Table of Contents. Frequently Used Abbreviation... xvii

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1 GPS Satellite Surveying, 2 nd Edition Alfred Leick Department of Surveying Engineering, University of Maine John Wiley & Sons, Inc (Navtech order #1028) Table of Contents Preface... xiii Frequently Used Abbreviation... xvii Chapter 1: Introduction The outcome of GPS positioning A performance review Some geodetic considerations Chapter 2: Elements of Satellite Surveying Geocentric coordinate systems and their motions Precession and nutation The conventional terrestrial reference system Time systems Time in orders of magnitude Astronomic time scales Atomic time Need for coordination Link to earth rotation Time and earth orientation services Satellite orbital motion Kepler elements Normal orbital theory Satellite visibility and topocentric motion Disturbed satellite motion Gravitational field of the earth Acceleration due to the sun and the moon Solar radiation pressure Chapter 3: The Global Positioning System Space segment GPS satellites Orbital configuration Satellite transmissions Overview Space vehicle and GPS time systems GPS signal structure The navigation message Control segment and other support Receivers Some fundamentals Bandwidth... 79

2 Power Filtering Frequency translation and multiplication Spread spectrum Cross-correlation Locking and tracking Modern geodetic receivers Pseudorange measurement accuracy Coping and antispoofing Squaring Code-aided squaring Cross-correlation Z tracking Chapter 4: Adjustment Computations 4.1 Elements Statistical nature of surveying measurement Elementary statistical concepts Observational errors Accuracy and precision Stochastic and mathematical models Propagation of mean and variance covariance Mixed adjustment model Linearization Minimization and solution Cofactor matrices A posteriori variance of unit weight Iterations Observation equation and condition equation models Sequential solution Weighed parameters and conditions between parameters Minimal and inner constrain adjustments Statistics in least-squares adjustments Multivariate normal distribution Distribution of V T PV Testing V T PV and ' V T PV General linear hypothesis Ellipses as confidence regions Properties of standard ellipses Other measures of precision Reliability Redundancy numbers Controlling type II error for a single blunder Internal reliability Absorption External reliability Correlated cases Blunder detection The W test Data snooping Changing weights of observations...174

3 Chapter 5: Least-Squares Adjustment Examples Introduction Adjustment of a simple network on the mapping plane Minimal constraint for network adjustment on the mapping Inner constraint for network adjustment on the mapping plane Adjustment of the complete network on the mapping plane Adjustment of the complete network with additional information Detecting poor network geometry: the dangerous circle Closed traverse adjustment on the mapping plane Open traverse adjustment on the mapping plane Adjustment of leveling observations Stochastic models for distances and angles Chapter 6: Links to Physical Observations Geoid Ellipsoid of revolution Location of the ellipsoid and reductions of observations Chapter 7: The Three-Dimensional Geodetic Model The partial derivatives Additional remarks An example Chapter 8: GPS Observables Pseudoranges The navigation solution DOP factors Carrier phases Undifferenced carrier phase observable Single differences Double differences Triple differences Delta ranges Evaluation The clock error terms Receiver clocks The question of simultaneity Satellite clock corrections Residual satellite clock error Summary of undifferenced expressions Singularities A priori position errors Cancellation of common mode errors Navigation solution Relative positioning Connection to other systems The Doppler connection The VLBI connection Selective availability...283

4 Chapter 9: Propagation Media, Multipath, and Phase Center The atmosphere in brief Elements of wave propagation Ionospheric effects on GPS observables Code delays and phase advanced Single frequency solutions Ionospheric plate model Daily cosine model Ionospheric point model Generalization in azimuth and altitude Broadcast message and ionospheric model Dual frequency ionospheric free solutions Dual frequency ionospheric solutions Tropospheric effects on GPS observables Multipath and phase center Chapter 10: Processing GPS Carrier Phases Getting acquainted with the observables Dual-frequency epoch solutions Geometry of epoch solutions Widelaning with undifferenced observations Widelaning and extra wide lancing with double-difference carrier phases Primary functions observables Description of a unified approach Static positioning Observation equations for double and trip differences Cycle slip detection and correction Ambiguity fixing An ordering scheme Testing complete sets Testing ambiguity differences Sequential reduction of ambiguity range Eliminating all position parameters Dual frequency ambiguities for short baselines Discernibility Primary and secondary satellites Normal points Ambiguity function Kinematic positioning Initialization on the ground Initialization on the fly Search volume and trial ambiguities Propagation of trial positions OTF techniques Kalman filtering formulation Long baselines Independent baselines Constraining the ionosphere Orbital relaxation Aspects of real-time GPS...402

5 Carrier phase and pseudorange corrections RTCM-104 standard WADGPS Chapter 11: Network Adjustments GPS vector networks A simulated example Combination through rotation and scaling A simulated example Accurate geoid undulations The normal gravity field Computing geoid undulations Discussion of selected GPS projects The Montgomery County geodetic network The SLC engineering survey The SSC ring Orange County densification Chapter 12: Ellipsoidal and Conformal Mapping Models Reductions to the ellipsoid The ellipsoidal surface model The conformal mapping model The transverse macerator model The Lambert conformal model State Plane Coordinate Systems (STC) Chapter 13: Useful Transformations Similarity transformation for nearly aligned coordinate systems Transforming ellipsoidal positions in a small region Chapter 14: Datums, Standards, and Specifications Reference frame Standards and specifications Existing classification standards The impact of GPS Recommendations Revision of the GPS Standards Position accuracy ACP Referencing Remarks concerning specifications To be continued Appendix A: Elements from Linear Algebra A.1 Determinants A.2 Eigenvalues and eigenvectors A.3 Diagonalization theorem A.4 Quadratic forms A.5 Inverse of a nonsingular matrix A.6 Differentiation of quadratic forms Appendix B: Linearization...512

6 Appendix C: One-Dimensional Distributions C.1 Chi-square distribution C.2 Normal distribution C.3 t distribution C.4 F distribution C.5 Distribution of selected functions C.5.1 The sum of normal distributed variables C.5.2 The square of standardized normal distribution C.5.3 The sum of chi-square distributed variables C.5.4 The sum of squares of standardized normal distributed variables C.5.5 The sum of squares of normal distributed variables C.6 Hypothesis tests C.7 Goodness-of fit test Appendix D: Rotation Matrices Appendix E: Selected Expressions from Spherical Trigonometry Appendix F: Sample Network Appendix G: GLONASS References Abbreviations for Frequently Used References Author Index Subject Index...555