Preface xiii
Preface to the First Edition 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 13
2.8 User Position in Spherical Coordinate System 15
2.9 Earth Geometry 16
2.10 Basic Relationships in an Ellipse 17
2.11 Calculation of Altitude 19
2.12 Calculation of Geodetic Latitude 20
2.13 Calculation of a Point on the Surface of the Earth 22
2.14 Satellite Selection 23
2.15 Dilution of Precision 24
2.16 Summary 27
Chapter 3 Satellite Constellation 30
3.1 Introduction 30
3.2 Control Segment of the GPS System 31
3.3 Satellite Constellation 31
3.4 Maximum Differential Power Level from
Different Satellites 33
3.5 Sidereal Day 33
3.6 Doppler Frequency Shift 34
3.7 Average Rate of Change of the Doppler
Frequency 38
3.8 Maximum Rate of Change of the Doppler
Frequency 39
3.9 Rate of Change of the Doppler Frequency Due to User Acceleration 40
3.10 Kepler’s Laws 40
3.11 Kepler’s Equation 42
3.12 True and Mean Anomaly 44
3.13 Signal Strength at User Location 46
3.14 Summary 48
Chapter 4 Earth-Centered, Earth-Fixed Coordinate System 51
4.1 Introduction 51
4.2 Direction Cosine Matrix 52
4.3 Satellite Orbit Frame to Equator Frame
4.4 Vernal Equinox 56
4.5 Earth Rotation 58
4.6 Overall Transform from Orbit Frame to Earth-Centered, Earth-Fixed Frame 59
4.7 Perturbations 60
4.8 Correction of GPS System Time at Time of Transmission 62
4.9 Calculation of Satellite Position 63
4.10 Coordinate Adjustment for Satellites 65
4.11 Ephemeris Data 66
4.12 Summary 67
Chapter 5 GPS C/A Code Signal Structure 68
5.1 Introduction 68
5.2 Transmitting Frequency 69
5.3 Code Division-Multiple Access (CDMA) Signals 71
5.4 P Code 71
5.5 C/A Code and Data Format 72
5.6 Generation of C/A Code 73
5.7 Correlation Properties of C/A Code 78
5.8 Navigation Data Bits 79
5.9 Telemetry (TLM) and Hand Over Word (HOW) 80
5.10 GPS Time and the Satellite Z Count 81
5.11 Parity Check Algorithm 82
5.12 Navigation Data from Subframe 1 88
5.13 Navigation Data from Subframes 2 and 3 90
5.14 Navigation Data from Subframes 4 and 5–Support Data 92
5.15 Ionospheric Model 97
5.16 Tropospheric Model 99
5.17 Selectivity Availability (SA) and Typical Position Errors 100
5.18 Summary 100
Chapter 6 Receiver Hardware Considerations 105
6.1 Introduction 105
6.2 Antenna 106
6.3 Amplification Consideration 107
6.4 Two Possible Arrangements of Digitization by Frequency Plans 110
6.5 First Component After the Antenna 111
6.6 Selecting Sampling Frequency as a Function of the C/A Code Chip Rate 111
6.7 Sampling Frequency and Band Aliasing for Real Data Collection 113
6.8 Down-Converted RF Front End for Real Data Collection 115
6.9 Direct Digitization for Real Data Collection 116
6.10 In-Phase (I) and Quadrant-Phase (Q) Down Conversion 118
6.11 Aliasing Two or More Input Bands into a Baseband 120
6.12 Quantization Levels 122
6.13 Hilbert Transform 122
6.14 Change from Complex to Real Data 124
6.15 Effect of Sampling Frequency Accuracy 125
6.16 Summary 126
Chapter 7 Acquisition of GPS C/A Code Signals 129
7.1 Introduction 129
7.2 Acquisition Methodology 130
7.3 Maximum Data Length for Acquisition 131
7.4 Frequency Steps in Acquisition 132
7.5 C/A Code Multiplication and Fast Fourier Transform (FFT) 133
7.6 Time Domain Correlation 134
7.7 Circular Convolution and Circular Correlation 136
7.8 Acquisition by Circular Correlation 138
7.9 Modified Acquisition by Circular Correlation 140
7.10 Delay and Multiply Approach 141
7.11 Noncoherent Integration 144
7.12 Coherent Processing of a Long Record of Data 144
7.13 Basic Concept of Fine Frequency Estimation 146
7.14 Resolving Ambiguity in Fine Frequency Measurements 147
7.15 An Example of Acquisition 151
7.16 Summary 155
Chapter 8 Tracking GPS Signals 160
8.1 Introduction 160
8.2 Basic Phase-Locked Loops 161
8.3 First-Order Phase-Locked Loop 163
8.4 Second-Order Phase-Locked Loop 164
8.5 Transform from Continuous to Discrete Systems 165
8.6 Carrier and Code Tracking 167
8.7 Using the Phase-Locked Loop to Track GPS Signals 169
8.8 Carrier Frequency Update for the Block Adjustment of Synchronizing Signal (BASS) Approach 170
8.9 Discontinuity in Kernel Function 171
8.10 Accuracy of the Beginning of C/A Code Measurement 174
8.11 Fine Time Resolution Through Ideal Correlation Outputs 176
8.12 Fine Time Resolution Through Curve Fitting 179
8.13 Outputs from the Bass Tracking Program 181
8.14 Combining RF and C/A Code 182
8.15 Tracking of Longer Data and First Phase Transition 183
8.16 Summary 183
Chapter 9 GPS Software Receivers 186
9.1 Introduction 186
9.2 Information Obtained from Tracking Results 187
9.3 Converting Tracking Outputs to Navigation Data 189
9.4 Subframe Matching and Parity Check 191
9.5 Obtaining Ephemeris Data from Subframe 1 192
9.6 Obtaining Ephemeris Data from Subframe 2 193
9.7 Obtaining Ephemeris Data from Subframe 3 194
9.8 Typical Values of Ephemeris Data 195
9.9 Finding Pseudorange 195
9.10 GPS System Time at Time of Transmission Corrected by Transit Time (tc) 202
9.11 Calculation of Satellite Position 202
9.12 Calculation of User Position in Cartesian Coordinate System 205
9.13 Adjustment of Coordinate System of Satellites 205
9.14 Changing User Position to Coordinate System of the Earth 206
9.15 Transition from Acquisition to Tracking Program 207
9.16 Summary 209
Chapter 10 Acquisition of Weak Signals 224
10.1 Introduction 224
10.2 Signal-to-Noise Ratio (S/N) 225
10.3 Limitation of Receiver Sensitivity 226
10.4 Probability of Detection and False Alarm Rate 229
10.5 Coherent Integration Gain 230
10.6 Noncoherent Integration 231
10.7 Noncoherent Integration Loss and Gain 232
10.8 Acquisition Considerations of Weak Signals 235
10.9 Output Sampling Rate 237
10.10 Coherent Integration for Periodic Signal 237
10.11 Recover Loss on in-between Frequencies 239
10.12 Time Frequency Adjustment in Noncoherent Integration 244
10.13 Threshold Determination for Gaussian Noise 247
10.14 Probability of Detection of Simulated Signals 256
10.15 Threshold Determination from Real Data 258
10.16 Fine Frequency Calculation 263
10.17 First Navigation Phase Transition Determination 266
Chapter 11 Tracking Weak Signals 271
11.1 Introduction 271
11.2 Frequency of Regenerating of Local C/A Code 272
11.3 Carrier Frequency Measurement Requirement 273
11.4 One Millisecond Data Processing and Input Data Selection 273
11.5 Generation of C/A Code 276
11.6 Generation of Local Code and Correlating on 1 ms Input Signal 279
11.7 Obtaining Navigation Data and Finding Carrier Frequency 281
11.8 Calculating Signal-to-Noise Ratio (S/N) 283
11.9 Basic Idea of Finding the Pseudorange 284
11.10 Obtaining the Summed Early and Late Peak Correlation Outputs (yes and yls ) 286
11.11 Actual Time Shifting in Tracking 289
11.12 Tracking Program with Regeneration of C/A Code Every Second 291
11.13 Tracking of Signals with Non-Integer Sampling Frequency 293
11.14 Cases Where an Initial C/A Code Point Matches the 1 ms Selected Data 297
11.15 Experimental Results of the Weak Signal Tracking 301
Chapter 12 GPS Receiver-Related Subjects 306
12.1 Introduction 306
12.2 Information from Almanac Data 306
12.3 Acquisition with Accurate Carrier Frequency Information 310
12.4 Circular Correlation by Partition 311
12.5 Sampling Frequency Correction through Wide Area Augmentation System (WAAS) Signal 316
12.6 Strong and Weak Signal Conditions 324
12.7 Simulation of GPS Signals 329
12.8 Acquisition Impact of Filter Bandwidth in Front of ADC 330
12.9 Number of ADC Bits Required Under Jamming 334
12.10 Real Time Operation of a Software Receiver 337
12.11 Passive Altimeter 337
12.12 Satellite Positions and Doppler Frequencies from Almanac Data 341
12.13 Emergency Geolocation with Cell Phone Operations 345
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