Improving Positional Accuracy Using Carrier Smoothing Techniques in Inexpensive GPS Receivers

101 Pages·2004·1.25 MB·English

IMPROVING POSITIONAL ACCURACY USING CARRIER SMOOTHING
TECHNIQUES IN INEXPENSIVE GPS RECEIVERS
BY
Sudha Neelima Thipparthi, B.Tech.
A thesis submitted to the Graduate School
in partial fulfillment of the requirements
for the Degree
Master of Science in Electrical Engineering
New Mexico State University
Las Cruces, New Mexico
February 2004
“Improving positional accuracy using carrier smoothing techniques in inexpen-
sive GPS receivers,” a thesis prepared by Sudha Neelima Thipparthi in partial
fulfillment of the requirements for the degree, Master of Science in Electrical En-
gineering, has been approved and accepted by the following:
Linda Lacey
Dean of the Graduate School
Charles D. Creusere
Chair of the Examining Committee
Date
Committee in charge:
Dr. Charles D. Creusere, Chair
Dr. Paul M. Furth
Dr. Raphael J. Lyman
Dr. Michael N. DeMers
Dr. Steven M. Shope (Industrial Advisor)
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Dedicated to my Mom and Dad
ACKNOWLEDGEMENTS
I wish to thank the president of US Positioning Group LLC, Dr. Steven
M. Shope for giving me an opportunity to work on this project, making this study
possible and for all his help, insight and encouragement. Many thanks to the rest
of the US Positioning Group for making my stay enjoyable.
Thanks also to my advisor at New Mexico State University, Dr. Charles D.
Creusere for helpful suggestions and comments during my work with the thesis.
I would like to express my great appreciation to my distinguished advisors,
Dr. Paul M. Furth and Dr. Jaime A. Ramirez, for their continued support and
encouragement throughout my M.S. program.
I’m very thankful to Dr. Michael DeMers and Dr. Raphael J. Lyman for
their valuable time.
Last but definitely not least I wish to thank my friend Krishna Pathipaka
for being supportive in every possible way.
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VITA
February 21, 1978 Born in Andhra Pradesh, INDIA.
May 1996 High School Diploma awarded by
KMJC, AP, INDIA.
1996–2000 Bachelor of Technology (B.Tech),
Kakatiya Institute of Technology and Science,
AP, INDIA.
May 2000–2001 Assistant Professor, ISS, AP, INDIA.
2001–2002 Teaching Assistant, Deptartment of ECE, NMSU.
January 2003–till date Co-op, US Positioning Group LLC, Arizona.
PROFESSIONAL AND HONORARY SOCIETIES
Institute of Navigation(ION.org)
FIELD OF STUDY
Electrical and Computer Engineering
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ABSTRACT
IMPROVING POSITIONAL ACCURACY USING CARRIER SMOOTHING
TECHNIQUES IN INEXPENSIVE GPS RECEIVERS
BY
Sudha Neelima Thipparthi, B.Tech.
Master of Science in Electrical Engineering
New Mexico State University
Las Cruces, New Mexico, 2004
Dr. Charles D. Creusere, Chair
Since it became fully operational in the mid-1990s, GPS has been used
as a stand-alone system for many land applications that require fast and precise
positioning such as mining, heavy construction, precision farming, and automated
highway systems as well as in other high-traffic land-based applications. However,
there are situations where GPS by itself does not provide the desired accuracy,
for example when satellite signals are blocked or when the achievable accuracy is
restricted by the geometry of the satellite constellation. In these situations, the
redundant data received by the GPS receiver can be used to enhance the avail-
ability, accuracy, and reliability of the GPS-derived position solution. Various
positioning techniques have been developed for enhancing the accuracy using the
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redundant data received, requiring expensive dual frequency receivers. This re-
search work focuses on developing, implementing and testing various techniques
on inexpensive single frequency receivers.
The performance of the carrier-smoothed code-phase differential GPS al-
gorithms is assessed experimentally on single frequency receivers. This thesis also
includes a regressive comparison of various techniques with experimental results.
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Contents
List of Tables xi
List of Figures xii
Chapter 1 INTRODUCTION 1
1.1 The Evolution of GPS . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Military Evolution of GPS . . . . . . . . . . . . . . . . . . . . . 1
1.2 How GPS Works . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Improved Accuracy with DGPS . . . . . . . . . . . . . . . . . . . 8
1.4 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.1 Thesis Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.2 Thesis Chapters Overview . . . . . . . . . . . . . . . . . . . . . 12
Chapter 2 POSITIONING METHODS 14
2.1 GPS Error Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Satellite Orbit Errors . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Satellite Clock Errors . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Receiver Clock Errors . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.4 Tropospheric Delay . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.5 Ionospheric Delay . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.6 Multipath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Satellite Geometry - Dilution of Precision . . . . . . . . . . . . . . 18
2.3 Measurement Models . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Satellite Signal Transmission . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Code Phase Measurements . . . . . . . . . . . . . . . . . . . . . 23
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2.3.3 Carrier Phase Measurements . . . . . . . . . . . . . . . . . . . . 24
2.3.4 Instructive Model for Code and Carrier Measurements . . . . . 28
Chapter 3 RECEIVER POSITION ESTIMATION 30
3.1 Position Estimation Using Least Squares . . . . . . . . . . . . . . 30
3.1.1 Mathematical Model for Positioning Using LLS . . . . . . . . . 33
3.1.2 Validity of Differential Corrections . . . . . . . . . . . . . . . . 38
3.2 Receiver Clock Offset . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chapter 4 CARRIER SMOOTHING 41
4.1 Time Differenced Carrier Phase . . . . . . . . . . . . . . . . . . . 42
4.1.1 Result and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Range Domain Hatch Filter (RDHF) . . . . . . . . . . . . . . . . 44
4.2.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Position Domain Hatch Filter(PDHF) . . . . . . . . . . . . . . . . 52
4.3.1 Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.3 Experimental Setup and Assumptions . . . . . . . . . . . . . . . 58
4.3.4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.5 Comparison of RDHF and PDHF . . . . . . . . . . . . . . . . . 61
4.3.6 Various factors effecting PDHF . . . . . . . . . . . . . . . . . . 63
Chapter 5 CONCLUSION 66
Chapter 6 FUTURE RESEARCH 69
Chapter 7 DEFINITIONS 71
Appendix A: Positioning methods 81
A.1 Ionospheric Refraction : . . . . . . . . . . . . . . . . . . . . . . . 81
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A.2 Taylor’s Series : . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A.3 Chain Rule : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A.4 Linear Least Squares : . . . . . . . . . . . . . . . . . . . . . . . . 82
Appendix B: Matlab Code for PDHF 83
REFERENCES 87
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