FAST PRECISE GPS POSITIONING IN THE PRESENCE OF IONOSPHERIC DELAYS

Transcription

1 FAST PRECISE GPS POSITIONING IN THE PRESENCE OF IONOSPHERIC DELAYS Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof.dr.ir. J.T. Fokkema, voorzitter van het College voor Promoties, in het openbaar te verdedigen op dinsdag 17 december 2002 om uur door Dennis ODIJK geodetisch ingenieur geboren te Utrecht

2 Abstract Samenvatting Curriculum vitae Acknowledgements xv xvii xx xxi 1 Introduction _ Background Research objective and limitations Outline of the thesis Contributions of this research Software implementation 4 2 Setting up the precise relative GPS model "Introduction GPS signals Electro-magnetic waves GPS codes and carriers GPS modernization GPS code and phase observables Code or pseudo-range observable Carrier-phase observable ' GPS processing models Positioning or geometry-based models Non-positioning or geometry-free models GPS observation equations Simplifications 15

3 2.5.2 Non-positioning observation equations 17 2:5.3 Positioning observation equations Computation of the satellite positions General mathematical model Gauss-Markov model Partitioning of the mathematical model The functional model without atmospheric errors The rank-deficient functional model Rank deficiencies and ways to remove them The full-rank functional model The stochastic model The stochastic properties of GPS observables The structure of the variance-covariance matrix Undifferenced vs. double-differenced model Transformation matrix Double-differenced observables and vc-matrix Double-differenced design matrix and parameters Concluding remarks 37 Procedure for solving the GPS model Introduction Integer property of the DD ambiguities Three-step processing procedure Estimation procedure _ Validation procedure Admissible integer ambiguity estimators Integer rounding Integer bootstrapping (sequential conditional rounding) Integer least-squares search Decorrelating ambiguity transformation On the quality of the integer and real solutions Probability distribution of the integer ambiguities Properties of the integer normal distribution Probability distribution of the ambiguity-fixed parameters On the quality of the ambiguity-fixed parameters Evaluating the ambiguity success rate The integer normal distribution evaluated 62

4 xi Closed-form expression for the ambiguity success rate "3.7.3 Bounding the ambiguity success rate The bias-affected success rate Concluding remarks 68 4 The ionospheric error in GPS observations Introduction Division of the Earth's atmosphere Non-ionized part of the atmosphere Ionized part of the atmosphere The variability of the ionospheric free electron density Atmospheric propagation of the GPS signals Atmospheric refraction Separation of the atmospheric refraction Tropospheric refraction effects Ionospheric refraction effects The inhomogeneous, anisotropic and dispersive ionosphere Refractive index for the ionosphere Ionospheric first-, higher-order and bending effects The first-order delay and the Total Electron Content A single-layer ionosphere approximation Ionospheric mapping function Sensitivity to the height of the ionospheric layer Approximating the higher-order/bending effects Approximating the ionospheric second-order delay Approximating the ionospheric third-order delay Approximating the ionospheric bending effect Absolute ionospheric effects for GPS: An example Relative ionospheric effects Single-differenced ionospheric effects Double-differenced ionospheric effects Worst-case relative ionospheric effects for GPS Worst-case conditions Results ionospheric-phase effects: Absolute and relative Concluding remarks The ionosphere-weighted GPS model Introduction 103

5 5.2 The tropospheric error in the GPS model Additional rank deficiencies Combined range/tropospheric pseudo-observables Parameterization of zenith tropospheric delays (ZTDs) The ionospheric error in the GPS model Neglecting ionospheric higher-order and bending effects Parameterizing the first-order ionospheric slant delays Ionospheric pseudo-observables The ionosphere-weighted model The ionosphere-fixed model (a l = 0) The ionosphere-float model (a t = oo) Relation to the ionosphere-free phase combination Redundancy of the ionosphere-weighted model Closed-form vc-matrices of the parameters The reduced normal equations Simplifying the normal equations The geometry-free vc-matrices The geometry-based vc-matrices Analyzing the (formal) coordinate precision Single-epoch coordinate precision Multi-epoch coordinate precision Analyzing the (formal) ambiguity success rates Judging the ambiguity success rate Example success rates Robustness of the ionosphere-fixed model Ionosphere-biased ambiguity and coordinate solutions Example Concluding remarks 144 Fast GPS positioning using ionospheric information Introduction Fast positioning using global ionospheric models Klobuchar's ionospheric model Performance of Klobuchar's model Fast network-based GPS positioning Single-baseline vs. network-based approach Geometric vs. physical approach for spatial prediction

6 xiii VRS-based vs. area correction-based approach Three-step procedure Network processing Parameters in the network model Three-step network processing Example: Network ionospheric delays Ionospheric prediction in the network processing Example: Instantaneous network processing Generation of virtual reference station data Generating the VRS observations VRS phase and code observation equations Stochastic model of the VRS observables Atmospheric interpolation method Least-squares collocation Kriging Choice of the covariance function Properties of the interpolation method User's processing Accounting for ionospheric residuals Accounting for tropospheric residuals Number of frequencies Fast VRS-based positioning results Simulations using SCIGN data AGRS.NL network: Case Cabauw AGRS.NL network: Case Damwoude Concluding remarks Conclusions and recommendations Conclusions Recommendations 206 Bibliography 209 A The Kronecker product 221 B Undifferenced - double-differenced models 223 C Adjustment and testing procedure in GPSveQ 111 C.I Reduction of the normal equations 227

7 xiv C.2 Uncorrelated observations in time 229 D Computation of some receiver/satellite-dependent matrices 237 E Ionospheric delay time series as stochastic process 239 E.I Random-walk process 239 E.2 Integrated random-walk process 240