GPS Stochastic Modelling: Signal Quality Measures and ARMA Processes

345 Pages·2013·15.39 MB·English

by  Xiaoguang Luo (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Xiaoguang Luo
GPS Stochastic
Modelling
Signal Quality Measures
and ARMA Processes
Springer Theses
Recognizing Outstanding Ph.D. Research
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Xiaoguang Luo
GPS Stochastic Modelling
Signal Quality Measures and ARMA
Processes
Doctoral Thesis accepted by
the Karlsruhe Institute of Technology, Karlsruhe, Germany
123
Author Supervisor
Dr.-Ing. XiaoguangLuo Prof.Dr.-Ing.habil.Dr.h.c.BernhardHeck
Geodetic Institute Geodetic Institute
Karlsruhe Instituteof Technology(KIT) Karlsruhe Instituteof Technology(KIT)
Karlsruhe Karlsruhe
Germany Germany
Co-Supervisor
Prof.Dr.-Ing. habil.HansjörgKutterer
Federal AgencyforCartography and
Geodesy (BKG)
Frankfurt amMain
Germany
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-642-34835-8 ISBN 978-3-642-34836-5 (eBook)
DOI 10.1007/978-3-642-34836-5
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012953558
(cid:2)Springer-VerlagBerlinHeidelberg2013
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Parts of this thesis have been published in the following journal and
proceedings articles:
Luo, X., Mayer, M., & Heck, B. (2011). On the probability distribution of GNSS
carrier phase observations. GPS Solutions, 15(4), 369–379. doi:10.1007/
s10291-010-0196-2.
Luo, X., Mayer, M., & Heck, B. (2011). Verification of ARMA identification for
modelling temporal correlations of GNSS observations using the ARMASA
toolbox. Studia Geophysica et Geodaetica, 55(3), 537–556. doi:10.1007/
s11200-011-0033-2.
Luo,X.,Mayer,M.,&Heck,B.(2008).ImprovingthestochasticmodelofGNSS
observations by means of SNR-based weighting. In: M. G. Sideris (Ed.),
Observing our changing Earth, Proceedings of the 2007 IAG General Assembly,
Perugia,Italy,2–13July,IAGSymposia,vol.133,Berlin:Springer,pp.725–734.
doi:10.1007/978-3-540-85426-5_83.
Luo, X., Mayer, M., & Heck, B. (2008). Erweiterung des stochastischen Modells
von GNSS-Beobachtungen unter Verwendung der Signalqualität. Zeitschrift für
Geodäsie, Geoinformation und Landmanagement (ZfV), 133(2), 98–107.
‘‘There is one thing even more vital to science
thanintelligentmethods;andthatis,thesincere
desiretofindoutthetruth,whateveritmaybe.’’
CharlesSandersPeirce(1839–1914)
AmericanMathematicianandLogician
Date of the oral examination: 14.02.2012
Supervisor’s Foreword
The Global Positioning System (GPS) has become an efficient tool for a wide
range of applications. However, when analysing GPS data, the stochastic model
characterising the precision and correlations of GPS observations is usually sim-
plified and incomplete. Extending the GPS stochastic model is the goal of this
thesis,usingsignal-to-noiseratio(SNR)measurementsandtimeseriesanalysisof
observation residuals.
First, this work proposes a novel SNR-based observation weighting model,
which sufficiently copes with weak signals, multipath effects and atmospheric
variations. Its employment in high precision, static relative positioning signifi-
cantly improves the results of ambiguity resolution, troposphere parameter esti-
mation and site coordinate determination. Next, applying autoregressive moving
average (ARMA) processes, the temporal correlation of GPS observation noise is
investigated in a mathematically rigorous manner. The outcomes are statistically
valid and physically interpretable, showing the influences of multipath effects,
satellite geometry and atmospheric conditions.
This study is a milestone and a key step towards a realistic GPS stochastic
model and provides an excellent example of statistical verification and physical
interpretation of results. Furthermore, this work includes a comprehensive
description of different methods, which are applicable to various other data sets.
Lastbutnotleast,thisthesisgivesanup-to-dateoverviewoftheGPSerroreffects
and an illustrative presentation of the stochastic components.
Karlsruhe, October 15, 2012 Prof. Dr.-Ing. habil. Dr. h.c. Bernhard Heck
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Acknowledgments
Although this dissertation represents an individual work, it would not have been
writtenwithoutthesincerehelpandsupport frommanypeople.Itisapleasureto
express mygratitude toall thosewho madethisthesis possible. Becauseofthem,
my graduate experience has become one that I will never forget and forever
appreciate.
In the first place, I owe my deepest gratitude to my supervisor, Prof. Dr.-Ing.
habil. Dr. h.c. B. Heck, who introduced me to the exciting world of research. He
gave me not only the freedom and courage to explore on my own, but also the
guidance and sympathy to overcome difficult situations. His thorough corrections
to my papers have considerably improved my writing skills, and his valuable
suggestions to the first version of this work are gratefully acknowledged. I have
beenveryfortunatetohavesuchacompetent,patientandsympatheticsupervisor.
I would also like to thank Prof. Dr.-Ing. habil. H. Kutterer for accepting to co-
supervise my Ph.D., as well as constructive discussions and valuable comments.
All of my colleagues at GIK (Geodetic Institute) and IPF (Institute of Photo-
grammetryandRemoteSensing)aredeeplyacknowledgedfortheircontributionto
anenjoyableworkingatmosphere.Iwouldliketoextendaspecialgratitudetothe
GNSS group headed by Dr.-Ing. M. Mayer for a great deal of support and
insightful discussions, helping me enrich my ideas and knowledge. Many thanks
also go to Dipl.-Ing. A. Knöpfler and Dipl.-Ing. T. Fuhrmann for performing site
quality assessments and providing PPP residuals, respectively. I benefited much
fromtheoutstandingworksdonebyHowind(2005)andTeusch(2006).Iammuch
delighted to thank Dr. K. Fleming for proofreading my thesis.
Furthermore, I am grateful to the German Research Foundation (DFG) for
supporting the project ‘‘Extending the stochastic model of GPS observations by
modelling physical correlations’’. The former University of Karlsruhe (TH) (now
Karlsruhe Institute of Technology, KIT) is acknowledged for granting me the
Scholarship in Accordance with the Law on Graduate Funding from the Federal
State of Baden-Württemberg (LGFG). In addition, I appreciate the financial sup-
portfromtheGermanAcademicExchangeService(DAAD)withintheframework
of the PROBRAL program with the Laboratory of Space Geodesy (LAGE) at the
Federal University of Paraná (UFPR), Curitiba, Brazil. For the successful col-
laborationandtheunforgettableexperiencesinBrazil,Iowemysincerethanksto
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