GPS Measurements and Its Impact on Geodetic Datum Maintenance

GPS Measurements and Its Impact on Geodetic Datum Maintenance

By

Eng. / ALI JAAFAR DAKHIL FARHAN

B.Sc. Building and Construction Department (2002-2003)

University of Technology, Baghdad, Iraq Eng. in Ministry of Higher Education and Scientific Research,

Al-Qadisiya University, Iraq

A Thesis Submitted to the Faculty of Engineering at Mansoura University

In Partial Fulfillment of the Requirements for the Degree of

Master of Sciencein Public Work Engineering

Supervisors

2015

FACULTY OF ENGINEERING

MANSOURA UNIVERSITY

MANSOURA – EGYPT

2015

Prof.Dr. Eng. MostafaRabah Head of Crustal Movement Lab

Department of Geodynamics

National Research Institute of

Astronomy & Geophysics

Helwan, Egypt

Prof. Dr. / Mahmoud El-Mewafi Shetiwi

Professor of surveying and geodesy,

Public Works Department,

Faculty of Engineering,

Mansoura University

Dr. Ahmed Ali Awad Public work Engineering

Department Faculty of Engineering, Mansoura

University

GPS Measurements And Its Impact on Geodetic Datum Maintenance

By

Eng. / ALI JAAFAR DAKHIL FARHAN

B.Sc. Building and Construction Department (2002-2003)

University of Technology, Baghdad, Iraq Eng. in Ministry of Higher Education and Scientific Research,

Al-Qadisiya University, Iraq

A Thesis Submitted to the Faculty of Engineering at Mansoura University

In Partial Fulfillment of the Requirements for the Degree of

Master of Sciencein Public Work Engineering

Approved by the Examining Committee:

Prof. Dr. Ali Abdel Azim Thoeilb External Examiner

Prof. Dr. Zaki Mohamed Zedan Internal Examiner

Prof. Dr. Eng. Mahmoud EL-Mewafi, Thesis Main Advisor...

Public work Engineering Department, Faculty of Engineering, MANSOURA University

Prof.Dr. Eng. MostafaRabah, Head of Crustal Movement Lab

Department of Geodynamics National Research Institute of Astronomy & Geophysics Helwan


MANSOURA UNIVERSITY MANSOURA – EGYPT

2015


MANSOURA UNIVERSITY

MANSOURA – EGYPT

2015

قرآ ية

(سورة البقرة 23)

Dedication

ƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯƯ

The spirit of the deceased

&&My Son Jaafar&&

&&&&&

Will never forget you

Ali Jaafar Dakhil

2015

IN THE NAME OF

ALLAH

THE BENEFICENT, THE MERCIFUL

"Praise to Allah, Who guided us to this;

And

in no way could we have been guided,

unless Allah has guided us"

(AL A'raf 43)

Acknowledgements

I

Acknowledgements

The author wishes to express his most sincere gratitude and thanks to Prof. Dr.

Mahmoud El-Mewafi, The head of Public Works Department, Faculty of

Engineering, Mansoura University, for his supervision, valuable guidance, enormous help,

and discussion throughout this study.

I would like to give my cordial thanks and respect to Prof. Dr. Mostafa Rabah, Head

of Crustal Movement Lab Department of Geodynamics National Research Institute of Astronomy

& Geophysics

And my cordial thanks and respect to Dr. Ahmed Ali Awad, Public work Engineering

Department Faculty of Engineering, Mansoura University

As I like to express my grateful thanks to the Ministryof Higher Education and

Scientific Research in Iraq for their role and support me in accomplishing this thesis.

And finally, "not least" I extend my thanks and gratitude to the Deanship of the Faculty of

Engineering, Mansoura University, represented by the person of Mr. Dean Prof. Dr.

Zaki Mohamed Zedan.

Ali Jaafar Dakhil

2015

Abstract

II

Abstract:

One of the fundamental goals of geodesy is to precisely define positions of

points on the surface of the Earth, so it is necessary to establish a well-defined geodetic

datum for geodetic measurements and positioning computations. Recently, a set of the

coordinates established by using Global Positioning System ( GPS ) and referred to

an international terrestrial reference frame could be used as a three-dimensional

geocentric reference system for a country. Based on this modern concept, in 1992, the

Egyptian Survey Authority (ESA) established two networks. The first net is called High

Accuracy Reference Network (HARN) and consisted of 30 stations, 200 km spacing.

The second network was established to cover the cultivated areas (Nile Valley and

Delta) so it is called the National Agricultural Cadastral Network (NACN) with spacing

30 to 40 km. To transfer the International Terrestrial Reference Frame to the HARN,

the HARN was connected with four International GNSS Service (IGS) stations,

namely MATE (Italy), KIT3 (Uzbekistan), HART (South Africa) andMASP in (Canary

Island). The results of analyzing both of HARN and NACN were defined in

International Terrestrial Reference Frame (ITRF1994) epoch 1996.The

processing results were 1:10,000,000 (Order A) for HARN and 1:1,000,000 (Order B)

for NACN relative network accuracy standard between stations defined in ITRF1994

Epoch 1996. The following studies were done by the current research:

To evaluate the specified part, the available, of HARN & NACN stations in the

Nile Delta and surroundings andto see for what extent can Precise Point

Positioning (PPP) be an alternative for the differential GNSS techniques, a

Processing was done by Canadian Spatial Reference System (CSRS-PPP) Service

based on utilizing Precise Point Positioning (PPP) and Trimble Business Center

(TBC). Additionally, seven test points were processed by Trimble Business Center

“TBC” Software, the product of Trimble, with considering the PPP solution of

PHLW as a reference station for the processing. Based upon the computed

results,one can easily see that the quality of PPP solution compared with the

Differential Global Positioning System (DGPS) solution,in spite of the processed

baselines are exceed several tens of kilometers to 120 km, PPP shows a good

harmony with the DGPS in mm level.

To see how the PPP can be used in updating the ITRF of the IGS points, several

IGS stations were computed by PPP solution in ITRF2008 at Epoch 2015.274 and

the results were compared with the published IGS ITRF2008 at the same Epoch.

Abstract

III

The differences between two solutions were: the absolute value of the maximum

differences does not exceed 17mm for the Y component of NicoStation, Cyprus,

while does not exceed few mm for the other stations.

The results confirm the usability of PPP in updating the frame.

To evaluate the IGS stations that were used in transferring the ITRF1994 to

HARN, by transferring their published ITRF2008 Epoch2015.422 coordinates

values and the related transformation parameter to ITRF1994 Epoch1996 and

compares the transferred values by the reported values of (Scott ,1997).We used

only in the previous processing the published values and models as specified by

IGS.The computed differences shows a tolerance ranged between -8.6 cm to

14.6 cm. The reasons behind these differences are mostly returning to that were

used in realizing the ITRF94 that leads to sub-optimal stations distribution and

small discontinuities between IGS realizations of ITRF, as clarified by (Ferland

and Kouba, 1996).

To see for what extent can the PPP be an alternative for the differential

techniques in updating the geodetic frame and to study its impact in analyzing

the geodetic applications that need an ultimate accuracy like the National HARN

of Egypt, a critical example is given to demonstrate this study. The example is

concerned with analyzing a part of Egypt HARN and NACN (National

Agriculture Cadastre) Networks that is located in and around Nile

Delta.Transferring the values of HARN & NACN networks that were defined in

ITRF2008 epoch 2015.274 to the original ITRF frame of HARN, namely

ITRF1994 epoch 1996 and compare the resulted values with the original

coordinate‟s values given by Scott (1997) exploiting the published 14

transformation parameters between different ITRF‟s Frames by IGS. The

differences were ranged in X-component from 34 to 37 cm, except 0Z18(66cm)

that was partially destroyed, and Y-component ranged from -8 cm to -11 cm and

for Z-component, the differences were ranged between -7 cm and -8 cm, except

0Z18.

One can say that PPP is the most feasible factor in performing datum

maintenance by time and cost.

The Egyptian HARN & NACN Networks need to update their frame, to be the

most recent one either by PPP or traditional approach.

IV

Contents

Subject Page

Acknowledgements……………………………………………………………………………. I

Abstract………………………………………………………………………………………… II

Table of Contents……………………………………………………………………………… IV

List of Figures………………………………………………………………………………….. VI

List of Tables…………………………………………………………………………………... VII

Chapter 1 – Introduction

1.1.Introduction……………………………………………………………………………….. 1

1.2.Statement of the Problem…………………………………………………………………. 2

1.3.Objectives of the Thesis…………………………………………………………………… 6

1.4.Scope of Thesis 7

Chapter 2 – Introduction to GPS Measurements

2.1. GPS Overview…………………………………………………………………………….. 8

2.2. The Precise Point Positioning “PPP” …………………………………………………….. 26

Chapter 3 – Introduction to Geodetic Datums

3.1. Introduction to Geodetic Datums…………………………………………………………. 43

3.2. Modern Geodesy and ITRS/ITRF………………………………………………………… 45

3.3. World Geodtic System (WGS84) ………………………………………………………… 52

3.4. The Datum Problem………………………………………………………………………. 53

V

Subject Page

3.5. Kinematic Transformation Parameters Using Rigid Plate Rotation Model………...…….. 57

Chapter 4 – Geodetic Control Networks

4.1. Network Establishment and Control Based on Hierarchial Orders……………………….. 61

4.2. Requirements for the Position of Control Points………………………………………….. 62

4.3. Erection of Survey Marks and Monument Setting………………………………………... 64

4.4. The Egyptian Geodtic Control Network…………………………………………………... 66

4.5. GPS Control Network……………………………………………………………………... 67

4.6. Marking the Position of the GPS Control Point…………………………………………... 70

4.7. Introduction to Network Adjustment……………………………………………………. 75

4.8. GPS Network Adjustments Procedures…………………………………………………. 77

4.9. Adjustment of GPS Network Models……………………………………………………. 81

4.10. Continuously Operating Reference System…………………………………………….. 83

Chapter 5 – Experimental Results & Evaluation

5.1. Transformation Parameters Terrestrial Reference Systems “TRS” …………………….. 90

5.2. PPP Solution……………………………………………………………………………... 93

5.3. The Evaluation Study……………………………………………………………………. 97

Chapter 6 – Conclusions and Recommendations

6.1. Conclusions………………………………………………………………………………

6.2. Recommendation………………………………………………………………………… 111

References…………………………………………………………………………………….. 112

107

VII

List of Figures

Caption

Figure No. Page

1.1.The Egyptian First Order Triangulation Networks ………………………………………. 3

1.2.The HARN & NACN Networks ………………………………………………… 4

1.3. Connecting parts of Egyptian HARN with four stations of IGS…………………………

2.1 The GPS satellite constellation ………………………………………………………10

5

2.2. The single-difference technique ………………………………………………………….. 16

2.3. The double-difference technique ………………………………………………………..... 18

2.4. The triple-difference technique…………………………………………………................ 19

3.1. Local datum with best fit ellipsoid ……………………………………………………….. 44

3.2. Geocentric datum with ellipsoid that is a best fit to the world …………………………… 45

3-3.Conventional Celestial System (CRS)……………………………………………………. 48

3-4.Conventional Terrestrial System (CTS)………………………………………………….. 49

3-5.International Terrestrial Reference System (ITRS)………………………………………. 49

3-6. World Geodetic System 1984 (WGS84)……… …………………………………………. 53

3-7.Rigid Plate Rotation ……………………………………………………..……………….. 58

4.1. Monumentation of the first- and second-order trig points………………………………… 65

4.2.The Egyptian First Order Triangulation Networks ………………………………………. 71

4.3. GPS survey network.……………………………………. …………………………. 83

4.4. The Monumentation of one Core Station ………………………………………... 84

VII

Caption

Figure No. Page

5.1 The Africa tectonics sub-plates …………………….……………………. 92

5.2 The location of the used part of Egypt HARN & NACN ………………. 99

5.3 Station set (13) used for IGS Realization of ITRF 92-93-94 …………… 103

VIII

List of Tables

Caption

Table No. Page

1. The offset in Helwan coordinate values by using the static datum…………………………. 6

2.1. The characteristics of the used linear combinations………………………………………. 21

4-2.Differences between reference systems…………………………………………………... 50

4.1. Accuracy and density of GPS control networks…………………………………………... 70

5.1. The Cartesian angular Velocity of Nubian Plate………………………………….............. 93

5.2. ITRF2008 STATION POSITIONS AT EPOCH 2005.0 AND VELOCITIES.................... 95

5.3. DATA SET EXPRESSED IN ITRF2008 FRAME

STATION POSITIONS AND VELOCITIES AT EPOCH 2015/04/10……………………….

95

5.4.the updated positioning for four IGS stations defined in ITRF2008 epoch 2015.274 by

IGS & PPP…………………..…………………..…………………..…………………..……...

96

5.5 The differences between DGPS & PPP solutions for the observed Stations 97

5.6. The coordinates of chosen points of the HARN and NACN Networks…………………... 98

5.7. The Part of HARN & NACN network updated in ITRF2000……………………………. 99

5.8. Transformation parameters Between ITRF2008 Epoch 2005 to ITRF 1994 Epoch 2000... 100

5.9. The coordinate values of the IGS four stations in ITRF1994, Epoch 1996 and the

published coordinate values for the nominated IGS stations in ITRF2008

Epoch2005……………………………………………………..…………………………….....

102

5.10 .The transferred coordinate values of the four stations to ITRF1994 Epoch2000……….. 102

XI

Caption

Table No.

Page

5.11. The values of the published coordinate values of the four IGS stations & the reported

values by (Scott, 1997) in ITRF1994 Epoch1996……………………………………………...

102

5.12. The differences between the published coordinate values of the four IGS stations & the

reported values by (Scott, 1997) in ITRF1994 Epoch1996…………………………………….

103

5.13. The Results of Transformation the HARN to ITRF 1994 Epoch 1997…...……………... 104

5.14. The computed velocities and the transferred coordinate values to ITRF 94 Epoch 96 of

the specified part of the Egyptian HARN………………………………………………………

105

5.15. The values of the computed PPP HARN transferred to ITRF 94 Epoch 96 and the given

values at the same epoch as computed by Scott (1997)………...……..… ……………………

105

5.16. The Difference between the computed PPP HARN transferred to ITRF 94 Epoch 96

and the given values at the same epoch as computed by Scott (1997)…………………………

106

List of Abbreviations

AFREF African Reference Frame

APC Antenna Phase Center

APREF Asia-Pacific Reference Frame

ARP Antenna Reference Point

C/A Code Coarse Acquisition

CEP Conventional Ephemeris pole

CIS Conventional Inertial System

CORS Continuously Operating Reference Station CRF Celestial Reference Frame

CRS Celestial Reference System

CTP Conventional Terrestrial Pole

CTS Coordinated Terrestrial System

DGPS Differential Global Positioning System

DMA United States Defence Mapping Agency

DoD US Department of Defense

ECEF Earth-Centered, Earth-Fixed

ECI Earth centered inertial

EPGN Egyptian Permanent GPS Network

ESA Egypt Survey Authority

ETRF European Terrestrial Reference Frame

Finmap Finnish Project in the Eastern Desert

GNSS Global Navigation Satellite System

GPS Global Positioning System

HARN High Accuracy Reference Network

IAG International Association of Geodesy

IAU International Astronomical Union

ICRS International Celestial Reference System ICRS International Celestial Reference System

IERS International Earth Rotation Service

IGS International GNSS Service

ITRF International Terestial Reference Frame

ITRS International Terrestrial Reference System

JPL NASA's Jet Propulsion Laboratory

LADGPS Local Area Global Positioning System

NACN National Agricultural Cadastral Network

NAD83 North American Datum 1983

NGIA National Geospatial -Intelligence Agency

NNR no-net-rotation

NRCan Natural Resources Canada

NRIAG National Research Institute for Astronomy and Geophysics

PMM Plate Motion Model

PPP Precise Point Positioning

PPS Precise Positioning Service

PRN Pseudo Random Noise

RTK Real-time, kinematic

SA Selective Availability

SIRGAS Sistema de Referencia Geocentrico para las America

SLR Satellite Laser Ranging

SNR Signal-to-Noise Ratio

SPS Standard Positioning Service

SRI Survey Research Institute

TBC Trimble Business Center

TRS Terrestrial Reference System

UNB University of New Brunswick

UTM Universal Transverse Mercator

VLBI Very Long Baseline Interferometry

WADGPS Wide Area Global Positioning System

WGS84 World Geodetic System of 1984

Chapter 1 - Introduction

Page 1

1.1. Introduction

In space geodetic positioning, where the observation techniques provide

absolute positions with respect to a consistent terrestrial reference frame, the

corresponding precise definition and realization of terrestrial and inertial reference

systems is of fundamental importance. Thanks to significant improvements in receiver

technology, to extension and densification of the global tracking network along with

more accurate determination of positions and velocities of the tracking stations and to

dramatically improved satellite orbits, GPS is today approaching 0.1 ppm precision for

longer baselines and it can be considered to be the main global geodetic positioning

system providing nearly instantaneous three-dimensional position at the cm accuracy

level. One of the fundamental goals of geodesy is to precisely define positions of points

on the surface of the Earth, so it is necessary to establish a well-defined geodetic datum

for geodetic measurements and positioning computations. Recently, a set of the

coordinates established by using GPS and referred to an international terrestrial

reference frame could be used as a three-dimensional geocentric reference system for a

country (Abidin, H. ,1993a).

In the classical sense, a geodetic datum is a reference surface, generally an

ellipsoid of revolution of adopted size and shape, with origin, orientation, and scale

defined by a geocentric terrestrial frame. Once an ellipsoid is selected, coordinates of a

point in space can be given in Cartesian or geodetic (curvilinear) coordinates (geodetic

longitude, latitude, and ellipsoid height).

Two types of geodetic datum can be defined namely a static and kinematic

geodetic datum. A static datum is thought of as a traditional geodetic datum where all

sites are assumed to have coordinates which are fixed or unchanging with time. This is

an incorrect assumption since the surface of the earth is constantly changing because of

tectonic motion. Static datum does not incorporate the effects of plate tectonics and

deformation events. Coordinates of static datum are fixed at a reference epoch and

slowly go out of the date, need to change periodically which is disruptive.

Datum's can either become fully kinematic (dynamic), or semi-kinematic. A

deformation model can be adopted to enable ITRF positions to be transformed into a

static or semi-kinematic system at the moment of position acquisition so that users do

Chapter 1 Introduction

Page 1

not see coordinate changes due to global plate motions. GNSS devices which use ITRF

or closely aligned systems position users in agreement with the underlying kinematic

frame, however, in practice there are a number of very significant drawbacks to a

kinematic datum. Surveys undertaken at different epochs cannot be combined or

integrated unless a deformation model is applied rigorously, or is embedded within the

data, and the data are correctly time-tagged. On the other hand, Semi–Kinematic datum

incorporates a deformation model to manage changes (plate tectonics and deformation

events). Coordinates fixed at a reference epoch, so the change to coordinates is

minimized. Many countries and regions which straddle major plate boundaries have

adopted a semi-kinematic (or semi-dynamic) geodetic datum in order to prevent

degradation of the datum as a function of time due to ongoing crustal deformation that

is occurring within the country.

High precision GNSS positioning and navigation is very rapidly highlighting the

disparity between global kinematic reference frames such as ITRF and WGS84, and

traditional static geodetic datum. The disparity is brought about by the increasingly

widespread use of PPP and the sensitivity of these techniques to deformation of the

Earth due to plate tectonics. In order for precision GNSS techniques to continue to

deliver temporally stable coordinates within a localized reference frame.

1.2. Statement of the Problem

Between 1853 and 1859 a survey of Egypt was made but did not depend on a

triangulation scheme (Shaker A.A.,1982). Later, many attempts were made for

constructing a geodetic triangulation, but they were not of higher order. In 1874 a

number of expeditions were led by British scientists to various European colonies in

Africa and the Indian Ocean in order to simultaneously observe the transit of Venus for

the purpose of precisely determining differences in longitude. Locations included

Mauritius, Rodrigues, Réunion, St. Paul and Egypt. Helwan Observatory situated on Az

Zahra Hill in the Al-Moqattam Hills, South of Cairo was utilized for the observations,

and the station was termed “F1” where: Φo = 30º 01‟ 42.8591” N, Λo = 31º 16‟ 33.6”

East of Greenwich, the initial La Place azimuth being measured from Station O1

(Helwân) to Station B1 (Saccara), αo = 72º 42‟ 01.20” from South, and Ho = 204.3 m,

based on mean sea-level at Alexandria. This is considered the origin of the “Old Egypt

Datum of 1907” (Clifford J. Mugnier ,2008).


Page 2

It just so happens that M. Sheppard, director general of the Survey of Egypt,

reported (in French) to the Secretary General of the Geodesy Section of the

International Union of Geodesy and Geophysics that the initial geodetic work

performed in Egypt was computed on the Clarke 1866 ellipsoid where: “a, demi-grande

axe equatorial =6.378.206m (sic), α = 1/295 (sic).” Sheppard went on to say that all

cultivated lands in the Nile Valley that were based on 2nd and 3rd order triangulations

(for cadastral applications) initially used this ellipsoid, but that a later controlling chain

of triangulation spanning the length of the Nile Valley was computed with the later

adopted Helmert (1906) ellipsoid where a, = 6.378.200 m, 1/f = 1/298.3. Everything

was later re-calculated on the Helmert ellipsoid and also on the International 1924

ellipsoid where a = 6,378, 388 m, 1/f = 297 (Bulletin géodésique, 1925) , (Clifford J.

Mugnier , 2008).

In 1907 it became possible to begin a new work for establishing a geodetic

triangulation frame for Egypt, which is considered to be the first national network to be

established in Africa (Moritz, 1981). From the cost point of view, it was decided to

carry out the network along the Nile Valley only (Shaker, 1982). The main reason to

carry it out was to fix, with a great possible accuracy, fundamental control-stations to be

a base for the cadastral survey and national mapping of the country. Egyptian network

was extended to Sudan and other African nations. The first order geodetic horizontal

control network of Egypt contains two main networks, Network (1) and Network (2),

(Cole, J., 1944). Figure (1.1) shows the first order triangulation networks.

In 1930, after a re-adjustment of the classical network, the New Egypt Datum of

1930 was published, also referenced to the Helmert1906 ellipsoid. The common

abbreviation for the new datum is “EG30.” This remains the current classical system

used in Egypt for civilian mapping purposes.

In 1992, an Egypt Survey Authority (ESA) steering committee developed a plan

for the creation of new datum for Egypt, with the following approach (Scott, 1997):

First, observe approximately 30 stations at approximately 200 km interval,

covering all of Egypt, creating a High Accuracy Reference Network (HARN).

Both high absolute and relative accuracies are required for these stations.

http://link.springer.com/journal/12357


Page 3

Second, establishing the Notational Agricultural Cadastral Network (NACN)

relative to these 30 stations, covering the green area of Egypt (Nile Valley and

the Delta) at 30-40 km intervals. This station spacing was selected to allow for

further densification with single frequency receivers, see figure (1.2).

Third, densify this network at a station spacing of approximately 5 km for use as

cadastral control at the governorate level.

Finally, replace the existing Egyptian Mercator grid with a new modified UTM

coordinate system.

Each station was observed for six sessions, every session was 6 hours with 30

seconds epoch interval. The observation time was planned to produce 1:10,000,000

(Order A) for HARN and 1:1,000,000 (Order B) for NACN relative network accuracy

standard between stations. The results of analyzing both of them were defined in

ITRF1994 epoch 1996.

Figure (1.1): The Egyptian First Order Triangulation Networks.


Page 4

Figure (1.2.): The HARN & NACN Networks

The ITRF1994 was transferred to Egypt‟s HARN network by connecting it with four

IGS stations, namely MATE (Italy), KIT3 (Uzbekistan), HART (South Africa) and

MASP in (Canary Island), see figure (1.3). Each HARN‟s station was observed for six

sessions, every session was 6 hours with 30 seconds epoch interval. The observation

time was planned to produce 1:10,000,000 (Order A) for HARN and 1:1,000,000 (Order

B) for NACN relative network accuracy standard between stations. The results of

analyzing both of them were defined in ITRF1994 epoch 1996.


Page 5

Figure (1.3): Connecting parts of Egyptian HARN with four stations of IGS

(Rabah et. al., 2015) proofed the drawback of the currently used Egypt static

datum, namely ITRF1994 Epoch 1996, based on GPS Observation Campaign 1996.

Because Helwan is considered the only station that was used in updating the ITRF2008

geodetic frame, the values of Helwan coordinates at any Epoch can be computed by

(http://itrf.ensg.ign.fr/site_info_and_select/solutions_extraction.php). So, Helwan

coordinate values was computed by IGS computing center Helwan IGS Station with in

ITRF2008 Epoch2015.274. Helwan was transferred by the published transformation

parameters, computed by (http://itrf.ign.fr/trans_para.php) to ITRF1994 Epoch 1996 The

related Reference Frame coordinate values, related velocity parameters and the

differences are tabulated in table (1.1). As it is indicated in the table, the differences

between Helwan coordinate values defined in ITRF2008 Epoch 2015 and the values

defined in ITRF1994 Epoch 1996 are: -41.8 cm for X component, 26 cm for Y

component and 31.6 cm for Z component. These discrepancies exceed any accuracy

requirements needed by any control works.

http://itrf.ensg.ign.fr/site_info_and_select/solutions_extraction.php


Page 6

Table (1.1.): The offset in Helwan coordinate values by using the static datum

Reference Frame HELWAN

IGS- ITRF2008 Epoch2015.274 4728141.098 2879662.549 3157147.092

Published ITRF2008 Epoch2005 4728141.309 2879662.406 3157146.932

Published Vx, Vy, Vz (m/year) -0.0211 0.0143 0.016

ITRF1994Epoch1996 4728141.516 2879662.289 3157146.776

Differences -0.418 0.260 0.316

1.3 Objectives of the Thesis

To study the situation of the HARN & NACN Network after passing more than

20 years, a check for existing HARN monuments in and around Delta. To

evaluate the PPP and answering wither PPP can be used as an alternative for

DGPS in geodetic Control Networks. Several (PPP) tests on several IGS station

were performed.

To see the quality of the HARN and NACN networks solution, the selected GPS

stations were estimated in its International Terrestrial Reference Frame (ITRF)

at the day of the observing campaign and site velocities given by the

International Earth Rotation Service (IERS) and then transformed to the original

processed ITRF datum, namely ITRF1994, epoch 1996.

To perform the required transformation processing, PPP GPS processing

techniques was utilized in the transformation process as well as a three

parameters kinematic rigid plate model.

To push Responsible authorities for maintenance of networks that represent the

references (datum)

To push the inevitability of updating of HARN and NACN according to the

latest frame by taking a modern observation to them and analyze it by PPP

To see the impact of tectonic and evaluate the results in terms of the required

level of accuracy.


Page 7

1.4 . Scope of Thesis

In addition to this chapter, the thesis consists of four chapters as follows:

1.4.1 Chapter Two: Introduction to GPS Measurements. This chapter contains GPS

Overviewand the principle of operation, segments of the system, error of

system, GPS Observation Equations, Relative Positioning Modes, The Precise

Point Positioning "PPP", Mathematical Model of Precise Point Positioning, and

adjustment of GPS processing.

1.4.2 ChapterThree: Introduction to Geodetic Datums, This chapter discusses the

different types of Geodetic datums and their relation to Modern Geodesy and

ITRS/ITRF, World Geodetic System (WGS84). It also explains the datum

problem, Kinematic Transformation Parameters Using Rigid Plate Rotation

Models.

1.4.3 ChapterFour: Introduction to Geodetic Control Networks, This chapter deals

with Geodetic Control Networks, Geodetic Horizontal Network Standards,

GPS Networks, Control Survey Requirements, Network Design, and

Introduction to Network Adjustments.

1.4.4 ChapterFive: This chapter explains how data were collected and analyzedand

as well as discussing and evaluating of the obtained results ,

1.4.5 Chapter six::Conclusions and Recommendations: Thischapter contains the

main conclusions that were derived from the research work and

recommendations for the future study.

Chapter 2 Introduction to GPS Measurements

Page 8

Chapter 2

Introduction to GPS Measurements

2.1 . GPS Overview

The Global Positioning System (GPS) is an all-weather, space-based navigation

system. This system is development by the US Department of Defense (DoD) to satisfy

the requirements of the military forces to accurately determine their position, velocity

and time in a common reference system, anywhere on or near the earth on a continuous

basis.

2.1.1 The principle of operation

The GPS satellites transmit radio signals giving the position of each satellite and

the time of transmitting the signal. These signals can be received on the earth with a

receiver. The distance between a satellite and the receiver can be computed by

multiplying the speed of light with difference between the times that the signal left the

satellite and the time that it arrives at the receiver. If the distances to four or more

satellites are measured simultaneously, then a three dimensional position on the earth

can be determined. GPS positioning capability is provided at no cost to civilian and

commercial users world-wide at an accuracy level of 100 meters. This accuracy level is

known as the Standard Positioning Service (SPS). The US military and its allies, and

other authorized users, receive a specified accuracy level of 21 meters, known as the

Precise Positioning Service (PPS). The full accuracy capability of GPS is denied to

users of the SPS through a process known as Selective Availability (SA). This

purposeful degradation in GPS accuracy is accomplished by intentionally varying the

precise time of the clocks on board the satellites and by providing incorrect orbital

positioning data in the GPS navigation message. SA is normally set to a level that will

provide 100 meter positioning accuracy to users of the Standard Positioning Service. In

practice, several additional sources of error other than SA can affect the accuracy of a

GPS-derived position. They include unintentional clock and ephemeris errors, errors

due to atmospheric delays, multipath errors, errors due to receiver noise, and errors due

to poor satellite geometry (Hofmann-Wellenhof, 1994).


Page 9

Differential GPS (DGPS) is the most widely used method of GPS augmentation

and significantly improves the positioning accuracy. DGPS makes use of GPS reference

stations at locations which have been geodetically surveyed and so are known with a

very high accuracy. These stations observe GPS signals in real time and compare their

measurements to the ranges expected to be observed at the fixed positions of the

stations. The differences between the observed and the predicted ranges are used to

compute the corrections to GPS parameters like error sources, resultant positions, or

observations. These differential corrections are then transmitted to GPS users, who

apply the corrections to their received GPS signals or the computed position. Depending

on the user application, DGPS reference stations can be permanent, elaborate

installations, or they can be small, mobile GPS receivers that can be moved to various

well surveyed locations. The equipment used to broadcast differential corrections, the

type of radio data link used, and the size of the geographic area covered by the DGPS

system also vary greatly with the application. Differential systems can be Local Area

(LADGPS) or Wide Area (WADGPS). The LADGPS broadcasts differential

corrections over a limited geographic area, while the WADGPS can cover a continent or

more. For civil applications, DGPS can provide sub-meter accuracy (Leick, 1995).

2.1.2 The segments of the system

The GPS system consists of three segments, the space segment consisting of

satellites which broadcast signals, the control segment managing the whole system, and

the user segment including the all types of receivers which receive the satellite signals.

2.1.2.1 Space Segment

The Space segment of the system consists of the GPS satellites. These satellites

send radio signals from space. The GPS operational constellation consists of 24

satellites: 21 navigational satellites and 3 active spares orbit the earth in 12 hour orbits

as shown in figure


Page 10

Figure (2.1.): The GPS satellite constellation.

These orbits repeat the same ground track (as the earth turns beneath them) once

each day. The orbit altitude is such that the satellites repeat the same track and

configuration over any point approximately every 24 hours (4 minutes earlier each day).

This is accomplished by satellites in nearly circular orbit with an altitude of about

20200 km above the earth. There are six orbital planes (with nominally four satellites in

each), equally spaced (60 degrees apart), and inclined at about fifty-five degrees with

respect to the equatorial plane. This constellation provides the user with between five

and eight satellites visible from any point on the earth. The GPS satellites provide a

platform for radio transceivers, atomic clocks, computers and various equipment used

for positioning requirements. The equipment of the satellites allows the user to operate a

receiver to measure simultaneously distances to more than three satellites. Each satellite

broadcasts a message which allows the user to determine the spatial position of the

satellite (US Department of Defense, 1996).

The satellites in the GPS constellation are arranged into six equally-spaced

orbital planes surrounding the Earth. Each plane contains four "slots" occupied by

baseline satellites. This 24-slot arrangement ensures users can view at least four

satellites from virtually any point on the planet.The Air Force normally flies more than

24 GPS satellites to maintain coverage whenever the baseline satellites are serviced or

decommissioned. The extra satellites may increase GPS performance but are not

considered part of the core constellation.


Page 11

In June 2011, the Air Force successfully completed a GPS constellation

expansion known as the "Expandable 24" configuration. Three of the 24 slots were

expanded, and six satellites were repositioned, so that three of the extra satellites

became part of the constellation baseline. As a result, GPS now effectively operates as a

27-slot constellation with improved coverage in most parts of the

world(Offi.US.Gov.info.GPS, 2015).

2.1.2.2 Control Segment

The Control Segment consists of a system of tracking stations located around the

world. The control segment monitors the functioning of the satellites and uploads

orbital, clock correction, and auxiliary data into the satellite memories. This segment

consists of two main parts, GPS Master Control, and Monitor Network. The Master

Control facility is located at Falcon Air Force Base in Colorado. The monitor stations

measure signals from the satellites which are incorporated into orbital models for each

satellite. The models compute precise orbital data (ephemeris) and satellite clock

corrections for each satellite. The Master Control station uploads ephemeris and clock

data to the satellites. The satellites then send subsets of the orbital ephemeris data to

GPS receivers over radio signals.

2.1.2.3 User Segment

The GPS User Segment consists of all the GPS receivers and the user

community. GPS receivers convert satellite signals into position, velocity, and time

estimates. Four satellites are required to compute the four dimensions of position (X, Y,

Z) and time. GPS receivers are used for navigation, positioning, time dissemination, and

other research. Navigation in three dimensions is the primary function of GPS.

Navigation receivers are made for aircraft, ships, ground vehicles, and for hand carrying

by individuals. Precise positioning is possible using GPS receivers at reference

locations providing corrections and relative positioning data for remote receivers.

Surveying, geodetic control, and plate tectonic studies are examples. Time and

frequency dissemination, based on the precise clocks on board the satellites and

controlled by the monitor stations, are another use for GPS. Astronomical observatories,

telecommunication facilities, and laboratory standards can be set to precise time signals

or controlled to accurate frequencies by special purpose GPS receivers.


Page 12

2.1.3 The satellite signals

The satellite transmits two microwave carrier signals. These signals are L1

frequency (1575.42 MHz) and L2 frequency (1227.60 MHz). The C/A Code (Coarse

Acquisition) modulates the L1 carrier phase. The C/A code is a repeating 1 MHz

Pseudo Random Noise (PRN) Code. This noise-like code modulates the L1 carrier

signal, "spreading" the spectrum over a 1 MHz bandwidth. The C/A code repeats every

1023 bits (one millisecond). There is a different C/A code PRN for each satellite. GPS

satellites are often identified by their PRN number, the unique identifier for each

pseudo-random-noise code. The C/A code that modulates the L1 carrier is the basis for

the civil SPS. The P-Code (Precise) modulates both the L1 and L2 carrier phases. The

P-Code is a very long (seven days) 10 MHz PRN code. In the Anti-Spoofing (AS) mode

of operation, the P-Code is encrypted into the Y-Code. The encrypted Y-Code requires

a classified AS module for each receiver channel and is for use only by authorized

users with cryptographic keys. The P (Y)-Code is the basis for the PPS. The Navigation

Message also modulates the L1-C/A code signal. The Navigation Message is a 50 Hz

signal consisting of data bits that describe the GPS satellite orbits, clock corrections,

and other system parameters. The GPS navigation message consists of time-tagged data

bits marking the time of transmission of each sub frame at the time they are transmitted

by the satellite. A data bit frame consists of 1500 bits divided into five 300-bit sub

frames. A data frame is transmitted every thirty seconds. Three six-second sub frames

contain orbital and clock data. Satellite clock corrections are sent in sub frame one and

precise satellite orbital data sets (ephemeris data parameters) for the transmitting

satellite are sent in sub frames two and three. Sub frames four and five are used to

transmit different pages of system data. An entire set of twenty-five frames (125 sub

frames) makes up the complete Navigation Message that is sent over a 12.5 minute

period. Data frames (1500 bits) are sent every thirty seconds. Each frame consists of

five sub frames. Data bit sub frames (300 bits transmitted over six seconds) contain

parity bits that allow for data checking and limited error correction. Navigation clock

data parameters describe the satellite clock and its relationship to GPS time. Ephemeris

data parameters describe satellite orbits for short sections of the satellite orbits. The

ephemeris parameters are used with an algorithm that computes the satellite position for

any time within the period of the orbit described by the ephemeris parameter set

(Hofmann-Wellenhof, 1994).


Page 13

2.1.4 The Biases

The GPS measurements are affected by both systematic errors and random

noise. The systematic errors can be modeled or eliminated by appropriate combinations

of the observables as will be explained in section 1.3.6 and 1.4.2. The systematic error

sources may be classified into three groups namely satellite related errors, propagation

medium related errors, and receiver related errors. The satellite related errors are the

clock bias and the orbital errors. The ionospheric and the tropospheric refraction are the

propagation medium related error. The antenna phase center variation and the clock bias

are considered the receiver related errors. The propagation medium related error

specially the ionospheric refraction is considered in this research.

The random noise contains mainly the observation noise and the multipath effects.

Multipath is interference between the direct and reflected signals. Multipath is difficult

to detect and sometimes hard to avoid. The multipath effect can be considerably

reduced by selecting sites protected from reflections and by an appropriate antenna

design.

2.1.4.1 Ionospheric refraction effect

The ionosphere is the part of the earth's atmosphere containing free electrons.

This part extends from about 50 to 1000 km above the surface of the earth. The

ionosphere is considered as a dispersive medium for the GPS radio signals (Seeber,

1993). The vertical ionospheric delay can be written as:

TECf

ionv 2

3.40 (2.1)

Where

ionv The vertical ionospheric delay in range units.

f The frequency of the signal.

TEC The total electron content.

The total electron content is a complicated quantity because it depends on the

sunspot activities, seasonal and diurnal variations, the line of sight which includes

elevation and azimuth of the satellite, and the position of the observation site. The total

electron content may be measured, estimated, or eliminated.


Page 14

2.1.4.2 The tropospheric effect

Troposphere is the lower part of the earth‟s atmosphere. It extends from the

surface of the earth to about 40 km. The troposphere is nondispersive for frequencies

below 30 GHz. Therefore the propagation of GPS signal in the troposphere is

frequency-independent and has the same effect on the phase and the code

measurements. The elimination of the tropospheric refraction by dual frequency

methods is not possible, so the tropospheric delay should be modeled.

There are various models developed to compute the tropospheric refraction.

These models differ primarily with respect to the assumptions made on the vertical

refractivity profile and the mapping of the vertical delay with elevation angle. In this

research the models of Hopfield, Saastamoninen, and the modified Hopfield models

(Seeber, 1993) have been used.

2.1.5 GPS Observation Equations

Two different models for the GPS observations can be applied: one model for

the code measurements and the other model for phase measurements.

The code observation is the difference between the transmission time of the

signal from the satellite and the arrival time of that signal at the receiver multiplied by

the speed of light. The time difference is determined by comparing the replicated code

with the received one. The time difference is the time shift essential to align these two

codes. The code observation represents the geometric distance between the GPS

satellite and the receiver plus the bias caused by the satellite and the receiver clock

offsets. Moreover, the atmospheric bias and the noise influence the code observations.

The basic observation equation related to the code measurement of receiver a to satellite

j can be written as:

R t t C t C t Ion t Trop ta

j

a

j j

a a

j

a

j( ) ( ) ( ) ( ) ( ) ( ) (2.2)

Where:

R ta

j ( ) The code observation in meter.

a

j t( ) The range between the receiver at station a and satellite j.

C Speed of light.


Page 15

j t( ) The bias of the satellite clock.

a t( ) The bias of the receiver clock .

a

j Ion t( ) The ionospheric delay in meter.

a

j Trop t( ) The tropospheric delay in meter.

The noise of the code measurement.

The phase measurement is the difference between the generated carrier phase

signal in the receiver and the received signal from the satellite. The phase measurement

is in range units when it is multiplied by the signal wave length. It represents the same

range and biases as the code observation, and additionally the range related to the

unknown integer ambiguities. The observation equation for the phase measurement can

be written as the following:

)(1

)(1

)( 1

)( 1

)(1

)( tTroptIontCtCNtt j

a

j

aa

jj

a

j

a

j

a (2.3)

The above equation can be modified to

a

j

a

j

a

j j

a a

j

a

jt t N f t f t Ion t Trop t( ) ( ) ( ) ( ) ( ) ( ) 1 1 1

(2.4)

Where:

a

j t( ) The phase measurements.

N a

j The unknown integer ambiguity.

The signal wave length.

f The signal frequency.

The noise of the phase measurements.

The ionospheric effect has the same absolute value for the code and phase

measurements but the signs are opposite. This behavior is due to the different

propagation modes for the code and the carrier phase (Hofmann-Wellenhof, 1994). The

code and the phase observation equation are valid for L1 and L2 signals.


Page 16

2.1.6 Relative Positioning Modes

Relative positioning aims at the determination of the vector between two stations

often called a baseline. The coordinates of one of those stations are known with very

high accuracy. Relative positioning techniques are always used to eliminate or at least

minimize the influence of the involved systematic biases. Relative positioning is an

observation technique based on using more than one observing station at the same time

rather than relying on the point positioning mode. The errors that influence GPS signals

can be greatly reduced or removed using difference modes. Difference modes are much

successful for short baselines, as a result from the existing correlation between signals

received at several stations simultaneously tracking the same satellites. Difference

modes can be performed either on code or carrier phase observations. The relative

positioning can be executed between receivers, between satellites, or between epochs,

as well as any combination among them leading to single-differences, double-

differences, and triple-differences.

2.1.6.1 Single-difference mode

The single-difference mode is executed between a pair of receivers and one satellite as

shown in figure 2.2.

Figure (2.2.): The single-difference technique.


Page 17

Denoting the stations by a and b and the satellite by i. The zero-difference model for

phase observations can be written as:

)( 1

)( 1

)()(1

)()( tTroptIontfNttft i

a

i

aa

ii

a

i

a

iii

a

(2.5)

b

i i i

b

i

b

i i

b b

i

b

it f t t N f t Ion t Trop t( ) ( ) ( ) ( ) ( ) ( )

1 1 1

The difference of the two equations is:

a

i

b

i

a

i

b

i

a

i

b

i i

b a

b

i

a

i

a

i

b

i

t t t t N N f t t

Ion t Ion t Trop t Trop t

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

1

1 1

(2.6)

By using the shorthand notations:

a b

i

a b

i

a b

i i

a b a b

i

a b

it t N f t Ion t Trop t, , , , , ,( ) ( ) ( ) ( ) ( ) 1 1 1

(2.7)

The single-difference removes the effect of the satellite clock offset ( )t and

reduces the effect of the satellite orbital error depending on the distance between the

stations. The atmospheric delay is significantly reduced especially with short base lines

and can be neglected. In this case the single-difference model for both L1 and L2

frequencies can be written as:

a b

i

a b

i

a b

i i

a bt t N f t, , , ,( ) ( ) ( ) 1

(2.8)

2.1.6.2 Double-difference mode

The double-difference mode is executed between a pair of receivers and pair of

satellites as shown in figure( 2.3) Denoting the stations by a and b and the satellites to

be involved by j, k. Two single-differences according to Equation (2.8) can be applied:

)()(1

)( ,,,, tfNtt ba

jj

ba

j

ba

j

ba

(2.9)

a b

k

a b

k

a b

k k

a bt t N f t, , , ,( ) ( ) ( ) 1


Page 18

These single-differences are subtracted to get the double-difference model as:

a b

j

a b

k

a b

j

a b

k

a b

j

a b

kt t t t N N, , , , , ,( ) ( ) ( ) ( ) 1

(2.10)

Using the shorthand notation as in the single-difference

a b

j k

a b

j k

a b

j kt t N,

,

,

,

,

,( ) ( ) 1

(2.11)

The result of this mode is the omission of the receiver clock offsets. The double-

difference model for long baselines when there is a significant difference in the

atmospheric effect between the two baselines ends can be expressed as:

a b

j k

a b

j k

a b

j k

a b

j k

a b

j kt t N Ion t Trop t,

,

,

,

,

,

,

,

,

,( ) ( ) ( ) ( ) 1 1 1

(2.12)

The double-difference model is the applied technique in this research.

Figure (2.3.): The double-difference technique.


Page 19

2.1.6.3 Triple-difference mode

The triple-difference mode is the change in the double-difference observable

between two epochs as shown in figure 2.4. Denoting two epochs by t t1 2, , the double-

difference model at each epoch is :

a b

j k

a b

j k

a b

j kt t N,

,

,

,

,

,( ) ( )1 1

1

(2.13)

a b

j k

a b

j k

a b

j kt t N,

,

,

,

,

,( ) ( )2 2

1

The corresponding triple-difference equation can be written as

a b

j k

a b

j kt t t t,

,

,

,( , ) ( , )1 2 1 2

1 (2.14)

Figure (2.4.): The triple-difference technique.

In the above equation it is assumed that the ambiguity remained unchanged

within the time. Therefore, the phase ambiguity bias is canceled. This is true if the

receive did not loose lock within the time and no cycle slip occurred.

2.1.7 Linear Combinations

The actual GPS observables are the carrier phases observationsL 1 , L 2 and the

code observations RL 1, RL 2 . Some other artificial observations can be created from the

actual observations by linearly combining them. The main applied linear combinations


Page 20

in this research will be e xplained. Any phase combination (Wübbena, 1989)can be

expressed as:

a b a b, 1 2 (2.15)

The corresponding frequency will be

f a f b fa b, 1 2 (2.16)

and the wave length is

a b a b,

1

1 2

(2.17)

The frequency-dependent biases such as the ionospheric delay and the multipath

will be affected by these combinations. The linear combinations have no effect on the

frequency-independent biases such as the tropospheric delay, the clock and the

ephemeris errors.

The linear combinations will alter the ionospheric delay by a ratio depending on

the integers a, b. The ionospheric delay can be written as:

Ion

a f Ion b f Ion

a f b fa b,

1 1 2 2

1 2

(2.18)

Substitute Equation(2.1), the ionospheric delay will be

Ion

TEC b f a f

f f a f b fa b,

.

40 3 1 2

1 2 1 2

(2.19)

The ratio between the ionospheric delay in the linear combination and in L1

observations will be:

ion

f b f a f

f a f b f

1 1 2

2 1 2

(2.20)


Page 21

Where: ion The ionospheric ratio.

The noise level is also affected by the linear combination. In this case the

standard deviation can be written in range units as:

a b a b a b, , 2

1

2 2

2

2 (2.21)

Where:

1 2, The standard deviation in L1 and L2 observations in cycles

respectively.

If the noise in L1 and L2 observations have the same standard deviation in

cycles, the ratio between the noise level in the linear combinations and L1 observation

can be written as:

noise

a b

a b

2

2

2 1

2

(2.22)

Where:

noise The noise ratio.

Table (2.1.): The characteristics of the used linear combinations.

Signal a B a,b (m) ion noise

L1 1 0 0.190 1.00 1

L2 0 1 0.244 1.65 1.3

Wide-lane 1 -1 0.862 -1.28 6.4

Narrow-lane 1 1 0.107 1.28 0.8

Ionosphere-free 77 -60 0.006 0.00 3.2

low ionospheric

effect 5 -4 0.101 -0.71 3.4

Very long wave

length -7 9 14.65 350.35 877.9


Page 22

Some different linear combinations are applied in this research. Table 2.1 shows the

characteristics of these linear combinations.

2.1.8 Wide-lane and narrow-lane linear combinations

There are two linear combinations which play an important role in the fixation

of the unknown ambiguities, namely the wide-lane and the narrow-lane linear

combination. The wide-lane linear combination can be expressed of L1 and L2 phase

observations as:

w 1 2 (2.23)

and the narrow-lane linear combination as:

n 1 2 (2.24)

The wave length of the wide-lane combination is about 86 cm which is approximately 4

times the wave length of L1 or L2 observations as shown in table 1.1. This means that

the ambiguity resolution process is generally much simpler when using such a

combination than using L1 or L2 observations.

There is some advantage in using the wide-lane and the narrow-lane linear

combination in the ambiguity resolution process. There is an even odd relation between

the wide-lane and the narrow-lane ambiguities. When the wide-lane ambiguity is odd

the corresponding narrow-lane ambiguity has also to be odd, similarly when the wide-

lane ambiguity is even the corresponding narrow-lane ambiguity has to be even. The

even odd relation implies that when one of the ambiguities of these combinations is

firstly resolved the effective wave length of the other combination will be increased by

a ratio of 2; consequently it can be resolved more easily.

2.1.9 Ionosphere-free linear combinations

The ionosphere-free is another important linear combination that used in this

investigation. To eliminate the effect of the ionospheric refraction a linear combination

between two signals with different frequencies is used. The ionosphere-free linear

combination of L1 and L2 phase observations can be expressed as:


Page 23

ion

f

f 1

2

1

2 (2.25)

The ionosphere-free linear combination has a significant disadvantage because

the resulting ambiguity is no longer an integer. This combination can be written in other

form as:

ion 77 601 2 (2.26)

The left hand side of Equation (2.25) and Equation (2.26) are different. The

above relation cannot be applied for ambiguity resolution because the wave length is

very short, about 0.63 cm. Such short wave length makes the ambiguity resolution

practically impossible. The estimated position using the ionosphere-free combination

after resolving the ambiguities is not influenced by the ionospheric effect. The

elimination of the ionospheric refraction is the huge advantage of this combination. This

method is the main reason why the GPS signal has two carrier waves L1 and L2

(Hofmann-Wellenhof, 1994).

2.1.10 The Mathematical Model for Relative Positioning

The double -difference is selected for treatment in detail, equation (2-44). The

canceling effect of the receiver clock biases is the reason why double differences are

preferably used. This cancellation resulted from the assumptions of simultaneous

observations and equal frequencies of the satellite signals . The final form of the double

difference equation is:

jk

AB )(t )(1

tR jk

AB

jk

ABN (2-49)

The model for the double –difference of equation (2-48), multiplied by , is

jk

AB )(t = )(tR jk

AB + jk

ABN (2-50)

Where the term: )(tR jk

AB , containing the geometry , is composed as

)(tR jk

AB = )(tR k

B - )(tR j

B - )(tR k

A + )(tR j

A (2-51)


Page 24

which reflects the fact of four measurement quantities for a double –difference.

Each of four terms must be linearized according to (Hofmann W. , 2001) yielding

)(tR jk

AB = )(0 tR k

B ( )

)(0 tR k

B

( )

)(0 tR k

B

( )

)(0 tR k

B

)(0 tR J

B

( )

)(0 tR j

B

( )

)(0 tR j

B

( )

)(0 tR j

B

)(0 tR k

A ( )

)(0 tR k

A

( )

)(0 tR k

A

( )

)(0 tR k

A

)(0 tR J

A ( )

)(0 tR j

A

( )

)(0 tR j

A

( )

)(0 tR j

A

(2-52)

Substituting (2-51) into (2-50) and rearranging leads to the linear observation equation

)(tR jk

AB = ( )

( )

(2-53)

Where the left side

)(tL jk

AB = jk

AB )(t - )(0 tR k

B + )(0 tR j

B + )(0 tR k

A - )(0 tR j

A (2-54)

Comprising both the measurement quantities and all terms computed from the

approximate values. On the right side of (2-53), the abbreviations have been used


Page 25

( )

( )

)(0 tR k

A

( )

)(0 tR j

A

( )

( )

)(0 tR k

A

( )

)(0 tR j

A

( )

( )

)(0 tR k

A

( )

)(0 tR j

A

(2-55)

( )

( )

)(0 tR k

B

( )

)(0 tR j

B

( )

( )

)(0 tR k

B

( )

)(0 tR j

B

( )

( )

)(0 tR k

B

( )

)(0 tR j

B

Note that the coordinates of one point (e.g.,A) must be known for relative

positioning. More specifically, the known point A reduces the number of unknowns by

three because of :

(2-56)

And leads to slight change in the left side term

)(tL jk

AB = jk

AB )(t - )(0 tR k

B + )(0 tR j

B + )(tR k

A - )(tR j

A (2-57)

Assuming now four satellites and two epoch , the matrix- vector system

[ ( )

( )

( )

( )

( )

( )]

[

]

(2-58)


Page 26

[

( ) ( )

( )

( )

( ) ( )

( )

( ) ( )

( )

( ) ( )

( )

( ) ( )

( )

( ) ( ) ]

is obtained which represents a determined and, thus , solvable system. Note that

for one epoch the system has more unknowns than observation equations.

2.2 The Precise Point Positioning "PPP"

Precise Point Positioning (PPP) is a satellite based positioning technique

aiming at highest accuracy in close to real-time. First investigations using dual

frequency data from a single GPS receiver data for a few cm-positioning in post-

processing mode have been published in 1997 by JPL. Utilizing the ionosphere free

linear combination the remaining required model information like precise orbits and

clocks issued by the IGS has been used. Within the last decade a number of approaches

have been carried out to serve applications in close to real- time by this technique.

Although traditionally a double-differencing processing tool, the Bernese

software is also capable of analyzing undifferenced GPS measurements in post

processing mode. BSW PPP is very fast and efficient in generating cm-level accuracy

station coordinates. Nevertheless, it is not possible to reach a coordinate quality as

obtained from a network analysis.

Since PPP is a technique with only one GPS receiver, no differences between

two receivers can be built to eliminate satellite specific errors such as clock and orbital

errors. Therefore it is necessary to use the most precise satellite clock corrections and

satellite orbits. Relevant products, available even in real-time, are for example IGS ultra

rapid precise ephemerides ensuring an orbital representation of 10-15 cm and better

than 1.5 ns clock accuracy over a prediction period of 2 hours and more. Beyond that

the use of the non-integer ionosphere free linear combinations leads to further effects.


Page 27

The combined code and phase noise is amplified compared to the noise of isolated

signals. Furthermore, the integer characteristics of the phase ambiguities get lost and

ambiguity fixing is prevented, which leads to even longer convergence times.

Convergence times are the time spans from start to a stably accurate solution. The

convergence time to reach decimeter accuracy is typically about 30 minutes

under normal conditions. To reach centimeter accuracies the PPP processor needs

significantly longer (Katrin et al, 2010).

In comparison with common techniques like DGPS or RTK, the costs are

reduced, because no base stations and no simultaneous observations are necessary. On

the other hand the necessary models have to be fetched either from globally acting

services like IGS (orbits, satellite clocks) or from regional GNSS service providers

(atmospheric delays) and standard interfaces (e.g. RTCM) have to be developed

toforward this information to the rover. Further problems still to be solved are

coordinate convergence periods of up to 2 hours as well as ambiguityresolution,

whichare harmed by non-integer calibration phase biases. These biases vanish

only in difference mode and have to be determined a priori.

PPP also provides a positioning solution in a dynamic, global reference frame

such as the International Terrestrial Reference Frame (ITRF) (Altamimi et al., 2011),

negating any local distortions associated with differential positioning techniques when

local coordinates are used at the Continuously Operating Reference Station (CORS).

However, it is important to fully understand the implications of transforming between a

global and a national or local datum for example, (Haasdyk and Janssen ,2011, 2012).

At present, post-processed PPP offers the most comparable accuracies

toDifferential GPS (DGNSS) positioning techniques. Free PPP post-processing services

such as Auto-GIPSY(http://apps.gdgps.net/) and CSRSPPP (http://www.geod.nrcan

.gc.ca/productsproduits/ ppp_e.php) provide converged float solutions at the centimeter-

level, thereby allowing PPP to offer a viable alternative to post-processed DGNSS

solutions. Users upload their observed RINEX data files to such online services, and the

coordinate solution for the (static or kinematic) GNSS receiver‟s position is computed

automatically. Note, however, that long observation session times (several hours) are

required to obtain “comparable accuracies”, and therefore the applications are typically


Page 28

restricted to the establishment of geodetic control using GNSS technology (Chris et al.

2012).

2.2.1 Mathematical Model of Precise Point Positioning

Recall that mainly, there are two types of GPS observables, namely the code

pseudoranges and carrier phase observables. In general, the pseudorange observations

are used for coarse navigation, whereas the carrier phase observations are used in high-

precision surveying applications. That is due to the fact that the accuracy of the carrier

phase observations is much higher than the accuracy of code observations,

(Leick, 1995). The pseudorange observation equations denoted in chapter two can be

written again in case of L1, and L2 as:

(2-27)

(2-28)

Where:

PL1, PL2 are the observed pseudorange on L1, L2 respectively.

is the unknown geometric satellite to receiver range.

C is speed of light

dt, dT are satellite and receiver clock errors respectively.

, are the ionosphere error on L1 and L2 respectively.

is the troposphere error.

dorb is the orbital error

PL1, PL2 are the code measurement noise on L1, L2 respectively.

Also, the phase observation equations are:

(2-29)

11)(1 LL porbtropionL ddddTdtcP

22)(2 LL porbtropionL ddddTdtcP

1Liond2Liond

tropd

11111 .)(LL orbtropionLLL dddNdTdtc


Page 29

(2-30)

Where:

L1, L2 are the observed phase on L1, L2 respectively.

λL1, λL2 are the L1, L2 carrier wavelength.

NL1, NL2 are the ambiguities on L1, L2.

εφL1, εφL1 are the phase measurement noise on L1, L2 respectively.

The GPS single point positioning model GPS-SPP is depending on eliminating

the ionospheric error from three linear combinations as follows:

1. The ionosphere-free phase combination consists of multiplying equation (2-29) by

and equation (2-30) by , and sum the two new equations. This gives:

(2-31)

Where:

is the ionosphere-free phase combination.

f1, f2 are the L1, L2 carrier frequencies .

2. Summation of equations (2-27), equation(2-28) and equation(2-29) , equation(2-30)

and multiplying the sum by 0.5 yield to ionosphere-free code-phase on both L1 and L2,

as follows:

(2-32)

(2-33)

22222 .)(LL orbtropionLLL dddNdTdtc

22

21

21

ff

f

22

21

22

ff

f

222

21

22

122

21

21 .. LLIF

ff

f

ff

f

)(5.0 1111 LLP PPLL

)(5.0 2222 LLP PPLL


Page 30

At this point the GPS-SPP model consists of three observations for each satellite.

Equations (2-31), (2-32)and (2-33) can be rewritten as:

(2-34)

(2-35)

(2-36)

Applying the IGS products on the above three equations, and use Saastamoinen

tropospheric model indicated , lead to removal of satellite clock error, orbital error, and

troposphere error. Thus, the equations can be rewritten again as:

(2-37)

(2-38)

(2-39)

Assume we have k satellites, then the observations equations (n) will be 3k, the

unknowns (u) will be the 3-D coordinates of the receiver point, the receiver clock error,

N1, N2 ambiguities for each satellite. To solve this system of equations

or simply . This means that, to solve an epoch by epoch SPP

model, at least four satellites must be tracked.

2.2.2 Variance Estimation

Typically, GPS observables are pseudoranges derived from code or phase

measurements. The accuracy of code ranges is at the sub-meter level, whereas the

accuracy of the carrier phase is in the millimeter range (Erickson, 1992). With high-

end GPS receivers, the code and phase noise levels are approximately 10cm and 0.3cm

respectively. Hence, one can assume the noise level of the pseudorange and phase for

both carrier signals as:

and (2-40)

IForbtropIF ddNff

fN

ff

fdTdtc

222

22

1

22

1122

21

21 ..)(

)(5.0.5.0)(1111 11 LLLL porbtropP NdddTdtcP

)(5.0.5.0)(2222 22 LLLL porbtropP NdddTdtcP

IFN

ff

fN

ff

fdtcIF

222

22

1

22

1122

21

21 ...

)(5.0.5.0.1111 11 LLLL pP NdtcP

)(5.0.5.0.2222 22 LLLL pP NdtcP

kk 2133 4k

cmLLL PPP 10

21 cm

LLL3.0

21


Page 31

Applying the variance propagation law, to determine the variance of the

ionosphere-free phase combination, one can get:

(2-41)

Analogously, the variance of the ionosphere-free from code and phase

combination after neglecting the phase noise can be deduced from:

(2-42)

2.2.3 Ambiguity Initialization

As stated before, the unknowns in the GPS-SPP model are the 3-D receiver

coordinates, and the receiver clock offset, and the double ambiguities for each satellite.

To solve the system of equations and applying the least squares principle, one must

have initial values for the unknowns. The approximate values for the 3-D receiver

coordinates along with the receiver clock offset are given in the navigation message. On

the other hand, the approximate values for the ambiguities unknown are deduced from

the following procedure:

1. get approximate values for the ionosphere error on L1, L2 by subtracting equation

(2-28) from equation (2-27), this yields to:

(2-43)

The ionosphere error is inversely proportional to the squaring frequency of the carrier

signal. Hence,

2

2

22

21

222

2

22

21

212 ..

ff

f

ff

fIF

2222 87.8.39.2.48.6 IF

2222222

4

1.5.0.5.0

2211ppPP

LLPLLP

2121 LL ionionLL ddPP


Page 32

(2-44)

Substituting equation (2-43) in equation (2-42), we can get an approximate solution for

the ionosphere error.

(2-45)

2. get the approximate values of the ambiguities from subtracting equation (2-27) from

equation

(2-29), leads to:

(2-46)

Substitute the approximate value of the ionosphere-free from equation (2-43) into

equation (2-45), one can get the approximate values of the ambiguities on the L1 carrier

from:

(2-47)

The same analysis can be done, to obtain the approximate values on the L2

carrier, and one can get the approximate values of the ambiguities on L2 carrier from:

(2-48)

12 22

21

LL ionion df

fd

22

21

21

11

f

f

PPd LL

ionL

12. 1111 LionLLLL dNP

22

21

211111

1

)(2.

f

f

PPPN LL

LLLL

21

22

122222

1

)(2.

f

f

PPPN LL

LLLL


Page 33

2.2.4 Least Squares Adjustment

Least squares adjustment is normally used at two different stages in the

processing of GPS carrier-phase measurements. First, it applied in the adjustment that

yields baseline components between stations from the redundant carrier-phase

observations. Recall that in this procedure, differencing techniques employed to

compensate for errors in the system and to resolve the cycle ambiguities. In the solution,

observation equations contain the differences in coordinates between stations as

parameters. The reference coordinate system for this adjustment is the Xe,Ye,Ze

geocentric system. A highly redundant system of equations obtained because a

minimum of four (and often more) satellites are tracked simultaneously using at least

two (and often more) receivers. Furthermore, many repeat observations taken. This

system of equations solved by least squares to obtain the most probable ∆X, ∆Y, and ∆Z

components of the baseline vectors. Software furnished by manufacturers of GPS

receivers will process observed phase changes to form the differencing observation

equations, perform the least squares adjustment, and output the adjusted baseline vector

components. The software will also output the covariance matrix, which expresses the

correlation between the ∆X, ∆Y, and ∆Z components of each baseline. The second stage

where least square employed in processing GPS observations is in adjusting baseline

vector components in networks. This adjustment made after the least squares adjustment

of the carrier-phase observations is completed. (Ghilani, D. and Wolf, R., 2006).

2.2.5 Standard Adjustment

There are numerous adjustment techniques that can be used, butleast squares

adjustment with parameters is the only one discussed here. It based on equations where

the observations expressed as a function of unknown parameters. A Taylor series

expansion usually performed in the case of nonlinear functions. This requires

approximate values for the parameters. The Taylor series expansion must truncated after

the second term to obtain a linear function with respect to the unknowns. The resulting

linear observation model can represent in a matrix-vector notation as (Hofmann W.,

2001):

L = Ax(2-59)

Where


Page 34

L is the vector of observations

A is the design matrix

x is the vector of unknowns.

By introducing in addition the definitions

2

0 is a priori variance

is the covariance matrix,

The cofactor matrix of observations is

Q1 = 2

0

1

(2-60)

and

P = Q 1

1

(2-61)

is the weight matrix. Assuming n observations and u unknown parameters leads

to a design matrix A comprising n rows and u columns. For n > u the system

Equation(2-58)is over determined and, in general, non-consistent because of

observational errors or noise. To assure consistency, the noise vector n is added to the

vector of observations and Equation(2-58) thus converts to

L+ n = Ax (2-62)

The solution of this system becomes unique by the least squares principle

(nT P n)= minimum. The application of this minimum principle on the observation

equations (4-35) leads to the normal equations

AT P Ax = A

T P L (2-63)

With the solution

x = (AT P A)

-1 A

T P L (2-64)

Which can be simplified to


Page 35

x = G-1

g (2-65)

where G = AT P A and g = A

T P L

the cofactor matrix Qx follows from x = G-1

AT P L by the covariance propagation law

as

Qx = (G-1

AT P) Q1 (G

-1 A

T P)

T(2-66)

and reduces to

Qx = G-1

= (AT P A)

-1(2-67)

by substituting Qx = P-1

2.2.6 Sequential Adjustment

Assume a partitioning of the observation model Equation (2-61) into two subsets

(Hofmann W., 2001):

L =

2

1

L

L n =

2

1

n

n A =

2

1

A

A (2-68)

Using the first set only, a preliminary solution xo can be calculated according to

Equation (2-83) and Equation(2-67)by

xo = ( P1 A1)

-1 A P1 L1 = G 1

1

g 1 ,

= ( P1 A1)

-1 = G 1

1

(2-69)

Provided that there is no correlation between the two subsets of observations, the

weight matrix

P =

1

1

0

0

P

P

(2-70)


Page 36

Is a block-diagonal matrix. The matrix G and the vector g for the adjustment of

the full set of observations result from adding the corresponding matrices and vectors

for the two subsets:

G = AT P A =(

P1 A1 + P2 A2 ) = G1+G2

g = AT P L =(

P1 L1 + P2 L2 ) = g1+g2 (2-71)

If the change of the preliminary solution xo due to the additional observation set

L2 is denoted as ∆x, then

(G1+G2)( xo + ∆x) = g1+g2 (2-72)

Is the appropriate formulation of the adjustment. This equation can slightly

rearranged to

(G1+G2) ∆x = g1+g2 - (G1+G2) xo (2-73)

where the right-hand side, cf. Equation(2-72), can be simplified because of the

relation g1 - G1 xo= 0 so that

(G1+G2) ∆x = g2 – G2 xo (2-74)

Results. Resubstituting from Equation(2-74)g2 = P2 L2 and G2=

P2 A2 yields

(G1+G2) ∆x = P2 L2 -

P2 A2 xo (2-75)

or

(G1+G2) ∆x = P2 (L2 – A2 xo) (2-76)

and

∆x =(G1+G2)-1

P2 (L2 – A2 xo) (2-77)

or finally

∆x =K (L2 – A2 xo) (2-78)


Page 37

Where:

K= (G1+G2)-1

A2 P2 (2-79)

Note that formally in Equation(2-78)the term A2 xo can be considered as

prediction for the observations L2

The goal of the next step is the computation of the change ∆Q with respect to the

preliminary cofactor matrix Q xo. Starting point is the relation

G Q xo= (G1+G2)( Q xo +∆Q)= I (2-80)

where I denotes the unit matrix. This equation reformulated as

(G1+G2) ∆Q = I- (G1+G2) Q xo (2-81)

and, since G1 Q xo = I, this reduces to

(G1+G2) ∆Q = - G2 Q xo (2-82)

or

∆Q= - (G1+G2)-1

G2 Q xo (2-83)

and, by using G2 = P2 A2, the relation

∆Q= - (G1+G2)-1

P2 A2 Q xo (2-84)

follows, comparing this equation with Equation(2-83)K may be substituted and

∆Q= -K A2 Q xo (2-85)

results. Matrix K which is denoted as gain matrix, satisfies the very remarkable relation

K= (G1+G2)-1

P2= G 1

1

( P2

-1 + A2G

1

1

)

-1 (2-86)

It is essential to learn from Equation(2-86) that the first form for K implies the

inversion of a u x u matrix if u is the number of unknown parameters; whereas, for the

second form an inversion of an n2 x n2 matrix is necessary when n2 denotes the number


Page 38

of observations for the second subset. Therefore, the second form is advantageous as

long as n2< u.

A final remark should conclude the section on the sequential adjustment. In the

equation of ∆x, cf. Equation(2-82), Equation(2-83), and in the equation for ∆Q, cf.

Equation(2-81), Equation (2-83), neither the design matrix A1 nor the vector L1 for the

first set of observations appears explicitly. Therefore, formally, the substitution e.g. A1

= I and L1 = xo may be performed and the model for the sequential adjustment is then

formulated as

xo + n1 = x

L2+ n2 =A2 x. (2-87)

Model Equation(2-87) reflects that the preliminary estimates xo for the unknown

parameters are introduced into the sequential adjustment as observations.

2.2.7 Epoch by Epoch Least Square Adjustment

The GPS-SPP model is depending on solving an epoch by epoch adjustment

solution. As stated before, for k satellites, we have 3k observations equations (n), and

4+2k unknowns (u). In case of 4 satellites, the observations will be 3*4=12, and the

number of known will be 3+1+2*4=12. For any number of satellites more than 4, the

number of observations will be greater than the number of unknowns, hence the system

of equations is an over-determined equation system, which must be solved using the

least-squares principles, to get the most reliable values for all the involved unknowns. In

this equation system, the observation vector L and the Parameter X can be given as:


Page 39

(2.88)

(2.89)

The parametric least squares adjustment solution becomes in matrix form:

(2-90)

Where: A is the design matrix, δ is the vector of corrections to the unknown parameters

X, is the misclosure vector, X0 is the vector of

approximate values for unknowns, and V is the vector of residuals. L is the vector of

observations.

The coefficient matrix A, which is defined as the first derivative of the involved

observation equations with respect to the unknowns, can be formed by a direct

differentiation of the observation equations (2.88) with respect to the involved

unknowns, given by equation (2- 89). The number of the rows in matrix A will be the

same as the number of the available observations, where the number of its columns will

be equivalent to the number of the involved unknowns. As a result, the coefficient

matrix A can be given as:

nsat

nsatLL

nsatLL

sat

satLL

satLL

sat

satLL

satLL

IF

P

P

IF

P

P

IF

P

P

n

P

P

P

P

P

P

L

#

#22

#11

2#

2#22

2#11

1#

1#22

1#11

)(

)(

)(

)(

)(

)(

1*

nsat

nsat

sat

sat

sat

sat

u

N

N

N

N

N

NtZYX

X

#

#

2#

2#

1#

1#

1*

2

1

2

1

2

1

0. VWA

LLLXfW 00 )(


Page 40

(2-91)

Where:

denoted for the first observation type .



, , , i=1,2,3 (2-92)

(2-93)

x,y,z are unknown receiver coordinates, Xs, Ys, Zs are the satellite

known coordinates.

,C is the speed of light. (2-94)

nsat

u

nsat

uuuuu

nsat

u

nsat

uuuuu

nsat

u

nsat

uuuuu

nsatnsatsatsat

nsatnsatsatsat

nsatnsatsatsat

un

N

f

N

f

t

f

Z

f

Y

f

X

f

N

f

N

f

t

f

Z

f

Y

f

X

f

N

f

N

f

t

f

Z

f

Y

f

X

f

N

f

N

f

N

f

N

f

t

f

Z

f

Y

f

X

f

N

f

N

f

N

f

N

f

t

f

Z

f

Y

f

X

f

N

f

N

f

N

f

N

f

t

f

Z

f

Y

f

X

f

A

##

#

1

#

11111

#

2

#

22222

#

3

#

3

1#

3

1#

33333

#

2

#

2

1#

2

1#

22222

#

1

#

1

1#

1

1#

11111

*

21

21

11

2121

1121

2121

1f11 LLPP

2f22 LLPP

3f IF

Xsx

X

f i

Xsx

X

f i

Xsx

X

f i

222 )()()( zZsyYsxXs

Ct

f i


Page 41

0 or 1 0 or 1 (2-95)

The coefficient matrix A is also known as the first design matrix. In addition to

this design matrix, there are two other design matrices that must be formed and used

with the matrix A in the process of the parametric least-squares adjustment. These two

matrices are called the weight matrix P and the misclosure vector W. The construction

of the three design matrices A, P and W is considered the core of the application of the

parametric least-squares adjustment process. The weight matrix can be written as:

(2-96)

Where is the apriori variance factor and ΣL is the variance-covariance

matrix of the observations. The weight matrix can be rewritten as:

.(2-97)

Where , , and

Finally, the misclosure vector W, can be formed as:

(2-98)

In which L0 is the vector of the observations, using the approximate values of

the unknowns X0, and L is the vector of observations. After formation of the three

design matrices A, P and W, the solution of the unknown correction vector can be

obtained as:

1N

f i

2N

f i

nn

nn LP*

120* .

20

21

21

21

23

22

21

*

#

#

#

1#

1#

1#

00000000

00000000

00000000000000000000000000000000

00000000

00000000

00000000

nsat

nsat

nsat

sat

sat

sat

nnP

221

11 LLPP 22

222 LLPP

223 IF

1*1*1*

0

nnnLLW


Page 42

(2-99)

Finally, the best estimator of all the considered unknowns, which is usually denoted as

can be obtained by adding the resulted correction vector to the pre-chosen

approximate values of the unknowns X0. Hence, the adjusted values of the unknowns

can be expressed as:

(2-100)

)..).(..(1*

WPAAPA tt

u

__

X

0__

XX

Chapter 3 Introduction to Geodetic Datums

Page 43

Chapter three

Introduction to Geodetic Datums

Geodesy is the science of measuring the shape and size of the Earth and

precisely locating points on its surface. As our society and economy becomes

increasingly dependent on complex technologies and the management of the space we

live in, the need for precise positioning and consistent, reliable spatial data has

intensified. As we move to a world where new technologies allow us to rapidly

determine the accurate position of features and points, we are developing the concept of

everything „geodetic‟. That is the development of a seamless geodetic cadastre and all

spatial datasets in terms of a common geodetic system.

For many countries subject to the effects of ground movements due to events

such as earthquakes, volcanic activity or plate tectonics, the ability to survey and record

these movements to maintain accuracy of the geodetic system is an important task. A

country‟s geodetic system provides the network of permanent ground reference points

and the associated intellectual and positional data that enables it to ensure all data

concerning land, resources, and location is managed in a systematic and orderly manner.

Fundamental to any geodetic system is the spatial reference frame upon which it

is based. Historically these were locally or regionally based, but as we have transitioned

to the use of globally based satellite positioning systems our reference frames have

become much more global in nature. A spatial reference frame allows a location to be

unambiguously identified through a set of coordinates (usually latitude and longitude or

northing and easting).

3.1 . Introduction to Geodetic Datums

A geodetic datum is a curved reference surface that is used to express the

positions of features consistently. Geodetic datums are usually classified into two

categories: local and geodetic.

A Local Geodetic Datum is a datum which best approximates the size and shape

of a particular part of the Earth‟s sea-level surface (Figure 3.1). It is defined by

specifying a reference ellipsoid, the position (latitude and longitude) of an initial station


Page 44

and an azimuth from that station. Invariably, the centre of its ellipsoid will not coincide

with the Earth‟s centre of mass. Until very recently, most national geodetic systems

were based on local geodetic datums.

Figure )3.1.(: Local datum with best fit ellipsoid

A Geocentric Datum is a datum which best approximates the size and shape of

the Earth as a whole. The centre of its ellipsoid coincides with the Earth‟s centre of

mass (Fig. 3.2). Geocentric datums do not seek to be a good approximation to any

single part of the Earth but on average they are a good fit. Global Navigation Satellite

Systems (GNSS) utilize geocentric datums to express their positions because of their

global extent. Multiple GNSS are now fully operational or being developed such as

GPS, GLONASS, GALILEO, and BEIDOU and each uses a slightly different

geocentric datum. The World Geodetic System 1984 (used by GPS) is an example of a

geocentric datum.


Page 45

Figure (3.2.): Geocentric datum with ellipsoid that is a best fit to the world.

Mean sea level is widely used as the reference surface for the measurement of height.

The contours on a map will usually show height above mean sea level. However,

heights in terms of a geodetic datum will be in relation to an ellipsoid.

3.2 . Modern Geodesy and ITRS/ITRF

The primary mission of Modern Geodesy is the definition and maintenance of

precise geometric and gravimetric reference frames and models, and the provision of

high accuracy positioning techniques for users in order to connect to these frames. The

International Association of Geodesy (IAG) has established services for all the major

satellite geodesy techniques that are vital to the definition of the terrestrial and celestial

reference systems. These reference systems are the foundation for all operational

geodetic applications associated with mapping and charting, navigation, spatial data

acquisition and management, as well as support for the geosciences.

The International Celestial Reference System (ICRS) forms the basis for describingcelestial

coordinates, and the International Terrestrial Reference System (ITRS) is thefoundation for the

definition of terrestrial coordinates to the highest possible accuracy.The definitions of these

systems include the orientation and origin of their axes, scale,physical constants and models

used in their realization, e.g., the size, shape and orientationof the reference ellipsoid that

approximates the geoid and the Earth‟s gravityfield model. The coordinate transformation

between the ICRS and ITRS is described by a sequence of rotations that account for

variations in the orientation of the Earth‟s rotation axis and its rotational speed.


Page 46

3.2.1. International Reference Systems, Frame and Datum maintenance

In space geodetic positioning, where the observation techniques provide

absolute positions with respect to a consistent terrestrial reference frame, the

corresponding precise definition and realization of terrestrial and inertial reference

systems is of fundamental importance. Thanks to significant improvements in receiver

technology, to extension and densification of the global tracking network along with

more accurate determination of positions and velocities of the tracking stations and to

dramatically improved satellite orbits, GPS is today approaching one ppb precision for

longer baselines and it can be considered to be a global geodetic positioning system

providing nearly instantaneous three-dimensional position at the 1 - 2 cm accuracy

level. With respect to this the reference system is one of the primary limiting error

sources.One of the fundamental goals of geodesy is to precisely define positions of

points on the surface of the Earth, so it is necessary to establish a well-defined geodetic

datum for geodetic measurements and positioning computations. Recently, a set of the

coordinates established by using GPS and referred to an international terrestrial

reference frame could be used as a three-dimensional geocentric reference system for a

country(Chang and Tseng, 1998).

3.2.2. Terrestrial Reference Systems and Frames

Reference System and Reference Frame are different concepts. The first one is

understood as “a theoretical definition”, including models and standards for its

implementation. The second one is its “practical implementation” through observations

and a set of reference coordinates (set of fundamental stars –for a Celestial Reference

Frame– or fiducial stations –for a Terrestrial Reference Framedescribed by a catalogue

of precise positions and motions(if measurable) at a specific epoch. A reference

systemis the complete conceptual definition of how a coordinate system is formed. It

defines the origin and the orientation of fundamental planes or axes ofthe system.

Satellite coordinates and user receivers must be expressed in a well-defined reference

system. Thence, an accurate definition and determination of such systems is essential to

assure a precise positioning in GNSS. Two of the main reference systems used in

satellite navigation are introduced bellow: The Conventional Celestial Reference

System (CRS) (also named Conventional Inertial System, CIS) and the Conventional

Terrestrial Reference System (also named Coordinated Terrestrial System, CTS)


Page 47

(Abidin, 2007). In satellite geodesy two fundamental systems are required: a space-

fixed, conventional inertial reference system (CRS) for the description of satellite

motion, and an Earth-fixed, conventional terrestrial reference system (CTS) for the

positions of the observation stations and for the description of results from satellite

geodesy(Seeber,G.,2003).

3.2.1.1. Conventional Celestial Reference System (CRS)

The concept of a celestial sphere and the definition of somebasic planes are

necessary for establishing a reference system for earthcenteredinertial (ECI)

coordinates. The celestial sphere is an imaginarysphere of infinite radius whose center

coincides with the center of massof the earth. The celestial poles and celestial equator

are, respectively,projections of the earth's north and south astronomic poles

andastronomic equator onto the celestial sphere. The vernal and autumnalequinoxes are

the points where the celestial equator intersects theecliptic.

This is a inertial reference system. It has its origin at the earth's centre of mass.

X-axis points in the direction of the mean equinox at J2000.0 epoch, Z-axis is orthogonal

to the plane defined by the mean equator at J2000.0 epoch (fundamental plane) and Y-

axis is orthogonal to the former ones figure (3.3), so the system is directly (right handed)

oriented. The practical implementation is called (conventional) Celestial Reference Frame

(CRF) and it is determined from a set of precise coordinates of extragalactic radio sources

(i.e., it is fixed with respect to distant objects of the universe). The mean equator and

equinox J2000.0 were defined by International Astronomical Union (IAU) agreements in

1976, with 1980 nutation series (Seildelmann, 1982).


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Figure (3.3.): Conventional Celestial System (CRS)

3.2.1.2. Conventional Terrestrial Reference System (CTS)

This is a reference system co-rotating with the earth in its diurnal rotation, also

called Earth-Centered, Earth-Fixed (ECEF). Its definition involves a mathematical model

for a physical earth in which point positions are expressed and have small temporal

variations due to geophysical effects (plate motion, earth tides, etc.). The CTS has its

origin in the earth's centre of mass. Z-axis is identical to the direction of the earth's

rotation axis defined by the Conventional Terrestrial Pole (CTP), X-axis is defined as the

intersection of the orthogonal plane to Z-axis (fundamental plane) and Greenwich mean

meridian, and Y-axis is orthogonal to both of them, making the system directly oriented

figure (3.4). In solving practical problems of navigation, geodesy, geodynamics,

geophysics and other geosciences it is necessary to have coordinate systems firmly

connected with the earth body. Therefore, it is necessary to define a terrestrial geocentric

system which would make it possible to solve global positioning problems at the highest

accuracy level. The Conventional Terrestrial Reference System adopted for either the

analysis of individual data sets by observation techniques.


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Figure (3.4.): Conventional Terrestrial System (CTS)

3.2.1.3. International Terrestrial Reference System (ITRS)

The ITRS represents the most precise global terrestrial reference system which

is a source system for the realization of other world reference systems (e.g. WGS84)

and of continental or regional reference systems (e.g. ETRS89 etc.). ( Jaroslav, Š. and

Jan,K. 2001). ITRS has its origin on the earth's centre of mass (including the Ocean

and atmosphere). Z axis pointing toward CTP known as IRP (IERS Reference Pole),

X axis on the Earth equator and IRM (IERS Reference Meridian passing Greenwich)

and Y-axis is orthogonal to X and Z axes figure (3.5). table (3.1) describes the

differences between reference systems.

Figure (3.5.): International Terrestrial Reference System (ITRS)


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Table (3.1.) Differences between reference systems

3.2.2. International Terrestrial Reference Frame (ITRF)

The realization of International Terrestrial Reference Systemis named

(conventional) Terrestrial Reference Frame (TRF) and it is carried out through the

coordinates of a set of points on the earth serving as reference points .A conventional

TRF is defined as a set of physical points with precisely determined coordinates in a

specific coordinate system that is the realization of an ideal TRS (Boucher and

Altamimi, 2001). An example of TRF is the International Terrestrial Reference Frame

(ITRF) introduced by the International Earth Rotation and Reference Systems Service

(IERS), which is updated every year (ITRF98, ITRF99, etc.). Other terrestrial reference

frames are the World Geodetic System 84 (WGS84), which is applied for GPS.The

types of different TRF can be described by the following:

Parameters

Reference System

CTS ITRS CIS

Origin Mass Center of the

Earth

Mass Center of the Earth

(including the Ocean

and atmosphere)

Mass Center of the Earth

Coordinate

System Earth –Fixed Earth -Fixed Space-Fixed

X-axis

On the Earth equator

and

Greenwich meridian

plane

On the Earth equator and

IRES Reference

meridian passing

Greenwich

On the Earth equator and

pointing to the Vernal

Equinox of J2000.0 epoch

Y-axis Orthogonal to X and Z

axis

Orthogonal to X and Z

axis

Orthogonal to X and Z

axis

Z-axis

Pointing Toward CTP

(Conventional

Terrestrial Pole)

Pointing Toward CTP

(IERS Reference Pole)

Pointing Toward CEP

(Conventional Ephemeris

pole of J2000.0 epoch

Example WGS 84 ITRF -------------


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Global Reference Frames

A global reference frame is typically the primary basis for the definition of a

coordinatesystem used in applied geodesy. Examples include the International

Terrestrial ReferenceFrame (ITRF) and the World Geodetic System 1984 (WGS 84).

These frames aregeocentric in nature, having the geocenter (the center of mass of the

Earth) as the originand orthogonal axes aligned with pole, equator and Greenwich

meridian accordingto IERS conventions. The ITRF is realized by the coordinates and

site velocities of anetwork of global stations and forms the basis for modern regional

and national referenceframes or geodetic datums. The most recent realizations of ITRF

have positionaluncertainties of contributing stations in the order of millimeters. ITRF

station velocitiesare described with respect to a no-net-rotation (NNR) condition where

the angular momentaof all of the global tectonic plates sum to zero.

Regional Reference Frames

Regional reference frames are denser networks of geodetic stations covering

continental areas. Examples include the European Terrestrial Reference Frame

(EUREF), North American Datum 1983 (NAD83), African Reference Frame (AFREF),

Sistema de Referencia Geocentrico para las America (SIRGAS) and the Asia-Pacific

Reference Frame (APREF). As with ITRF, regional reference frames are defined by the

coordinates and site velocities of contributing stations. The key difference with some

regional reference frames (e.g. EUREF and NAD83) and ITRF is that the site velocities

may be with respect to the dominant tectonic plate encompassed by the frame and not a

NNR condition. This approach minimizes site velocities. Regional frames not

constrained by the motion of a single tectonic plate are closely aligned with ITRF.

National Reference Frames

Modern national reference frames are typically a static realization of ITRF or a

regional reference frame. In most countries the coordinates of a national reference frame

(or geodetic datum) form the basis for all surveying, positioning and mapping within

national borders. Because surveying/ GIS software and spatial data are not generally

designed to deal with continuously changing coordinates, the epoch for national datums

is fixed and the coordinates are considered to be invariant with time.


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The key-element of the ITRF combinations is the availability of co-location sites

where two or more space geodesy instrumentsare operating and where differential

coordinates(local ties) between the measuring reference points of theseinstruments are

determined. While any individual spacegeodesy technique Very Long

BaselineInterferometry (VLBI), Satellite Laser Ranging (SLR),Global Positioning

System (GPS) and Doppler OrbitographyRadiopositioning Integrated by Satellite

(DORIS) (Altamimi,2002). Global NavigationSatellite Systems (GNSS) including

Galileo in the future) isable to provide all the necessary information of the

datumdefinition of the Terrestrial Reference Frame (TRF) (origin,scale, orientation),

combination of reference frames providedby independent techniques has long been the

standard methodto implement global terrestrial reference frames.The latest realization

of the international terrestrial reference frame during this study is known as ITRF2005,

but now is ITRF2008 and is derived from several spaced-based, geodetic techniques

such as Global Navigation Satellite Systems (GNSS).

3.3. World Geodetic System (WGS84)

WGS84 or the World Geodetic System 1984 isthe geodetic reference system

used by theGNSS - “GPS”. WGS84 was developed for theUnited States Defence

Mapping Agency (DMA), now called NGA (National Geospatial -Intelligence Agency).

WGS84 is the default "native" system used by the GlobalPositioning System (GPS) and

commercial GPS receivers. Although the nameWGS84 has remained the same, it has

beenenhanced on several occasions to a point whereit is now very closely aligned to

ITRF andreferenced as WGS 84 (G1150). It was used as the reference frame for

broadcast GPS Ephemerides (orbits) beginning January 23, 1987. At 0000 GMT It was

redefined again and was more closely aligned with International Earth Rotation Service

(IERS) Terrestrial Reference Frame (ITRF).Theorigin of the WGS 84 Coordinate

System is the center of mass of the earth;Z-axis is parallel to the direction of the CTP

for polarmotion, as defined by the Bureau International de ĹHeure (BIH) on the basis of

the coordinates adopted forthe BIH stations; the X-axis is the intersection of the WGS

84 referencemeridian plane and the plane of the CTP's equator, the reference

meridianbeing parallel to the Zero Meridian defined by the BIH on the basis of

thecoordinates adopted for the BIH stations; and, the Y-axis, measured in theplane of

the above equator, 90" east of the X-axis, completes a right-handed,earth-fixed,


Page 53

orthogonal coordinate system figure (3.6). The use of global kinematic reference frames

such as ITRF and WGS84 in positioning, navigation and mapping is now widespread.

Positions within these reference frames can be acquired with a precision of between a

few millimetres and several meters depending upon the choice of GNSS receiver,

differential service or processing method.

A major dilemma arises when these positioning technologies are used to

reposition fixed locations on the Earth‟s surface (e.g. land surveying, airborne laser

scanning, deformation monitoring, precision agriculture and automated mining).

Coordinates of fixed locations within a kinematic reference frame (or “dynamic datum”)

change by up to 100 mm/yr due to plate tectonics. Where large earthquakes occur,

coordinate changes of up to several meters in magnitude are possible. Unmodelled

deformation is undesirable if surveys referenced to different measurement epochs of a

kinematic datum are to be integrated or correlated.( Jaroslav, Š. and Jan,K. 2001).

Figure (3.6.): World Geodetic System 1984 (WGS84)

3.4. The Datum Problem


ellipsoid ofrevolution of adopted size and shape, with origin, orientation, and scale

defined by ageocentric terrestrial frame. Once an ellipsoid is selected, coordinates of a


longitude, latitude, and ellipsoid height). Geodetic coordinates are preferred in

cartographic and mapping applications. Furthermore, the classical concept of geodetic


Page 54

datum implies that a datum‟s coordinates are fixed and do not change with time except

for the effect of local tectonic motion (episodic motions, land subsidence, volcanic

activity, etc.). Thus, the coordinate frame of a geodetic datum should be somewhat

attached to the plate and move with it in such a way that the coordinates of the points

will not change as a consequence of plate rotation.

However, in actuality, the reverse process is implemented; that is, the coordinate

frame is fixed to the Earth‟s mantle while the plates are rotated to their original position

at epoch D t (the datum epoch). This is achieved by applying the same type of

correction at every point. The magnitude of this correction is determined through the

angular velocity matrixassociated with the continental plate where the points are

located. (Roberts et al. 2009). In essence, all points are moved back to their location at

epoch D t on theframe ITRF which, in ourexample, is assumed to be the adopted datum

frame and, by definition, remains fixed. In other words, the plate and the points on it are

assumed frozen in space at the epoch when the datum frame was defined; all

coordinates determined at epoch t should be taken back to epoch D t , the datum epoch.

3.4.1. Limitations of Static Geodetic Datums





tectonic motion.Static datumdoes not incorporate the effects of plate tectonics and



The concept of dynamic (or kinematic) datum has been introduced to represent a

coordinate datum where the coordinates of sites change as a function of time (Paul

andRussell,1999). Dynamic datum incorporates a deformation model to manage

changes (plate tectonics and deformation events). Coordinates change continuously and

can be confusing and difficult to manage.

Countries and regions located on relatively stable tectonic landmasses such as

Egypt, South Africa, Brazil, Eastern USA, Germany and the UK have geodetic datum

that do not deform significantly as a function of time. Typically, baselines measured


Page 55

between any stable geodetic monuments in these countries change by less than a few

centimeters on decadal time scales. This stability has supported the adoption of a static

geodetic datum for such regions.

The major limitation with a static geodetic datum arises from the ongoing

divergence between ITRF and the fixed coordinates of a static geodetic network due to

rigid plate motion. While the network may not necessarily be deforming internally to

any significant degree, the lithospheric plate on which the network sits is moving as a

rigid body over the Earth‟s asthenospheric mantle. The impact of this deformation is

noticeable where precision GNSS techniques are used to compute ITRF coordinates.

Another limitation of a static datum arises from the processing of long GNSS

baselines. If the static coordinates of a reference station are held fixed, rigid plate

rotation of a long baseline will degrade the precision of the point computation as a

function of time (Dawson and Woods, 2010).

Global PPP systems and post-processing services such as OmniStar, and

NRCan, provide instantaneous ITRF coordinates which will be invariably misaligned

from any static realization of ITRF, unless the position is also explicitly stated in a static

datum (e.g. NAD83 for OPUS and NRCan; GDA94 for AUSPOS). Using a simplified

plate based transformation model can enable the ITRF solution to be related to a fixed

epoch. If such a transformation strategy could be implemented, users could either

choose a static epoch, or use a database of existing datum with defined reference epochs

and origin translations. A polygon file for each rigid plate can define the extents of rigid

plates and deforming zones, so that the correct parameter set and deformation model

can be implemented depending upon the user‟s position. Alternatively, datum specific

online processing services could be developed, so that users are spared the need to

perform additional transformations(Stanaway and Roberts,2010). So, datum's can

either become fully kinematic (dynamic), or semi-kinematic. A deformation model can

be adopted to enable ITRF positions to be transformed into a static or semi-kinematic

system at the moment of position acquisition so that users do not see coordinate changes

due to global plate motions.

3.4.2 Limitations of Kinematic Geodetic Datum


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GNSS devices which use ITRF or closely aligned systems position users in

agreement with the underlying kinematic frame, however, in practice there are a number

of very significant drawbacks to a kinematic datum. Surveys undertaken at different

epochs cannot be combined or integrated unless a deformation model is applied

rigorously, or is embedded within the data, and the data are correctly time-tagged.

Three-dimensional data sets acquired by laser scanning techniques (e.g. airborne or

terrestrial laser scanning) are often several terabytes in size and comparison of point

clouds offset by a different realization within a kinematic system imposes an increased

computational workload and potential for error. High-precision automated GNSS

techniques are rapidly being adopted in the agricultural, mining and transport sectors

(e.g. aviation, lane control and shipping). Unless spatial models of farm machinery

tracks, mine infrastructure, berths and runways also move several centimetres a year to

maintain alignment with a kinematic system, the limitations of a kinematic datum soon

become apparent as kinematic and ground-fixed coordinates become misaligned

(Stanaway et al, 2012a).

3.4.3. Benefits of a Semi-Kinematic Datum

Semi –Kinematicdatum incorporates a deformation model to manage changes

(plate tectonics and deformation events). Coordinates fixed at a reference epoch, so the

change to coordinates is minimized. Many countries and regions which straddle major

plate boundaries have adopted a semi-kinematic (or semi-dynamic) geodetic datum in

order to prevent degradation of the datum as a function of time due to ongoing crustal

deformation that is occurring within the country .The two major drivers for the adoption

of a semi-kinematic datum in these countries have been: (1) the widespread adoption of

precision GNSS techniques for surveying and positioning and, (2) the need to maintain

consistency of coordinates to support combination and integration of spatial information

acquired at different epochs.( Pearson et al., 2010).







Page 57

deliver temporally stable coordinates within a localized reference frame,(Stanaway et

al, 2012a)

Also, PPP, global RTK and GNSS post-processing services are now used

extensively to provide realizations of ITRF and WGS84 globally with a precision of a

few centimeters. Unless these instantaneous realizations are transformed to a static or

semi-kinematic datum using a suitable kinematic transformation model, repeat surveys

using these techniques will result in datum divergence as a function of time arising from

the effects of unmodelled tectonic plate motion. Africa has a very sparse CORS

infrastructure, and this limitation supports the use of PPP and related techniques. At

present, there is no kinematic transformation applied through these services to maintain

consistency of coordinate solutions, which account for plate motion.The simplified

transformation method can be easily coded into GNSS algorithms to enable a reference

epoch to be chosen by the user. All of these services initially compute positions in the

latest realization of the International Terrestrial Reference Frame (ITRF) or closely

aligned WGS84 (G1150) (NGA, 2004).

3.5. Kinematic Transformation Parameters Using Rigid Plate Rotation

Model

Transformations from kinematic ITRF to a static datum are conventionally done

by either using the site velocity (measured directly or computed from a plate motion

model) to compute the displacement between the reference and current epochs or by a

conformal transformation augmented with time dependent parameters to account for

rigid plate motion Fig (3.7) e.g., Geoscience Australia‟s 14-parameter model (Dawson

and Steed, 2004).The precision achievable is often several millimetres on a decadal

time scale within any rigid plate.


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Fig (3.7.): Rigid Plate Rotation

Most larger tectonic plates (e.g. the Pacific and Australian Plates) move as a rigid

body with almost insignificant intraplate deformation away from the plate boundaries (with

the exception of spasmodic and rare intraplate earthquakes) (Beavan et al, 2002). Plate

movement is conventionally defined by a rotation rate about an Euler Pole.

The Earth‟s surface is comprised of a number of tectonic plates .These plates

collide, rift apart, or slip past adjoining plates along the plate margins at rates of up to

several centimetres a year. Major earthquakes and volcanic activity predominantly occur

within these plate boundary zones. In general, tectonic plates are internally rigid and stable

away from the plate boundaries. Baselines measured between any two geologically and

structurally stable geodetic stations located on a rigid plate are unlikely to change by more

than a few mm/yr. Conversely, within plate boundary zones and regions of diffuse

deformation (e.g. Tibetan plateau and the Eastern Mediterranean), baseline changes become

significant and highly variable depending upon the strain regime prevalent within the

deformation zone.

Approximately 94% of the Earth‟s surface lies on rigid tectonic plates where

localized deformation rarely exceeds more than a few mm/yr (Stanaway and Roberts,

2009). Rigid plates consist of segments of the Earth‟s crust rotating over the mantle.

Rigidplate motion can be parameterized by three parameters, either by definition of the

Euler pole of rotation, or the rotation of the Cartesian axes with respect to the inertial

Earth frame.ITRF or WGS84 coordinates can be transformed to a regional static


Page 59

geocentric datum by using a four parameter model derived from absolute rigid plate

kinematic models .Within tectonically stable areas.

A site velocity in Cartesian format ( )(in metres) can be computed for

any given location (X, Y, Z in meters) on a rigid plate defined by (ΩX, ΩY, ΩZ in

radians per million years) using:

[

] [

] 1E-6

By introducing a reference epoch and an epoch of measurement t (epochs in

decimal years), the ITRF coordinates of any point on a rigid plate at a reference epoch

( , , in meters) can be computed from the coordinates at epoch t ( , , in

meters) using:

[

] [[

] [

] ( ) ]

The above equation can also be used to realize a static geocentric datum aligned

with ITRF at a specific reference epoch. Instantaneous ITRF positions measured at

different locations and at different epochs on the same rigid plate can be related to the

static datum at the reference epoch by using the same parameters ( , , , ). In

instances where a geocentric datum is offset from ITRF (for example, a datum aligned

with an earlier realization of ITRF or WGS84), three additional parameters ( , , )

can be added to the transformation model to account for the translation of the ITRF

origin from the datum at the reference epoch using:

[

] [

] [[

] [

] ( ) ]

The above equations are accurate within rigid plate zones, however within

deforming zones additional parameters derived from deformation models (e.g. Finite

Element Model and Fault Locking models) are required in order to maintain consistency

between different epochs (Dow et al ,2009). In addition, co-seismic and post seismic


Page 60

terms need to be added. This topic and its impact on the High Accurate Reference

Network (HARN) in Egypt will explain in detail in the next chapter.

Chapter 4 Geodetic Control Networks

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Chapter Four

Geodetic Control Networks

A national horizontal control network is a fundamental construction project.

Wetherefore need to proceed from the real situations of a nation, properly handle

therelationship between quality, quantity, time, and expenditure according to theoryand

the real experience of network establishment, and work out specific principlesas the

basis for designing and establishing the geodetic control networks.

4.1 Network Establishment and Control Based on Hierarchical Orders

A national horizontal control network can be established based either on a

singleorder or several different orders. The single-order control network can

servedirectly as the basis for mapping control and is usually established in countrieswith

smaller territories to ensure more homogeneous accuracy throughout thenetwork and

facilitate adjustment computations. Countries with vast territoriesoften adopt the

method of establishing networks from higher to lower orders.

They usually first build a nationwide primary control network with higher

accuracyand lower density as a consistent control framework, and then continue to

densifythe control network in a piecemeal fashion according to the needs of different

areas.The side lengths of control networks become shorter and the accuracies get lower

asthe order changes from higher to lower. Using such a method to establish

othertriangulation networks successively in different areas within one consistent

coordinate

system can not only satisfy the desired accuracy but also achieve theeffective results at a

faster pace and lower cost.

4.1.1 Sufficient Accuracy

Apart from being the control framework of the national unified coordinates,

thefirst- and second-order networks, in the process of establishing the national

horizontalcontrol network, have to meet the requirements for mapping of the basicscale

topographic maps and the development of modern technology, such as spacetechnology,

precise engineering, earthquake monitoring, and geodynamics,whereas the third- and


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fourth-order horizontal control networks are used chieflyfor a higher-level control of the

topographic mapping control points and to satisfythe needs of fundamental engineering

construction. Control points of variousorders, therefore, must cater for the actual

demands. For example, the accuracy ofthe first- and second-order control points should

meet the needs of a 1:50,000 scaletopographic map, while that of the third- and fourth-

order control points shouldmeet the needs of topographic mapping at a scale of

1:10,000.

4.1.2 Necessary Density

Density of the control points in the control network means that there is usually

onesingle point every several square kilometers on average. It can also be expressed

bythe average side length of midpoints in the control network. The shorter the

sidelength, the denser the geodetic points will be. The controlling area Q of each point

isexpressed by the average side length S, namely:

(4.1)

which is the relationship between the side length and the controlling area.

The density of the points is required to be different according to

differentmapping scales and methods. On average, three or four geodetic points are

generallyrequired to densify control points for each map sheet. For different

engineeringprojects, however, the desired density of points will presumably be different

andshould be determined according to real situations.

4.2 Requirements for the Position of Control Points

The position of horizontal control points should satisfy the following

requirementsfor either technical design or reconnaissance for control point selection:

1. The side lengths, angles, and graphical structures formed between Control

Points should completely conform to the requirements in the corresponding

technical standards.

2. The control points should be marked where the sites can be extended easily and

lower-order points are conveniently densified.


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3. The position should be selected where the survey mark can be well preserved

over time and it will be safe and convenient to erect the monument and to

observe it. Therefore, the position should be selected in high land with solid soil

and a fine drainage system, and should be a suitable distance away from

highways, railways, high-voltage wires, and other buildings.

4. The line of sight should go beyond or deviate from obstacles by a certain

distance which, for first- and second-order, respectively, should be no less than 4

m and 2 m in mountainous areas while no less than 6 m and 4 m in plain areas.

4.2.1 Technical Design

Data Collection

Data relevant to the survey areas should be collected before planning,

includingmaps of various scales, aerial photo maps, traffic maps and meteorological

information,existing results of geodetic points, natural and social geographical

environmentsof the survey areas, transportation and material supplies, and so on.

Thesedata should be analyzed and studied as the basis and reference for the

technicaldesign.

Drawing Up Designs

Drawing up designs is a key aspect in technical design that deserves careful

consideration in order to facilitate site selection. Fieldwork will otherwise bedifficult.

Drawing up designs usually follows the steps and methods listed below:

1. Splicing the 1/50,000 or 1/100,000 scale topographic maps of the survey area

and marking the already established triangulation chains, GPS networks,

traverse networks, and leveling lines on the map.

2. Extending outward from the points of known control in a pointwise manner

according to the requirements for positions of control points while considering

creating the best figure possible. The points are laid out from higher to lower

orders, from points of known control to unknown control, and from the interior

to exterior in a pointwise fashion.

3. Drawing up the leveling connection lines according to the density requirements

for the zero elevation surface provided in the corresponding technical standards;


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Trying to utilize the old network points already existing and to propose the plans

for a connection survey.

4. Ensuring intervisibility during the site selection. Several alternative plans should

be drawn up for the uncertain positions of points or directions.

4.3 Erection of Survey Marks and Monument Setting

Erection of Survey Marks

National triangulation points or traverse points are way apart from each other

andinvisible in general conditions; geodetic survey marks are therefore needed to

showthe specific position of the point as the target. Geodetic survey marks are

usuallyclassified into ordinary survey marks and tower structures. The former is only

usedas the target point with a height of 4.3 m and 6.3 m, while towers are chiefly used

toelevate the instrument and position of the target point when two adjacent points arenot

intervisible.

Monument Setting

The survey mark is a permanent mark of the control point position. Field

observationis referred to the center of the mark, and the plane coordinates and height of

thepoint obtained will be the position of the survey mark center. If the mark isdestroyed

or displaced, the surveying results and position coordinates will bemeaningless. Hence,

when the monument is set, one should firmly abide by theprinciple of “quality first.”

Meanwhile, the monument should be stable to ensurepermanence.


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Figure (4.1.): Monumentation of the first- and second-order trig points

A monument can be classified as that of the first- and second-order

triangulation(traverse) points or that of the third- and fourth-order triangulation

(traverse) points.

A monument is generally filled with concrete chiseled from granite, bluestone, orother

hard stones with identical specifications. Monuments consist of disks andpillars, both

with a mark sunken into the center of their top surfaces. The surveymark can be made of

metal or vitreous enamel. There are many types of monuments,which are different in

terms of the different orders and places ofmonumentation under the principle of

ensuring their stability and permanence.

Generally, a monument of first- and second-order points is composed of

pillarsand upper and lower disks, as shown in figure (4.1), while that of third- and

fourthorderpoints is composed of pillars and one disk.

Completion of the technical design and erection of survey marks and

monumentsmarks the position of each control point in the horizontal control network on

theEarth‟s surface. However, extensive distance and angle measurements, as well

asadjustment computations, still need to be made before the coordinates of the

controlpoints can be determined.


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4.4 The Egyptian Geodetic Control Network

The Egyptian Geodetic Control Network Between 1853 and 1859 a survey of

Egypt was made but did not depend on a triangulation scheme [Shaker, 1982]. Later,

many attempts were made for constructing a geodetic triangulation, but they were not of

higher order. In 1907 it became possible to begin a new work for establishing a geodetic

triangulation frame for Egypt, which is considered to be the first national network to be

established in Africa (Moritz, 1981). From the cost point of view, it was decided to

carry out the network along the Nile Valley only (Shaker, 1982). The main reason to

carry it out was to fix, with a great possible accuracy, fundamental control-stations to be

a base for the cadastral survey and national mapping of the country. Egyptian network

was extended to Sudan and other African Nations. The first order geodetic horizontal

control network of Egypt contains two main networks, Network (1) and Network (2),

(Cole, 1944). Figure (1.1) shows the first order triangulation networks.

4.4.1 Network (1)

It started in the year 1907 and was finished in 1945. It consists of ten sections

contain 195 stations and the general form as (T) shape, with initial point on the

Mokattem hills to the east of Cairo, figure (1.1). The nearly horizontal part from (T)

shape contains five sections covering the north area from Al-arish in the East to Al-

salom in the West and passing through Cairo region. The nearly vertical part from (T)

shape contains the other five sections covering the cultivated area of the Nile valley

from Cairo to Adindan near Sudanese borders. Each section starts from a base line and

ends at another base line. Station Z5 (Adindan) in the south is the origin of the Sudanese

geodetic network.

4.4.2 Network (2)

In 1952, the Egyptian Survey Authority (ESA) set out a plan for observing the

second geodetic Network (2) to cover South Sinai, the area of the Red sea, and to cover

also part of the Western Desert, in order to cultivate and inhabit these areas

(Elhussainy, 1982). Network (2) was constructed and observed from 1955 and finished

in 1968. This network consists of 207 stations forming three basic blocks which are

divided into 13 sections. The two Networks were linked by 19 common stations in

different regions, figures (1.1).


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4.4.3 Description of Treating Network 1 and Network 2

The geodetic observations of Network 1 and Network 2 were taken while the

geoid in Egypt was unknown. So the gravimetric reductions to the collected

observations were neglected. The gravimetric reductions are needed to relate the

observations to the ellipsoidal (geodetic) gravity field which the observations will be

computed in. The Network 1 is adjusted section by section, not as one block, so the

errors in the network are not homogeneously distributed. The coordinates of Network 2

stations are just computed from the collected observations without gravimetric

reductions and without any kind of adjustment. Therefore it is expected that Network 1

has some distortions and inconsistency. It is expected also that Network 2 has more

distortions and inconsistency.

4.5 . GPS Control Network

GPS can be used like any other surveying tool; it can accomplish certain goals if

we are conscious of its strengths and limitations. When surveying with GPS, we do not

need to have inter-visibility between the stations to measure a baseline. The only

constraint to receive the signals is having a clear view of the sky.

4.5.1 Principles for Establishment of GPS Control Networks

Establishment Based on Hierarchical Orders

Setting GPS network into different orders is conductive to stage-wise

establishmentaccording to the immediate needs and long-term development of survey

areas.Moreover, this principle enables the network structure to combine the long

andshort sides. Compared to the Short-Side GPS Control Network, the

networkestablished in such a way can reduce the accumulation of errors at its edge

andallows data processing and results checking of GPS networks to be carried outeasily

in a piecemeal fashion.

For instance, we can first use GPS to establish a nationwide high-

precisionbackbone control network with low density (A- and B-order networks or

firstandsecond-order networks) and then further densify the network using GPS


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orconventional methods based on the survey areas needed. In further densification,with

the help of GPS technology it is unnecessary to establish an overall geodeticnetwork in

advance. Instead, one can establish and use the network at any timeaccording to the

accuracy required by users. We can obtain directly the knownpoints from hundreds of

kilometers away by GPS measurement, which not onlysaves a lot of manpower and

material resources but also fulfills the practical needs.

Density

Different task requirements and service targets have different requirements

forestablishing the GPS network. For example, the national super-network (AA-order)

datum points are mainly used to provide national datums for orbit determination,precise

ephemeris calculations, and large-scale ground deformation monitoring,with an average

distance of hundreds of kilometers. The network required by ageneral engineering

survey with an average side length of several kilometers oreven shorter (within

hundreds of meters) should cater for the needs of mappingdensification and engineering

survey. Taking the above factors into account, a rulefor the distance between two

adjacent points in GPS networks is made dependent onvarious needs: the average

distance between adjacent points in GPS at all ordersshould meet the requirements of

the data in table (4.1); the shortest distance betweenadjacent points can be 1/3 to 1/2 of

the average distance while the longest is 2–3times. Under special circumstances,

depending on the network‟s task and target, thedistance between some points can

require specific rules for the distribution of GPSstations.

Accuracy

In the design of GPS networks, the order and accuracy standard should be

designedbased on the size of survey areas and the use of the networks. The accuracy

standardof general GPS measurement is commonly expressed by the mean square error

ofthe distance between adjacent points in the networks as follows:

Where: σ is the mean square error of distance (mm), a is the constant error

(mm), b isthe coefficient of the ratio error, and d is the distance between adjacent points


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(km).The national “GPS survey specifications” classify GPS measurement into

sixorders, namely AA, A, B, C, D, E (as shown in table 4.1). The Table lists

thedistances between points and their accuracy indicators in GPS networks of

differentorders (SBSM , 2009).

4.5.2 Technical Design of GPS Control Networks

Design of GPS Control Network Datum

The design of the GPS control network datum is fundamental to the

implementationof GPS measurement. It aims to find the best possible solution in terms

of accuracy, reliability, and economic efficiency of the network. With GPS

measurement we canobtain the GPS baseline vector between surface points, which

belongs to the three- dimensional coordinate system of WGS84 or ITRF. Practical

engineering applicationsrequire national coordinate systems like Beijing Coordinate

System 1954, Xi‟an Coordinate System 1980, China Geodetic Coordinate System 2000,

oranother independent local coordinate system. Therefore, in the technical design,the

coordinate system and the initial data of the GPS network have to be specified,which

means making clear the datum adopted by the GPS network.

The GPS network datum consists of position datum, azimuth datum, and

scaledatum. Position datum is usually determined by the coordinates of known

initialpoints. Azimuth datum can be determined by the value of the known

startingazimuth or the azimuth of the GPS baseline vector. Scale datum can be

determinedby the side of the electromagnetic wave distance measurement on the

Earth‟ssurface, by the distance between two initial points, or by the distance of the

GPSbaseline vectors. So, the design of the GPS network datum is essentially the issue

ofdetermining the position datum of the network.

Point Selection

Since GPS observation stations do not require intervisibility with each other,

theselection of points is much simpler than for conventional measurements. The

choiceof GPS points has a significant influence on the smooth operation of GPS

observationsand the acquisition of reliable results. As a result, we should collect and

fullyunderstand the geographical conditions of the survey areas and the distribution


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andmaintenance of existing control points based on the purpose of measurement andthe

requirements of coverage, accuracy, and density of the survey areas so as toproperly

choose the positions of the GPS points. The following principles should befollowed in

the selection of GPS point positions:

1. It should be convenient to install antennae and GPS receivers around the point.

The point should be located where the view is not obstructed and the elevation

angle of the surrounding obstacles is less than 15o.

2. The point should be far away from high-power radio emission sources and high

voltage wires to avoid interference from magnetic fields close to the signal.

3. In order to weaken multipath effects, there should be no objects that strongly

reflect or absorb electromagnetic waves around the point.

4. To improve operational efficiency, the point should be located where

transportation is convenient.

Table (4.1.): Accuracy and density of GPS control networks

5. Points should be selected taking into account the convenience of using other

measurement techniques for connection and extension.

6. The point should be located in solid soil or, better, an outcrop of rock in order to

be better preserved.

7. The integrity and stability of the survey mark should be checked before using

old points.

Additionally, other conditions such as the nearby communication facilities

andpower supplies should also be considered for the connections between points andthe

electricity for equipment.

4.6 Marking the Position of the GPS Control Point

For long-term preservation, the GPS control point should usually be located on

thesurvey mark (monument) with an identifier in the center to mark the point precisely.


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Both the survey mark and the identifier should be stable and firm. The mark can besunk

into the ground or built into an observation stake or a stake with forcedcentering

devices.

4.6.1 Monument for GPS Control Point

A large stone engraved with Circle and Dot, will be embedded in the ground firmly.

It will act as a lower mark. A cement concrete pillar of dimension 1m×1m×1.2m will be

constructed in such a manner that it is 0.7m below the ground level and 0.5m above

ground. A „Survey Reference Mark‟ made of Gun Metal/brass as shown in the figure

(4.2) will be embedded at the centre of pillar, flushed with the top surface of the pillar,

see figure (4.2)

Figure (4.2): Design of a good GPS network observation scheme


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4.6.2 Measurement Operations of GPS Control Networks

GPS measurement includes field observations and indoor data processing work.

The former consists of installation of antennae, observation operations, and recording of

field observation results whereas the latter consists of data extraction from instruments,

baseline solution, and adjustment calculations of three-dimensional GPS control

networks, etc. Below is an overview of field observations. For the extraction of

observation data and the indoor work of data processing, please refer to annexed

instructions and other relevant data (S.I.H.T, 2009).

Installation of Antennae

The precise installation of antennae is one of the prerequisites for precise

positioning and should satisfy the following conditions:

1. Normally, the antenna should be installed in the vertical direction of the mark

center on a tripod, directly centered. Only in exceptional cases can eccentric

observations be allowed, where the centering elements should be precisely

determined by analytical methods.

2. When installing an antenna on the platform of the tower, in order to avoid

interference to signals, the top of the tower should be removed and the mark

center be projected onto the platform. Then the antenna can be placed according

to the projection point.

3. When there is an ordinary tower at the point and the distance between

observation stations is less than 10 km, an antenna is allowed to be installed

upon the tower, but the time of observation should be extended.

4. The pointer of the antenna should be directed to the true north. The effect of

local magnetic declination should be considered and the orientation error should

be no more than ±5o.

5. The level bubble at the bottom of the antenna must be centered.

6. While installing an antenna in thunderstorm weather, the bottom of the antenna

must be grounded to avoid lightning strikes. In a thunderstorm, observation

operations should be stopped and the antenna removed.

After installation of the antenna, its height should be measured both before and

after each time interval of observation. The difference between the results of thetwo


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measurements should be less than 3 mm. The average can be determined as thefinal

height of the antenna. If the difference is larger than the tolerance, we should identify

the causes, put forward suggestions, and note down the observation records.

The antenna height refers to the height from the average antenna phase center to

the surface of the central mark of the observation station, which can be divided into two

parts. One part covers the height from the phase center to the bottom of the antenna (i.e.,

the antenna reference point, ARP), which is a constant provided by manufacturers; the

other part covers the height from the ARP to the surface of the central mark of the

observation station, which should be measured by users on thespot. The specific

measurement methods can be categorized into direct measurement and slant range

measurement, according to the methods and types of antenna installation. Please refer to

the receiver user manual for details. The final value ofthe antenna height is the sum of

the heights of the parts.

Observational Operations

Observational operations are mainly aimed at capturing, tracking, receiving,

andprocessing GPS satellite signals to obtain the required data on positioning

andobservations.The operation of GPS receivers is highly automated. Its specific

methods andprocedures of operation vary with the types and operating modes of

receivers.

Detailed information is included in the attached operation manuals. During

operation, observers only need to follow the instructions in the operation

manual.Generally, the following aspects should be noted:

1. Observers at each receiver should work within the regulated observation time to

ensure the realization of simultaneous observation of the same group of

satellites.

2. After correct connection of the external power supply, the cable and antenna are

confirmed, and the power can be switched on; when the receiver is in the right

preset state it can be started.

3. When the data on the receiver‟s panel display is normal, observers can begin the

self-test and input control information for observation stations and intervals of

observation time.


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4. When the receiver begins to record data, the observer should use function keys

and selection menus to check information on observation stations, number of

received satellites, satellite catalog number, channel SNR (signal-to-noise ratio),

phase measurement residuals, results and changes in real-time positioning,

records of storage media, etc.

5. During the period of observation, the receiver should not be turned off and

restarted. The antenna height and limits of the elevation angle of satellites

should not be changed. Observers are supposed to prevent vibration and

especially displacement of the receiving devices. The antenna or signals should

not be touched or obstructed.

6. When all the operation projects are confirmed to have been completed as

required, the station can be moved.

7. In long-distance GPS measurements at higher levels, meteorological elements

should be measured as required.

Observational Records

Observational records are automatically formed by GPS receivers onto

storagemedia, which include carrier phase observations, pseudo-range observations,

corresponding GPS time, parameters of GPS satellite ephemeris, clock

offsetparameters, and initial information of observation stations such as name,

cataloguenumber, time intervals, approximate coordinates, antenna height, and so on.

Theinformation on observation stations is generally first input by observers into

thereceivers or recorded manually in measurement handbooks (S.I.H.T, 2009).

Some GPS Networks in Egypt

GPS surveys for producing geodetic control points have been performed within

the Egyptian Survey Authority (ESA) through the Finnish Project in the Eastern Desert

(Finmap), the American Project in the Delta and along the River Nile with some

extensions in the Eastern Desert. In addition, the Survey Research Institute (SRI)

established some GPS points. Some other GPS control points were available from the

German Project in Aswan area. A High Accurate Reference Network (HARN) is

observed in 1995 and a new Egyptian Datum is based on it. GPS observations were

taken at triangulation stations in a project belong to the Aviation Authority. The

National Research Institute for Astronomy and Geophysics (NRIAG) established two


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GPS networks to follow the crustal movements in Sinai and Greater Cairo area in the

years 1994 and 1995 respectively.

4.7 Introduction to Network Adjustment

When performing network adjustments of GPS baselines, a least squares

adjustment of thegenerated baselines is often performed once processing is complete

and should follow themanufacturer‟s recommended procedures. These networks may

comprise static andkinematic baselines. The network adjustment procedure has several

functions in the GPSsurveying process. The adjustment provides a single set of

coordinates based on all themeasurements acquired, as well as providing a mechanism

by which baselines that have notbeen resolved to sufficient accuracy can be detected. A

series of loop closures should beperformed before the network adjustment procedure to

eliminate erroneous baselinesentering the adjustment process. A further feature of the

network adjustment stage is thattransformation parameters relating the GPS vectors to a

local coordinate system can beestimated as part of the adjustment. The adjustment

process can be done in several ways.The following sections highlight the major

elements of the adjustment process.

4.7.1 Minimally Constrained Adjustment

Once the processed Cartesian vectors have been loaded into the adjustment

module, anadjustment should be performed where one or no coordinates are

constrained. Theadjustment should be performed using the WGS84 datum and

appropriate estimates ofstation centering error. This solution provides a mechanism by

which GPS baselines, whichare not sufficiently accurate, can be detected. Once the

minimally constrained adjustmenthas been performed, the surveyor should analyze the

baseline residuals and statisticaloutputs (which will differ between adjustment

programs) and ascertain whether anybaselines should be removed from subsequent

adjustments. This process relies on thebaseline network being observed in such a

manner to ensure that redundant baselines exist.Redundant baselines enable erroneous

baselines.

4.7.2 Fully Constrained Adjustment


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Once the minimally constrained adjustment has been performed and all

unsatisfactorybaseline solutions removed, a fully constrained adjustmentcan be

performed. The constrained adjustment is performed to compute transformation

parameters, if required, and yield coordinates of all unknown points in the desired

coordinate system. The surveyor must ensure that sufficient points with known

coordinates are occupied as part of the survey. The user should analyze the statistical

output of the processor to ascertain the quality of the adjustment. Large residuals at this

stage, after the minimally constrained adjustment has been performed, will indicate that

the control points are non-homogeneous. It is, therefore, important that additional

control points are occupied to ensure that such errors can be detected.

4.7.3 Error Ellipses

The standard deviation of the estimated coordinates is derived from the inverse

of thenormal matrix generated during formulation of the least squares process. Error

ellipses foreach point can be computed from the elements of this matrix. The ellipse

presents a twostandard deviation confidence region (95% certainty) in which the most

probable solutionbased on the measurements will fall. Surveyors should base the quality

of the adjustmentprocess on the magnitude of these ellipses. Many contracts will specify

the magnitude oferror ellipses for both the minimally constrained and fully constrained

adjustments as amethod of prescribing required accuracy levels. The product

documentation for theadjustment program will further indicate the manner in which the

ellipse values aregenerated.

4.7.4 Independent Baselines (Non-Trivial Baselines)

For the least squares adjustment process to be successful, the surveyor must

ensure thatindependent baselines have been observed. If more than one session is used

to build thebaseline network, then independent baselines will exist. In instances where

one session isobserved and all baselines adjusted, the measurement residuals will all be

extremely small.

This is due to the correlation that exists between the baseline solutions as they

are derivedfrom common data sets. This is not a problem as long as the surveyor is

aware of theoccurrence and does not assume that the baselines are of as high accuracy

as implied fromthe network adjustment results. For each observing session, there are n-


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1 independentbaselines where n is the number of receivers collecting data

simultaneously, withmeasurements inter-connecting all receivers during a session. If the

mathematicalcorrelation between two or more simultaneously observed vectors in a

session is not carriedin the variance-covariance matrix, the trivial baselines take on a

bracing functionsimulating the effect of the proper correlation statistics, but at the same

time introducing afalse redundancy in the count of the degrees of freedom.

4.7.5 Error Analysis

The local accuracies of property corners are based upon the results of a least

squaresadjustment of the survey observations used to establish their positions. They can

becomputed from elements of a covariance matrix of the adjusted parameters, where the

known NSRS control coordinate values have been weighted using their one-sigma

networkaccuracies.

The 95% confidence circle representing a local accuracy can be derived from the

major andminor semi-axis of the standard relative ellipse between two selected points. It

is closelyapproximated from the major (a) and minor (b) semi-axis parameters of the

standard ellipseand a set of coefficients. For circular error ellipses, the circle coincides

with the ellipse. Forelongated error ellipses, the radius of the circle will be slightly

shorter than the majorsemi-axis of the ellipse. The radius of an error circle is equal tothe

major semi-axis of an associated error ellipse. The value of the largest error circle

radiusin the project should be adopted for reporting local project accuracy (Lee et al.,

1987; Paul and Charles, 1997 ; Rizos, 1996).

4.8 GPS Network Adjustments Procedures

4.8.1 Acquisition and check of GPS observation data

GPS observation data necessary for baseline processing and precise ephemeris of

GPS satellite necessary for baseline processing of long baseline should preferentially be

secured for GPS network adjustment. Besides, for accurate estimation of unknown point

coordinate with GPS network adjustment, the process of checking the quality of

observation data such asobserved antenna height, observed station name, receipt interval

of data & receipt time,receipt state of data is indispensable. Especially, in antenna

height case, checkup of thelocation that measured APC(Antenna Phase Center),


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ARP(Antenna Reference Point), and ofoffset of antenna receiver by manufacturer is

necessary. And a checkup of receiving time andstate needs to be done by all means for

the minute application of mathematical difference indifference to the observed value of

carrier value obtained from the two points while baselineprocessing. A checkup of

receipt time & receipt state is required for the minute application ofmathematical double

difference to the carrier wave observed value gotten from the two pointswhile baseline

processing.

4.8.2 GPS baseline processing

GPS network is adjusted by using 3-dimensional baseline vector between two

pointsgenerated from observed GPS data processing and VCV matrix. Baseline vector

and VCVmatrix can be calculated through GPS processing, a mathematical method and

procedureestimating baseline vectors ΔX, ΔY, ΔZ between two points by least square

method passingthrough the determination of integer ambiguity process after the

application of mathematicaldouble difference to the carrier wave observed value

obtained from the two points at the sametime effect of ionospheric and tropospheric,

error of satellite track need to be fully checkedup to raise the accuracy of baseline

processing, and baseline processing S/W should beselected suitable for the purpose for

use. Besides, after GPS processing, misclosure of baselinevector needs to be examined

if there exists outlier in baseline vector or not.

4.8.3 Minimally constrained adjustment

Minimally constrained adjustment is conducted to cover the following:

To detect outlier in GPS network that hasn't been detected in the miscloser

checkup that carried out after baseline processing,

to calculate approximate accuracy of GPS network, and

to determine the statistical model of GPS network that will be used in the

final adjustment.

One point fixed adjustment and free adjustment are mainly used for minimally

constrained adjustment, approximate accuracy of GPS network is assessed through

RMSE or arithmetic mean through calculation of the size of relative error ellipse

between points obtained after minimally constrained adjustment for certain

probability(generally 95%).


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4.8.4 Outlier detection (tau-test)

In order to checkup outlier within GPS network, standardized residual should be

calculatedunder the assumption that VCV matrix of measured value is unknown and

then compare themwith critical value determined by confidence interval and degree of

freedom supposing theyconform to students‟ distribution and then tau test was used for

outlier detection. Taudistribution is used to estimate the confidence interval of the

average of comparatively smallmother group, and mainly used to check up the propriety

of the average for certain part aftercomparison with the mother group average (Lee et

al., 1987; Paul and Charles, 1997).

4.8.5 Empirical stochastic modeling

Random error components could be included in the corrected VCV matrix, but

the errorsincluded in the estimation of effect of atmosphere and antenna height

estimation that haven'tbeen fully modeled in baseline processing S/W couldn't be

included in stochastic model, andso stochastic model is determined through Empirical

stochastic modeling which corrects thevariance, the diagonal element of VCV matrix by

recalculating it for reflection of actualaccuracy of GPS network. Empirical stochastic

modeling was done in the way of changing aand b in (4.1) by dividing it into

horizontal(N, E) and vertical(H) until it passed χ2 test, a fidelitytest for model. S is

standard deviation of baseline vector, a is absolute error different to thepoints observed,

b is relative error of ppm unit in proportion to baseline length, L is baselinelength

(Rizos, 1996).

(4-1)

4.8.6 Propriety test for stochastic model (χ2 test)

Stochastic test for variance factor is necessary for the propriety of mathematical

model andstochastic model that used for estimation or detection of outlier, and for this

test, attest forcertain confidence needs to be carried out. The result can‟t pass the χ2 test

if inappropriatemathematical model or stochastic model was used or the measured value

contains outlier.χ2 test is the density function for the distribution of variance estimated

from the degree offreedom selected by mother group, a critical value of distribution


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should be arranged into stochastic table for distribution use and stochastic test to

determine confidence interval for thevariance of mother group(Paul and Charles

,1997).

4.8.7 Over constrained adjustment

Over constrained adjustment is a way of determining the coordinate of unknown

point andfinal adjustment results by using the coordinate of unknown point and the size

of baselinevector between points & variation of VCV matrix. Function model,

determined by relationalexpression of coordinate difference for each baseline made up

of baseline vector is used forthe determined coordinate of unknown point by over

constrained adjustment. Function modelcould be formulated as observed equation and

in case, the number of observed equationexceeds that of unknown quantity, solution

could be obtained by least square methodprinciple(Lee et al., 1987; Leick, 2004;

Rizos, 1996).

4.8.8 Checkup of adjusted result and assessment of accuracy

The comparison of check result with reliable accuracy and coordinate difference

needs to beconducted along with comparison with individual applied point, and

stochastic calculationsuch as RMSE, standard deviation, mean for the coordinate

difference needs to be carried outfor the checkup of adjusted results. Besides, the

assessment of adjusted results accuracy isavailable through estimation of absolute error

ellipsoid generated from GPS networkadjustment. The accuracy of horizontal location

of absolute error ellipsoid could be seenconsidering the correlation of east and west (E)

and south and north (N), and the size andshape of error ellipsoid varies to the size of

standard deviation of measured value andcovariance between components.

Checkup and Analyze Loop Misclosure

Loop misclosure can be used to detect "bad" observations. (A bad observation

can includea misread antenna height, not being plumb over a point or observing the

wrong point). Iftwo loops with a common base line have large misclosure, this may be

an indication that thecommon base line is an outlier. Since users must repeat base lines

on different days and atdifferent times of the day, there are several different loops that

can be generated from theindividual base lines. If a repeat base line difference is greater


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than 2 cm then comparing theloop misclosure involved with the base line may help

determine which base line is theoutlier. According to NGS guidelines, if a repeat base

line difference exceeds 2 cm then oneof the base lines must be observed again, and base

lines must be observed at least twice ontwo different days and at two different times of

the day.

4.9 Adjustment of GPS Network Models

For the past five decades, NASA and the US military participated in space

research program a precise GPS navigation. System used six satellites of the first

generation, called transit countries, and is based on the Doppler principle. Transit is

available for commercial use in 1967, and shortly thereafter began to be used in the

survey. The creation of a global network of control centers between applications at the

earliest and the most valuable. GPS using transit required very long sessions control

point, and accuracy to level 1-m. Thus, in the survey it was only suitable for business

control over networks that consist of spaced points on a large scale. It was not

satisfactory to clear applications such as engineering or planning transit every day.

Encouraged by the success of transit, a new research program developed which

ultimately led to the creation of GPS in the NAVSTAR system (GPS). This system uses

GPS and navigation of the second-generation constellation of 24 satellites orbits.

Positioning accuracy have improved considerably compared to the transit system,

depriving the long monitoring sessions, also canceled. Although the developed

countries for military applications, and civilians, including surveyors, also found uses

the global positioning system.

Since its introduction, it used widely GPS. They are reliable and efficient and

able to generate a very high accuracy. Notes can be taken to determine the sites day or

night and in any weather. A great feature for GPS it is not necessary to see the dots

surveyed. Thus is avoided process takes a long time to scan the horizon lines. Al-

though most of the first applications of GPS in the work of monitoring, system

improvements now comfortable and practical for use in almost every type of study,

including surveys of ownership and topographic mapping, and staking of the building.

In practice, when surveys are done by observing carrier phases, four ormore satellites

are observed simultaneously using two or more receivers locatedon ground stations.

Also, the observations are repeated many times.


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This produces a very large number of redundant observations, from whichmany

difference combinations can be computed.Of the two GPS observing procedures,

pseudo ranging yields a somewhat lower order of accuracy, but it is preferred for

navigation use because it givesinstantaneous point positions of satisfactory accuracy.

The carrier-phase techniqueproduces a higher order of accuracy and is therefore the

choice forhigh-precision surveying applications. The differencing techniques used in

carrier-phase observations, describedbriefly above, do not yield positions directly for

the points occupied by receivers.Rather, baselines (vector distances between stations)

are determined.These baselines are actually computed in terms of their coordinate

differencecomponents ΔX, ΔY, and ΔZ. To use the GPS carrier-phase procedure in

surveying, at least two receiverslocated on separate stations must be operated

simultaneously. For example,assume that two stations A and B were occupied for an

observing session,that station A is a control point, and that station B is a point of

unknownposition. The session would yield coordinate differences ΔXAB, ΔYAB, and

ΔZABbetween stations A and B. The X,Y,Z coordinates of station B can then

beobtained by adding the baseline components to the coordinates of A as

XB=XA+ΔXAB

YB= YA+ ΔYAB (4.2)

ZB= ZA+ ΔZAB

Because carrier-phase observations do not yield point positions directly,but

rather, give baseline components, this method of GPS surveying is referredto as relative

positioning. In practice, often more than two receivers are usedsimultaneously in

relative positioning, which enables more than one baselineto be determined during each

observing session. Also, after the first observingsession, additional points are

interconnected in the survey by moving thereceivers to nearby stations. In this

procedure, at least one receiver is left onone of the previously occupied stations. By

employing this technique, a networkof interconnected points can be created. Figure

(4.3) illustrates an example of a GPS network. In this figure, stations A and B are

control stations,and stations C, D, E, and F: are points of unknown position. Creation

of suchnetworks is a common procedure employed in GPS relative positioning work.


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Figure (4.3): GPS survey network.

4.10 Continuously Operating Reference System

The Continuously Operating Reference System (CORS) is a major technique

forestablishing regional three-dimensional geodetic datums. Thanks to the rapid

development of satellite positioning technology, information technology, and

networktechnology, CORS networks have appeared all over the world, includingglobal

large-scale networks and regional small-scale networks. The classical horizontaldatum

is defined and extended by the geodetic origin and horizontal controlnetwork. Similarly,

the three-dimensional coordinate datum is defined andextended by CORS and GPS

networks (Hoffman-Wellenhof, 2001; Leick, 2004).

4.10.1 Basic Components of CORS

As the datum of the three-dimensional control network, CORS is the product

ofsophisticated new technologies, such as satellite positioning technology,

computernetwork technology, digital communication technology, and so on. It is

composedof a datum station network, see figure (4.4), data processing center, data

transmission system,positioning and navigation data broadcast system, and user

application system, see figure (4.5).


Page 84

Figure (4.4): The Monumentation of one Core Station


Page 85

Figure (4.5): The configuration of CORE networks

Every datum station is connected to the monitoring and analysis center through

thedata transmission system, constituting a special purpose network.

The datum station network, made up of datum stations distributed evenly

withina certain scope, is used to collect observational data from GPS satellites,

transmitthem to the data processing center, and provide services for monitoring the

systemintegrity.

The data processing center, as the control center of the system, is used to

receivedata from every datum station and form multiple datum stations‟ differential

positioning data for users through data processing. Then, the data files formed with a

certain format are distributed to users. The data processing center is the essential part of

CORS as well as the key to realizing high-precision real-time dynamic positioning.

After a continuous around-the-clock solution of the whole modeling within an

area based on real-time observational data collected by every datum station, the center

automatically generates a virtual reference station (including the coordinates of datum

stations and GPS observations) corresponding to the mobile station and provides

various users who are in need of measurement and navigation with code phase/carrier


Page 86

phase differential correction information in a universal common format via the existing

data communication networks and wireless data broadcast systems so as to calculate the

exact real-time position of mobile stations.

The data transmission system, where data from every datum station are

transmitted to the monitoring and analysis center through fiber lines. The system

comprises hardware devices for data transmission and software control module. The

data broadcast system broadcasts positioning and navigation data to users in the form of

mobile networks, UHF radio, Internet, etc.

The user application system consists of a user information receiving system,

anetwork-based RTK (real-time, kinematic) positioning system, a fast and

postprocessingprecision positioning system, an autonomous navigation system,

positioningmonitoring system, and so on. According to different application

accuracies,the user service subsystem ranges from millimeter-level, centimeter-

level,decimeter-level, to meter-level whereas, according to different user applications,

itcan be categorized into surveying and mapping and engineering users

(centimeteranddecimeter-level), vehicle navigation and positioning users (meter-level),

highprecisionusers (post-processing), and meteorology users.

CORS is not only a kinematic and continuous positioning reference frame

butalso an important technical means for rapid and high-precision acquisition of

spatialdata and geographic features. CORS is more often applied in small areas,

forinstance, a city, to provide three-dimensional datum. Within an area, it

provideshighly precise, reliable, and real-time positioning information to a large number

ofusers simultaneously and unifies the surveying and mapping data in the city.

Forexample, the application of CORS in cities will exert a profound and

lastinginfluence on the collection of modern urban geographic information and

theapplication system. Not only can it establish and maintain a reference frame ofthe

surveying and mapping in cities, it can also provide automatically all-weatherreal-time

spatial and temporal information of high-precision, serving as the basis ofregional

planning, management, and decision-making. It can also provide differentialpositioning

information and develop new applications of transportationnavigation; again it enables

high-precision, high-spatial-and-temporal-resolution,all-weather, near-real-time, and

continuous variable sequences in precipitable watervapor, which will gradually form a


Page 87

regional severe weather monitoring and forecastingsystem. CORS can also be used in

the high-precision time synchronizationin communication and power systems and will

provide the services of monitoringand predicting land subsidence, geological disasters,

and earthquakes and will studythe temporal and spatial evolution of natural disasters.

Currently, CORS systems have been established in many developed countries

worldwide, Egypt, KSA, UAE, Bahrain and Jordan(Zhiping Lu,& at el,2014).

4.10.2 CORS Network in Egypt

NRIAG CORE NETWORK

In 2006, NRIAG started the establishment of the Egyptian Permanent GPS

Network (EPGN). Basically, the site selection was aimed to cover geographically all the

Egyptian territory but also considering the tectonic setting of Egypt. As shown in

figure(4.6), three stations were located in the Eastern Desert at the Red Sea coast, two

stations in Sinai Peninsula, four stations in the Western Desert, three stations at the Nile

and six stations around Cairo and the Nile Delta.

https://www.google.com.eg/search?num=20&tbm=bks&q=inauthor:%22Zhiping+Lu%22&sa=X&ei=2oyfVZKPMMLTygP_3oCABQ&ved=0CCEQ9AgwAA


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Figure (4.10.): Geographic distribution of the NRIAG CORE Network

The EPGN operation started by four stations in 2007 to 18 stations was

achievable at the end of 2014 (4 in 2007, 2 in 2008, 3 in 2010, and 6 stations in 2011,

three station in 2014). In addition to these 18stations, it was started 2015 to install

another four stations in south of Aswan two in Eastern side of Nasser Lake, and two in

the western side of the lake to continuous monitor of seismic activities around the High

Dam(A.F.R.E.F,2007).

ESA CORE NETWORK

Unfortunately, nothing was published about it. What is known that ESA started

installing it 2008 and consists of 40 CORE station covered the Nile Delta and Nile

Valley, most of it, installed on the branches of ESA in different Governorates with

Trimble NET R5 GNSS receivers.

Chapter 5 Experimental Results & Evaluation

Page 89

Chapter Five

Experimental Results & Evaluation

In space geodetic positioning, where the observation techniques provide absolute

positions with respect to a consistent terrestrial reference frame, the corresponding

precise definition and realization of terrestrial and inertial reference systems is of

fundamental importance. Thanks to significant improvements in receiver technology, to

extension and densification of the global tracking network along with more accurate

determination of positions and velocities of the tracking stations and to dramatically

improved satellite orbits, GPS is today approaching 0.1 ppm precision for longer

baselines and it can be considered to be the main global geodetic positioning system

providing nearly instantaneous three-dimensional position at the cm accuracy level. One

of the fundamental goals of geodesy is to precisely define positions of points on the

surface of the Earth, so it is necessary to establish a well-defined geodetic datum for

geodetic measurements and positioning computations. Recently, a set of the coordinates

established by using GPS and referred to an international terrestrial reference frame

could be used as a three-dimensional geocentric reference system for a country (Chang

and Tseng, 1998b).


ellipsoid of revolution of adopted size and shape, with origin, orientation, and scale

defined by a geocentric terrestrial frame. Once an ellipsoid is selected, coordinates of a


longitude, latitude, and ellipsoid height).





tectonic motion. Static datum does not incorporate the effects of plate tectonics and



89


Page 90

Datum's can either become fully kinematic (dynamic), or semi-kinematic. A

deformation model can be adopted to enable ITRF positions to be transformed into a

static or semi-kinematic system at the moment of position acquisition so that users do

not see coordinate changes due to global plate motions. GNSS devices which use ITRF

or closely aligned systems position users in agreement with the underlying kinematic

frame, however, in practice there are a number of very significant drawbacks to a

kinematic datum. Surveys undertaken at different epochs cannot be combined or

integrated unless a deformation model is applied rigorously, or is embedded within the

data, and the data are correctly time-tagged. On the other hand, Semi–Kinematicdatum

incorporates a deformation model to manage changes (plate tectonics and deformation

events). Coordinates fixed at a reference epoch, so the change to coordinates is

minimized. Many countries and regions which straddle major plate boundaries have

adopted a semi-kinematic (or semi-dynamic) geodetic datum in order to prevent

degradation of the datum as a function of time due to ongoing crustal deformation that

is occurring within the country.






deliver temporally stable coordinates within a localized reference frame.

5.1 Transformation Parameters Terrestrial Reference Systems “TRS”

Recall that Transformations from kinematic ITRF to a static datum are

conventionally done by either using the site velocity (measured directly or computed

from a plate motion model) to compute the displacement between the reference and

current epochs or by a conformal transformation augmented with time dependent

parameters to account for rigid plate motion. Rigid Plate movement is conventionally

defined by a rotation rate about an Euler Pole and , where , are the latitude and

longitude of the pole, and is the rate of rotation of the plate around the pole in degrees

per million years. Equivalent rotation rates about the Cartesian axes ( and ) can

be computed from the Euler pole definition using equations (5.1-5.3) ( , , and ) are

first converted from decimal degrees to radians):


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Ω (Φ) ( ) (5.1)

Ω (Φ) ( ) (5.2)

Ω (Φ) (5.3)

A site velocity in Cartesian format ( ) can be computed for any given

location (X, Y, Z in meters) on a rigid plate defined by (ΩX, ΩY, ΩZ in radians per

million years) using:

[

] [

Ω Ω Ω Ω Ω Ω

] 1E-6 (5.4)

By introducing a reference epoch and an epoch of measurement t (epochs in

decimal years), the ITRF coordinates of any point on a rigid plate at a reference epoch

( , , in meters) can be computed from the coordinates at epoch t ( , , in

meters) using:

[

] [[

] [

] ( ) ] (5.5)

For any location on a rigid plate, instantaneous ITRF coordinates can be transformed to

a fixed reference epoch using equation (5-18) (Stanaway and Roberts, 2009).

[

] [

] [[

] [

Ω Ω Ω Ω Ω Ω

] ( ) ] (5.6)

Where:

( ): are the ITRF Cartesian coordinates at the reference epoch

(in decimal years),

( ): are instantaneous ITRF Cartesian coordinates at epoch (epoch

in decimal years),


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( ): is the translation of the reference frame origin (from ITRF to

local system),

(Ω Ω Ω ): are the Cartesian rigid plate/block rotation parameters, is the

reference frame

: is scale factor (from ITRF to local).

As it is seen in figure (5.1), the African continent is broadly divided into two major

tectonic plates. Most of Africa, west of the East African Rift lies on the Nubian Plate.

The Somalian Plate lies east of the African Rift. A very small section of North Africa

along the Maghreb coast in Algeria and Morocco lies on the Eurasian Plate and the

Dankalia region of Eritrea lies on the Arabian Plate.

Figure (5.1.): The Africa tectonics sub-plates

Analysis of the ITRF2005 solution (Altamimi et al., 2007; IERS, 2010)

indicates that ITRF site velocities for any location within Africa are between 24 and 31

mm/yr due to rigid motion of the African plates over the underlying mantle. These site

velocities degrade the accuracy of absolute positions like PPP if the measurement epoch


Page 93

is misinterpreted as a reference epoch for the underlying datum realization in use at the

time Equations (5.1, 5.2 and 5.3) were used to compute (ΩX, ΩY, ΩZ) for the Nubian

Plate using the Euler parameters determined by ITRF2008 PMM “Plate Motion Model”

(Altamimi Z., et al. (2012) and Egypt‟s Deformation Model (Saleh,M. , Becker, M.,

2013), the results were depicted in table (5.1).

Table (5.1.): The Cartesian angular Velocity of Nubian Plate

Deformation

Model

Absolute Pole Cartesian angular Velocity for Nubian Plate

(Rad/Ma) (Rad/Ma) (Rad/Ma)

ITRF2008-PMM 0.000461 -0.00290 0.003506

5.2. PPP Solution

PPP has received increased attention in the past several years within the GPS

community due to its great operational flexibility and accuracy promise. The major

advantages of PPP lie in two aspects: system simplicity at the user‟s end and global

consistency in terms of positioning accuracy. PPP-based approach significantly reduces

the equipment and personnel costs, pre-planning, and logistics compared to

conventional GPS network-based approaches. Applying PPP, a single survey team can

establish a CORS network across a PPP has received increased attention in the past

several years within the GPS community due to its great operational flexibility and

accuracy promise (A. Elhattab, 2014).

The major advantages of PPP lie in two aspects: system simplicity at the user‟s

end and global consistency in terms of positioning accuracy. PPP-based approach

significantly reduces the equipment and personnel costs, pre-planning, and logistics

compared to conventional GPS network-based approaches. Applying PPP, a single

survey team can establish a control network across a large area, rather than the

complicated logistics and communications needed to organize multiple survey teams to

occupy stations simultaneously. It also reduces the needs to analyze the data using

scientific software packages, which are not generally too accessible to inexperienced

users.

https://www.researchgate.net/researcher/2066035923_Matthias_Becker


Page 94

Measurements from the IGS global tracking network are processed by the IGS

Analysis Centers to provide the highest quality satellite orbit and clock parameters.

These parameters are freely available from the Internet and are the basis for PPP

development. These IGS products can be applied to significantly reduce the errors in

GPS satellite orbits and clocks, which are two of the most significant error sources in

GPS positioning. Combining precise satellite positions and clocks with a dual frequency

GPS receiver to remove the first order effect of the ionosphere, PPP is able to provide

position solutions at centimeter level. Coordinates estimated with PPP will be in the

same global reference frame as the satellite orbits. When using orbits from IGS,

estimated receiver coordinates are referred to the IGS realization of ITRF.

Last decades several PPP post-processing software have been developed based

on the above observation models. Also online web services from different organizations

such as the Precise Point Positioning Software Center (http://gge.

unb.ca/Resources/PPP/index.htm) which has been created under the auspices of the

Canadian Geomatics for Informed Decisions Network of Centers of Excellence

provides users easy access to online PPP services as CSRS-PPP

by Natural Resources Canada (NRCan),GPS Analysis and Positioning Software

(GAPS)by University of New Brunswick (UNB),Automatic Precise Positioning Service

(APPS)by Jet Propulsion Laboratory (JPL),and magic GNSS by GMV (privately owned

technological business group).

5.2.2 Evaluating the PPP Solution

The solution of CSRS-PPP SW is now used extensively to provide realizations

of ITRF globally with a precision of a few centimeters. Four groups of data from IGS

stations, namely MALI (Malindi, Kenya) on the Somalian plate, RABT (Moracco) on

the Nubian plate, RAMON (occupied Palestine) on the Arabian plate and NICO

(Nicosia, Cyprus) on the Eurasian plate, distributed over the different sub-plates of

Africa and their positioning was computed and published by the IGS data centers at

ITRF 2008 Epoch2005 and given in table (5.2). The data of the four groups of IGS

stations was downloaded from ftp://garner.ucsd.edu/pub/rinex/2015/100/ for Day 100,

2015 and processed using the Precise Point Positioning module of CSRS-PPP. To

transfer the IGS published coordinates from Epoch2005, as: = 2005, to the epoch of

ftp://garner.ucsd.edu/pub/rinex/2015/100/


Page 95

the PPP solutions, ITRF 2008 Epoch2015.274 as t, Epoch2015.274, the following

formula (Altamimi. Z, 2006), is used:

P ( t0 ) = P( t ) + P˙( t0- t) (5.7)

Where:

P(t0) = is the positioning at a reference epoch ITRF 2008 Epoch 2005

P(t) = is the positioning value at time t, defined by PPP at epoch 2015.274

P˙ = Velocity

Table (5.2.): ITRF2008 STATION POSITIONS AT EPOCH 2005.0 AND

VELOCITIES

DOMES

SITE

X/Vx Y/Vy Z/Vz Sigmas

--------------------/m/y-----------

35001M002 Rabat RABT 5255617.683 -631745.687 3546322.552 0.001 0.001 0.001

35001M002 -0.0088 0.0174 0.0142 0.0001 0.000 0.0001

33201M001 MALINDI MALI 4865366.354 4110737.599 -331121.569 0.001 0.001 0.001

33201M001 -0.0172 0.02 0.0167 0.0001 0.0001 0.0000

20703S001 Mitz

RAMON RAMO 4514721.855 3133507.841 3228024.716 0.001 0.001 0.001

20703S001 -0.0205 0.0141 0.0177 0.0001 0.0001 0.0001

14302M001 NICOSIA NICO 4359415.713 2874117.066 3650777.829 0.001 0.001 0.001

14302M001 -0.0179 0.0116 0.0126 0.0001 0.0001 0.0001

The transferred coordinates of the four IGS stations defined in ITRF2008 Epoch

2015.274 are tabulated in table (5.3).

Table (5.3.): IGS Data Set Expressed in ITRF2008 Frame Station Positions and

Velcocities at Epoch 2015/04/10

DOMES NB SITE

NAME ID

SOL

N X Y Z

SIGMA

x

SIGMA

y

SIG

MA z

35001M002 RABTRABT 1 5255617.683 -631745.687 3546322.552 0.001 0.001 0.001

33201M001 MALINDI MALI 1 4865366.177 4110737.805 -331121.398 0.001 0.001 0.001

14302M001

NICOSIA-

ATHALASS

A

NICO 1 4359415.525 2874117.189 3650777.949 0.001 0.001 0.001

20703S001 Mitzpe

Ramon

RAM

O 1 4514721.645 3133507.986 3228024.898 0.001 0.001 0.001


Page 96

To see how the PPP can be used in updating the ITRF of the IGS points, the

solution of PPP with the transferred published IGS ITRF2008 at Epoch 2015.274 are

given in table (5.4). The differences between two solutions are computed and outlined

in table (5.4). As it is shown in the table, the absolute value of the maximum differences

does not exceed 17mm for the Y component of Nico Station, while does not exceed few

mm for the other stations.

Table (5.4.): the updated positioning for four IGS stations defined in ITRF2008 epoch

2015.274 by IGS & PPP

Rabat

Sol. Type X Y Z

PPP- Solution 5255617.590 -631745.508 3546322.700

IGS-Solution 5255617.593 -631745.508 3546322.698

Differences -0.003 0.000 0.002

Mali

Sol. Type X Y Z

PPP- Solution 4865366.174 4110737.798 -331121.393

IGS-Solution 4865366.177 4110737.805 -331121.398

Differences -0.003 -0.007 0.005

Nico

Sol. Type X Y Z

PPP- Solution 4359415.522 2874117.172 3650777.950

IGS-Solution 4359415.525 2874117.189 3650777.949

Differences -0.003 -0.017 0.001

Ramo

Sol. Type X Y Z

PPP- Solution 4514721.636 3133507.978 3228024.886

IGS-Solution 4514721.641 3133507.982 3228024.891

Differences -0.005 -0.004 -0.005

By comparing the differences of the two solutions for the four IGS stations, one

can easily see that, how the PPP is precise in expressing the epochwise solution of the

ITRF frame.

Additionally to see for what extent PPP can be an alternative for the differential

techniques, seven test points were processed by Trimble Business Center “TBC”

Software, the product of Trimble, with considering the PPP solution of PHLW as a

reference station for the processing. The results of the processing were demonstrated in

table (5.5).


Page 97

As it is shown in table (5.5), one can easily see the quality of PPP solution

compared with the DGPS solution. In spite of the processed baselines are exceed

several tens of kilometers to 120 km, PPP shows good harmony with the DGPS in mm

level except the station 0Z20 which has differences of 2.3 to 3.2 cm that may be it has

the longest baseline as well as it gives the worst accuracy of PPP that is may be come

from the surrounding environments around the station.

Table (5.5.): The differences between DGPS & PPP solutions for the observed Stations

St.

DGPS Sol.

PPP Sol.

Differences bet

DGPS & PPP

X Y Z X Y Z dX dY dZ

PHL

W 4728141.180 2879662.608 3157147.159

4728141.180 2879662.608 3157147.159

0.000 0.000 0.000

0Z18 4657081.787 2807150.058 3322370.152 4657081.784 2807150.059 3322370.156 0.003 -0.001 -0.004

0Z20 4796793.729 2651830.764 3250924.993 4796793.697 2651830.738 3250924.970 0.032 0.026 0.023

0Z89 4745737.252 2795140.347 3205858.805 4745737.246 2795140.341 3205858.797 0.006 0.006 0.008

0Z94 4739314.560 2828743.551 3186027.207 4739314.553 2828743.544 3186027.199 0.007 0.007 0.008

Burg 4765954.276 2704546.183 3252949.202 4765954.269 2704546.174 3252949.193 0.007 0.009 0.009

O1 4728219.038 2879743.411 3156930.682 4728219.033 2879743.402 3156930.676 0.005 0.009 0.006

5.3. The Evaluation Study

In 1992, an ESA steering committee developed a plan for the creation of new

datum for Egypt, with the following approach (Scott, 1997):











coordinate system.


Page 98

The ITRF1994 was transferred to Egypt‟s HARN network by connecting it with

four IGS stations, namely MATE (Italy), KIT3 (Uzbekistan), HART (South Africa) and

MASP in (Canary Island), depicted in chapter one figure (1.3). Each HARN‟s station

was observed for six sessions, every session was 6 hours with 30 seconds epoch

interval. The observation time was planned to produce 1:10,000,000 (Order A) for

HARN and 1:1,000,000 (Order B) for NACN relative network accuracy standard

between stations. The results of analyzing both of them were defined in ITRF1994

epoch 1996.


techniques and its impact in analyzing the geodetic applications that need an ultimate

accuracy like the National High Accuracy Reference Networks, a critical example is

given to demonstrate this study. The example is concerned with analyzing a part of

Egypt HARN and NACN (National Agriculture Cadastre) Networks that is located in

and around Nile Delta. The geometric location of this part is illustrated in figure (5.2)

and the position of the aforementioned points as given in HARN analysis report (Scott,

1997) is depicted in table (5.6). Additionally, this section deals with the computing

techniques that are used in transferring the terrestrial frame from epoch to epoch in to

different frames. Three days campaigns were conducted in June 2015 from 3 to 6, to

convert this part of HARN & NACN network in the most recent ITRF available frame

at the epoch of observation campaigns, namely ITRF 2008 epoch 2015.422. However,

we use the aforementioned approach, equation (5.7) in transferring the PPP solution of

the specified part of HARN to the ITRF 2000 epoch 2000, utilizing the three

parameters of Nubian plate as defined by ITRF2005-PMM (Altamimi et al. (2007).,

table (5.1). The results are given in table (5.7).

Table (5.6.): The coordinates of chosen points of the HARN and NACN Networks

ITRF 1994, epoch 1996 (Scott, 1997).

Station X Y Z

OZ94 4745737.755 2795140.173 3205858.575

OZ89 4739315.089 2828743.36 3186026.976

OZ18 4657082.606 2807149.887 3322369.803

OZ20 4796794.204 2651830.557 3250924.750


Page 99

Figure (5.2): The location of the used part of Egypt HARN & NACN

Table (5.7.): The Part of HARN & NACN network updated in ITRF2000

ST.

PPP Results Coordinate at Epoch 2015.422

Transformed PPP Coordinates at ITRF2008

Epoch 2005

X Y Z X Y Z

PHLW 2879662.632 2879662.632 3157147.186 2879662.851 2879662.483 3157147.019

0Z18 4657081.784 2807150.059 3322370.156 4657082.003 2807149.91 3322369.989

0Z20 4796793.697 2651830.738 3250924.970 4796793.916 2651830.589 3250924.803

0Z89 4745737.246 2795140.341 3205858.797 4745737.465 2795140.192 3205858.63

0Z94 4739314.553 2828743.544 3186027.199 4739314.772 2828743.395 3186027.032

Burg 4765954.269 2704546.174 3252949.193 4765954.488 2704546.025 3252949.026

O1 4728219.033 2879743.402 3156930.676 4728219.252 2879743.253 3156930.509

The evaluation strategy is based upon:

1. Evaluating the IGS stations that were used in transferring the ITRF to HARN,

by using their published ITRF2008 Epoch2015.422 coordinates values and the

related transformation parameter to ITRF1994 Epoch1996 and compares the

transferred values by the reported values of (Scott, 1997).

2. Transferring the values of HARN & NACN networks that were defined in

ITRF2008 epoch 2005 to the original ITRF frame of HARN, namely ITRF1994

epoch 1996 and compare the resulted values with the original coordinate‟s

values given by (Scott, 1997). The aforementioned transformation is performed


Page 100

by exploiting the published 14 transformation parameters between different

ITRF‟s Frames by IGS (John, D.and Jim S., 2004). However, the

transformation process from ITRF 2008 epoch 2015.422 to ITRF 1994 epoch

1996 will be performed in the following steps:

1. Transforming the PPP values of HARN & NACN networks that defined in

ITRF2008 epoch 2015.422 to ITRF2008 Epoch2005 using the published

Absolute Pole Cartesian angular Velocity for Nubian Plate, as outlined

before.

2. Transferring the ITRF2008 Epoch2005 to ITRF1994 Epoch 2000 using the

published parameters in table (5.8).

3. Updating the values specified in the table (5.8) to be in Epoch 1996 instead

of Epoch2000.

4. Compute the differences

Table (5.8.): Transformation parameters Between ITRF2008 Epoch 2005 to ITRF 1994

Epoch 2000

EPOCH R1

R1

R1

D

Ppb

T3

mm

T2

mm

T1

mm

SOLUTIO

N

UNITS…

…

/Y

/Y

/Y

Ppb/Y

mm/Y

mm/y

mm/y

RATES

UNITS…

…

2000 0.06

0.02

0.00

0.00

0.00

0.00

2.92

0.09

-33.2

-3.2

2.6

-0.05

4.8

0.1

ITRF94

rates

5.3.1 Evaluating the IGS Stations that was Used in Transferring the

ITRF to HARN

Before digging into applying the above procedures, a check for the published

transformation parameters are done. This step is so necessary to check the quality of the

published data by IGS as well as to see the size of errors embedded in the stations that

were used by (Scott, 1997) in transferring the ITRF1994 frame to Egypt‟s HARN,

namely MATE (Italy), KIT3 (Uzbekistan), HART (South Africa) and MASP in

(Canary Island), see figure (1.3). table (5.9) depicts the coordinates of the four IGS

stations defined in ITRF1994 Epoch 1996 as given by (Scott, 1997) and the published

by IGS in ITRF2008, Epoch2005.


Page 101

It was stated in http://itrf.ign.fr/rel_trs.php that the standard relation of

transformation between two reference systems is an Euclidian similarity of seven

parameters: three translation components, one scale factor, and three rotation angles,

designated respectively, T1, T2, T3, D, R1, R2, R3, and their first times derivations: 1,

2, 3, , 1, 2, 3. The transformation of coordinate vector X1, expressed in a reference

system (1), into a coordinate vector X2, expressed in a reference system (2), is given by

the following equation:

(5.8)

With: (

) and (

)

It is assumed that equation (5.7) is linear for sets of station coordinates provided

by space geodetic technique (origin difference is about a few hundred meters, and

differences in scale and orientation are of 10-5 level). Generally, X1, X2, T, D, R are

function of time. Differentiating equation (5.7) with respect to time gives:

(5.9)

D and R are of 10-5

level and is about 10 cm per year, the terms D 1 and

R 1 arenegligible which represent about 0.0 mm over 100 years. Therefore,

equation (5.9) could be written as:

+ (5.10)

http://itrf.ign.fr/rel_trs.php


Page 102

Table (5.9.): The coordinate values of the IGS four stations in ITRF1994, Epoch 1996

and the published coordinate values for the nominated IGS stations in ITRF2008

Epoch2005

Statio

n ITRF2008 Epoch2005

ITRF1994 Epoch 1996 (as given by

Scott, 1997)

MATE 4641949.557 1393045.422 4133287.465 4641949.737 1393045.262 4133287.317

KIT3 1944945.139 4556652.244 4004326.007 1944945.390 4556652.199 4004325.973

HART 5084625.288 2670366.383 -2768494.401 5084625.460 2670366.404 -2768494.470

MAS1 5439192.215 -1522055.484 2953454.847 5439192.277 -1522055.641 2953454.694

The four stations in table (5.7) were transferred from ITRF2008 Epoch2005 to

ITRF1994 Epoch2000 using the transformation parameters given in table (5.8) and

equation (5.8). The results were demonstrated in table (5.10). Also the velocities of the

specified IGS stations in ITRF1994 were also depicted in table (5.10).

Table (5.10.): The transferred coordinate values of the four stations to ITRF1994

Epoch2000

Station ITRF1994 Epoch2000 Velocity m/y

MATE 4641949.557 1393045.429 4133287.444 -0.0191 0.0202 0.0121

KIT3 1944945.149 4556652.26 4004325.985 -0.028 0.0163 0.0064

HART 5084625.308 2670366.394 -2768494.442 -0.0015 0.0164 0.018

MAS1 5439192.236 -1522055.486 2953454.822 0.0001 0.0154 0.0152

To transfer the computed IGS coordinates from Epoch2000, as: = 2000, to the

epoch of the HARN solutions, ITRF 1994 Epoch1996 as t, equation (5.7) was used. The

results of the transformation were given in table (5.11). To see the differences between

the original coordinate values of the used IGS four stations as given by Scott (1997),

defined in ITRF1994 Epoch1996, as outlined in table (5.7), the differences between the

two ITRFs were computed and recorded in table (5.11) and the differences in table

(5.12).

Table (5.11.): The values of the published coordinate values of the four IGS stations &

the reported values by (Scott, 1997) in ITRF1994 Epoch1996

St.

ITRF1994 Epoch1996 transferred from IGS

published values in ITRF2008 Epoch2005

ITRF1994 Epoch1996 as reported by Scott

(1997)

X Y Z X Y Z

MATE 4641949.633 1393045.348 4133287.396 4641949.737 1393045.262 4133287.317

KIT3 1944945.261 4556652.195 4004325.959 1944945.390 4556652.199 4004325.973

HART 5084625.314 2670366.328 -2768494.514 5084625.460 2670366.404 -2768494.470

MAS1 5439192.236 -1522055.548 2953454.761 5439192.277 -1522055.641 2953454.694


Page 103

Table (5.12.): The differences between the published coordinate values of the four IGS

stations & the reported values by (Scott, 1997) in ITRF1994 Epoch1996

St.

Differences

Bet. ITRF1994 Epoch1996 transferred from IGS published values in ITRF2008

Epoch2005&ITRF1994 Epoch1996 as reported by Scott (1997)

dX dY dZ

MATE 0.104 -0.086 -0.079

KIT3 0.129 0.004 0.014

HART 0.146 0.076 0.044

MAS1 0.041 -0.093 -0.067

As it is shown in table (5.12), in spite of we have already used only in the

previous processing the published values and models as specified by IGS, one can see a

tolerance ranged between -8.6 cm to 14.6 cm. The reasons behind these differences are

mostly returning to the limited number of stations, only 13 stations - see figure (5.4)-,

that were used in realizing the ITRF94 that leads to sub-optimal stations distribution and

small discontinuities between IGS realizations of ITRF, as clarified by (Ferland and

Kouba, 1996).

Figure (5.3): Station set (13) used for IGS Realization of ITRF 92-93-94


Page 104

5.3.2. Transferring the Solved PPP Part of HARN Network to the

ITRF 1994 Epoch 1996

Firstly, transfer the tested part of HARN and NACN from ITRF2008

epoch2005, specified in table (5.5), to HARN ITRF1994 epoch 2000, with the

aforementioned steps in sub-chapter 5.4 by using equation (5.8) and table (5.8).The

computation results are given in table (5.13).

Table (5.13.): The Results of Transformation the HARN to ITRF 1994 Epoch 1997

St. PPP at ITRF2008 Epoch 2005 PPP at ITRF1994Epoch 2000

X Y Z X Y Z

PHLW 4728141.399 2879662.459 3157146.992 4728141.418 2879662.47 3157146.968

0Z18 4657082.003 2807149.91 3322369.989 4657082.021 2807149.921 3322369.966

0Z20 4796793.916 2651830.589 3250924.803 4796793.935 2651830.599 3250924.779

0Z94 4745737.465 2795140.192 3205858.63 4745737.484 2795140.203 3205858.606

0Z89 4739314.772 2828743.395 3186027.032 4739314.791 2828743.406 3186027.008

Burg 4765954.488 2704546.025 3252949.026 4765954.507 2704546.036 3252949.002

O1 4728219.252 2879743.253 3156930.509 4728219.271 2879743.264 3156930.485

To transfer the resulted coordinate‟s values of the tested part of HARN from

ITRF1994 Epoch2000 to ITRF1994 Epoch 1996, there is a need to define the Nubian

Plate Velocity in the same ITRF1994. Equation (5.10) can be used in computing the

velocities of the Egyptian stations in ITRF1994, provided that the stations velocities

should be defined in ITRF2008. This can be performed by applying equation (5.4) and

table (5.4). The resulted velocities are represented in table (5.14). So the HARN stations

can be converted to ITRF1994 Epoch1996, by using equation (5.7) and considering

Epoch2000 as: = 2000, and Epoch1996 as t = 1996. The results are depicted also in

table (5.13). The differences between the reported part of HARN by Scott (1997) and

the computed part based on PPP techniques and the IGS related transformation

parameters and velocities defined in IREF1994 Epoch 1996 is displayed in table (5.14).


Page 105

Table (5.14.): The computed velocities and the transferred coordinate values to ITRF

94 Epoch 96 of the specified part of the Egyptian HARN

St. Velocities at ITRF1994 m/y PPP at ITRF1994Epoch 1996

VX VY VZ X Y Z

PHLW -0.0187 0.0149 0.0121 4728141.343 2879662.53 3157147.016

0Z18 -0.0190 0.0146 0.0119 4657081.945 2807149.979 3322370.013

0Z20 -0.0182 0.0151 0.0122 4796793.862 2651830.66 3250924.828

0Z94 -0.0186 0.0150 0.0121 4745737.409 2795140.263 3205858.655

0Z89 -0.0187 0.0149 0.0121 4739314.716 2828743.466 3186027.057

Burg -0.0184 0.0150 0.0122 4765954.433 2704546.096 3252949.051

O1 -0.0187 0.0149 0.0121 4728219.196 2879743.324 3156930.533

As it is shown in table (5.16), the differences in X-component ranged from 34 to

37 cm, except 0Z18 that was partially destroyed, and Y-component ranged from -8 cm

to -11 cm and for Z-component, the differences were ranged between -7 cm and -8 cm,

except 0Z18. Finally, one can see that size of error budget that affects the original

processing of Egyptian HARN network which stem from connecting parts of Egyptian

HARN with four stations of IGS that were far away from EGYPT, namely HART,

KIT3, MAS1 and MAT, forming very long baselines as depicted in figure (4). Also the

errors in the definition of ITRF1994 itself, that was reached 7 to14 cm as computed in

chapter 4.1. Additionally, within the plate boundary regions (e.g. in the vicinity of the

African Rift and in the northern coastal areas) there will be inter-seismic deformation

of up to a 3-4 mm/year which will not be modeled using a rigid plate transformation

model (Stanaway and Roberts, 2009).

Table (5.15.): The values of the computed PPP HARN transferred to ITRF 94 Epoch

96 and the given values at the same epoch as computed by Scott (1997)

St.

PPP Sol transferred to ITRF1994Epoch

1996 ITRF 1994, epoch 1996 (Scott, 1997)

X Y Z X Y Z

0Z18 4657081.945 2807149.979 3322370.013 4657082.606 2807149.887 3322369.803

0Z20 4796793.862 2651830.66 3250924.828 4796794.204 2651830.557 3250924.750

0Z94 4745737.409 2795140.263 3205858.655 4745737.755 2795140.173 3205858.575

0Z89 4739314.716 2828743.466 3186027.057 4739315.089 2828743.36 3186026.976


Page 106

Table (5.16.): The Difference between the computed PPP HARN transferred to ITRF

94 Epoch 96 and the given values at the same epoch as computed by Scott (1997)

St. Differences bet. PPP Sol transferred to ITRF1994Epoch 1996 & ITRF

1994, epoch 1996 (Scott, 1997)

dX dY dZ 0Z18 0.6606 -0.0923 -0.2101

0Z20 0.3421 -0.1029 -0.0782

0Z94 0.3458 -0.0897 -0.0797

0Z89 0.3731 -0.1058 -0.0806

Chapter 6 Conclusions and Recommendations

Page 107

Chapter six

Conclusions and Recommendations

6.1. Conclusions

In 1874 a number of expeditions were led by British scientists to various

European colonies in Africa and the Indian Ocean in order to simultaneously observe

the transit of Venus for the purpose of precisely determining differences in longitude.

Locations included Mauritius, Rodrigues, Réunion, St. Paul and Egypt. Helwan

Observatory situated on Az Zahra Hill in the Al-Moqattam Hills, South of Cairo was

utilized for the observations, and the station was termed “F1” where: Φo = 30º 01‟

42.8591” N, Λo = 31º 16‟ 33.6” East of Greenwich, the initial La Place azimuth being

measured from Station O1 (Helwân) to Station B1 (Saccara), αo = 72º 42‟ 01.20” from

South, and Ho = 204.3 m, based on mean sea-level at Alexandria. This is considered the

origin of the “Old Egypt Datum of 1907” (Clifford J. Mugnier ,2008).

In 1930, after a re-adjustment of the classical network, the New Egypt Datum of

1930 was published, also referenced to the Helmert1906 ellipsoid. The common

abbreviation for the new datum is “EG30.” This remains the current classical system

used in Egypt for civilian mapping purposes. In 1992, an ESA steering committee

developed a plan for the creation of new datum for Egypt, with the following approach

(Scott, 1997):











Page 108


coordinate system.

Each station was observed for six sessions, every session was 6 hours with 30

seconds epoch interval. The observation time was planned to produce 1:10,000,000

(Order A) for HARN and 1:1,000,000 (Order B) for NACN relative network accuracy

standard between stations. The results of analyzing both of them were defined in

ITRF1994 epoch 1996.

(Rabah, M., et. al., 2015) proofed the drawback of the currently used Egypt

static datum, namely ITRF1994 Epoch 1996, based on GPS Observation Campaign

1996. Because Helwan is considered the only station that was used in updating the

ITRF2008 geodetic frame, the values of Helwan coordinates at any Epoch can be

computed by (http://itrf.ensg.ign.fr/site_info_and_select/solutions_extraction.php). So,

Helwan coordinate values were computed by IGS computing center Helwan IGS Station

with in ITRF2008 Epoch2015.274. Helwan was transferred by the published

transformation parameters, computed by (http://itrf.ign.fr/trans_para.php) to ITRF1994

Epoch 1996 The related Reference Frame coordinate values, related velocity parameters

and the differences are tabulated in table (1). (Rabah, M., et. al., 2015) computed the

differences between Helwan coordinate values defined in ITRF2008 Epoch 2015 and

the values defined in ITRF1994 Epoch 1996. The differences were: -41.8 cm for X

component, 26 cm for Y component and 31.6 cm for Z component. Hence, these

discrepancies exceed any accuracy requirements needed by any control works.

Since 1990, positioning technology has undergone a dramatic improvement in

terms of accuracy and accessibility. Prior to 1990, national geodetic datums were

considered to be static, with fixed coordinates assigned to the datum origin by

convention. Datum coordinates were dynamic only as a consequence of re-observation

and re-adjustment, or localized disturbance. This strategy has been suitable for

terrestrial surveys within stable continental areas. The accessibility of Precise Point

Positioning “PPP” is now widespread with the provision of free online processing

facilities by various geodetic agencies. Such ready accessibility to a global datum has

serious implication for this technology with static geocentric datums. Unless the local

geocentric datums are kept in step with global terrestrial reference frames, discrepancies

between the two will increase in magnitude over time and will become discernable,

http://itrf.ensg.ign.fr/site_info_and_select/solutions_extraction.php


Page 109

even using PPP. The PPP users nowadays are unaware of this datum offset and

incorrectly assume a coordinated datum monument is in error if there is found to be a

disagreement greater than the level of accuracy of the positioning technique.

To evaluate the performance of the PPP processing engine, several PPP tests on

several African IGS station were performed to transfer them to ITRF2005 Epoch 2000

using three parameters kinematic rigid plate model and comprising the results of the

IGS stations published IERS values in the same Epoch. The differences were just a few

centimeters. The results confirm the usability of PPP with the kinematic rigid plate

model in updating the frame.

By applying the published IGS transformation parameters and related sites

velocities, that were computed to transfer from ITRF2008 Epoch2015 toITRF1994

Epoch1996, the Egypt‟s HARN frame, the difference between the computed and the

given original values were in X-component ranged from 34 to 37 cm, and Y-component

ranged from -8 to -11 cm and Z-component, the differences were ranged between -7 and

-8 cm. So, based upon this study and related results, the following conclusions can be

drawn:

To evaluate the performance of the PPP processing engine, several PPP tests on

several IGS station were performed in ITRF2008, Epoch2015 and transfer them

to ITRF2008 epoch 2005 using the IGS plate model, velocities of sites, and

comprising the results of the IGS stations published IERS values in the same

epoch. The differences were just a few centimeters.

To see how the PPP can be used in updating the ITRF of the IGS points, the IGS

stations PPP solution in ITRF2008 at Epoch 2015.274 was compared with the

computed published IGS ITRF2008 at Epoch 2015.274. The differences

between two solutions are computed where we found that the absolute value of

the maximum differences does not exceed 17mm for the Y component of

NicoStation, Cyprus, while does not exceed few mm for the other stations.

The results confirm the usability of PPP in updating the frame.

Additionally to see for what extent PPP can be an alternative for the differential

GNSS techniques, seven test points were processed by Trimble Business Center

“TBC” Software, the product of Trimble, with considering the PPP solution of

PHLW as a reference station for the processing. Based upon the results of the


Page 110

processing,one can easily see the quality of PPP solution compared with the

DGPS solution,in spite of the processed baselines are exceed several tens of

kilometers to 120 km, PPP shows a good harmony with the DGPS in mm level

except the station 0Z20 which has differences of 2.3 to 3.2 cm that may be it has

the longest baseline as well as it gives the worst accuracy of PPP that is may be

come from the surrounding environments around the station.


techniques and its impact in analyzing the geodetic applications that need an

ultimate accuracy like the National HARN of Egypt, a critical example is given

to demonstrate this study. The example is concerned with analyzing a part of

Egypt HARN and NACN (National Agriculture Cadastre) Networks that is

located in and around Nile Delta.Transferring the values of HARN & NACN

networks that were defined in ITRF2008 epoch 2015 to the original ITRF frame

of HARN, namely ITRF1994 epoch 1996 and compare the resulted values with

the original coordinate‟s values given by (Scott ,1997) exploiting the published

14 transformation parameters between different ITRF‟s Frames by IGS. The

differences were ranged in X-component from 34 to 37 cm, except 0Z18(66cm)

that was partially destroyed, and Y-component ranged from -8 cm to -11 cm and

for Z-component, the differences were ranged between -7 cm and -8 cm, except

0Z18.

To evaluating the IGS stations that were used in transferring the ITRF to HARN,

by using their published ITRF2008 Epoch2015.422 coordinates values and the

related transformation parameter to ITRF1994 Epoch1996 and compares the

transferred values by the reported values of (Scott ,1997) ,we have already used

only in the previous processing the published values and models as specified by

IGS, one can see a tolerance ranged between -8.6 cm to 14.6 cm. The reasons

behind these differences are mostly returning to that were used in realizing the

ITRF94 that leads to sub-optimal stations distribution and small discontinuities

between IGS realizations of ITRF, as clarified by(Ferland and Kouba, 1996).

One can say that PPP is the most feasible factor in performing datum

maintenance by time and cost.


most recent one either by PPP or traditional approach.


Page 111

To transfer the coordinates for the part of HARN and NACN to any ITRF

Frame, two different GPS processing techniques can be utilized in the

transformation process. The first technique is based on using PPP as a GPS

processing engine and the second is based on the classical DGPS network

processing.

As a closing conclusion for the overall results, one can say that PPP is the most

feasible factor in performing datum maintenance by time and cost.

6.2. Recommendations


most recent one either by PPP or DGPS. In case of ESA still has the old

collected data, we recommend using the PPP, because most of the available

reference points are at a far distant from Egypt, hence its errors contribution will

be more than the expected error of PPP in updating the frame.

Responsible authorities for maintenance of networks that represent the

references (datum) must safeguard the network points in terms of the restoration,

protection and Coding and re-renovation described Graphics and to prevent any

obstacles hindering the process of observation and to be consistent with modern

appliances.

Updating of HARN and NACN according to the latest frame by taking a modern

observation to them and analyze it by PPP to transfer it to any period of time

(epoch) by the impact of sub plate of tectonic and evaluate the results in terms of

the required level of accuracy and finally make a unified center for the issue of

related geodetic information to be available to all researchers.

There is no doubt that world has become a small village due to rapid advances in

technology, communications and satellite monitoring so we should keep up with this

development through the establish of permanent network or at least a set of points

covering Egypt like global points (IGS) and be fitted with a correct Egypt's atmosphere

sector, which I think is possible. Egypt has already begun doing continuous tracking

networks either done by ESA and NRIAG which actually performs daily update its

datum; hence a kinematic datum or at least semi-kinematic datum must be realized.

References

Page

References

Abidin, H. (1993a): Computational and Geometrical Aspects of On-the Fly Ambiguity

Resolution. Ph.D. dissertation, Department of Surveying Engineering

Technical Report NAO.164, University of New Brunswick, Fredericton,

Canada.

Abidin, Z. Hasanuddin, (2007): Reference of Coordinates, Research center for

Seismology, Volcanology and Disaster Mitigation Graduate school of

Environmental of studies Nagoya University, 22 January 2007.

Altamimi, Z .(2002): Discussion on How to Express a Regional GPS Solution in the

ITRF. Institut Geographique National (IGN); Ecole Nationale des

Sciences Geographiques; 6 et 8 avenue Blaise Pascal; 77455 Marne la

Value Cedex 2 – France .

Altamimi, Z., Collileux, J., Legrand, J., Garayt, B., and Boucher, C. (2007):

ITRF2005: A new release of the International Terrestrial Reference

Frame based on time series of station positions and Earth Orientation

Parameters, Journal of Geophysical Research, Vol. 112, B09401,

doi:10.1029/2007JB004949.

Altamimi, Z. (2006): IGS reference frames: Status and future improvements, Institute

Geographique National, France.

Altamimi Z, Métivier L, Collilieux X (2012): ITRF2008 plate motion model. J

Geophys Res 117, B07402. doi: 10.1029/2011JB008930

A.F.R.E.F, 2007, AFRICAN GEODETIC REFERENCE FRAME -NEWSLETTER,

Secretariat: Regional Centre for Mapping of Resources for Development

(RCMRD) P.O.Box 632-00618, Ruaraka Nairobi, Kenya. Tel:+254-20-

8560227/8561775Fax:254-20-8561673.

Beavan, J., Tregoning, P., Bevis, M., Kato, T., and Meertens, C. (2002): Motion and

rigidity of the Pacific Plate and implications for plate boundary

112

References

Page 113

deformation, Journal of Geophysical Research, Vol. 107, B10, 2261,

doi:10.1029/2001JB000282.

Boucher, C. and Altamimi, Z., (2001). ITRS, PZ- 90 and WGS 84: current

realizations and the related transformation parameters. Journal of

Geodesy 75, pp. 613–619.

Bulletin géodésique (1925): Errata au Bulletin GÉodÉsique, AnnÉe 1925 , Journal

Volume 8, Issue 1 , p 698

Clifford J. Mugnier (2008): Grids & Datum of Arab Republic of Egypt,

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING,

November 2008, pp 1307-1309.

Chang , C. and Tseng, L., (1998) : A Geocentric Reference System in Taiwan , Survey

Review, Department of Surveying and Mapping Engineering Chung

Cheng Institute of Technology, Taiwan, ROC.

Chang, C. and Tseng, L., (1998) : A Geocentric Reference System in Taiwan , Survey

Review, Department of Surveying and Mapping Engineering Chung

Cheng Institute of Technology, Taiwan, ROC.

Cole, J., 1944, Geodesy in Egypt, Egyptian Survey Authority, Government Press,

Cairo, Egypt.

Dawson, J., and Steed, J. (2004): International Terrestrial Reference Frame (ITRF) to

GDA94 Coordinate Transformations, Geosciences Australia.

Dawson and Woods, (2010): ITRF to GDA94 coordinate transformations, Journal of

Applied Geodesy, Vol. 4, Issue 4, pp. 189-199, 2010. Australia.

Dow J.M., Neilan R. E., and Rizos C., (2009): The International GNSS Service in a

changing landscape of Global Navigation Satellite Systems. J. Geodesy,

83(3-4):191–198, DOI: 10.1007/s00190-008-0300-3 .

Elhattab, A. (2014):Assessment of PPP for establishment of CORS network for

municipal surveying in Middle East. Port Said University, Faculty of

Engineering, Egypt.

http://link.springer.com/journal/12357

http://link.springer.com/journal/12357/8/1/page/1

References

Page 114

Erickson, C. (1992): Investigation of C/A Code and Carrier Measurement and

Techniques for Rapid Static GPS Surveys, UCGE Report Number 20044,

University of Calgary, 180pp.

Ferland, R. and Kouba, J., (1996):IGS ITRF Realization and Transformations.

Geodetic Survey Division Natural Resources Canada (NRCan) Ottawa,

Canada K1A OE9.

Ghilani, D. and Wolf, R. (2006): Adjustment Computations, Spatial Data Analysis,

John Wiley & Sons, p1-12, pp. 310-328.

Haasdyk, J., Janssen, V. (2011) :The many paths to a common ground: A comparison

of transformations between GDA94 and ITRF, Proc. IGNSS2011,

Sydney, Australia, 15-17November, 16pp. (e.g. accessible from

http://www.ignss.org/Conferences/PastPapers/tabid/64/Default.aspx).

Haasdyk, J., Janssen,V. (2012) : Choosing the best path: Global to national coordinate

transformations, Coordinates, 8(2), 10-16.

Hofmann-Wellenhof. (1994). GPS: theory and practice. In B. &., GPS: theory and

practice. New York: 3rd edSpringer-Verlag.

Hoffman-Wellenhof, B., et al. (2001): GPS Theory and Practice, 5th ed., Springer-

Verlag, New York.

IERS, (2010):http://itrf.ensg.ign.fr/ITRF_solutions/2005/doc/ITRF2005_GPS.SSC.txt

(accessed, 11th November, 2010).

Jaroslav, Š. and Jan, K. (2001): Modern Geodetic Network and Datum in Europe.

Research Institute of Geodesy, Topography and Cartography, Geodetic

Observatory Pecný.

John D. and Jim (2004): International Terrestrial Reference Frame (ITRF) to GDA94

Coordinate Transformations Minerals and Geohazards Division

Geosciences Australia Version 01.03.2004 .

Katrin, H. , Florian, H., Christoph, A., Ana, K. , Robert, W. and Philipp, B. (2010)

: PPP: Precise Point Positioning – Constraints and Opportunities, Facing the

Challenges – Building the Capacity Sydney, Australia, 11-16 April 2010

References

Page 115

Lee, S.C., Ko, Y.H., Lee, Y.J., (1987): “Outliers Identification and Reliabilities in

Geodetic Networks”, KSCE Journal of Civil Engineering, Vol.7, No.1,

pp.67-75.

Leick, A. (1995). In GPS Satellite Surveying. New York: John Willey & Sons.Inc.

Leick, A., (2004): GPS Satellite Surveying, John Wiley & Sons.Washington State

Department of Natural Resources 2004, GPS Guide Book standards and

Guidelines for Land Surveying Using Global Positioning System

Methods http://www.wsrn3.org/CONTENT/Reference/Reference_GPS-

Guidebook-WADNR.pdf

Moritz H. (1981): “Continental African Network as a Part of the World Geodetic

System”. Presented at Second Symposium on Geodesy in Africa, Nairobi

Paul, R.W., Charles D.G., (1997): Adjustment Computation, John Wiley & Sons.

Paul, T., Russell, J. (1999): The need for Dynamic .Geomatics Research Australasia,

No 71 December,1999,pp87-102 .

Pearson, C., McCaffrey, R., Elliott, J. and Snay, R. : (2010): HTDP 3.0 Software for

Coping with the Coordinate Changes Associated with Crustal Motion, J.

Surv. Eng., 136, 80, 2010.

Rabah, M., Shaker, A., and Farhan, M. (2015): Towards Semi Kinematic Datum for

Egypt,Published Online August 2015 (Vol. 6 No. 3) in SciRes.

http://www.scirp.org/journal/pos

Rizos, C., (1996): Principle and Practice of GPS Surveying, School of Surveying and

SIS, the University of New South Wales, Sydney, Australia.

Roberts, C., Ozdemir, S. and McElroy, S. (2009): Where is Positional Uncertainty?

Proceedings of SSC 2009 Spatial Diversity: The National Biennial

Conference of the Spatial Sciences Institute, Adelaide, Oct 2009.

Saleh,M, , · Becker, M., 2013: A new velocity field from the analysis of the Egyptian

Permanent GPS Network (EPGN) , Arabian Journal of Geosciences

11/2013; 7(11):4665-4682. DOI:10.1007/s12517-013-1132-x.

http://www.wsrn3.org/CONTENT/Reference/Reference_GPS-Guidebook-WADNR.pdf

http://www.wsrn3.org/CONTENT/Reference/Reference_GPS-Guidebook-WADNR.pdf

http://www.scirp.org/journal/pos

https://www.researchgate.net/researcher/2066035923_Matthias_Becker

https://www.researchgate.net/publication/271951391_A_new_velocity_field_from_the_analysis_of_the_Egyptian_Permanent_GPS_Network_%28EPGN%29?ev=prf_pub

https://www.researchgate.net/publication/271951391_A_new_velocity_field_from_the_analysis_of_the_Egyptian_Permanent_GPS_Network_%28EPGN%29?ev=prf_pub

References

Page 116

SBSM,CAI, R. H., SU, L. Q., YANG, Y. T., & WANG, J. X. (2009). 2 (1.

Department of Survey and Geo-Informatics, Tongji University, Shanghai

200092, China; 2. Key Laboratory of Advanced Engineering Surveying

of Shanghai 200092, China; 3. NO. 1 Surveying and Mapping Institute of

Zhejiang Province, Hangzhou, 310012, China); RTK Testing and

Analysis of Zhejiang Provincial Level CORS System [J]. Gnss World of

China, 3.

Scott, M. (1997): Results of Final Adjustment of New National Geodetic Network,

Geodetic Advisor for the Egyptian Survey Authority.

Seeber, G., (1993) : Satellite Geodesy: Foundations, Methods, and Applications,

Walter de Gruyter, Berlin New York.

Seeber, G. (2003): Satellite Geodesy: Foundations, Methods, and Applications, de 2nd

completely revised and extended edition. Walter de Gruyter ·Berlin ·New

York.

Seidelmann, P.K, (1982): IAU Theory of Nutation -the Final Report of the IAU

Working Group on Nutation" Celestial Mechanics; Vo1. 27, No. 1; May

1982.

Shaker A.A. (1982): “Three-Dimensional Adjustment and Simulation of Egyptian

Geodetic Network”. Ph.D. Thesis, Technical University, Graz.

S.I.H.T , Survey of India, Handbook of Topography, Controlby GPS &Triangulation

/ Trilateration, Corrected upto 2009.

Stanaway, R. , Roberts, C. Blick , G. (2012a): Realisation of a Semi-Kinematic

Geodetic Datum using an Absolute Deformation Model (ADM) . School

of Surveying and Spatial Information Systems, University of New South

Wales Sydney, NSW, 2052, Australia;

Stanaway,R. and Roberts ,C. (2010): CORS Network and Datum Harmonisation in

the Asia-Pacific Region. TS 6C – Global Geodetic Observing System

and APREF I Richard Stanaway and Craig Roberts CORS Network and

Datum Harmonisation in the Asia-Pacific Region FIG Congress 2010

Facing the Challenges – Building the Capacity Sydney, Australia, 11-16

April 2010

References

Page 117

US Department of Defense , (1996). Retrieved from Official U.S. Government

information (2015). about the Global Positioning System (GPS) and

related topics: http://www.gps.gov/systems/gps/space/

Wübbena, G. (1989). The GPS adjustment software package-GEONAP-concepts and

models. In The GPS adjustment software package-GEONAP-concepts

and models (pp. 452-461). Las Cruces, New Mexico: In Proceedings of

the fifth international symposium on satellite positioning.

Zhiping Lu • Yunying Qu • Shubo Qiao,2014, Geodesy, Introduction to Geodetic

Datum and Geodetic Systems, Springer Heidelberg New York Dordrecht

London , Library of Congress Control Number: 2014939507 , Springer-

Verlag Berlin Heidelberg 2014.

http://www.gps.gov/systems/gps/space/

يهخص انرضانت

Page 118


إشبء لبعذح ث١ببد أ أذاف اغ١د٠غ١ب رؾذ٠ذ أبو امبط ع عطؼ األسع ثذلخ ربخ, زا فئ

ؤخشا ر أع اعزخذا امب١٠ظ اغ١د٠غ١خ ؽغبثبد رؾذ٠ذ الع. ب"ضشس٠ ا"أش ٠عزجشع١غد٠غ١خ ؾىخ

( أشبسد االؽظبئ١بد إ GPSظب ازضع اعب ) إشبء غعخ اإلؽذاص١بد ع طش٠ك اعزخذا

إىب١خ ع ظب شعع أسض د صالص األثعبد ذخ ب. ثبء ع زا اف اؾذ٠ش, فمذ لبذ ا١ئخ

ثبع اشجىخ اشعع١خ عب١خ ب األ . رعشفع١د٠غز١ ثئشبء شجىز١ 2991اظش٠خ اعبخ غبؽخ عب

اغبؽبد اضسعخ اشجىخ اضب١خ رغط و١زش. 133ؾطخ رغط غبؽخ 03( رزى HARNذلخ )ا

– 03( رغط غبؽخ NACNاد ا١ اذزب( زه ف رعشف ثبع اشجىخ اط١خ اغبؽ١خ اضساع١خ )ث)

و١زش. 03

( فمذ ر رط١ اشجىخ ثأسثعخ HARN)ى ٠ز رؾ٠ اإلطبس األسض اشعع اعب شجىخ

)عضس MASP)عة أفش٠م١ب( HART)أصثبوغزب( KIT3)إ٠طب١ب( IGS ,MATEؾطبد

. وبذ زبئظ 2991عب ITRF1994ف HARN NACNاىبس(. لذ ر رؾذ٠ذ زبئظ رؾ١ و شجىز

)اظب ة( ثبغجخ شجىخ HARN 2:203330333)اظب أ( ثبغجخ شجىخ 2:2303330333اعبغخ

NACN عب١٠ش اذلخ اشجى١خ اغج١خ ث١ اؾطز١ از ر رؾذ٠ذب فITRF1994 لذ ر 2991عب .

ازط ذساعبد ازب١خ خالي اجؾش اؾب:

أع رم١١ اغضء اؾذد ازبػ ؾطز HARN NACN طك اؾ١طخ, ف دزب ا١ اب

أ رى ثذ٠خ زم١بد ازفبرخ اخبطخ PPP عشفخ إ أ ذ ٠ىزم١خ "دلخ رؾذ٠ذ االع"

ثبالسرىبص ع CSRS-PPP ثبـظب اعب غار االؽخ, لذ ر إعشاء عبغخ ع طش٠ك خذخ

, TBCخبطجـ"شوض رش٠ج ازغبس" اجشبظ ا PPPو١ف١خ االعزفبدح رم١خ "دلخ رؾذ٠ذ االع"

ؽ١ش وب ازظ اخبص ثششوخ رش٠ج ع اضع ف االعزجبس اؾ اخبص ثز١خ دلخ رؾذ٠ذ االع

وؾطخ شعع١خ عبغخ. اعزبدا إ ازبئظ اؾغثخ ٠غ الؽظخ أ اؾ ع PHLWاخبص ثـ

و١زشا, ثبمبسخ ع 213اى١زشاد طال إ طش٠ك رم١خ دلخ رؾذ٠ذ االع لذ رغبص عششاد

, ب ٠ضؼ االغغب اغ١ذ ث١ و DGPSاؾ ع طش٠ك رم١خ "ظب ازضع اعب ازفبر"

.mm رم١خ دلخ رؾذ٠ذ االع رم١خ ظب ازضع اعب ازفب ف غز

االع" عشفخ و١ف١خ اعزخذا رم١خ "دلخ رؾذ٠ذPPP ف رؾذ٠ش اـITRF ف مبط ايIGS فمذ ر ,

ITRF2008ف PPPع طش٠ك اعزخذا رم١خ "دلخ رؾذ٠ذ االع" IGSؽغبة اعذ٠ذ ؾطبد اـ

ف فظ اعب. وبذ االخزالفبد IGS ITRF2008, لذ ر مبسخ ازبئظ ثبز ر ششب ف 1322عب

ؾطخ ١ى Y ى 21 رزغبص ام١خ اطمخ أللظ لذس االخزالفبد ث١ اؾ١ وبزب:

ثغض٠شح لجشص, ف ؽ١ رزغبص عذد ل١ ا١زشاد ف اؾطبد األخش.


Page 119

ثذلخ رؤوذ ازبئظ اىب١خ اعزخذا رم١خ رؾذ٠ذ العPPP .ف رؾذ٠ش اإلطبس

أع رم١١ ؾطبد خذخ اـ GNSS اعب١خIGS از اعزخذذ ف مITRF1994 إ ؾطخ

HARN ع طش٠ك م ,ITRF2008 ام١ اإلؽذاص١خ اشسح اخبطخ ثب عخ ازؾ٠ 1322عب

. لذ Scott(1997)مبسخ ام١ امخ ثزه از روشب 2991عب ITRF1994اشرجطخ ثب إ

غبثمخ ام١ اشسح فمظ ابرط از ر رؾذ٠ذب ع طش٠ك ؾطبد خذخ اـ اعزخذب ف اع١خ ا

GNSS اعب١خIGS ع. 20.1ع إ 6.1. لذ أظشد االخزالفبد اؾغثخ رفبرب ٠زشػ ث١

از ٠ؤد ITRF94اغجت ساء ره االخزالفبد ٠شعع ف اغبت ىب وبذ رغزخذ ف اعز١عبة

, ب ITRFـ IGSص٠ع اؾطبد د اغز األض االمطبعبد اظغ١شح ث١ إدسان إ ر

.(Ferland and Kouba, 1996ضؾ )

زم١خ دلخ رؾذ٠ذ االع عشفخ إ أ ذ ٠ىPPP أ رى ثذ٠خ زم١بد اخزفخ اغزخذخ ف

ازطج١مبد اغ١د٠غ١خ از رؾزبط إ دلخ زب١خ ض رؾذ٠ش اإلطبس اغ١د٠غ دساعخ رأص١شب ف رؾ١

ف ظش, فمذ ر طشػ ضبي ثبغ األ١خ أع اجشخ HARN" اشجىخ اشعع١خ عب١خ اذلخ "

اظش٠ز١, االعز١ HARN NACNز اذساعخ. اضبي ٠شرىض ع رؾ١ عضء ؾطز

از ر اإلشبسح إ١ب ف HARN NACNؽي دزب ا١. ع طش٠ك م ام١ اخبطخ ثؾطز

ITRF2008 إلطبس 2015عبITRF األط ؾطخHARN اعشف ثبع ,ITRF1994 عب

بعزغالي اعبد ث Scott(1997)مبسخ ام١ ابرغخ ع ظ١شرب األط١خ از أعطبب 2991

. رشاؽذ االخزالفبد ف اى IGSع طش٠ك ITRFاألسثعخ عشش اشسح ث١ اإلطبساد اخزفخ ـ

X 0ع, ثبعزضبء 01 00ب ث١Z18 (11 از ر رؾط١ عضء , رشاؽذ ف اى )عY ب

.0Z18ع, ثبعزضبء 6ع إ 1, رشاؽذ االخزالفبد ث١ Zع ف اى 22ع إ 6ث١

" دلخ رؾذ٠ذ االع ٠ى امي ثأ رم١خ "PPP اعب األوضش عذ ف إعشاء ط١بخ اغذ

ؽ١ش الذ ازىفخ.

أو بأي PPPف مصر إلى تحدث إطارها لإلطار األحدث إما عن طرق تقنة NACNو HARNوتحتاج محطت

طرقة تقلدة.

Page 120

ديرـــــوتق رــــشك

أعزبر , نألضتار انذكتىر يذىد يىافأعشة ع خبض ازب شىش أد أ

, األشغبي اعبخ, و١خ اذعخ, عبعخ اظسح لغاغبؽخ اغ١د٠غ١ب ف

. إلششاف رع١بر ام١خ ع اىج١ش , بلشخ ع١ع أعضاء ز اذساعخ

سئ١ظ لغ خزجش , ضتار انذكتىر يصطفى رباحنألأد أ أعشة ع ازب

إلششاف ى١خ اغ١ف١ض٠م١خ ف ؽا , جؾس افاثعذ ؽشوخ امششح األسض١خ,

. رع١بر ام١خ ع اىج١ش , بلشخ ع١ع أعضاء ز اذساعخ

, اذسط ثمغ عىض عه نهذكتىر أدذوب أد أ أعشة ع ازب اؽزشا

. ألشغبي اعبخ , و١خ اذعخ , عبعخ اظسحذعخ ا

ف نىزارة انتعهى انعان وانبذج انعه ازب أ٠ضب أد أ أعشة ع شىش

اعشاق ذسب دعب ف إغبص ز اشعبخ.ثذ

عبدح و١خ اذعخ عبعخ اظسح االزب ارمذ ثبشىش ١ظ اخشا" "اخ١شا

يذذ زذااالضتار انذكتىر زك زضخ ثشخض اغ١ذ اع١ذ

مــفر داخــ جعــو.عه

5102

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ــــإ سػ اشؽ

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"داــــــــــــن أنساك أبل

جايعت انصىرة كهت انهذضت

وتأحرها ف تذذج ضطخ انعانأرصاد ظاو تذذذ انىاقع

االضاد انجىدط

رضانت يقذيت ي

/ املهندس

(5112-5115واإلشاءاث ) هذضت انباءرىش قطى ىبكان

راقــــانع –ذاد ـــــبغ –انجايعت انتكىنىجت

انتعهى انعان وانبذج انعهيهذش ف وزارة

راقـــــانع –ت ـــــجايعت انقادض

يقذيت

هذضت األشغال انعايت ف درجت اناجطتر كجسء ي يتطهباث انذصىل عهى

إشــــــــــراف

يصطفى يىضى رباح /أ.د. يذىد انىاف شتىي /أ.د.

رئص قطى يختبر دركت انقشرة األرضت أضتار انطادت وانجىدطا

يعهذ انبذىث انفهكت وانجىفسقت , دهىا ضت انصىرةذه –قطى األشغال انعايت

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GPS Measurements and Its Impact on Geodetic Datum Maintenance

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