Improved Covariance Modeling of Gravimetric, GPS, and Leveling Data in High-Resolution Hybrid Geoids

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Improved Covariance Modeling of Gravimetric, GPS,
and Leveling Data in High-Resolution Hybrid Geoids

• Daniel R. Roman, Ph.D.
• Research Geodesist

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Abstract
Hybrid geoids are created from gravimetric geoids
and GPS-derived ellipsoidal heights at
spirit-leveled Bench Marks (GPSBM's). Modeling of
the residuals between the GPSBM's and gravimetric
values was previously accomplished nationally
using single values for correlation length and
signal amplitude in Least Squares Collocation
(LSC). The most recent high resolution hybrid
geoid (GEOID99) converts heights between the NAD
83 and NAVD 88 datums at about 2.5 cm RMS
accuracy, which represents the remaining
correlated signal in the residuals. While this
signal is lower in power compared to the initial
residuals (21 cm RMS) and the features implied by
it are generally narrow, these features can have
great lateral extent (100's to 1000's of km).
Hence it is desirable to further reduce this
correlated signal, and more elaborate LSC
modeling techniques were explored to do this. The
two most promising are the of progressively
reduced correlation lengths signal amplitudes
and also combination of multiple covariance
matrices in a single pass. The results of these
tests demonstrate that the correlated signal of
the residuals can be reduced to 1.5 - 2.0 cm RMS.
These results are discussed in relation to error
sources deriving from the observed heights above
the NAVD 88 and NAD 83 datums (the GPSBM's) as
well as those from the gravimetric geoid model.
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Outline

• Introduction
• Unresolved issues after GEOID99
• Alternative LSC modeling
• Separation of error sources
• Conclusions

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Empirical () versus Gaussian Function (line) for
GPSBM-G99SSS
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Empirical () versus Gaussian Function (line) for
GPSBM-GEOID99
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Empirical Error Statistics for GEOID96 (100 km
range)
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Empirical Error Statistics for GEOID96 (1000 km
range)
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First empirical covariance function for
iterative-LSC
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Second empirical covariance function for
iterative-LSC
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Empirical covariance function for MM-LSC
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Empirical covariance function for
Gaussian-Sinusoidal combination function
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Error Sources

• GPS Obs.
• Short/Int. ?
• Statewide adjustments (HARNs)
• CORS
• National adjustment

• Gravimetric Geoid
• Faye anomalies
• DEM resolution and accuracy
• Remove-and- Restore (EGM96)
• 1D FFT solution
• New DEM/gravity
• Combined data Fourier solution

• Leveling (BM)
• Long/Int. ?
• Quality of initial gravity
• The effect is greatest in the mountains
• Propagation
• GPS/Leveling

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Summary Outlook

• More complex models of the Gaussian function
  better emulate GPSBM residuals
• Further near term improvements will derive from
  readjusting and improving input data
• Long term improvements require revising the
  entire approach taken to generate the underlying
  gravimetric geoid