GPS theory, algorithms and applications

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1. Verfasser: Xu, Guochang (VerfasserIn)
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Sprache:English
Veröffentlicht: Berlin [u.a.] Springer 2007
Ausgabe:2. ed.
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adam_text Contents 1 Introduction .............................................................................. 1 1.1 A Key Note of GPS ........................................................................ 2 1.2 A Brief Message About GLONASS ..................................................... 3 1.3 Basic Information of Galileo............................................................4 1.4 A Combined Global Navigation Satellite System .................................... 5 2 Coordinate and Time Systems .......................................................7 2.1 Geocentric Earth-Fixed Coordinate Systems ........................................ 7 2.2 Coordinate System Transformations .................................................10 2.3 Local Coordinate System ...............................................................11 2.4 Earth-Centred Inerţial Coordínate System ..........................................13 2.5 Geocentric Ecliptic Inerţial Coordinate System ....................................17 2.6 Time Systems .............................................................................17 3 Satellite Orbits ..........................................................................21 3.1 Keplerian Motion ........................................................................21 3.1.1 Satellite Motion in the Orbital Plane .........................................24 3.1.2 Keplerian Equation ..............................................................27 3.1.3 State Vector of the Satellite .....................................................29 3.2 Disturbed Satellite Motion .............................................................31 3.3 GPS Broadcast Ephemerides...........................................................32 3.4 IGS Precise Ephemerides ...............................................................34 3.5 GLONASS Ephemerides ................................................................35 4 GPS Observables .......................................................................37 4.1 Code Pseudoranges ......................................................................37 4.2 Carrier Phases ............................................................................39 4.3 Doppler Measurements .................................................................41 5 Physical Influences of GPS Surveying .............................................43 5.1 Ionospheric Effects ......................................................................43 5.1.1 Code Delay and Phase Advance ...............................................43 5.1.2 Elimination of the Ionospheric Effects ......................................45 5.1.3 Ionospheric Models .............................................................48 5.1.4 Mapping Functions ..............................................................51 XIV Contents 5.2 Tropospheric Effects .....................................................................55 5.2.1 Tropospheric Models............................................................56 5.2.2 Mapping Functions and Parameterisation ..................................59 5.3 Relativistic Effects .......................................................................62 5.3.1 Special Relativity and General Relativity ....................................62 5.3.2 Relativistic Effects on GPS .....................................................64 5.4 Earth Tide and Ocean Loading Tide Corrections ..................................67 5.4.1 Earth Tide Displacements of the GPS Station ..............................67 5.4.2 Simplified Model of the Earth Tide Displacements ........................68 5.4.3 Numerical Examples of the Earth Tide Effects .............................70 5.4.4 Ocean Loading Tide Displacement ...........................................72 5.4.5 Computation of the Ocean Loading Tide Displacement ..................75 5.4.6 Numerical Examples of Loading Tide Effects ...............................75 5.5 Clock Errors ..............................................................................76 5.6 Multipath Effects .........................................................................78 5.6.1 GPS-Altimetry, Signals Reflected from the Earth-Surface ................79 5.6.2 Reflecting Point Positioning ...................................................80 5.6.3 Image Point and Reflecting Surface Determination .......................81 5.7 Anti-Spoofing and Selective Availability Effects ...................................82 5.8 Antenna Phase Centre Offset and Variation .........................................82 5.9 Instrumental Biases .....................................................................85 6 GPS Observation Equations and Equivalence Properties ...................87 6.1 General Mathematical Models of GPS Observations ..............................87 6.2 Linearisation of the Observational Model ...........................................89 6.3 Partial Derivatives of Observational Function .....................................90 6.4 Linear Transformation and Covariance Propagation ..............................94 6.5 Data Combinations ......................................................................95 6.5.1 Ionosphere-Free Combinations ...............................................97 6.5.2 Geometry-Free Combinations .................................................98 6.5.3 Standard Phase-Code Combination ........................................ 100 6.5.4 Ionospheric Residuals ......................................................... 101 6.5.5 Differential Doppler and Doppler Integration ............................ 102 6.6 Data Differentiations .................................................................. 104 6.6.1 Single Differences .............................................................. 105 6.6.2 Double Differences ............................................................ 107 6.6.3 Triple Differences .............................................................. 110 6.7 Equivalence of the Uncombined and Combining Algorithms ................. Ill 6.7.1 Uncombined GPS Data Processing Algorithms ........................... 112 6.7.2 Combining Algorithms of GPS Data Processing ......................... 114 6.7.3 Secondary GPS Data Processing Algorithms .............................. 119 6.7.4 Summary ........................................................................ 122 6.8 Equivalence of Undifferenced and Differencing Algorithms ................... 122 6.8.1 Introduction .................................................................... 122 6.8.2 Formation of Equivalent Observation Equations ........................ 123 6.8.3 Equivalent Equations of Single Differences ............................... 125 Contents XV 6.8.4 Equivalent Equations of Double Differences .............................. 128 6.8.5 Equivalent Equations of Triple Differences ............................... 130 6.8.6 Method of Dealing with the Reference Parameters ...................... 130 6.8.7 Summary of the Unified Equivalent Algorithm .......................... 131 7 Adjustment and Filtering Methods .............................................. 133 7.1 Introduction ............................................................................ 133 7.2 Least Squares Adjustment ............................................................ 133 7.2.1 Least Squares Adjustment with Sequential Observation Groups ...... 135 7.3 Sequential Least Squares Adjustment .............................................. 137 7.4 Conditional Least Squares Adjustment ............................................ 138 7.4.1 Sequential Application of Conditional Least Squares Adjustment .... 140 7.5 Block-Wise Least Squares Adjustment ............................................. 141 7.5.1 Sequential Solution of Block-Wise Least Squares Adjustment ........ 143 7.5.2 Block-Wise Least Squares for Code-Phase Combination ............... 145 7.6 Equivalently Eliminated Observation Equation System ........................ 146 7.6.1 Diagonalised Normal Equation and the Equivalent Observation Equation ......................................................... 148 7.7 Kalman Filter ........................................................................... 150 7.7.1 Classic Kalman Filter .......................................................... 150 7.7.2 Kalman Filter - A General Form of Sequential Least Squares Adjustment .................................................... 151 7.7.3 Robust Kalman Filter .......................................................... 152 7.7.4 Adaptively Robust Kalman Filtering ....................................... 155 7.8 A Priori Constrained Least Squares Adjustment ................................. 159 7.8.1 A Priori Parameter Constraints ............................................. 159 7.8.2 A Priori Datum ................................................................. 160 7.8.3 Quasi-Stable Datum ........................................................... 161 7.9 Summary ................................................................................ 163 8 Cycle Slip Detection and Ambiguity Resolution ............................. 167 8.1 Cycle Slip Detection ................................................................... 167 8.2 Method of Dealing with Cycle Slips ................................................ 168 8.3 A General Criterion of Integer Ambiguity Search ............................... 169 8.3.1 Introduction .................................................................... 169 8.3.2 Summary of Conditional Least Squares Adjustment .................... 170 8.3.3 Float Solution ................................................................... 171 8.3.4 Integer Ambiguity Search in Ambiguity Domain ........................ 172 8.3.5 Integer Ambiguity Search in Coordinate and Ambiguity Domains ..................................................... 174 8.3.6 Properties of the General Criterion ........................................ 175 8.3.7 An Equivalent Ambiguity Search Criterion and its Properties ........ 176 8.3.8 Numerical Examples of the Equivalent Criterion ........................ 178 8.3.9 Conclusions and Comments ................................................. 181 8.4 Ambiguity Function ................................................................... 182 8.4.1 Maximum Property of Ambiguity Function .............................. 183 XVI Contents 9 Parameterisation and Algorithms of GPS Data Processing ............... 187 9.1 Parameterisation of the GPS Observation Model ................................ 187 9.1.1 Evidence of the Parameterisation Problem of the Undifferenced Observation Model ............................................................ 187 9.1.2 A Method of Uncorrelated Bias Parameterisation ....................... 189 9.1.3 Geometry-Free Illustration .................................................. 195 9.1.4 Correlation Analysis in the Case of Phase-Code Combinations ....... 195 9.1.5 Conclusions and Comments ................................................. 197 9.2 Equivalence of the GPS Data Processing Algorithms ............................ 198 9.2.1 Equivalence Theorem of GPS Data Processing Algorithms ............ 198 9.2.2 Optimal Baseline Network Forming and Data Condition .............. 200 9.2.3 Algorithms Using Secondary GPS Observables .......................... 201 9.3 Non-Equivalent Algorithms .......................................................... 203 9.4 Standard Algorithms of GPS Data Processing .................................... 203 9.4.1 Preparation of GPS Data Processing ....................................... 203 9.4.2 Single Point Positioning ...................................................... 204 9.4.3 Standard Un-Differential GPS Data Processing .......................... 209 9.4.4 Equivalent Method of GPS Data Processing .............................. 211 9.4.5 Relative Positioning ........................................................... 212 9.4.6 Velocity Determination ....................................................... 212 9.4.7 Kalman Filtering Using Velocity Information ............................ 215 9.5 Accuracy of the Observational Geometry ......................................... 217 10 Applications of GPS Theory and Algorithms .................................. 219 10.1 Software Development ................................................................ 219 10.1.1 Functional Library ............................................................. 219 10.1.2 Data Platform ................................................................... 223 10.1.3 A Data Processing Core ....................................................... 225 10.2 Concept of Precise Kinematic Positioning and Flight-State Monitoring ..... 226 10.2.1 Introduction .................................................................... 226 10.2.2 Concept of Precise Kinematic Positioning ................................ 229 10.2.3 Concept of Flight-State Monitoring ........................................ 233 10.2.4 Results, Precision Estimation and Comparisons ..................... 235 10.2.5 Conclusions ..................................................................... 240 Π Perturbed Orbit and its Determination ........................................ 243 11.1 Perturbed Equation of Satellite Motion ............................................ 243 11.1.1 Lagrangian Perturbed Equation of Satellite Motion 244 11.1.2 Gaussian Perturbed Equation of Satellite Motion ....................... 246 11.2 Perturbation Forces of Satellite Motion ............................................ 249 11.2.1 Perturbation of the Earth s Gravitational Field ........................... 249 11.2.2 Perturbation of the Sun and the Moon as well as Planets 254 11.2.3 Earth Tide and Ocean Tide Perturbations ................................. 255 11.2.4 Solar Radiation Pressure ................................ 258 11.2.5 Atmospheric Drag ...................................................... 262 11.2.6 Additional Perturbations ............................................ 265 Contents XVII 11.2.7 Order Estimations of Perturbations ........................................ 267 11.2.8 Ephemerides of the Moon, the Sun and Planets .......................... 267 11.3 Analysis Solution of the C20 Perturbed Orbit ..................................... 271 11.4 Orbit Correction ....................................................................... 277 11.5 Principle of GPS Precise Orbit Determination ................................... 281 11.5.1 Algebra Solution of the Variation Equation ............................... 283 11.6 Numerical Integration and Interpolation Algorithms ........................... 284 11.6.1 Runge-Kutta Algorithms ...................................................... 284 11.6.2 Adams Algorithms ............................................................. 289 11.6.3 Cowell Algorithms ............................................................. 291 11.6.4 Mixed Algorithms and Discussions ........................................ 293 11.6.5 Interpolation Algorithms ..................................................... 294 11.7 Orbit-Related Partial Derivatives ................................................... 294 12 Discussions ............................................................................. 305 12.1 Independent Parameterisation and A Priori Information ...................... 305 12.2 Equivalence of the GPS Data Processing Algorithms ............................ 307 Appendix 1 IAU 1980 Theory of Nutation ...................................................... 309 Appendix 2 Numerical Examples of the Diagonalisation of the Equations ........... 311 References ............................................................................. 317 Subject Index .......................................................................... 337
adam_txt Contents 1 Introduction . 1 1.1 A Key Note of GPS . 2 1.2 A Brief Message About GLONASS . 3 1.3 Basic Information of Galileo.4 1.4 A Combined Global Navigation Satellite System . 5 2 Coordinate and Time Systems .7 2.1 Geocentric Earth-Fixed Coordinate Systems . 7 2.2 Coordinate System Transformations .10 2.3 Local Coordinate System .11 2.4 Earth-Centred Inerţial Coordínate System .13 2.5 Geocentric Ecliptic Inerţial Coordinate System .17 2.6 Time Systems .17 3 Satellite Orbits .21 3.1 Keplerian Motion .21 3.1.1 Satellite Motion in the Orbital Plane .24 3.1.2 Keplerian Equation .27 3.1.3 State Vector of the Satellite .29 3.2 Disturbed Satellite Motion .31 3.3 GPS Broadcast Ephemerides.32 3.4 IGS Precise Ephemerides .34 3.5 GLONASS Ephemerides .35 4 GPS Observables .37 4.1 Code Pseudoranges .37 4.2 Carrier Phases .39 4.3 Doppler Measurements .41 5 Physical Influences of GPS Surveying .43 5.1 Ionospheric Effects .43 5.1.1 Code Delay and Phase Advance .43 5.1.2 Elimination of the Ionospheric Effects .45 5.1.3 Ionospheric Models .48 5.1.4 Mapping Functions .51 XIV Contents 5.2 Tropospheric Effects .55 5.2.1 Tropospheric Models.56 5.2.2 Mapping Functions and Parameterisation .59 5.3 Relativistic Effects .62 5.3.1 Special Relativity and General Relativity .62 5.3.2 Relativistic Effects on GPS .64 5.4 Earth Tide and Ocean Loading Tide Corrections .67 5.4.1 Earth Tide Displacements of the GPS Station .67 5.4.2 Simplified Model of the Earth Tide Displacements .68 5.4.3 Numerical Examples of the Earth Tide Effects .70 5.4.4 Ocean Loading Tide Displacement .72 5.4.5 Computation of the Ocean Loading Tide Displacement .75 5.4.6 Numerical Examples of Loading Tide Effects .75 5.5 Clock Errors .76 5.6 Multipath Effects .78 5.6.1 GPS-Altimetry, Signals Reflected from the Earth-Surface .79 5.6.2 Reflecting Point Positioning .80 5.6.3 Image Point and Reflecting Surface Determination .81 5.7 Anti-Spoofing and Selective Availability Effects .82 5.8 Antenna Phase Centre Offset and Variation .82 5.9 Instrumental Biases .85 6 GPS Observation Equations and Equivalence Properties .87 6.1 General Mathematical Models of GPS Observations .87 6.2 Linearisation of the Observational Model .89 6.3 Partial Derivatives of Observational Function .90 6.4 Linear Transformation and Covariance Propagation .94 6.5 Data Combinations .95 6.5.1 Ionosphere-Free Combinations .97 6.5.2 Geometry-Free Combinations .98 6.5.3 Standard Phase-Code Combination . 100 6.5.4 Ionospheric Residuals . 101 6.5.5 Differential Doppler and Doppler Integration . 102 6.6 Data Differentiations . 104 6.6.1 Single Differences . 105 6.6.2 Double Differences . 107 6.6.3 Triple Differences . 110 6.7 Equivalence of the Uncombined and Combining Algorithms . Ill 6.7.1 Uncombined GPS Data Processing Algorithms . 112 6.7.2 Combining Algorithms of GPS Data Processing . 114 6.7.3 Secondary GPS Data Processing Algorithms . 119 6.7.4 Summary . 122 6.8 Equivalence of Undifferenced and Differencing Algorithms . 122 6.8.1 Introduction . 122 6.8.2 Formation of Equivalent Observation Equations . 123 6.8.3 Equivalent Equations of Single Differences . 125 Contents XV 6.8.4 Equivalent Equations of Double Differences . 128 6.8.5 Equivalent Equations of Triple Differences . 130 6.8.6 Method of Dealing with the Reference Parameters . 130 6.8.7 Summary of the Unified Equivalent Algorithm . 131 7 Adjustment and Filtering Methods . 133 7.1 Introduction . 133 7.2 Least Squares Adjustment . 133 7.2.1 Least Squares Adjustment with Sequential Observation Groups . 135 7.3 Sequential Least Squares Adjustment . 137 7.4 Conditional Least Squares Adjustment . 138 7.4.1 Sequential Application of Conditional Least Squares Adjustment . 140 7.5 Block-Wise Least Squares Adjustment . 141 7.5.1 Sequential Solution of Block-Wise Least Squares Adjustment . 143 7.5.2 Block-Wise Least Squares for Code-Phase Combination . 145 7.6 Equivalently Eliminated Observation Equation System . 146 7.6.1 Diagonalised Normal Equation and the Equivalent Observation Equation . 148 7.7 Kalman Filter . 150 7.7.1 Classic Kalman Filter . 150 7.7.2 Kalman Filter - A General Form of Sequential Least Squares Adjustment . 151 7.7.3 Robust Kalman Filter . 152 7.7.4 Adaptively Robust Kalman Filtering . 155 7.8 A Priori Constrained Least Squares Adjustment . 159 7.8.1 A Priori Parameter Constraints . 159 7.8.2 A Priori Datum . 160 7.8.3 Quasi-Stable Datum . 161 7.9 Summary . 163 8 Cycle Slip Detection and Ambiguity Resolution . 167 8.1 Cycle Slip Detection . 167 8.2 Method of Dealing with Cycle Slips . 168 8.3 A General Criterion of Integer Ambiguity Search . 169 8.3.1 Introduction . 169 8.3.2 Summary of Conditional Least Squares Adjustment . 170 8.3.3 Float Solution . 171 8.3.4 Integer Ambiguity Search in Ambiguity Domain . 172 8.3.5 Integer Ambiguity Search in Coordinate and Ambiguity Domains . 174 8.3.6 Properties of the General Criterion . 175 8.3.7 An Equivalent Ambiguity Search Criterion and its Properties . 176 8.3.8 Numerical Examples of the Equivalent Criterion . 178 8.3.9 Conclusions and Comments . 181 8.4 Ambiguity Function . 182 8.4.1 Maximum Property of Ambiguity Function . 183 XVI Contents 9 Parameterisation and Algorithms of GPS Data Processing . 187 9.1 Parameterisation of the GPS Observation Model . 187 9.1.1 Evidence of the Parameterisation Problem of the Undifferenced Observation Model . 187 9.1.2 A Method of Uncorrelated Bias Parameterisation . 189 9.1.3 Geometry-Free Illustration . 195 9.1.4 Correlation Analysis in the Case of Phase-Code Combinations . 195 9.1.5 Conclusions and Comments . 197 9.2 Equivalence of the GPS Data Processing Algorithms . 198 9.2.1 Equivalence Theorem of GPS Data Processing Algorithms . 198 9.2.2 Optimal Baseline Network Forming and Data Condition . 200 9.2.3 Algorithms Using Secondary GPS Observables . 201 9.3 Non-Equivalent Algorithms . 203 9.4 Standard Algorithms of GPS Data Processing . 203 9.4.1 Preparation of GPS Data Processing . 203 9.4.2 Single Point Positioning . 204 9.4.3 Standard Un-Differential GPS Data Processing . 209 9.4.4 Equivalent Method of GPS Data Processing . 211 9.4.5 Relative Positioning . 212 9.4.6 Velocity Determination . 212 9.4.7 Kalman Filtering Using Velocity Information . 215 9.5 Accuracy of the Observational Geometry . 217 10 Applications of GPS Theory and Algorithms . 219 10.1 Software Development . 219 10.1.1 Functional Library . 219 10.1.2 Data Platform . 223 10.1.3 A Data Processing Core . 225 10.2 Concept of Precise Kinematic Positioning and Flight-State Monitoring . 226 10.2.1 Introduction . 226 10.2.2 Concept of Precise Kinematic Positioning . 229 10.2.3 Concept of Flight-State Monitoring . 233 10.2.4 Results, Precision Estimation and Comparisons . 235 10.2.5 Conclusions . 240 Π Perturbed Orbit and its Determination . 243 11.1 Perturbed Equation of Satellite Motion . 243 11.1.1 Lagrangian Perturbed Equation of Satellite Motion 244 11.1.2 Gaussian Perturbed Equation of Satellite Motion . 246 11.2 Perturbation Forces of Satellite Motion . 249 11.2.1 Perturbation of the Earth's Gravitational Field . 249 11.2.2 Perturbation of the Sun and the Moon as well as Planets 254 11.2.3 Earth Tide and Ocean Tide Perturbations . 255 11.2.4 Solar Radiation Pressure . 258 11.2.5 Atmospheric Drag . 262 11.2.6 Additional Perturbations . 265 Contents XVII 11.2.7 Order Estimations of Perturbations . 267 11.2.8 Ephemerides of the Moon, the Sun and Planets . 267 11.3 Analysis Solution of the C20 Perturbed Orbit . 271 11.4 Orbit Correction . 277 11.5 Principle of GPS Precise Orbit Determination . 281 11.5.1 Algebra Solution of the Variation Equation . 283 11.6 Numerical Integration and Interpolation Algorithms . 284 11.6.1 Runge-Kutta Algorithms . 284 11.6.2 Adams Algorithms . 289 11.6.3 Cowell Algorithms . 291 11.6.4 Mixed Algorithms and Discussions . 293 11.6.5 Interpolation Algorithms . 294 11.7 Orbit-Related Partial Derivatives . 294 12 Discussions . 305 12.1 Independent Parameterisation and A Priori Information . 305 12.2 Equivalence of the GPS Data Processing Algorithms . 307 Appendix 1 IAU 1980 Theory of Nutation . 309 Appendix 2 Numerical Examples of the Diagonalisation of the Equations . 311 References . 317 Subject Index . 337
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author Xu, Guochang
author_facet Xu, Guochang
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illustrated Illustrated
index_date 2024-07-02T17:43:58Z
indexdate 2024-07-09T20:58:16Z
institution BVB
isbn 9783540727149
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3540727140
language English
oai_aleph_id oai:aleph.bib-bvb.de:BVB01-015676929
oclc_num 154712362
open_access_boolean
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physical XXII, 340 S. Ill., graph. Darst.
publishDate 2007
publishDateSearch 2007
publishDateSort 2007
publisher Springer
record_format marc
spelling Xu, Guochang Verfasser aut
GPS theory, algorithms and applications Guochang Xu
2. ed.
Berlin [u.a.] Springer 2007
XXII, 340 S. Ill., graph. Darst.
txt rdacontent
n rdamedia
nc rdacarrier
Global Positioning System
GPS (DE-588)4216824-7 gnd rswk-swf
GPS (DE-588)4216824-7 s
DE-604
Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015676929&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle Xu, Guochang
GPS theory, algorithms and applications
Global Positioning System
GPS (DE-588)4216824-7 gnd
subject_GND (DE-588)4216824-7
title GPS theory, algorithms and applications
title_auth GPS theory, algorithms and applications
title_exact_search GPS theory, algorithms and applications
title_exact_search_txtP GPS theory, algorithms and applications
title_full GPS theory, algorithms and applications Guochang Xu
title_fullStr GPS theory, algorithms and applications Guochang Xu
title_full_unstemmed GPS theory, algorithms and applications Guochang Xu
title_short GPS
title_sort gps theory algorithms and applications
title_sub theory, algorithms and applications
topic Global Positioning System
GPS (DE-588)4216824-7 gnd
topic_facet Global Positioning System
GPS
url http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015676929&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv AT xuguochang gpstheoryalgorithmsandapplications