Heft 73/2001

Schriftenreihe
des Instituts für Geodäsie



Heft 73/2001

SCHÜLER, Torben

On Ground-Based GPS Tropospheric Delay Estimation

Dissertation
364 S.

Auflage:  150

ISSN:  0173-1009

Inhaltsverzeichnis

Abstract

Zusammenfassung


 


Vollständiger Abdruck der von der Fakultät für Bauingenieur- und Vermessungswesen der Universität der Bundeswehr München zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften (Dr.-Ing.) eingereichten Dissertation.

Promotionsausschuss  
Vorsitzender: Univ.-Prof. Dr.-Ing. B. Eissfeller
1. Berichterstatter: Univ.-Prof. Dr.-Ing. G. W. Hein
2. Berichterstatter: Univ.-Prof. Dr.-Ing. G. Seeber

Die Dissertation wurde am 18. Oktober 2000 bei der Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, D-85577 Neubiberg eingereicht.

Tag der mündlichen Prüfung:  1. Februar 2001
 



Inhaltsverzeichnis
(in Englisch)

Abstract 2
Zusammenfassung 3
Table of Contents 4
List of Figures 10
List of Tables 18
List of Symbols 22
List of Acronyms 33
 
1.  Introduction 37
     1.1  Importance of Atmospheric Water Vapor for the Climate
            System

37
            1.1.1  Hydrological Cycle and Greenhouse Effect 37
            1.1.2  Trends 38
     1.2  The Role of Water Vapor in GPS Geodesy and Navigation 38
            1.2.1  NAVSTAR GPS 38
            1.2.2  Tropospheric Delays and GPS 39
     1.3  Water Vapor Observing Systems 39
            1.3.1  Description of Selected Sensors 39
            1.3.2  Synopsis 43
     1.4  Objectives and Structure of this Thesis 43
            1.4.1  Objectives of this Thesis 43
            1.4.2  Structure of this Thesis 44
 
2.  Principles of GPS Data Processing 47
     2.1  Processing Overview 47
            2.1.1  Pre-Processing 47
            2.1.2  Network Filtering 48
            2.1.3  Post-Filter Processing 48
            2.1.4  Realization 49
     2.2  Observations and Observation Equations 50
            2.2.1  Pseudo-Ranges 50
            2.2.2  Carrier Phase Measurements 51
                  2.2.2.1  Double Differences 53
                  2.2.2.2  Synchronization Problem 54
                  2.2.2.3  Degradation due to Selective Availability 55
                  2.2.2.4  Antenna Orientation Problem 57
                  2.2.2.5  Hardware Biases 58
                  2.2.2.6  Relativistic Effects 59
            2.2.3  Linear Combinations 60
            2.2.4  Ionospheric Error 62
                  2.2.4.1  First Order Effect 63
                  2.2.4.2  Second Order Effect 64
                  2.2.4.3  Interpolation in IONEX-Files 65
                        2.2.4.3.1  Computation of Ionospheric Points 66
                        2.2.4.3.2  Horizontal Interpolation 66
                        2.2.4.3.3  Temporal Interpolation 66
            2.2.5  Cycle Slip Detection and Repair 67
            2.2.6  Multipath Detection 68
     2.3  Site Displacements and Corrections 69
            2.3.1  Velocity Correction 70
            2.3.2  Solid Earth Tides 71
            2.3.3  Pole Tide 73
            2.3.4  Ocean Loading 73
            2.3.5  Antenna Eccentricity 74
            2.3.6  Antenna Phase Center Corrections 74
                  2.3.6.1  Antenna Phase Center Offset 75
                  2.3.6.2  Elevation-Dependent Phase Center
                               Variations

76
     2.4  Handling Precise Orbits 76
            2.4.1  Format Conversion of Broadcast Orbits 77
            2.4.2  Orbit Interpolation 79
            2.4.3  Epoch of Signal Transmission and Receiver
                      Clock Check

81
                  2.4.3.1  Epoch of Signal Transmission 81
                  2.4.3.2  Check of Receiver Clock Error Behavior 85
            2.4.4  Antenna Phase Center Eccentricity Correction 86
            2.4.5  Eclipsing Season 88
     2.5  Parameter Estimation Techniques 91
            2.5.1  Least-Squares Adjustment 91
                  2.5.1.1  Observation Vector, Design Matrix and
                               Stochastic Model

92
                  2.5.1.2  Adjustment Algorithm 93
                  2.5.1.3  Iterating on a Previous Solution 95
                  2.5.1.4  Blunder Detection 95
                        2.5.1.4.1  Global Test 95
                        2.5.1.4.2  Blunder Detector of Residual-Type 96
                        2.5.1.4.3  Blunder Detector of Baarda- or
                                        Pope-Type

96
            2.5.2  Kalman Filtering 98
                  2.5.2.1  Observations and Covariance Matrix 98
                  2.5.2.2  State Vector, Transition and Prediction
                               of State

101
                  2.5.2.3  Design Matrix 103
                  2.5.2.4  Filter Update 105
                  2.5.2.8  Tuning of Stochastic Model 106
                  2.5.2.7  Backward Filtering 107
                        2.5.2.7.1  Optimal Estimation 107
                        2.5.2.7.2  Sub-Optimal Estimation 107
                  2.5.2.8  Blunder Detection 108
                        2.5.2.8.1  Level-D: Check of Innovations 109
                        2.5.2.8.2  Level-U: Check of Stochastic Model
                                        of the State Vector

110
                        2.5.2.8.3  Analysis of Post-Fit Residuals 111
                  2.5.2.9  Summarizing Coordinates 111
                        2.5.2.9.1  Arithmetic Weighted Mean 112
                        2.5.2.9.2  Median 112
                        2.5.2.9.3  Jump Detection 112
     2.6  Ambiguities 113
            2.6.1  Direct Fixing 113
            2.6.2  Indirect Fixing of the Ionosphere-Free Signal 115
                  2.6.2.1  Wide Lane Fixing 115
                        2.6.2.1.1  Code-Carrier-Combination 115
                        2.6.2.1.2  IONEX-Supported Carrier Solution 117
                  2.6.2.2  Narrow Lane Fixing 117
                  2.6.2.3  Nominal LC-Ambiguity 118
            2.6.3  Ambiguity Back-Tracing 118
     2.7  Geodetic Datum 119
            2.7.1  Datum Transformation 120
            2.7.2  Similarity Transformation 121
     2.8  Network Composition 123
            2.8.1  Centered Networks 123
            2.8.2  Shortest Baseline Networks 123
            2.8.3  Site Isolation Logic 124
     2.9  Network Partitioning 126
 
3.  Modeling and Estimating Tropospheric Propagation Delays 129
     3.1  Brief Overview of the Lower Atmosphere 129
            3.1.1  Pressure 129
            3.1.2  Temperature 131
            3.1.3  Water Vapor 131
     3.2  Modeling of Tropospheric Delays 131
            3.2.1  Generalized Functional Description 132
            3.2.1  Modeling Zenith Delays 133
                  3.2.1.1  Zenith Hydrostatic Delay 136
                        3.2.1.1.1  Hopfield Hydrostatic Delay Model 136
                        3.2.1.1.2  Saastamoinen Hydrostatic Delay Model 140
                        3.2.1.1.3  MOPS Hydrostatic Delay Model 142
                        3.2.1.1.4  Comparison of Hydrostatic Models 144
                  3.2.1.2  Zenith Wet Delay 145
                        3.2.1.2.1  Hopfield Wet Delay Model 146
                        3.2.1.2.2  Ifadis Wet Delay Model 147
                        3.2.1.2.3  Mendes Wet Delay Model 147
                        3.2.1.2.4  MOPS Wet Delay Model 147
                        3.2.1.2.5  Comparison of Wet Delay Models 149
            3.2.2  Projecting Zenith Delays into Slant Direction 149
                  3.2.2.1  Hydrostatic Mapping Functions 151
                        3.2.2.1.1  Saastamoinen Mapping Function 152
                        3.2.2.1.2  Chao Hydrostatic Mapping Function 153
                        3.2.2.1.3  Black Hydrostatic Mapping Function 153
                        3.2.2.1.4  Davis Hydrostatic Mapping Function 154
                        3.2.2.1.5  Ifadis Hydrostatic Mapping Function 155
                        3.2.2.1.6  Herring Hydrostatic Mapping Function 156
                        3.2.2.1.7  Niell Hydrostatic Mapping Function 157
                  3.2.2.2  Wet Mapping Functions 158
                        3.2.2.2.1  Chao Wet Mapping Function 158
                        3.2.2.2.2  Black Wet Mapping Function 158
                        3.2.2.2.3  Ifadis Wet Mapping Function 159
                        3.2.2.2.4  Herring Wet Mapping Function 159
                        3.2.2.2.5  Niell Wet Mapping Function 160
                  3.2.2.3  Gradient Mapping Functions 160
     3.3  Estimation of Tropospheric Parameters 161
            3.3.1  Zenith Wet Delays 161
            3.3.2  Horizontal Gradients 162
            3.3.3  Mapping Function Coefficients 163
            3.3.4  Error Budget and Stochastic Modeling 164
                  3.3.4.1  Position Error 164
                  3.3.4.2  Orbit Error 165
                  3.3.4.3  Convergence Error 165
                        3.3.4.3.1  Network Considerations for Absolute
                                        Delay Estimation

166
                        3.3.4.3.2  Relative Tropospheric Delay Estimation 167
                  3.3.4.4  Multipath 169
                  3.3.4.5  Hydrostatic Delay 169
                  3.3.4.6  Mapping Function 170
                  3.3.4.7  Measurement Noise 172
     3.4  Stochastic Properties of Zenith Wet Delays 172
            3.4.1  Stochastic Filtering 173
            3.4.2  Stochastic Processes 174
                  3.4.2.1  First Order Gauss-Markov Process 175
                  3.4.2.2  Random Walk 176
            3.4.3  Mean Process Noise Parameters from Time
                      Series Analysis

177
                  3.4.3.1  Results for the IGS Tracking Network 177
                  3.4.3.2  Process Noise Values 178
            3.4.4  Dynamic Tuning and Maximum Tuning 180
                  3.4.4.1  Methods of Dynamic and Maximum Process
                               Noise Definition

182
                  3.4.4.2  Validation Study 182
     3.5  Conversion of Wet Delays into Precipitable Water 184
            3.5.1  Relation between Integrated Water Vapor and
                      Zenith Wet Delay

184
            3.5.2  Relation between Precipitablöe Water and
                      Zenith Wet Delay

185
            3.5.3  Mean Temperature and Conversion Factor Q 186
                  3.5.3.1  Global Functions 187
                  3.5.3.2  Regional Functions 187
                  3.5.3.3  Individual Functions 188
                  3.5.3.4  Height Dependency 188
            3.5.4  Conversion Uncertainty 189
 
4.  Application of Numerical Weather Models 193
     4.1  Contents of Numerical Weather Fields 193
            4.1.1  Contents and Resolution of GDAS-Fields 194
            4.1.2  Height Systems 194
            4.1.3  Horizontal Coordinates 196
     4.2  Surface Data Extraction 197
            4.2.1  Surface Pressure 197
                  4.2.1.1  Interpolation Sequences 197
                  4.2.1.2  Vertical Interpolation 199
                  4.2.1.3  Horizontal Interpolation 201
                  4.2.1.4  Temporal Interpolation 203
            4.2.2  Surface Temperature 203
            4.2.3  Surface Humidity 204
     4.3  Mapping Function Coefficients and Horizontal Gradients 205
            4.3.1  Ray-Tracing Algorithm 205
                  4.3.1.1  Ray-Tracing 205
                  4.3.1.2  Alternative Ray-Tracing Algorithm 207
                  4.3.1.3  Horizontal Resolution 208
                  4.3.1.4  Vertical Resolution 208
            4.3.2  Ray-Tracing Analysis 208
     4.4  Gridded Tropospheric Correction Files (TROPEX) 209
            4.4.1  Contents and Structure of TROPEX Files 211
            4.4.2  Zenith Hydrostatic Delay 211
                  4.4.2.1  Surface Pressure 211
                  4.4.2.2  Vertical Profile Modeling 212
            4.4.3  Zenith Wet Delay 212
                  4.4.3.1  Integral Evaluation 212
                  4.4.3.2  Vertical Profile Modeling 213
            4.4.4  Other Atmospheric Properties 213
                  4.4.4.1  Mean Temperature of Troposphere 213
                  4.4.4.2  Temperature Lapse Rate 214
                  4.4.4.3  Height of the Tropopause 214
            4.4.5  Horizontal Interpolation in TROPEX Files 218
                  4.4.5.1  Distance Weighting 219
                  4.4.5.2  Gauss-Markov Weighting 219
                  4.4.5.3  Best Linear Unbiased Estimator (BLUE) 220
     4.5  Combination of NWM Data and GPS Estimates 221
            4.5.1  Observations, Parameters and Stochastic Model 222
            4.5.2  Functional Model 223
            4.5.4  Stochastic Optimization 225
                  4.5.4.1  Sensing Inconsistencies (Outlier Detection) 225
                  4.5.4.2  Variance Component Estimation 225
                  4.5.4.3  Pre-Weighting Approach 227
 
5.  Validation of Numerical Weather Model Data 229
     5.1  Surface Meteorological Data 229
            5.1.1  Surface Pressure 230
                  5.1.1.1  Impact of Vertical Interpolation 232
                  5.1.1.2  Long-Term Comparison 232
            5.1.2  Surface Temperature 232
            5.1.3  Relative Humidity 234
            5.1.4  Results for High-Resolution Weather Fields 238
     5.2  Temperature Lapse Rate 240
     5.3  Mean Temperature of the Troposphere 241
     5.4  NWM-derived Mapping Functions 241
 
6.  GPS Validation Experiments 247
     6.1  Long-term Experiment 248
            6.1.1  Availability Statistics 248
            6.1.2  Outlier Statistics 251
            6.1.3  Comparison with IGS Neutral Delays 251
            6.1.4  Systematic Effects 256
     6.2  Experiment OBER-I 256
            6.2.1  Availability and Reliability 256
            6.2.2  Comparison with IGS Zenith Neutral Delays 257
            6.2.3  Evaluation of Tropospheric Mapping Functions 262
            6.2.4  Horizontal Gradients 262
            6.2.5  Ionospheric Impact 263
            6.2.6  Elevation Masking 266
            6.2.7  Comparison with Radiosonde Data 266
     6.3  Experiment OBER-II 267
            6.3.1  Impact of Orbit Accuracy 267
            6.3.2  Comparison with Radiosonde Data 269
     6.4  EUREF/GREF Experiment 269
            6.4.1  Comparison with IGS Delays 269
            6.4.2  Conversion into Integrated Water Vapor 271
            6.4.3  Comparison of Integrated Water Vapor Results 272
            6.4.4  Comparison with Integrated Water Vapor from
                      Numerical Weather Fields
276
     6.5  Multipath Experiment / Receiver Comparison 276
     6.6  WVR Validation Experiment 280
            6.4.1  Integrated Water Vapor 281
                  6.4.1.1  Comparison of Results 281
                  6.4.1.2  Comparison of Different Configuration Settings 281
            6.4.2  Mapping Function Coefficients 285
            6.4.3  Horizontal Gradients 285
            6.4.4  Process Noise Definition 287
 
7.  Quality Assessment of TROPEX Data 291
     7.1  Vertical Reduction 291
            7.1.1  Pressure Scale Height 291
                  7.1.1.1  Impact of Scale Height on Hydrostatic Delay 291
                  7.1.1.2  Internal Consistency of Numerical Weather
                              Model

296
            7.1.2  Water Vapor Scale Height 297
            7.1.3  Summary 297
     7.2  Zenith Neutral Delays from GDAS Weather Fields 299
     7.3  Combined GDAS/GPS Solution Fields 312
 
8.  Résumé 315
     8.1  GPS Tropospheric Delay Estimation 315
            8.1.1  Error Budget 315
            8.1.2  Meteorological Inputs 317
     8.2  Gridded Tropospheric Correction Data 318
            8.2.1  NWM-derived Zenith Neutral Delays 318
            8.2.2  Combination of NWM and GPS Data Sets 319
     8.3  Economical and Technical Aspects 319
     8.4  Summary and Outlook 320
 
9.  References 323
 
Appendices 333
     Appendix I:    Process Noise Parameters 333
     Appendix II:   Conversion Coefficients for Mean Temperature 336
     Appendic III:  Comparison of IWV Conversion Uncertainties 339
     Appendix IV:  Mean Values for Water Vapor 342
     Appendix V:   Mean Values for Water Vapor Scale Heights 353
     Appendix VI:  TROPEX Format Description 355
 
Index of Keywords 361
 
Acknowledgements 364
 

 
Abstract

NAVSTAR GPS has become an important aid in navigation and precise space geodesy. Permanent tracking networks like the global IGS net of the International GPS Service for Geodynamics and regional densifications like the German Reference Frame GREF have become very valuable for many scientific applications. For parameter estimation in largescale networks, two major error sources have to be reduced, namely the orbit error of the GPS space vehicles and the propagation delay in the troposphere. In 1992, the IGS started to produce precise GPS orbits which became a standard product of high precision that virtually eliminated orbit uncertainties from the list of significant contributors to the overall error budget. The remaining problem is that of modeling wet delays with high precision. All conventional models have to fail in this task due to the impossibility of modeling wet delays solely from surface measurements like temperature and relative humidity. Actually, the non-hydrostatic component of the tropospheric propagation delay is highly influenced by the distribution of water vapor in the lower troposphere which cannot be sufficiently predicted with sole help of surface measurements. A work-around is to include atmospheric parameters as additional unknowns in the analysis of GPS data from permanent monitor stations that turns out to improve the quality of position estimates. Moreover, knowledge of zenith wet delays allows to obtain a highly interesting value for climatology and meteorology: integrated or precipitable water vapor being important for the energy balance of the atmosphere and holds share of more than 60% of the natural greenhouse effect. GPS can thereby contribute to the improvement of climate models and weather forecasting.

This work outlines the application of ground-based GPS to climate research and meteorology without omitting the fact that precise GPS positioning can also highly benefit from using numerical weather models for tropospheric delay determination for applications where GPS troposphere estimation is not possible, for example kinematic and rapid static surveys. In this sense, the technique of GPS-derived tropospheric delays is seen as mutually improving both disciplines, precise positioning as well as meteorology and climatology.

Chapters 1 to 4 constitute the theoretical part of this study with first introducing the reader to the importance of water vapor and tropospheric delays (Chapter 1) and outlining the principles of GPS data processing (Chapter 2) with special emphasis on tropospheric delay modeling (Chapter 3). Furthermore, a brief introduction to numerical weather models and extraction methods for needed data is given (Chapter 4) and approaches to combine both data sets - tropospheric delays from numerical weather fields and GPS delays - are described.

Chapters 5 to 7 describe several experiments to validate and assess the quality of numerical weather model data (Chapter 5), GPS-derived troposphere propagation delays (Chapter 6) and combined solutions (Chapter 7). Finally, a summary of the application of ground-based GNSS for tropospheric delay estimation is given (Chapter 8).
 


 
Zusammenfassung

NAVSTAR GPS ist inzwischen zu einer wichtigen Hilfe für die Navigation und präzise geodätische Raumverfahren herangewachsen. Permanente Netzwerke wie das IGS Netz des Internationalen GPS Service für Geodynamik und regionale Verdichtung wie beispielsweise das Deutsche Referenznetz DREF haben sich für viele wissenschaftliche Aufgaben als ausgesprochen wertvoll erwiesen. Zwei wesentliche Fehlerquellen müssen zum Zwecke genauer Parameterschätzung in großen Netzen jedoch reduziert werden: die Orbitfehler der GPS-Satelliten und die Laufzeitverzögerungen in der Troposphäre. 1992 begann der IGS mit der Produktion genauer GPS Bahnen und verschiedene Verbesserungen führten dazu, dass dieses Standardprodukt Orbit- Unsicherheiten in der praktischen Nutzung des GPS fast vollständig von der Liste der bedeutenden Fehlereinflüsse eliminiert hat. Es verbleibt das Problem, die feuchte Komponente der troposphärischen Laufzeitverzögerung mit hoher Genauigkeit zu modellieren. Alle konventionellen Modelle müssen in dieser Hinsicht zwangsläufig versagen, denn in der Tat wird die nicht-hydrostatische Komponente der troposphärischen Laufzeitverzögerung maßgeblich von der Verteilung des Wasserdampfes in der unteren Troposphäre beeinflusst, die nicht auf Grund der alleinigen Kenntnis von Oberflächen-Messungen wie Temperatur und relativer Luftfeuchtigkeit prädiziert werden kann. Aus diesem Grunde wird versucht, die feuchte Laufzeitverzögerung als zusätzliche Unbekannte in die Analyse der GPS-Daten von Permanentstationen aufzunehmen und die so erzielten Ergebnisse verbessern zweifelsohne die Qualität der Positionsbestimmung. Weiterhin erlaubt die Kenntnis der feuchten Laufzeitverzögerung aber auch die Ableitung einer für Klimatologie und Meteorologie interessanten Größe, nämlich der des integrierten Wasserdampf-Gehaltes, die für den Energiehaushalt der Atmosphäre von großer Bedeutung und verursacht mehr als 60% des natürlichen Treibhaus-Effektes. GPS kann damit zur Verbesserung von Klima- und Wettervorhersage-Modellen beitragen.

Diese Arbeit stellt die Anwendung des bodengestützten GPS für Klimaforschung und Meteorologie dar, ohne dabei die Tatsache zu vernachlässigen, dass die präzise GPS Positionierung ebenfalls stark von der Nutzung numerischer Wettermodelle zum Zwecke der Bestimmung des Troposphären-Fehlers profitieren kann, nämlich bei Anwendungen, welche die Mitschätzung dieses Fehlers nicht erlauben, beispielsweise im Bereich des kinematischen GPS. In diesem Sinne wird die Technik der GPS-basierten Bestimmung troposphärischer Laufzeitverzögerungen als für beide Disziplinen gewinnbringend betrachtet, für die präzise Positionsbestimmung genauso wie für Meteorologie und Klimatologie.

Kapitel 1 bis 4 bilden den theoretischen Teil dieser Arbeit. Zunächst wird der Leser in die Thematik eingeführt (Kapitel 1) und anschließend werden die Grundlagen der GPS Daten- Prozessierung beschrieben (Kapitel 2), wobei besonderer Wert auf die Modellierung der troposphärischen Laufzeitverzögerung gelegt wird (Kapitel 3). Weiterhin wird eine kurze Einführung in numerische Wettermodelle sowie in die Methoden zur Extraktion der benötigten Daten gegeben (Kapitel 4) und Ansätze zur Kombination beider Datensätze - troposhärischer Verzögerungen aus numerischen Wetterfeldern und GPS Verzögerungen - werden beschrieben.

Kapitel 5 bis 7 beschreiben verschiedene Experimente zur Validierung und Qualitätsabschätzung von numerischen Wettermodell-Daten (Kapitel 5), GPS-basierten troposphärischen Laufzeitverzögerungen (Kapitel 6) und kombinierten Lösungen (Kapitel 7). Schließlich wird eine Zusammenfassung der Anwendung von GNSS für bodengestützte Bestimmung troposphärischer Parameter gegeben (Kapitel 8).
 


 
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