b
Synchroniz essing, a p ence frame epoch to ne in zero mate the re ons were w
t al., 2007, p
ds of form mon observ
n the node ines were SVEA so th erested sta
baselines be zation priori coord
e IGS00 and epoch for
differencin eceiver cloc written dir p. 108‐109
ming base vation betw es, or other
created u hat the sing
ation (SVE
etween SVE
dinates hav d the IGS0
each cam ng by using ck correcti rectly into 9].
elines in t ween the t r criteria [R
sing the st gle differen EA) to the
EA station
ve been cal 0 velocity mpaign. Th
g the ionos on differen the Berne
the Bernes two nodes Rolf, et al., 2
tar method nce has bee
reference
and the IGS
lculated us model to t he receive sphere free nce. The re ese GPS so
se GPS So for each b 2007, p. 11 d because n used to f IGS station
S stations.
sing the transfer r clock e linear esulting oftware
oftware baseline 3‐115].
we are
form six
ns, (see
3.3 The processing steps
3.3.4 Preprocessing Phase Observations
The main goal of the pre‐processing phase observation is to detect the cycle slips at the phase observation files in a single difference level. In this step, the cycle slips have been screened using the COMBINED mode due to the longer baseline. This mode is mandatory as there is only the ionosphere‐free linear combination of the
and observations.
In the COMBINED mode, the residuals and between the first and second epochs for and can be expressed in the following [Rolf, et al., 2007, p. 118‐
130]:
3.1 3.2
is the ionosphere refraction by the carrier at time . is the ambiguity difference from epoch to .
The residual of the ionosphere‐free linear combination was tested under the assumption that the integer ambiguity remains the same from epoch to as the following:
| | 3 3.3
3.4
, 3.5 Where , are the standard errors of observations, respectively. The factor = √8 =√2 is caused by the fact in triple –difference, there are two satellites and two receivers and two epochs.
3.3.5 Screening of PostFit Residuals
In this step, the data with low–quality (the data was collected under extremely bad conditions or that the pre–processing at the last step was not successfully performed) has been regarded as out layers.
By applying the least squares' theory in the Bernese GPS software the residuals have been estimated in a double difference level with sampling rate (zero) “because we are interesting at all observations” and without ambiguity resolution, the residuals were marked and removed from the observation data [ Rolf, et al., 2007,p.
130‐137].
3. Data Processing
3.3.6 First Network Solution
After the cycle slips and the outliers are detected and removed from the observation, a linear ionosphere‐free combination L with unresolved ambiguity has been used to estimate the troposphere parameters by choosing the following options for each session [ Rolf, et al., 2007, p. 239]:
• Cut off angle (10 degree).
• Elevation dependent weight cos , Correlation strategy (Base line).
• ZPD model and mapping function (dry Niell).
• Site‐specific mapping function (with Niell) with parameters spacing (1 hour).
• Horizontal gradient estimation model (Tilting) with parameters spacing (24 hours).
3.3.7 Ambiguity Resolution
The most important criteria in selecting the ambiguity resolution strategy are the observation time period and the base line length. In this thesis, the observation time period was one day (24 hours) and the base line lengths were greater than 2000 km (as in Table 1.2). The Quasi Ionosphere‐Free (QIF) ambiguity resolution strategy with the ionosphere model from CODE and the estimated troposphere model from the last step has been used to fix the ambiguity [ Rolf, et al., 2007, p. 167‐182].
The ambiguities were resolved for each individual base line separately and the IGS stations were regarded as fixed during the fixing of the ambiguities. In general the percentage of the fixed ambiguity was from 66 % to 83% (see the appendix). Some ambiguities could not be resolved due to the fact that those satellite signals were interrupted by trees, multipath, or severe ionosphere activity [Sjöberg, et al., 2002].
3.3.8 Final network Solution
After the loop over all baselines are completed and the ambiguities are resolved, the
network has been adjusted by constrained all IGS stations coordinate (relate to the
reference frame IGS00) to 0.01 mm, the results of this step are the adjusted
coordinates and normal equation for each session. These sessions’ normal equations
were saved for the next work [ Rolf, et al., 2007, p. 149‐152].
3.3 The processing steps
3.3.9 Flow Diagram for the Processing Steps
Figure 3.2 shows the flow diagram of the action performed in this thesis to process the GPS data. This diagram provides a summary of the steps from Section 3.3.1 to 3.3.8. The solid rectangles (the left side) refer to the tasks or the steps and the dash rectangles (the right side) are the corresponding results of these tasks.
Figure 3.2: The flow diagram shows a summary of the processing strategy (for each session) using the Bernese GPS software.
Orbit Generation
Receiver Clock Synchronization
Preprocessing Phase Observation
Screening of postFit Residuals
Ambiguity Resolution (QIF) First Network Solution
Final Network Solution
Baselines creation (star strategy)
Standard Orbit (Orbit in Bernese format)
+ Satellite clock information
Receiver clock error
Baselines
Cycle Slips detection
Residuals file (outliers)
Troposphere Parameters
Fixed ambiguity
Adjusted coordinates +
Normal Equations (NEQ)
