Fundamentals of
Global Positioning
System Receivers
Fundamentals of
Global Positioning
System Receivers
A Software Approach
SECOND EDITION
JAMES BAO-YEN TSUI
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright 2005 by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data
Tsui, James Bao-yen.
Fundamentals of global positioning system receivers : a software approach / James
Bao-yen Tsui. – 2nd ed.
p. cm.
Includes bibliographical references (p. ).
ISBN 0-471-70647-7 (cloth)
1. Global Positioning System. I. Title.
G109.5.T85 2005
.285 – dc22
910
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1
2004053458
Contents
Preface
Preface to the First Edition
Chapter 1 Introduction
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Introduction
History of GPS Development
A Basic GPS Receiver
Approaches of Presentation
Software Approach
Potential Advantages of the Software Approach
Organization of the Book
References
Chapter 2 Basic GPS Concept
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
Introduction
GPS Performance Requirements
Basic GPS Concept
Basic Equations for Finding User Position
Measurement of Pseudorange
Solution of User Position from Pseudoranges
Position Solution with more than Four Satellites
User Position in Spherical Coordinate System
Earth Geometry
Basic Relationships in an Ellipse
Calculation of Altitude
xiii
xv
1
1
1
2
3
3
4
5
5
7
7
7
8
10
11
12
13
15
16
17
19
v
vi
CONTENTS
2.12
2.13
2.14
2.15
2.16
Calculation of Geodetic Latitude
Calculation of a Point on the Surface of the
Earth
Satellite Selection
Dilution of Precision
Summary
References
Chapter 3 Satellite Constellation
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
Introduction
Control Segment of the GPS System
Satellite Constellation
Maximum Differential Power Level from
Different Satellites
Sidereal Day
Doppler Frequency Shift
Average Rate of Change of the Doppler
Frequency
Maximum Rate of Change of the Doppler
Frequency
Rate of Change of the Doppler Frequency Due
to User Acceleration
Kepler’s Laws
Kepler’s Equation
True and Mean Anomaly
Signal Strength at User Location
Summary
References
Chapter 4 Earth-Centered, Earth-Fixed Coordinate System
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
Introduction
Direction Cosine Matrix
Satellite Orbit Frame to Equator Frame
Transform
Vernal Equinox
Earth Rotation
Overall Transform from Orbit Frame to
Earth-Centered, Earth-Fixed Frame
Perturbations
Correction of GPS System Time at Time of
Transmission
Calculation of Satellite Position
Coordinate Adjustment for Satellites
20
22
23
24
27
27
30
30
31
31
33
33
34
38
39
40
40
42
44
46
48
49
51
51
52
54
56
58
59
60
62
63
65
CONTENTS
4.11
4.12
Ephemeris Data
Summary
References
Chapter 5 GPS C/A Code Signal Structure
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
Introduction
Transmitting Frequency
Code Division-Multiple Access (CDMA) Signals
P Code
C/A Code and Data Format
Generation of C/A Code
Correlation Properties of C/A Code
Navigation Data Bits
Telemetry (TLM) and Hand Over Word (HOW)
GPS Time and the Satellite Z Count
Parity Check Algorithm
Navigation Data from Subframe 1
Navigation Data from Subframes 2 and 3
Navigation Data from Subframes 4 and
5–Support Data
Ionospheric Model
Tropospheric Model
Selectivity Availability (SA) and Typical
Position Errors
Summary
References
Chapter 6 Receiver Hardware Considerations
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
Introduction
Antenna
Amplification Consideration
Two Possible Arrangements of Digitization by
Frequency Plans
First Component After the Antenna
Selecting Sampling Frequency as a Function of
the C/A Code Chip Rate
Sampling Frequency and Band Aliasing for Real
Data Collection
Down-Converted RF Front End for Real Data
Collection
Direct Digitization for Real Data Collection
In-Phase (I) and Quadrant-Phase (Q) Down
Conversion
vii
66
67
67
68
68
69
71
71
72
73
78
79
80
81
82
88
90
92
97
99
100
100
101
105
105
106
107
110
111
111
113
115
116
118