Fundamentals of Global Positioning System Receivers A Software Approach

matlix

Contents
Preface xiii
Notations and Constants xv
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 History of GPS Development 1
1.3 A Basic GPS Receiver 2
1.4 Approaches of Presentation 3
1.5 Software Approach 3
1.6 Potential Advantages of the Software Approach 4
1.7 Organization of the Book 5
Chapter 2 Basic GPS Concept 7
2.1 Introduction 7
2.2 GPS Performance Requirements 7
2.3 Basic GPS Concept 8
2.4 Basic Equations for Finding User Position 10
2.5 Measurement of Pseudorange 11
2.6 Solution of User Position from Pseudoranges 12
2.7 Position Solution with More Than Four Satellites 14
2.8 User Position in Spherical Coordinate System 16
2.9 Earth Geometry 17
2.10 Basic Relationships in an Ellipse 18
2.11 Calculation of Altitude 20
2.12 Calculation of Geodetic Latitude 21
2.13 Calculation of a Point on the Surface of the Earth 24
2.14 Satellite Selection 25
2.15 Dilution of Precision 27
2.16 Summary 28
viii CONTENTS
Chapter 3 Satellite Constellation 32
3.1 Introduction 32
3.2 Control Segment of the GPS System 33
3.3 Satellite Constellation 33
3.4 Maximum Differential Power Level from Different
Satellites 34
3.5 Sidereal Day 35
3.6 Doppler Frequency Shift 36
3.7 Average Rate of Change of the Doppler Frequency 40
3.8 Maximum Rate of Change of the Doppler
Frequency 41
3.9 Rate of Change of the Doppler Frequency Due
to User Acceleration 42
3.10 Kepler’s Laws 43
3.11 Kepler’s Equation 45
3.12 True and Mean Anomaly 47
3.13 Signal Strength at User Location 50
3.14 Summary 52
Chapter 4 Earth-Centered, Earth-Fixed Coordinate System 54
4.1 Introduction 54
4.2 Direction Cosine Matrix 55
4.3 Satellite Orbit Frame to Equator Frame Transform 57
4.4 Vernal Equinox 60
4.5 Earth Rotation 61
4.6 Overall Transform from Orbit Frame to Earth-
Centered, Earth-Fixed Frame 63
4.7 Perturbations 64
4.8 Correction of GPS System Time at Time of
Transmission 66
4.9 Calculation of Satellite Position 68
4.10 Coordinate Adjustment for Satellites 69
4.11 Ephemeris Data 71
4.12 Summary 71
Chapter 5 GPS C/ A Code Signal Structure 73
5.1 Introduction 73
5.2 Transmitting Frequency 74
5.3 Code Division-Multiple Access (CDMA) Signals 76
5.4 P Code 76
5.5 C/ A Code and Data Format 77
5.6 Generation of C/ A Code 78
5.7 Correlation Properties of C/ A Code 83
CONTENTS ix
5.8 Navigation Data Bits 84
5.9 Telemetry (TLM) and Hand Over Word (HOW) 85
5.10 GPS Time and the Satellite Z Count 86
5.11 Parity Check Algorithm 88
5.12 Navigation Data from Subframe1 90
5.13 Navigation Data from Subframes 2 and3 94
5.14 Navigation Data from Subframes 4 and 5—Support
Data 96
5.15 Ionospheric Model 102
5.16 Tropospheric Model 104
5.17 Selectivity Availability (SA) and Typical Position
Errors 104
5.18 Summary 105
Chapter 6 Receiver Hardware Considerations 109
6.1 Introduction 109
6.2 Antenna 110
6.3 Amplification Consideration 111
6.4 Two Possible Arrangements of Digitization by
Frequency Plans 114
6.5 First Component After the Antenna 115
6.6 Selecting Sampling Frequency as a Function of the
C/ A Code Chip Rate 115
6.7 Sampling Frequency and Band Aliasing for Real
Data Collection 117
6.8 Down-converted RF Front End for Real Data
Collection 119
6.9 Direct Digitization for Real Data Collection 121
6.10 In-Phase (I) and Quadrant-Phase (Q) Down
Conversion 122
6.11 Aliasing Two or More Input Bands into a Baseband 123
6.12 Quantization Levels 126
6.13 Hilbert Transform 127
6.14 Change from Complex to Real Data 129
6.15 Effect of Sampling Frequency Accuracy 130
6.16 Summary 131
Chapter 7 Acquisition of GPS C/ A Code Signals 133
7.1 Introduction 133
7.2 Acquisition Methodology 134
7.3 Maximum Data Length for Acquisition 135
7.4 Frequency Steps in Acquisition 136
7.5 C/ A Code Multiplication and Fast Fourier
Transform (FFT) 137
x CONTENTS
7.6 Time Domain Correlation 138
7.7 Circular Convolution and Circular Correlation 140
7.8 Acquisition by Circular Correlation 143
7.9 Modified Acquisition by Circular Correlation 144
7.10 Delay and Multiply Approach 146
7.11 Noncoherent Integration 149
7.12 Coherent Processing of a Long Record of Data 149
7.13 Basic Concept of Fine Frequency Estimation 150
7.14 Resolving Ambiguity in Fine Frequency
Measurements 151
7.15 An Example of Acquisition 156
7.16 Summary 159
Chapter 8 Tracking GPS Signals 165
8.1 Introduction 165
8.2 Basic Phase-locked Loops 166
8.3 First-Order Phase-locked Loop 168
8.4 Second-Order Phase-locked Loop 169
8.5 Transform from Continuous to Discrete Systems 171
8.6 Carrier and Code Tracking 173
8.7 Using the Phase-locked Loop to Track GPS
Signals 175
8.8 Carrier Frequency Update for the Block Adjustment
of Synchronizing Signal (BASS) Approach 176
8.9 Discontinuity in Kernel Function 178
8.10 Accuracy of the Beginning of C/ A Code
Measurement 180
8.11 Fine Time Resolution Through Ideal Correlation
Outputs 182
8.12 Fine Time Resolution Through Curve Fitting 186
8.13 Outputs from the BASS Tracking Program 188
8.14 Combining RF and C/ A Code 189
8.15 Tracking of Longer Data and First Phase Transition 190
8.16 Summary 190
Appendix 190
Chapter 9 GPS Software Receivers 193
9.1 Introduction 193
9.2 Information Obtained from Tracking Results 194
9.3 Converting Tracking Outputs to Navigation Data 196
9.4 Subframe Matching and Parity Check 198
9.5 Obtaining Ephemeris Data from Subframe1 199
9.6 Obtaining Ephemeris Data from Subframe2 200
9.7 Obtaining Ephemeris Data from Subframe3 201
CONTENTS xi
9.8 Typical Values of Ephemeris Data 202
9.9 Finding Pseudorange 202
9.10 GPS System Time at Time of Transmission
Corrected by Transit Time (tc) 209
9.11 Calculation of Satellite Position 210
9.12 Calculation of User Position in Cartesian Coordinate
System 212
9.13 Adjustment of Coordinate System of Satellites 213
9.14 Changing User Position to Coordinate System of
the Earth 214
9.15 Transition from Acquisition to Tracking Program 215
9.16 Summary 217
Index 235
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