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Improving the Precision and Accuracy of Geodetic GPS:

Improving the Precision and Accuracy of Geodetic GPS:. Applications to Multipath and Seismology. Andria Bilich Ph.D. Defense August 24, 2006. Main Topics. Global Positioning System (GPS) principles High-rate GPS positioning for seismology

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Improving the Precision and Accuracy of Geodetic GPS:

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  1. Improving the Precision and Accuracy ofGeodetic GPS: Applications to Multipath and Seismology Andria Bilich Ph.D. Defense August 24, 2006

  2. Main Topics • Global Positioning System (GPS) principles • High-rate GPS positioning for seismology • Carrier phase multipath identification and correction using signal-to-noise ratio (SNR)

  3. Global Positioning System Principles • Satellite navigation system • Determine range from 4 satellites = position of GPS receiver • Important for high precision/accuracy: • Dual-frequency • Carrier and code • Satellite orbits Department of Defense

  4. Estimated parameters Receiver position Clocks Carrier phase biases Troposphere GIPSY from JPL Least squares Best fit of model to data Models: Earth, observation, and GPS equipment Data: range to satellite (code and carrier) Residuals: unmodeled and mismodeled factors Estimating Position with GPS

  5. High-rate GPS Positioning Determining displacement history from the Denali Fault earthquake

  6. Outline: High-rate GPS Positioning • Introduction to high-rate GPS • Noise/error reduction methodology = repeating errors • Modified sidereal filtering (MSF) • Data equalization • Spatial filtering • Denali Fault event • GPS network • GPS seismograms • Noise and signal: GPS vs. seismometers

  7. GPS Data Rates and Analysis Strategies

  8. Repeating Errors • Multipath, residual PCV, and satellite distribution repeat with satellite-receiver geometry • Satellite-receiver geometry repeat • Sidereal day (~23hr 56min) • Orbital repeat period of individual GPS satellites

  9. Orbital Periods of GPS Satellites • Orbital period: • Approximately sidereal (86400-236s) • DoD constraint for GPS orbits 246s • Varies in practice • Repeat period of errors: • Determined by dominant satellite • Slowly-varying errors, similar satellites = use mean value

  10. Modified Sidereal Filtering (MSF) • Errors at a station: • Repeat each day • Repeat period depends on satellites in solution • Use error profile on other days to correct day of interest

  11. Data Equalization • For MSF to work, errors must repeat between days • Function of satellites in solution • Constellation must repeat • Edit data on sidereal filter days for consistency

  12. Spatial Filtering • Systematic errors remain after MSF • Common to all stations in network • Distributed reference station errors • Spatial filter • Common-mode error profile using distant stations • Subtract profile from stations of interest

  13. Denali Fault Earthquake • 3 November 2002 • Magnitude 7.9, shallow strike-slip with long rupture • SE directivity • Large Love waves Source: USGS Photo: USGS Photo: Patty Craw, DGGS

  14. Denali GPS Network & Research Goals • 25 GPS stations • 1 sample/second • Different azimuths and distances • Goals: • Minimize noise • Understand noise • Develop seismograms

  15. Denali Seismograms

  16. Disadvantages GPS noise sets lower magnitude limit of observability Estimate of displacement Requires filtering to reduce noise Advantages: No upper limit to observable displacement Displacements (not acceleration) GPS Seismograms

  17. Noise Floor:GPS vs. Seismometer

  18. Research Contributions • Seismograms for Denali event • High-rate GPS filtering • Refinements to sidereal and spatial filtering • Importance of data equalization to MSF • Unimportance of bias fixing • Long-period trend • Largely addressed by filtering steps

  19. Carrier Phase Multipath Identification and Correction Using the Signal-to-Noise Ratio (SNR)

  20. Outline: Multipath Research • Multipath principles • Signal-to-noise ratio (SNR) • When is it useful? • What does it tell us? • Understanding multipath errors through mapping of SNR • Correcting for multipath error by modeling SNR

  21. Multipath Principles • Multipath introduces range error • Why is multipath such an issue? • Difficult to model • Systematic error • Potentially large-magnitude error • How can we understand or remove multipath? SNR!

  22. SNR – Phasor Diagram • Recorded SNR = direct + multipathed signal • Phase error: relate SNR measurements to phase errors

  23. Time-evolving Multipath • Carrier-phase multipath • Linked to SNR • Changes with time • Different for every satellite, day, time, etc. • Use SNR to • Understand multipath environment • Correct for multipath errors

  24. SNR: Theory vs. Reality • Theory: oscillations in SNR tell you about phase errors • Practice: quality of SNR data impacts what is possible

  25. Database of 525 geodetic GPS stations: August 16, 2005 5 manufacturers 11 receiver models Different antennas Characteristics of SNR Lacking precision Dropouts Same on both frequencies Relation of SNR to pseudorange multipath Should be in-phase and well-correlated Establishes link to phase multipath When are SNR measurements useful?

  26. GPS Receivers & SNR

  27. Multipath Assessment:Power Spectral Maps • Idea: frequency and power content of SNR  multipath environment • Method: • Power spectra of small data sections • Assign to satellite azimuth/elevation • Plot all points on a grid

  28. Mauna Kea (MKEA)

  29. MKEA Power Maps 22-28s 15-17s 52-77s • Frequency (distance to reflector) changes with satellite position • High power returns from cinder cones

  30. Sliding-window FFT (SWFFT) Estimate frequency w for short sections of SNR data Size of data section varies w used to estimate multipath phase (y) Adaptive least squares (ALS) Filter SNR data with w as input Estimate amplitudes and y Estimation of Phase Multipath Errors

  31. Salar de Uyuni, Boliva • Large salt flat • Sub-decimeter topography • Experimental setup: • 3 Ashtech Z-12 receivers • 2 flush with ground • 1 tripod (~1.4m height) • 12-18m baselines • 10s sampling • 10 hour occupation

  32. Multipath Errors • Residuals • No errors for ground • Big, systematic errors for tripod • SNR • Same frequency content as L1 residual • Data problematic >30

  33. Multipath Corrections • SNR • Modeled data 30 • Reasonable fit between original and reconstructed SNR • Phase errors and corrections • Reasonable correspondence to residual error • Applying corrections to phase data • Whitens residuals • Benefits high-rate positions

  34. Multipath: Research Contributions • Better understanding of SNR data • Graphical method for multipath identification • Requires no knowledge of environment • Spatially and temporally dynamic • Numerical method for multipath correction • Great potential for carrier phase error mitigation • Many difficulties to modeling process must be addressed; currently requires user intervention

  35. Acknowledgements • Fabulous colleagues: Kristine Larson, Penny Axelrad, Kevin Choi, Herb Dragert, Paul Bodin, Jim Davis, Pedro Elosegui, Duncan Agnew, Honn Kao, and many many others. • IGS, JPL, UNAVCO, NGS, CORS, SOPAC, CDDIS • Geodetic Survey, Natural Resources Canada; Base Mapping & Geomatics Services, B.C.; AeroMap Surveying • Funding from NSF Graduate Research Fellowship and NSF geophysics program

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