University of Moratuwa 
TROPOSPHERIC RANGE ERROR CORRECTIONS 
FOR THE GLOBAL POSITIONING SYSTEM 
IN SRI LANKA 
Submitted in partial fulfillment for the Degree of Master of Engineering in 
Electronic & Telecommunication Engineering 
ATHULA SENEVIRATNE 
• ? 2 <1 
072440 " /•0,«, Hp. OO 
University of Moratuwa 
June 2000 
72440 
The work presented in this dissertation has not been submitted for the 
fulfillment of any other degree 
(Supervisors) 
The author is indebted to 
Prof. I. J. Dayawansa for all the valuable guidance, inspiration and most of all for proposing this title 
for the dissertation 
Dr. S.A.D. Dias for all the advice, encouragement and most of all for enlightening me on how to 
undertake a dissertation of this nature 
Dr. J.A.K.S. Jayasinghe and Mr. B.S. Samarasiri for the valuable comments and suggestions 
provided at the periodic reviews 
Dr. Mohottala, Mr. Jayathilaka Banda and others at the Department of Meteorology 
for all the help and assistance provided in collecting lifeline data for the project 
Wipula, my boss, my batchmate, my partner and my friend for the sharing, brotherhood and support 
Ajith, Biyan a n d Athauda my colleagues at Airport & Aviation Services (Sri Lanka) Ltd., for the 
numerous assistance provided in sourcing useful information 
My beloved mother who is not among the living, for her jewels of wisdom, my father for the 
wheels of courage and my sister for the rays of hope 
Dinindu and Chinthani my children for their boundless patience and understanding 
Manjula my wife, for Everything !!! 
ABSTRACT 
The Global Positioning System is the most accurate positioning and 
navigation system in use today. It uses the time of arrival of radio signals 
transmitted from satellites placed in high altitude orbits around the globe. 
The ideal GPS theory assumes free space radio propagation whereas in 
reality, the signals have to propagate through the atmosphere. When 
propagating through the atmosphere, the finite refractive index of the various 
layers of the atmosphere causes the electromagnetic waves to travel 
distances that are longer than the corresponding free space distances. This 
causes an error in the observed time of arrival which is carried on to the 
positional computation. 
The error due to refraction in the troposphere is of particular interest. Unlike 
the ionosphere, the troposphere is non-dispersive. Its refractive properties 
depend more on physical parameters such as pressure and temperature. Due 
to this reason, the refractivity tends to depend on the location as well. It has 
been shown that a good correlation exists between the refractivity at the 
surface of the earth and the range error. Hence this error may be determined 
using the refractivity at the surface of the earth. 
In this dissertation, the effect of the troposphere on GPS observations made 
within the geographical extent of Sri Lanka is studied. The range errors at 
reference locations within Sri Lanka are determined for different parts of the 
year. The results are compared with established results for the region and 
reasons for discrepancies are briefly discussed. 
The design of a conceptual GPS receiver processor that can self-correct 
tropospheric range errors at the surface of the earth by sensing the pressure 
and the temperature is proposed. A computer program is used to simulate the 
operation of this receiver. 
LIST OF FIGURES 
No. Title Page 
2.1 Pseudo-range observation from ith satellite. 06 
5.1 Tropospheric delay as observable in Colombo 36 
5.2 Tropospheric delay as observable in Galle 36 
5.3 Tropospheric delay as observable in Nuwara'eliya 37 
5.4 Tropospheric delay as observable in Batticaloa 37 
5.5 Tropospheric delay as observable in Anuradhapura 38 
5.6 Space average tropospheric delay in Sri Lanka 38 
5.7 Least square estimated variation of tropospheric path delay 39 
with latitude within Sri Lanka 
5.8 Variation of tropospheric path delay with altitude within Sri 39 
Lanka 
6.1 Variation of Range Error with Angle of Elevation 42 
6.2 Computation of Angle of Elevation using receiver position 43 
7.1 Conceptual receiver capable of self-correcting tropospheric 48 
range error 
7.2 Flowchart of simulation program 49 
ii 
LIST OF TABLES 
No. Title Page 
2.1 Ephemeris data at time=150000 seconds of GPS week 12 
3.1 Typical values for GPS range errors 18 
3.2 Standard Error Model with no SA 19 
3.3 Standard Error Model with SA 19 
3.4 Precise Error Model 19 
4.1 Surface refractivity as a function of Latitude and Month 26 
5.1 Variation of Surface Refractivity with Latitude in Sri Lanka 29 
5.2 Weather stations in Sri Lanka 30 
5.3 Atmospheric Pressure during each month of the year 1999 31 
5.4 Temperature during each month of the year 1999 32 
5.5 Surface refractivity in Sri Lanka 32 
5.6 Trcpospheric path delay for zenith observations within Sri Lanka 34 
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iii 
LIST OF ABBREVIATIONS USED 
4 
CEP Circular Error Probable 
DRMS RMS Radial Distance Error 
GDOP Geometric dilution of precision 
GPS Global Positioning System 
PDOP Position dilution of precision 
SA Selective Availability 
SEP Spherical Error Probable 
TDOP Time dilution of precision 
TOA Time of Arrival 
UERE User Equivalent Range Error 
UTC Universal Time Transfer 
4 
IV 
CONTENTS 
Abstract 
1. Introduction 
1.1 Use of GPS in Sri Lanka 
1.2 Research background 
1.3 Present work 
1.4 About this report 
2. Operating Principle of the GPS 
2.1 Classical GPS theory 
2.2 Selection of the best satellites for tracking 
2.3 Worked example 
2.4 Inclusion of Error Correction 
3. GPS error sources and their effects 
3.1 Sources of error 
3.1.1 Ephemeris data 
3.1.2 Satellite clock 
3.1.3 Atmosphere 
3.1.4 Multipath effects 
3.1.5 The receiver itself as a source of error 
3.2 Parameters for assessment of errors 
3.2.1 Circular error probable (CEP) 
3.2.2 Spherical error probable (SEP) 
3.2.3 RMS radial distance error (DRMS) 
3.2.4 User equivalent range error (UERE) 
3.3 Standard error models 
3.4 Standard error model without selective availabil 
4. Effects of the troposphere on GPS 
4.1 Tropospheric effects 
4.1.1 Tropospheric attenuation 
4.1.2 Rainfall attenuation 
4.1.3 Tropospheric Scintillation 
4.1.4 Tropospheric Delay 
4.2 Definitions 
4.2.1 Elevation angle 
4.2.2 Refractivity 
4.2.3 Surface refractivity 
A 
CONTENTS (Continued...) 
4. 4.3 Work of Saastamoinen 24 
4.4 Work of Hopfield and Black 24 
4.5 Work of Smith and Weintraub 25 
4.6 Work of Black and Eisner 25 
4.7 Work of Hanseen and Feijt 26 
4.8 Work of Altshuler and kalaghan 26 
5. Modeling the troposphere above Sri Lanka 28 
5.1 Seasonal variation in pressure and temperature 28 
5.2 Weather stations in Sri Lanka 30 
5.3 Computations using actual data 31 
5.4 Possible reasons for the discrepancy between values of Altshuler 33 
and kalaghan and the values computed 
5.5 Tropospheric delay for radio propagation in Sri Lanka 34 
6. Iterative model for range error correction 41 
6.1 Variation of range error with angle of elevation 41 
6.2 Computing angle of elevation from position estimate 42 
6.3 Inclusion of range error correction in the iterative loop 44 
6.4 Application of the model to off-line observations 44 
6.5 Worked example 45 
7. The simulation program 47 
7.1 Conceptual receiver model 47 
7.2 Inputs to the program 49 
7.3 Conditions for convergence 50 
8. Discussion & Conclusions 51 
8.1 Discussion on the tropospheric range error in Sri Lanka 51 
8.2 Discussion on the simulation program 53 
8.3 Suggestions for future work 54 
8.4 Acknowledgements 54 
List of references 56 
ANNEX - Source listing of simulation program 57 
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