Basic Observation Equations

This chapter introduces the fundamental observation equations for multiconstellation global navigation satellite systems (GNSS s). It starts with an introduction of the basic observation equations for pseudorange, carrier-phase, and Doppler measurements. In the remainder of the chapter, the parameters used in modeling the basic observation equations are discussed. The parameters covered in the discussion are relativistic effects, atmospheric delays, the carrier-phase wind-up effect, antenna phase-center offset and variation, pseudorange and carrier-phase biases, and finally multipath errors and receiver noise.

[1]  Gerhard Wübbena,et al.  Tests of phase center variations of various GPS antennas, and some results , 2002 .

[2]  O. Montenbruck,et al.  Spin rate estimation of sounding rockets using GPS wind-up , 2008 .

[3]  W. I. Bertiger,et al.  Effects of antenna orientation on GPS carrier phase , 1992 .

[4]  Flavien Mercier,et al.  Zero-difference Integer Ambiguity Fixing on Single Frequency Receivers , 2009 .

[5]  J. W. Marini,et al.  Correction of Satellite Tracking Data for an Arbitrary Tropospheric Profile , 1972 .

[6]  Ling Huang,et al.  On the Convergence of Ionospheric Constrained Precise Point Positioning (IC-PPP) Based on Undifferential Uncombined Raw GNSS Observations , 2013, Sensors.

[7]  Oliver Montenbruck,et al.  The Effect of Correlator and Front-End Design on GNSS Pseudorange Biases for Geodetic Receivers , 2015 .

[8]  Alan Dodson,et al.  Ambiguity resolution in precise point positioning with hourly data , 2009 .

[9]  Wei Wang,et al.  A Study on the Beidou IGSO/MEO Satellite Orbit Determination and Prediction of the Different Yaw Control Mode , 2013 .

[10]  Noriyasu Inaba,et al.  Design and development of the first Quasi-Zenith Satellite attitude and orbit control system , 2009, 2009 IEEE Aerospace conference.

[11]  Peter Steigenberger,et al.  Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite , 2012, GPS Solutions.

[12]  Richard B. Langley,et al.  Evaluation of High-Precision, Single-Frequency GPS Point Positioning Models , 2004 .

[13]  I. Shapiro,et al.  Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length , 1985 .

[14]  H. Schuh,et al.  Short Note: A global model of pressure and temperature for geodetic applications , 2007 .

[15]  Kefei Zhang,et al.  Short Note: On the Relativistic Doppler Effect for Precise Velocity Determination using GPS , 2006 .

[16]  Yoaz E. Bar-Sever,et al.  A new model for GPS yaw attitude , 1996 .

[17]  Dmitry Kozlov,et al.  CENTIMETER-LEVEL, REAL TIME KINEMATIC POSITIONING WITH GPS + GLONASS C/A RECEIVERS , 1998 .

[18]  H. Schuh,et al.  Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data , 2006 .

[19]  Jan Kouba,et al.  Improved relativistic transformations in GPS , 2004 .

[20]  Peter Steigenberger,et al.  Generation of a consistent absolute phase-center correction model for GPS receiver and satellite antennas , 2007 .

[21]  Richard B. Langley,et al.  High-Precision Single-Frequency GPS Point Positioning , 2003 .

[22]  Per K. Enge,et al.  Global positioning system: signals, measurements, and performance [Book Review] , 2002, IEEE Aerospace and Electronic Systems Magazine.

[23]  Bernhard Hofmann-Wellenhof,et al.  GNSS - Global Navigation Satellite Systems , 2008 .

[24]  Oliver Montenbruck,et al.  A study on the dependency of GNSS pseudorange biases on correlator spacing , 2016, GPS Solutions.

[25]  Jan Kouba,et al.  A simplified yaw-attitude model for eclipsing GPS satellites , 2009 .

[26]  G. D. Thayer,et al.  An improved equation for the radio refractive index of air , 1974 .

[27]  B Görres,et al.  Absolute calibration of GPS antennas: laboratory results and comparison with field and robot techniques , 2006 .

[28]  Peter Teunissen,et al.  Review and principles of PPP-RTK methods , 2015, Journal of Geodesy.

[29]  C. Mo ller,et al.  The Theory of Relativity , 1953 .

[30]  Jan Askne,et al.  Estimation of tropospheric delay for microwaves from surface weather data , 1987 .

[31]  Neil Ashby,et al.  Relativity in the Global Positioning System , 2003, Living reviews in relativity.

[32]  Martin Schmitz,et al.  Results of Absolute Field Calibration of GPS Antenna PCV , 1998 .

[33]  M. Rothacher,et al.  Estimation of elevation-dependent satellite antenna phase center variations of GPS satellites , 2003 .

[34]  G. Gendt,et al.  Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations , 2008 .

[35]  Avram K. Tetewsky,et al.  Carrier Phase Wrap-Up Induced by Rotating GPS Antennas , 1996 .

[36]  Martin Schmitz,et al.  Automated Absolute Field Calibration of GPS Antennas in Real-Time , 2000 .

[37]  I. Simmonds,et al.  Modeling δ18O in tropical precipitation and the surface ocean for present‐day climate , 2006 .

[38]  Ch. Reigber,et al.  Satellite antenna phase center offsets and scale errors in GPS solutions , 2003 .

[39]  René Warnant,et al.  Reliability of the TEC Computed Using GPS Measurements — The Problem of Hardware Biases , 1997, Acta Geodaetica et Geophysica Hungarica.

[40]  H. S. Hopfield.  Two- quartic tropospheric refractivity profile for correcting satellite data , 1969 .

[41]  Ben A. van der Pluijm,et al.  Mineralogical characterization of protolith and fault rocks from the SAFOD Main Hole , 2006 .

[42]  Martin Schmitz,et al.  A NEW APPROACH FOR FIELD CALIBRATION OF ABSOLUTE GPS ANTENNA PHASE CENTER VARIATIONS , 1997 .

[43]  Oliver Montenbruck,et al.  Code Biases in Multi-GNSS Point Positioning , 2013 .

[44]  Jing Guo,et al.  Precise orbit determination for COMPASS IGSO satellites during yaw maneuvers , 2013 .

[45]  Andrew Simsky,et al.  Origin and Compensation of GLONASS Inter-frequency Carrier Phase Biases in GNSS Receivers , 2012 .

[46]  A. Niell.  Global mapping functions for the atmosphere delay at radio wavelengths , 1996 .

[47]  Florian Dilssner,et al.  The GLONASS-M satellite yaw-attitude model , 2011 .

[48]  J.-P. Berthias,et al.  Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination , 2007 .

[49]  Gerald L. Mader,et al.  GPS Antenna Calibration at the National Geodetic Survey , 1999, GPS Solutions.

[50]  Alessandro Caporali,et al.  An analysis of intersystem biases for multi-GNSS positioning , 2015, GPS Solutions.

[51]  Markus Rothacher,et al.  Comparison of Absolute and Relative Antenna Phase Center Variations , 2001, GPS Solutions.

[52]  Gerhard Wübbena,et al.  GPS Block II/IIA Satellite Antenna Testing using the Automated Absolute Field Calibration with Robot , 2007 .

[53]  Pawel Wielgosz,et al.  Accounting for Galileo–GPS inter-system biases in precise satellite positioning , 2014, Journal of Geodesy.

[54]  Peter Steigenberger,et al.  QZS-1 Yaw Attitude Estimation Based on Measurements from the CONGO Network , 2011 .

[55]  Blair Fonville,et al.  ACCOUNTING FOR TIMING BIASES BETWEEN GPS, MODERNIZED GPS, AND GALILEO SIGNALS , 2005 .

[56]  R. Langley,et al.  Limiting Factors in Tropospheric Propagation Delay Error Modelling for GPS Airborne Navigation , 1996 .

[57]  Tim Murphy,et al.  GPS Antenna Group Delay Variation Induced Errors in a GNSS Based Precision Approach and Landing Systems , 2007 .

[58]  Lambert Wanninger,et al.  Carrier-phase inter-frequency biases of GLONASS receivers , 2012, Journal of Geodesy.

[59]  A. E. Niell,et al.  Improved atmospheric mapping functions for VLBI and GPS , 2000 .

[60]  O. Ovstedal,et al.  Absolute Positioning with Single-Frequency GPS Receivers , 2002 .

[61]  J. Saastamoinen.  Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging Satellites , 2013 .

[62]  Martin Schmitz,et al.  Precise GPS Positioning Improvements by Reducing Antenna and Site Dependent Effects , 1998 .

[63]  Xiaojie Li,et al.  Accuracy Analyses of Precise Orbit Determination and Timing for COMPASS/Beidou-2 4GEO/5IGSO/4MEO Constellation , 2013 .

[64]  Per Enge,et al.  Gps Navigation Algorithms , 1996 .

[65]  Paul Collins,et al.  Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing , 2010 .

[66]  T. Springer,et al.  GPS IIF yaw attitude control during eclipse season , 2011 .

[67]  Jan Kouba,et al.  Relativistic Time Transformations in GPS , 2002, GPS Solutions.

[68]  Bruce R. Schupler,et al.  Signal Characteristics of GPS User Antennas , 1994 .

[69]  Peter Teunissen,et al.  Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution , 2013, GPS Solutions.

[70]  Frank van Graas,et al.  GPS Antenna Phase and Group Delay Corrections , 2004 .

[71]  H. Schuh,et al.  Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium‐Range Weather Forecasts operational analysis data , 2006 .