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Bernese GNSS Software
Version 5.2
Edited by
Rolf Dach, Simon Lutz,
Peter Walser, Pierre Fridez
November 2015
AIUB
Astronomical Institute, University of Bern
User manual of the Bernese GNSS Software, Version 5.2
Please send comments on the Bernese GNSS Software and
this manual as well as requests for copies to:
PD Dr. Rolf Dach
Astronomical Institute Phone: +41 − 31 − 631 85 91 (secretary)
University of Bern E-mail: rolf.dach@aiub.unibe.ch
Sidlerstrasse 5
CH–3012 Bern
Switzerland
For contact and support send e-mail to:
Pierre Fridez Phone: +41 − 31 − 631 85 93
E-mail: bernese@aiub.unibe.ch
ISBN: 978-3-906813-05-9 ; University of Bern, Bern Open Publishing.
DOI: 10.7892/boris.72297
Freely available online at http://www.bernese.unibe.ch .
This is an open access book licensed under a Creative Commons Attribution-
NonCommercial 4.0 Internationa l license (CC BY-NC 4.0). This license allows anyone
to download, share, reuse, reprint, adapt, distribute and/or copy the work providing the
original authors and source ar e credited and the purpose is non-commercial. No permis-
sion is required from the authors or the publisher in these cases. Further details about CC
BY–NC licenses are available at https://creativecommons.org/licenses/by-nc/4.0/
Copyright
c
Astronomical Institute, University of Bern
November 2015
Produced in Digital Print by Publikation Digital AG, Biel in December 2015.
Bernese GNSS Software
Version 5.2
Astronomical Institute, University of Bern
R. Dach,
F. Andritsch, D. Arnold, S. Bertone, P. Fridez, A. Jäggi,
Y. Jean, A. Maier, L. Mervart, U. Meyer, E. Orliac,
E. Ortiz–Geist, L. Prange, S. Scaramuzza, S. Schaer,
D. Sidorov, A. Sušnik, A. Villiger, P. Walser,
C. Baumann, G. Beutler, H. Bock, A. Gäde, S. Lutz,
M. Meindl, L. Ostini, K. Sośnica, A. Steinbach, D. Thaller
Important Ex ternal Contributors:
Federal Office of Topography swisstopo, Wabern, Switzerland
E. Brockmann, D. Ineichen, S. Lutz, S. Schaer
IAPG, Technische Universität München, Germany
U. Hugentobler, C. Rodriguez–Solano, P. Steigenberger
Federal Agency for Cartography and Geodesy, BKG, Germany
D. Thaller
IPG, Technische Universität Dresden, Germany
M. Fritsche, A. Rülke
The Version 5.2 is based on the Version 5.0 that had been developed
until May 2004 by many former institute members and several external
contributors.
Contents
1. Introduction and Overview 1
1.1. From Version 3 to Version 5 . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Main Objectives and General Characteristics . . . . . . . . . . . . . . . . 3
1.3. Program Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4. About this Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2. Fundamentals 19
2.1. Global Navigation Satellite Systems — A Shor t Review . . . . . . . . . . 19
2.1.1. GPS System Description . . . . . . . . . . . . . . . . . . . . . 20
2.1.1.1. GPS Satellites and Their Constellation . . . . . . . 20
2.1.1.2. The Satellite Signal . . . . . . . . . . . . . . . . . . 22
2.1.1.3. Signal Processing . . . . . . . . . . . . . . . . . . . 26
2.1.2. GLONASS System Description . . . . . . . . . . . . . . . . . . 27
2.1.2.1. GLONASS Satellites and Their Constellation . . . . 27
2.1.2.2. The Signals of the GLONASS Satellites . . . . . . . 30
2.1.2.3. Comparison between GPS and GLONASS . . . . . 31
2.2. GNSS Satellite Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.2. Celestial Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.2.1. The Keplerian Orbit . . . . . . . . . . . . . . . . . . 36
2.2.2.2. The Osculating Orbital Elements . . . . . . . . . . . 38
2.2.2.3. Deterministic Orbit Parameterizatio n . . . . . . . . 42
2.2.2.4. Pseudo–Stochastic Orbit Parameterization . . . . . 44
2.2.2.5. Variational Equations . . . . . . . . . . . . . . . . . 45
2.2.3. Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . 46
2.3. Observation Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.1. Code Pseudoranges . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.2. Phase Pseudoranges . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.3. Measurement Biases . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.4. Forming Differences . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.5. Receiver Clocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3.6. Linear Combinations of Observations . . . . . . . . . . . . . . . 51
2.3.6.1. Ionosphere–Free Linear Combination L
3
. . . . . . . 51
2.3.6.2. Geometry–Free Linear Combination L
4
. . . . . . . 52
2.3.6.3. Wide–Lane Linear Combination L
5
. . . . . . . . . 52
2.3.6.4. Melbourne–Wübbena Linear Combination L
6
. . . . 53
2.3.7. GLONASS Single–Difference Bias Term . . . . . . . . . . . . . 53
Page I
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