Heft 73/2001

des Instituts für Geodäsie

Heft 73/2001


On Ground-Based GPS Tropospheric Delay Estimation

364 S.

Auflage:  150

ISSN:  0173-1009





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.

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

(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

            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
          Double Differences 53
          Synchronization Problem 54
          Degradation due to Selective Availability 55
          Antenna Orientation Problem 57
          Hardware Biases 58
          Relativistic Effects 59
            2.2.3  Linear Combinations 60
            2.2.4  Ionospheric Error 62
          First Order Effect 63
          Second Order Effect 64
          Interpolation in IONEX-Files 65
                Computation of Ionospheric Points 66
                Horizontal Interpolation 66
                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
          Antenna Phase Center Offset 75
          Elevation-Dependent Phase Center

     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

          Epoch of Signal Transmission 81
          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
          Observation Vector, Design Matrix and
                               Stochastic Model

          Adjustment Algorithm 93
          Iterating on a Previous Solution 95
          Blunder Detection 95
                Global Test 95
                Blunder Detector of Residual-Type 96
                Blunder Detector of Baarda- or

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

          Design Matrix 103
          Filter Update 105
          Tuning of Stochastic Model 106
          Backward Filtering 107
                Optimal Estimation 107
                Sub-Optimal Estimation 107
          Blunder Detection 108
                Level-D: Check of Innovations 109
                Level-U: Check of Stochastic Model
                                        of the State Vector

                Analysis of Post-Fit Residuals 111
          Summarizing Coordinates 111
                Arithmetic Weighted Mean 112
                Median 112
                Jump Detection 112
     2.6  Ambiguities 113
            2.6.1  Direct Fixing 113
            2.6.2  Indirect Fixing of the Ionosphere-Free Signal 115
          Wide Lane Fixing 115
                Code-Carrier-Combination 115
                IONEX-Supported Carrier Solution 117
          Narrow Lane Fixing 117
          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
          Zenith Hydrostatic Delay 136
                Hopfield Hydrostatic Delay Model 136
                Saastamoinen Hydrostatic Delay Model 140
                MOPS Hydrostatic Delay Model 142
                Comparison of Hydrostatic Models 144
          Zenith Wet Delay 145
                Hopfield Wet Delay Model 146
                Ifadis Wet Delay Model 147
                Mendes Wet Delay Model 147
                MOPS Wet Delay Model 147
                Comparison of Wet Delay Models 149
            3.2.2  Projecting Zenith Delays into Slant Direction 149
          Hydrostatic Mapping Functions 151
                Saastamoinen Mapping Function 152
                Chao Hydrostatic Mapping Function 153
                Black Hydrostatic Mapping Function 153
                Davis Hydrostatic Mapping Function 154
                Ifadis Hydrostatic Mapping Function 155
                Herring Hydrostatic Mapping Function 156
                Niell Hydrostatic Mapping Function 157
          Wet Mapping Functions 158
                Chao Wet Mapping Function 158
                Black Wet Mapping Function 158
                Ifadis Wet Mapping Function 159
                Herring Wet Mapping Function 159
                Niell Wet Mapping Function 160
          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
          Position Error 164
          Orbit Error 165
          Convergence Error 165
                Network Considerations for Absolute
                                        Delay Estimation

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

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

          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

            3.5.2  Relation between Precipitablöe Water and
                      Zenith Wet Delay

            3.5.3  Mean Temperature and Conversion Factor Q 186
          Global Functions 187
          Regional Functions 187
          Individual Functions 188
          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
          Interpolation Sequences 197
          Vertical Interpolation 199
          Horizontal Interpolation 201
          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
          Ray-Tracing 205
          Alternative Ray-Tracing Algorithm 207
          Horizontal Resolution 208
          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
          Surface Pressure 211
          Vertical Profile Modeling 212
            4.4.3  Zenith Wet Delay 212
          Integral Evaluation 212
          Vertical Profile Modeling 213
            4.4.4  Other Atmospheric Properties 213
          Mean Temperature of Troposphere 213
          Temperature Lapse Rate 214
          Height of the Tropopause 214
            4.4.5  Horizontal Interpolation in TROPEX Files 218
          Distance Weighting 219
          Gauss-Markov Weighting 219
          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
          Sensing Inconsistencies (Outlier Detection) 225
          Variance Component Estimation 225
          Pre-Weighting Approach 227
5.  Validation of Numerical Weather Model Data 229
     5.1  Surface Meteorological Data 229
            5.1.1  Surface Pressure 230
          Impact of Vertical Interpolation 232
          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
     6.5  Multipath Experiment / Receiver Comparison 276
     6.6  WVR Validation Experiment 280
            6.4.1  Integrated Water Vapor 281
          Comparison of Results 281
          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
          Impact of Scale Height on Hydrostatic Delay 291
          Internal Consistency of Numerical Weather

            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


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).


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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