A Software-Defined GPS and Galileo Receiver: A Software-Defined GPS and Galileo Receiver.jpg

Cover design by Joseph Sherman.
MATLABR
and Simulink R
are registered trademarks of The MathWorks, Inc.
Mathematics Subject Classification (2000): 34B27, 49-XX, 49R50, 65Nxx
Library of Congress Control Number: 2006932239
ISBN-10 0-8176-4390-7 e-ISBN-10: 0-8176-4540-3
ISBN-13 978-0-8176-4390-4 e-ISBN-13: 978-0-8176-4540-3
Printed on acid-free paper.

c 2007 Birkha¨user Boston
All rights reserved. This work may not be translated or copied in whole or in part without the written
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The use in this publication of trade names, trademarks, service marks and similar terms, even if they
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Preface ix
List of Figures xiii
List of Tables xvii
Abbreviations xix
1 Signals and Systems 1
1.1 CharacterizationofSignals . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Continuous-Time Deterministic Signals . . . . . . . . . . 2
1.1.2 Discrete-TimeDeterministicSignals . . . . . . . . . . . . 3
1.1.3 Unit Impulse . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.4 Rectangular Pulse . . . . . . . . . . . . . . . . . . . . . . 4
1.1.5 Random Signals . . . . . . . . . . . . . . . . . . . . . . 6
1.1.6 Random Sequence of Pulses . . . . . . . . . . . . . . . . 7
1.2 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 CharacterizationofSystems . . . . . . . . . . . . . . . . . . . . 9
1.4 LinearTime-InvariantSystems . . . . . . . . . . . . . . . . . . . 12
1.5 Representation of Bandpass Signals . . . . . . . . . . . . . . . . 14
2 GPS Signal 17
2.1 Signals andData . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 GPSSignalScheme . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 C/ACode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
vi Contents
2.3.1 GoldSequence . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 GoldSequenceGeneration—Overview . . . . . . . . . . 21
2.3.3 GoldSequenceGeneration—Details . . . . . . . . . . . . 22
2.3.4 CorrelationProperties . . . . . . . . . . . . . . . . . . . 25
2.4 Doppler Frequency Shift . . . . . . . . . . . . . . . . . . . . . . 26
2.5 CodeTracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6 NavigationData . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6.1 TelemetryandHandoverWords . . . . . . . . . . . . . . 29
2.6.2 Data inNavigationMessage . . . . . . . . . . . . . . . . 30
3 Galileo Signal 31
3.1 SignalTheoreticalConsiderations . . . . . . . . . . . . . . . . . 31
3.2 Galileo L1 OS Signal . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 SignalGeneration. . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Coherent Adaptive Subcarrier Modulation . . . . . . . . . 35
3.2.3 Binary Offset Carrier Modulation . . . . . . . . . . . . . 37
3.3 MessageStructure . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.1 Frames andPages . . . . . . . . . . . . . . . . . . . . . . 42
3.3.2 Cyclic Redundancy Check . . . . . . . . . . . . . . . . . 42
3.3.3 Forward Error Correction and Block Interleaving . . . . . 43
3.4 MessageContents . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Time andClockCorrectionParameters . . . . . . . . . . 46
3.4.2 ConversionofGSTtoUTCandGPST . . . . . . . . . . . 48
3.4.3 ServiceParameters . . . . . . . . . . . . . . . . . . . . . 49
3.5 The Received L1 OS Signal . . . . . . . . . . . . . . . . . . . . . 50
4 GNSS Antennas and Front Ends 53
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 GNSS L1 Front-End Components . . . . . . . . . . . . . . . . . 55
4.2.1 GNSSAntenna . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.3 Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.4 Mixer/Local Oscillator . . . . . . . . . . . . . . . . . . . 59
4.2.5 Analog-to-DigitalConverter . . . . . . . . . . . . . . . . 61
4.3 Resulting Sampled Data . . . . . . . . . . . . . . . . . . . . . . 64
4.4 GNSSFront-EndASIC . . . . . . . . . . . . . . . . . . . . . . . 66
5 GNSS Receiver Operation Overview 69
5.1 Receiver Channels . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.1 Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1.2 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1.3 NavigationDataExtraction . . . . . . . . . . . . . . . . . 72
5.2 Computation of Position . . . . . . . . . . . . . . . . . . . . . . 73
6 Acquisition 75
6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Contents vii
6.2 Serial Search Acquisition . . . . . . . . . . . . . . . . . . . . . . 76
6.2.1 PRNSequenceGeneration . . . . . . . . . . . . . . . . . 77
6.2.2 CarrierGeneration . . . . . . . . . . . . . . . . . . . . . 77
6.2.3 IntegrationandSquaring . . . . . . . . . . . . . . . . . . 78
6.3 Parallel Frequency Space Search Acquisition . . . . . . . . . . . 78
6.4 Parallel Code Phase Search Acquisition . . . . . . . . . . . . . . 81
6.5 DataSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.6 ExecutionTime . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.7 ParameterEstimation . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Carrier and Code Tracking 87
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2 Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.3 Second-Order PLL . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.3.1 DampingRatio . . . . . . . . . . . . . . . . . . . . . . . 92
7.3.2 NoiseBandwidth . . . . . . . . . . . . . . . . . . . . . . 92
7.4 CarrierTracking . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.5 CodeTracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.6 Multipath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.7 CompleteTrackingBlock . . . . . . . . . . . . . . . . . . . . . . 106
7.8 Pseudorange Computations . . . . . . . . . . . . . . . . . . . . . 107
8 Data Processing for Positioning 109
8.1 NavigationDataRecovery . . . . . . . . . . . . . . . . . . . . . 109
8.1.1 Finding the Bit Transition Time and the Bit Values . . . . 109
8.2 NavigationDataDecoding . . . . . . . . . . . . . . . . . . . . . 110
8.2.1 LocationofPreamble . . . . . . . . . . . . . . . . . . . . 110
8.2.2 ExtractingtheNavigationData . . . . . . . . . . . . . . . 111
8.3 Computation of Satellite Position . . . . . . . . . . . . . . . . . . 114
8.4 Pseudorange Estimation . . . . . . . . . . . . . . . . . . . . . . . 119
8.4.1 The Initial Set of Pseudoranges . . . . . . . . . . . . . . 119
8.4.2 Estimation of Subsequent Pseudoranges . . . . . . . . . . 120
8.5 Computation of Receiver Position . . . . . . . . . . . . . . . . . 121
8.5.1 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.5.2 Linearizationof theObservationEquation . . . . . . . . . 122
8.5.3 UsingtheLeast-SquaresMethod . . . . . . . . . . . . . . 123
8.5.4 Real-TimePositioningAccuracy . . . . . . . . . . . . . . 125
8.6 TimeSystemsRelevant forGPS . . . . . . . . . . . . . . . . . . 125
8.7 CoordinateTransformations . . . . . . . . . . . . . . . . . . . . 127
8.8 UniversalTransverseMercatorMapping . . . . . . . . . . . . . . 129
8.9 DilutionofPrecision . . . . . . . . . . . . . . . . . . . . . . . . 130
8.10 World Geodetic System 1984 . . . . . . . . . . . . . . . . . . . . 133
8.11 Time and Coordinate Reference Frames for GPS and Galileo . . . 134
Problems 137
viii Contents
A MATLAB Code 143
A.1 Structureof theCode . . . . . . . . . . . . . . . . . . . . . . . . 143
A.2 The settingsStructure . . . . . . . . . . . . . . . . . . . . . . . . 144
A.3 Acquisition Function . . . . . . . . . . . . . . . . . . . . . . . . 145
A.4 TrackingFunction . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A.5 Function postNavigation . . . . . . . . . . . . . . . . . . . . . . 148
A.5.1 Pseudorange Computation . . . . . . . . . . . . . . . . . 149
A.5.2 Position Computation . . . . . . . . . . . . . . . . . . . 150
B GNSS Signal Simulation 153
B.1 GPSSignalSimulation . . . . . . . . . . . . . . . . . . . . . . . 153
B.2 SimulinkImplementation . . . . . . . . . . . . . . . . . . . . . . 154
B.2.1 C/ACodeGeneration . . . . . . . . . . . . . . . . . . . . 155
B.2.2 NavigationDataGeneration . . . . . . . . . . . . . . . . 157
B.2.3 PCodeGeneration . . . . . . . . . . . . . . . . . . . . . 158
B.2.4 Combining the Signal Components . . . . . . . . . . . . 158
B.2.5 Upper-Level Implementation . . . . . . . . . . . . . . . . 158
B.3 Galileo Signal Generator . . . . . . . . . . . . . . . . . . . . . . 159
B.4 Differences in Processing GPS and Galileo Signals . . . . . . . . 161
B.4.1 SignalDifferences . . . . . . . . . . . . . . . . . . . . . 162
B.5 Differences inSignalProcessing . . . . . . . . . . . . . . . . . . 164
Bibliography 167
Index 171

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