GPSfor LandSurveyors

THIRD EDITION

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CRC Press is an imprint of theTaylor & Francis Group, an informa business

Boca Raton London New York

GPSfor LandSurveyors

Jan Van Sickle

THIRD EDITION

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CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742

© 2008 by Taylor & Francis Group, LLCCRC Press is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S. Government worksVersion Date: 20110725

International Standard Book Number-13: 978-0-203-30522-5 (eBook - PDF)

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v

ContentsPreface to the Third Edition ...................................................................................xixAbout the Author ....................................................................................................xxi

Chapter 1 The GPS Signal ....................................................................................1

Global Positioning System (GPS) Signal Structure ...................................................1GPS and Trilateration .....................................................................................1

A Passive System .................................................................................1Time .....................................................................................................1Control .................................................................................................2

The Navigation Code ......................................................................................2Wavelength ...........................................................................................3Codes ...................................................................................................3GPS Time .............................................................................................4Satellite Clocks ....................................................................................5GPS Week ............................................................................................5Julian Date ...........................................................................................6The Broadcast Ephemeris ....................................................................6Atmospheric Correction.......................................................................7Antispoofing and Coordinated Universal Time (UTC) .......................7The Almanac .......................................................................................7Satellite Health .....................................................................................7

The P and Coarse/Acquisition (C/A) Codes ...................................................8Pseudorandom Noise (PRN) ................................................................8P Code ..................................................................................................8C/A Code ..............................................................................................8Standard Positioning Service (SPS) and Precise Positioning

Service (PPS) ..........................................................................8The Production of a Modulated Carrier Wave ...............................................9

EDM Ranging ......................................................................................9GPS Ranging........................................................................................9Oscillators .......................................................................................... 11

A Chain of Electromagnetic Energy ............................................................ 11Phase Shift ......................................................................................... 12The Cycle Ambiguity Problem .......................................................... 14

Two Observables ...................................................................................................... 15Encoding by Phase Modulation ......................................................... 15

Pseudoranging .......................................................................................................... 17Propagation Delay .............................................................................. 17Code Correlation ................................................................................ 17

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Autocorrelation ............................................................................................. 18Correlation Peak ........................................................................................... 19Lock and the Time Shift ............................................................................... 21

Imperfect Oscillators ......................................................................... 21A Pseudorange Equation............................................................................... 21The One-Percent Rule of Thumb ..................................................................23

Carrier Phase Ranging .............................................................................................24Carrier Phase Comparisons ..........................................................................24

Phase Difference ................................................................................24Beat ....................................................................................................25

The Doppler Effect .......................................................................................26GPS and the Doppler Effect ...............................................................26A Carrier Phase Approximation ........................................................26An Illustration of the Cycle Ambiguity Problem...............................29

Exercises ..................................................................................................................30Answers and Explanations ....................................................................................... 32

Chapter 2 Biases and Solutions ........................................................................... 35

The Error Budget ..................................................................................................... 35A Look at the Biases in the Observation Equations ..................................... 35

The Biases .......................................................................................... 35User Equivalent Range Error ............................................................. 35

The Satellite Clock Bias, dt .......................................................................... 35Relativistic Effects on the Satellite Clock .........................................36Satellite Clock Drift ...........................................................................36

The Ionospheric Effect, dion .......................................................................... 37Group and Phase Delay ...................................................................... 37Total Electron Content ....................................................................... 37Ionosphere and the Sun ...................................................................... 38Ionospheric Gradients ........................................................................ 38Satellite Elevation and Ionospheric Effect ......................................... 38The Magnitude of the Ionospheric Delay .......................................... 39The Ionosphere Affects Codes and the Carrier Differently .............. 39Different Frequencies Are Affected Differently ............................... 39Broadcast Correction .........................................................................40

The Receiver Clock Bias, dT ........................................................................40Typical Receiver Clocks ....................................................................40

The Orbital Bias, d ......................................................................................40Forces Acting on the Satellites ..........................................................40Tracking Facilities ............................................................................. 41

The Tropospheric Effect, dtrop ...................................................................... 42Multipath ....................................................................................................... 43

Limiting the Effect of Multipath ....................................................... 45Antenna Design and Multipath .......................................................... 45

Receiver Noise .............................................................................................. 45

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Contents vii

Differencing .............................................................................................................46Classifications of Positioning Solutions ........................................................46

Kinematic GPS ..................................................................................46Static GPS .......................................................................................... 47Hybrid Techniques in GPS................................................................. 47Relative and Point Positioning ........................................................... 47The Navigation Solution .................................................................... 47Four Unknowns .................................................................................. 47Four Satellites and Four Equations ....................................................48

Relative Positioning ...................................................................................... 49Correlation ......................................................................................... 49Baselines ............................................................................................ 49Networks ............................................................................................ 49Differencing ....................................................................................... 49

Single Difference .......................................................................................... 49Elimination of the Satellite Clock Errors .......................................... 49Other Errors Remain.......................................................................... 51

Double Difference ........................................................................................ 51Elimination of the Receiver Clock Errors ......................................... 51No Clock Errors at All ....................................................................... 51

Triple Difference ........................................................................................... 51Integer Cycle Ambiguity .................................................................... 51

Summary ......................................................................................................56Typical Techniques ............................................................................56Pseudorange and Carrier Phase .........................................................56Kinematic GPS ..................................................................................56Other Techniques ...............................................................................56Differencing .......................................................................................56Biases ................................................................................................. 57

Exercises .................................................................................................................. 57Answers and Explanations .......................................................................................60

Chapter 3 The Framework .................................................................................. 63

Technological Forerunners ...................................................................................... 63Consolidation ................................................................................................ 63Terrestrial Radio Positioning ........................................................................ 63

Radar .................................................................................................. 63Distance by Timing............................................................................ 63Shoran Surveying ...............................................................................64Hiran Surveying .................................................................................64Sputnik ...............................................................................................64Satellite Advantages ...........................................................................64

Optical Systems ............................................................................................65Triangulation with Photographs.........................................................65

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Laser Ranging ....................................................................................65Optical Drawbacks .............................................................................66

Extraterrestrial Radio Positioning ................................................................66Satellite Tracking ...............................................................................66Prime Minitrack .................................................................................66Very Long Baseline Interferometry ...................................................66

Very Long Baseline Interferometry ......................................................................... 67Transit ......................................................................................................................68

The Doppler Shift ..............................................................................68TRANSIT Shortcomings ...................................................................68TRANSIT and GPS ...........................................................................69Linking Datums .................................................................................69

Navstar GPS .............................................................................................................69Orbits and Clocks ...............................................................................69Increased Accuracy ............................................................................69Military Application ..........................................................................69Secure, Passive, and Global ............................................................... 70Expense and Frequency Allocation ................................................... 70Large Capacity Signal ........................................................................ 70The Satellite Constellation ................................................................. 71The Perfect System? ........................................................................... 71

GPS in Civilian Surveying ........................................................................... 71Federal Specifications ........................................................................ 72Interferometry .................................................................................... 72Civil Applications of GPS .................................................................. 72

GPS Segment Organization ..................................................................................... 73The Space Segment....................................................................................... 73

GPS Constellation .................................................................................................... 73Orbital Period ............................................................................................... 73

Design ................................................................................................ 74Dilution of Precision .......................................................................... 74

Bad Dilution of Precision ............................................................................. 74Good Dilution of Precision ........................................................................... 76

Outages .............................................................................................. 76Satellite Positions in Mission Planning ............................................. 76Satellite Names .................................................................................. 78Block I ................................................................................................ 79Block II and Block IIA ...................................................................... 79Block IIR ............................................................................................ 79Block IIF ............................................................................................ 79

Block II GPS Satellite ...................................................................................80Signal Deterioration ...........................................................................80GPS Satellites.....................................................................................80

The Control Segment ............................................................................................... 81Master Control Station ....................................................................... 81Other Stations .................................................................................... 81

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Contents ix

Kalman Filtering ................................................................................ 82An Analogy ........................................................................................ 82Constant Tracking .............................................................................. 82Postcomputed Ephemerides ............................................................... 82GPS for Orbit Calculation .................................................................. 83

The User Segment ......................................................................................... 83Constantly Increasing Application of GPS ........................................ 83

Exercises ..................................................................................................................84Answers and Explanations .......................................................................................86

Chapter 4 Receivers and Methods ...................................................................... 91

Common Features of GPS Receivers ....................................................................... 91A Block Diagram of a Code Correlation Receiver ....................................... 91

Receivers for GPS Surveying ............................................................. 91The Antenna .................................................................................................92

Bandwidth ..........................................................................................93Nearly Hemispheric Coverage ...........................................................93Antenna Orientation ..........................................................................94Height of Instrument ..........................................................................94

The Radio Frequency (RF) Section ..............................................................94Channels ............................................................................................95Multiplexing and Sequencing ............................................................96Tracking Loops ..................................................................................96Pseudoranging ....................................................................................96Carrier Phase Measurement ...............................................................97Carrier Tracking Loop .......................................................................97Doppler Shift ......................................................................................97

Typical GPS Doppler Shift ...........................................................................97The Typical Change in the Doppler Shift ..........................................98Continuously Integrated Doppler .......................................................98Integer Ambiguity ..............................................................................99Signal Squaring ..................................................................................99

The Microprocessor .................................................................................... 100Differential Positioning.................................................................... 100Differential GPS .............................................................................. 101Positional Accuracies ....................................................................... 101Kinematic and Real-Time Kinematic .............................................. 101

The Control and Display Unit (CDU) ......................................................... 101Typical Displays ............................................................................... 101

The Storage ................................................................................................. 102Downloading .................................................................................... 102

The Power ................................................................................................... 102Battery Power ................................................................................... 102

Choosing a GPS Receiver ...................................................................................... 103Trends in Receiver Development ................................................................ 104

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High Accuracy Early ....................................................................... 104Another Direction ............................................................................ 104More Convenience ........................................................................... 104Multichannel and Code-Correlating ................................................ 105Dual-Frequency ............................................................................... 105Adding Codeless Capability ............................................................ 105Adding P Code Tracking ................................................................. 105Typical GPS Surveying Receiver Characteristics ............................ 106GPS Receiver Costs ......................................................................... 106

Some GPS Surveying Methods .............................................................................. 106Static ........................................................................................................... 106

Prerequisites for Static GPS ............................................................. 106Productivity ...................................................................................... 108Session Length ................................................................................. 108Large Amounts of Data ................................................................... 108Resolution of the Cycle Ambiguity .................................................. 108Preprogrammed Observations ......................................................... 108Observation Settings ........................................................................ 109Data Interval .................................................................................... 109Compatible Receivers ...................................................................... 109Receiver Capabilities and Baseline Length ..................................... 109

Differential GPS ......................................................................................... 110Kinematic ................................................................................................... 110

Reference Receiver and Rover Receivers......................................... 110Leapfrog Kinematic ......................................................................... 110Kinematic Positional Accuracy ....................................................... 110Maintaining Lock ............................................................................ 111Reconnaissance ................................................................................ 111Applications ..................................................................................... 111Most Carrier Phase Receivers Capable of Kinematic GPS ............. 111Wideband ......................................................................................... 111Practical Considerations in Kinematic GPS .................................... 112

Pseudokinematic ......................................................................................... 112Double Occupation .......................................................................... 112No Need for Continuous Lock ......................................................... 112Best Used in Easy Access Situations ............................................... 113Mostly Radial Surveys ..................................................................... 113

Rapid-Static ................................................................................................ 113Wide Laning .................................................................................... 113

On-the-Fly .................................................................................................. 114Accurate Initial Positions ................................................................. 114Photogrammetry without Ground Control....................................... 114

Real-Time Kinematic (RTK) ...................................................................... 114Exercises ................................................................................................................ 115Answers and Explanations ..................................................................................... 117

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Contents xi

Chapter 5 Coordinates ...................................................................................... 121

A Few Pertinent Ideas About Geodetic Datums for GPS ...................................... 121Plane Surveying .......................................................................................... 121

Development of State Plane Coordinate Systems ............................ 121GPS Surveyors and Geodesy ........................................................... 122

Some Geodetic Coordinate Systems........................................................... 122Three-Dimensional (3-D) Cartesian Coordinates............................ 122Polar Motion .................................................................................... 122The Conventional Terrestrial System (CTS) in GPS ....................... 123Latitude and Longitude .................................................................... 123

Elements of a Geodetic Datum ...................................................................124The Deflection of the Vertical .........................................................124

Geocentric, Geodetic, and Astronomic Latitude ........................................ 125Datums ............................................................................................. 127Development of the Ellipsoidal Model ............................................ 127

Biaxial Ellipsoidal Model of the Earth ....................................................... 128The Role of an Ellipsoid in a Datum ............................................... 128

Regional Ellipsoids ..................................................................................... 130Measurement Technology and Datum Selection ............................. 130

Position Derived from GPS ........................................................................ 131The Development of a Geocentric Model ........................................ 131

The Geoid ................................................................................................... 132An Equipotential Surface ................................................................ 133Geoidal Undulation .......................................................................... 133

The Modern Geocentric Datum ................................................................. 133World Geodetic System 1984 (WGS84) .......................................... 134

North American Datum 1983 ..................................................................... 135NAD27 ............................................................................................. 135The Development of the North American Datum 1983

(NAD83) ............................................................................. 135The International Terrestrial Reference System (ITRS) .................. 136ITRF00, WGS84, and NAD83 ........................................................ 136The Management of NAD83 ........................................................... 137Transformations from NAD27 to NAD83 ....................................... 137Densification and Improvement of NAD83 ..................................... 138High Accuracy Reference Networks ................................................ 138Height Modernization and Base Networks ...................................... 139Continuously Operating Reference Stations .................................... 140

State Plane Coordinates ......................................................................................... 140NAD83 Positions and Plane Coordinates ................................................... 140Map Projection............................................................................................ 141Distortion .................................................................................................... 143

Decreasing Distortion ...................................................................... 144Secant and Cylindrical Projections ............................................................ 144

Secant Projections ............................................................................ 144Choices ............................................................................................. 145

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State Plane Coordinate System (SPCS) Map Projections ........................... 147SPCS27 to SPCS83 ..................................................................................... 148

Changes in Zones ............................................................................. 149State Plane Coordinates Scale and Distance .............................................. 150

Geodetic Lengths to Grid Lengths .................................................. 150Universal Transverse Mercator Coordinates .............................................. 158Universal Transverse Mercator (UTM) Zones of the World ...................... 158

Heights ................................................................................................................... 162Ellipsoidal Heights ..................................................................................... 162Orthometric Heights ................................................................................... 163

Spirit Leveling ................................................................................. 163Evolution of a Vertical Datum .................................................................... 164

Sea Level .......................................................................................... 164Diurnal Tide ................................................................................................ 165

A Different Approach ...................................................................... 166The Zero Point ................................................................................. 167

The Geoid ................................................................................................... 167Geoid Models ................................................................................... 169

Exercises ................................................................................................................ 171Answers and Explanations ..................................................................................... 173

Chapter 6 GPS Surveying Techniques .............................................................. 177

Static GPS Surveying ............................................................................................. 177Planning ...................................................................................................... 177

New Standards ................................................................................. 177New Design Criteria ........................................................................ 177The Lay of the Land ........................................................................ 178Maps ................................................................................................. 178

National Geodetic Survey (NGS) Control .................................................. 178NGS Control Data Sheets ................................................................ 178Survey Order and Class ................................................................... 181Coordinates ...................................................................................... 181The Station Mark ............................................................................. 182Significance of the Information ....................................................... 182

Control from Continuously Operating Networks ....................................... 182NGS Continuously Operating Reference Stations ........................... 183NGS CORS Reference Points .......................................................... 183NGS CORS Precise Orbits .............................................................. 184International Global Navigation Satellite System (GNSS)

Service (IGS) ...................................................................... 184Project Design ............................................................................................. 184

Horizontal Control ........................................................................... 184Station Location ............................................................................... 185Vertical Control ............................................................................... 185

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Contents xiii

Preparation .................................................................................................. 186Plotting Project Points ..................................................................... 186Evaluating Access ............................................................................ 187Planning Offsets .............................................................................. 188Planning Azimuth Marks................................................................. 188Obtaining Permissions ..................................................................... 188

Some GPS Survey Design Facts ................................................................. 189Software Assistance ......................................................................... 189Position Dilution of Precision (PDOP) ............................................ 189Polar Plot .......................................................................................... 190An Example ..................................................................................... 190Choosing the Window...................................................................... 192Ionospheric Delay ............................................................................ 192An Example ..................................................................................... 192Naming the Variables ...................................................................... 194

Drawing the Baselines ................................................................................ 194Horizontal Control ........................................................................... 194Julian Day in Naming Sessions ....................................................... 195Independent Lines ............................................................................ 197Redundancy ..................................................................................... 198Federal Geodetic Control Committee (FGCC) Standardsfor

Redundancy ........................................................................ 199Forming Loops ................................................................................ 199Finding the Number of Sessions ...................................................... 199Ties to the Vertical Control ..............................................................202

Real-Time Kinematic (RTK) and Differential GPS (DGPS) ................................202The General Idea ........................................................................................202Radial GPS .................................................................................................203

The Correction Signal ......................................................................204DGPS .....................................................................................................................204

Real-Time....................................................................................................204Local and Wide Area DPGS ......................................................................205

Maritime DGPS ...............................................................................206Wide Area Augmentation System (WAAS) ....................................206

Latency .......................................................................................................206Identical Constellation ................................................................................207Geographic Information Systems (GIS) Applications for DGPS ...............207

RTK ........................................................................................................................208Fixing the Integer Ambiguity in RTK ........................................................208Radio License ............................................................................................. 210Cell Phones ................................................................................................. 211Typical RTK ............................................................................................... 211The Vertical Component in RTK ............................................................... 212Some Practical RTK Suggestions ............................................................... 212

Typical Satellite Constellations ........................................................ 212Dual-Frequency Receiver ................................................................ 213

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Setting up a Base Station ................................................................. 213After the RTK Survey ...................................................................... 213

Comparing RTK and DGPS ....................................................................... 213Multipath in RTK and DGPS ........................................................... 213Initialization ..................................................................................... 214Base Station ..................................................................................... 214Radio Technical Commission for Maritime (RTCM) Services

Version 3 ............................................................................. 215Real-Time Network Services ................................................................................. 215

Precise Point Positioning ............................................................................ 217Summary .................................................................................................... 218

Exercises ................................................................................................................ 219Answers and Explanations .....................................................................................223

Chapter 7 Observing and Processing ................................................................ 229

Static GPS Control Observations ........................................................................... 229Equipment ................................................................................................... 229

Conventional Equipment .................................................................. 229Safety Equipment .............................................................................230Communications ..............................................................................230GPS Equipment ................................................................................ 231Auxiliary Equipment ....................................................................... 232Papers ............................................................................................... 232

Station Data Sheet....................................................................................... 232Station Name ....................................................................................234Rubbings .......................................................................................... 235Photographs...................................................................................... 235Quad Sheet Name ............................................................................ 235To-Reach Descriptions ..................................................................... 235Flagging and Describing the Monument ......................................... 236

Visibility Diagrams .................................................................................... 236An Example ..................................................................................... 236Drawing Obstructions ...................................................................... 237Working around Obstructions .......................................................... 238Approximate Station Coordinates ................................................... 238Multipath ..........................................................................................240Point Offsets.....................................................................................240Look for Multipath ...........................................................................240

Monumentation ........................................................................................... 241Logistics ...................................................................................................... 241

Scheduling ....................................................................................... 241Observation .................................................................................................242

Arrival ..............................................................................................242Setup ................................................................................................242Height of Instrument ........................................................................ 243

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Contents xv

Observation Logs ............................................................................. 243Weather ............................................................................................245

Daily Progress Evaluation ..........................................................................245Real-Time Kinematic (RTK) and Differential GPS (DGPS) Observations ..........245

Point Offsets.....................................................................................246Dynamic Lines ................................................................................. 247Planning ........................................................................................... 247

A Few RTK Procedures ..............................................................................248Site Calibration ...........................................................................................248

Processing ..............................................................................................................249Postprocessing GPS Static Control Surveys ...............................................249

Correlation of Biases ........................................................................250Quantity of Data .........................................................................................250

Organization Is Essential .................................................................250File Naming Conventions ................................................................250

Downloading ..............................................................................................250Making Room .................................................................................. 251

Control ........................................................................................................ 251The First Position ........................................................................................ 251Triple Difference ......................................................................................... 252

Components of a Triple Difference ................................................. 252Double Difference ...................................................................................... 252

The Integer Ambiguity .................................................................... 252The Float Solution ............................................................................ 253The Fixed Solution ........................................................................... 253

Cycle Slip Detection and Repair................................................................. 253Cycle Slip Causes .............................................................................254Repairing Cycle Slips ......................................................................254

Fixing the Integer Ambiguity and Obtaining Vector Solutions ................. 255Least-Squares Adjustment ..........................................................................256Using a Processing Service ......................................................................... 257

Exercises ................................................................................................................ 257Answers and Explanations ..................................................................................... 261

Chapter 8 GPS Modernization and Global Navigation Satellite System (GNSS) ............................................................................................. 267

GPS Modernization ............................................................................................... 267Block I, Block II, and Block IIR Satellites ................................................. 267Power Spectral Density Diagrams ..............................................................268L1 Signal .....................................................................................................269L2 Signal .....................................................................................................269New Signals ................................................................................................269The M-Code ................................................................................................ 270L2C ............................................................................................................. 271

Civil-Moderate (CM) and Civil-Long (CL) ..................................... 272

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CNAV ............................................................................................... 272Multiplexing ..................................................................................... 273Phase-Locked Loop ......................................................................... 273

Practical Advantages .................................................................................. 273L5 ........................................................................................................................... 274

The L5 Carrier ............................................................................................ 274The Block IIF Satellites .............................................................................. 276Summary of Coarse Acquisition (C/A), L2C, and L5 ................................ 276New Signal Availability .............................................................................. 276

Availability ....................................................................................... 276Ionospheric Bias ............................................................................... 278Correlation Protection ...................................................................... 278

Another Civil Signal—L1C ........................................................................ 278Global Navigation Satellite System (GNSS) .......................................................... 279GLONASS .............................................................................................................280

GLONASS Uragan M and K ......................................................................280GLONASS Constellation ................................................................. 281

GLONASS Signals .....................................................................................282Code Division Multiple Access (CDMA) and Frequency

Division Multiple Access (FDMA) ....................................282Changes to FDMA ...........................................................................284

GLONASS Time .........................................................................................284GALILEO ...................................................................................................284GIOVE-A and GIOVE-B ............................................................................285

GALILEO Signals and Services ......................................................285Interoperability ...........................................................................................286GALILEO Signals ......................................................................................287

Frequency Coincidence ....................................................................287BEIDOU/COMPASS .............................................................................................288

Frequencies .................................................................................................288The Quasi-Zenith Satellite System (QZSS) ................................................289

The Future ..............................................................................................................289More Satellites ............................................................................................289

Accessibility .....................................................................................290Flexibility .........................................................................................290Reliability .........................................................................................290Faster Positioning .............................................................................290Faster Initialization ..........................................................................290GPS Accuracy ..................................................................................290GNSS Accuracy—Faster ................................................................. 291Simplification ...................................................................................292

Interoperability ......................................................................................................292GPS–GALILEO–GLONASS Constellations .............................................292

Inconsistency ....................................................................................292

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Contents xvii

Consistency ......................................................................................292Robust Solutions ..............................................................................292

Summary .................................................................................................... 293Exercises ................................................................................................................294Answers and Explanations .....................................................................................296

References .............................................................................................................299

Glossary ................................................................................................................ 301

Index ...................................................................................................................... 325

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