Improving the Precision and Accuracy of Geodetic GPS

374 Pages·2012·25.52 MB·English

Improving the Precision and Accuracy of
Geodetic GPS:
Applications to Multipath and Seismology
by
Andria L. Bilich
B.S., University of Texas at Austin, 1999
M.S., University of Colorado, 2004
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulflllment
of the requirements for the degree of
Doctor of Philosophy
Department of Aerospace Engineering Sciences
2006
This thesis entitled:
Improving the Precision and Accuracy of
Geodetic GPS:
Applications to Multipath and Seismology
written by Andria L. Bilich
has been approved for the Department of Aerospace Engineering Sciences
Kristine M. Larson
Penina Axelrad
Date
The flnal copy of this thesis has been examined by the signatories, and we flnd that both the
content and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.
Bilich, Andria L. (Ph.D., Aerospace Engineering Sciences)
Improving the Precision and Accuracy of
Geodetic GPS:
Applications to Multipath and Seismology
Thesis directed by Prof. Kristine M. Larson
TheGlobalPositioningSystem(GPS)enablespreciseandaccuratedeterminationofposi-
tionanywhereontheEarth,aboontothefleldofgeodesy. Althoughgreatadvancesingeodetic
GPSpositioningprecisionandaccuracyhavebeenmadeoverthelastdecade,improvementscan
still be made. This dissertation addresses GPS positioning error from two difierent directions
{ understanding and taking advantage of the repeating nature of some errors, or understand-
ing and taking advantage of the relationship between errors in difierent contemporaneous GPS
observables.
In the area of high-rate GPS positioning, repeating errors have a substantial impact
on the solution. In this dissertation, I study high-rate GPS error reduction using data from
the 2002 Denali Fault earthquake. I apply the techniques of modifled sidereal flltering and
spatial flltering to positions from 25 GPS stations throughout northwestern North America,
and I develop improvements to these methods such as data equalization and careful selection
of sidereal flltering sites. Substantial reduction in noise magnitude is achieved through proper
application of sidereal and spatial fllters, and the resulting ‘GPS seismograms’ show excellent
agreement to records from seismometers.
Multipath, where GPS signals arrive by more than one path and thereby create a range
error,canbeunderstoodthroughtheGPSobservables. MultipathefiectsonGPScarrierphase,
pseudorange,andsignal-to-noiseratio(SNR)measurementsaredifierentbutlinkedbythesame
underlying principles. In this dissertation, I explain multipath efiects on the GPS observables
and deflne multipath in terms of conditions speciflc to geodetic GPS installations and receivers.
I develop two approaches to multipath errors, both using SNR measurements { a graphical
iv
method for multipath assessment, and a computational method for multipath modeling and
carrier phase error reduction. The graphical method shows great promise for understanding
spatial and temporal variability in multipath errors, but provides no avenue for removing these
errors. ThetheorybehindSNRmodelingisrobust,butcomplicatedtoimplementwithgeodetic
GPSmeasurementsofSNR.Idiscussthedi–cultiesinherentinSNRmodelinganddemonstrate
how this technique is of limited utility for geodetic GPS even in the most simple of multipath
environments.
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Acknowledgements
Foremost, I would like to acknowledge the help of my primary advisor, Kristine Larson,
and co-investigator and advisor, Penny Axelrad. Both have been extremely supportive, knowl-
edgeable, inflnitely accessible, and smart beyond my comprehension. Never assuming that I
didn’tknowwhattheyweretalkingabout,KristineandPennypushedmetoexpandmyknowl-
edgeandtothinkcriticallyasonlythebestofadvisorscan. Botharetrulyamazingrolemodels
for an up-and-coming female researcher. In addition, Kristine has always gone to great lengths
to take care of me as her student { encouraging professional development through conference
presentations,makingsureIhadfunding,anddemonstratingunderstandingwhenIneededsome
timeofi. Icannotimaginehavinggonethroughthisexperiencewithouttheirguidanceandhelp.
My fellow students from the last flve years, John Plumb and Kyuhong (Kevin) Choi,
deserve special recognition. We struggled through the GPS learning process together, helped
each other to master GPS analysis strategies, and provided a sounding board for ideas (both
good and bad) while developing our research programs and dissertations. I owe a great debt to
John and Kevin.
I would also like to acknowledge the kind help of many other colleagues over the years;
without their aggregate knowledge and patient explanations, this dissertation would not have
beenpossible. PaulBodin,ChuckMeertens,andJohnWahrforservingonmydefensecommittee
andcontributingtheirconstructivecomments,scientiflccuriousity,andpatience. DuncanAgnew
and Honn Kao, for their patient teaching of seismology and noise analysis principles. Herb
Dragert, Jefi Freymueller, the Geodetic Survey of Natural Resources Canada, and AeroMap
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Surveyingfortheircontributionstothehigh-rateDenaliGPSdatasetIcouldnothaveobtained
otherwise. VladimirKostoglodovandMarcoGuzman,forthetriptoChiapasinwhichIlearned
much about the vagaries of campaign GPS data collection. Sara Ivonne Franco, for her GIPSY
questions which helped me to also gain a better understanding of the software. Joan Gomberg,
Jennifer Hasse, and especially Paul Bodin, for their hard work transforming seismic data into
something easily comparable to GPS positions, something I can understand. Jan Weiss, Steve
Anderson, and Farheen Rizvi, for creating simulation software and simulated multipath data
sets included in my dissertation. Ken Austin, for doing the math for PBO monument heights.
Adrian Borsa, for the kind use of the salar de Uyuni data collected for his own dissertation.
Finally, I would like to thank my very important support network of friends and loved
ones { my family, my spouse Jason Vogel, my good friend Elizabeth Lowham, and all my other
Boulderite buddies. The combined efiorts of all these folks { through friendship, bike rides,
happy hours, and extreme understanding when I ceased to exist as a person for the last 6
months of my graduate career { is beyond appreciated.
MyresearchwasfundedbyaNationalScienceFoundationGraduateResearchFellowship
(2002-2005)andNationalScienceFoundationgrantsformultipath(EAR-0003943)andhigh-rate
GPS(EAR-0337206). GPSdataforthe2002DenaliFaultnetworkassembledforthisdissertation
arearchivedatUNAVCO(http://facility.unavco.org/data/data.html),anddisplacement
results from the high-rate GPS analysis are archived at IRIS (http://www.iris.edu/mda/GD)
as \geodetic displacements".
Contents
Chapter
1 Introduction 1
1.1 Global Positioning System Background . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 GPS Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Position Estimation with GIPSY . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Satellite Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Earth and Observation Models . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.3 Removing Ionospheric Efiects . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.4 Unmodeled Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.5 Position Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Overview of High-Rate Positioning Research 12
2.1 Comparision of GPS and Seismologic Measurements . . . . . . . . . . . . . . . . 12
2.2 Previous Work in GPS Seismology . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Case Study: 2002 November 3 Denali Fault Event . . . . . . . . . . . . . . . . . 15
2.3.1 Denali Fault earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 GPS network and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3 Error-reduction methodology . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 High-rate GPS Techniques 22
3.1 Sidereal Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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3.1.1 Orbital repeat period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Modifled sidereal flltering (MSF) method . . . . . . . . . . . . . . . . . . 24
3.1.3 Variables in sidereal flltering process . . . . . . . . . . . . . . . . . . . . . 26
3.2 Additional Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Ambiguity resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2 Data editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Spatial Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Common-mode errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Spatial flltering method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.3 Spatial flltering sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.4 Role of the reference site and fllter order . . . . . . . . . . . . . . . . . . . 56
4 High-rate GPS Results and Discussion 64
4.1 Surface Waves Recorded by GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Positioning Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.1 Noise (cid:176)oor of GPS receivers . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.2 Generalized noise in GPS positions . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Comparison to Seismic Recordings . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5 Overview of Multipath Research 79
5.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Research Motivation and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Principles of Multipath and SNR 87
6.1 GPS Receiver Signal Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Multipath Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
ix
6.3 Multipath Efiects on GPS Observables . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3.1 Pseudorange multipath . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3.2 Carrier phase multipath . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.3.3 Efiect of multipath on SNR . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.4 Summary of Multipath Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7 Multipath Under Geodetic GPS Conditions 100
7.1 Multipath Geometry for the Geodetic Case . . . . . . . . . . . . . . . . . . . . . 100
7.1.1 Multipath geometry and errors . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1.2 Time-varying behavior of ˆ and SNR . . . . . . . . . . . . . . . . . . . . 105
7.1.3 Multipath geometry and periodicity . . . . . . . . . . . . . . . . . . . . . 106
7.1.4 Resolvable multipath frequencies . . . . . . . . . . . . . . . . . . . . . . . 107
7.1.5 Multipath phasor spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.1.6 Direct and multipath amplitudes . . . . . . . . . . . . . . . . . . . . . . . 114
7.1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.2 Geodetic GPS Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.2.1 Computation and reporting of SNR . . . . . . . . . . . . . . . . . . . . . 122
7.2.2 Characteristics of geodetic GPS SNR. . . . . . . . . . . . . . . . . . . . . 123
7.2.3 Correlation of SNR and pseudorange multipath . . . . . . . . . . . . . . . 134
7.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8 Multipath Assessment for Permanent GPS Stations 145
8.1 SNR Power Spectral Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.1.1 Spectral power estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.1.2 Representation of gridded spectral power . . . . . . . . . . . . . . . . . . 154
8.2 Examples of Power Spectral Maps . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2.1 TASH: tall pillar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2.2 MKEA: re(cid:176)ections from angled surfaces . . . . . . . . . . . . . . . . . . . 156
x
8.2.3 CHUR: variable topography . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.3 Discussion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
9 Estimation of SNR-based Multipath Corrections 168
9.1 Direct Signal Amplitude and SNR Due to Multipath . . . . . . . . . . . . . . . . 169
9.2 Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9.3 Multipath Frequency Estimation Via Sliding-Window Fast Fourier Transform
(SWFFT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
9.4 Amplitude and Multipath Phase Estimation Via Adaptive Least Squares (ALS) . 178
9.5 Construction of SNR and Multipath Corrections . . . . . . . . . . . . . . . . . . 183
9.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10 Phase Multipath Mitigation for GPS Stations 204
10.1 Salar de Uyuni Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
10.1.1 Phase errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
10.1.2 Phase multipath corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 216
10.1.3 Efiect of corrections on residuals and positions . . . . . . . . . . . . . . . 218
10.2 TASH/KIT3 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
10.2.1 SNR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
10.2.2 Phase multipath corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 233
10.2.3 Phase errors and corrections. . . . . . . . . . . . . . . . . . . . . . . . . . 234
10.3 Discussion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
11 Conclusions 246