Data fusion for geoid computation

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Data fusion for geoid computation numerical
tests in Texas area(preliminary results)

• Yan Ming Wang Xiaopeng Li
• National Geodetic Survey, NOAA, USA
• International Symposium on Gravity, Geoid and
  Height Systems October 9-12, 2012Venice, Italy

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Outline

• Objective of study
• Combination methods used
• Preliminary results
• Future work

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Objective of study

• Many types of gravity related data sets
  available today
• - satellite gravity models (long wavelength)
• - Airborne gravity (medium wavelength)
• - Surface gravity (short wavelength)
• - High resolution digital elevation and density
  models (Ultra short wavelength)
• - Geopotential numbers from leveling (short
  wavelength)
• - Deflections of the vertical (short wavelength)
• Goal To combine data in an optimal way (old
  topic, but a new challenge can it reach 1 cm
  geoid accuracy?)

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Few words on the use of geopotential numbers C (1)

• The ellipsoidal height is NOT known at most
  historical leveling benchmarks, so that the
  disturbing potential can not be computed directly
  for all benchmarks
• To use the geopotential number C in determination
  of the gravity field, we compute initial
  disturbing potential as
• T0 W0 C (U0 ?0h0) - C ?0h0
• and h0 H ? H N

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Few words on the use of geopotential numbers C (2)

• Gravity anomaly can be computed from the
  geopotential numbers

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Combination methods(1)

• Over determined boundary values problems
• Least squares collocation
• Observation equation
• l ... observation
• L linear operator
• n observation error
• The least squares solution

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Combination methods(2)

• Use of harmonic (Eigen) functions
• Task using observations l to determine
  coefficients .
• Solution in matrix form

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Airborne and surface gravity Data
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Geopotential numbers

• The gravity anomaly dg can be computed from
  geopotential numbers as
• D(T0 )/Dh g ?0 dg (?0 - ?Q)
• ?Q normal gravity on the telluroid.

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Empirical Covariance functions
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Residual gravity anomaly (LSC)
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Airborne Surface Air
Surface
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Residual disturbing potential
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Conclusions

• Surface data show rich high frequency of gravity
  field, but it shows also systematical difference
  from the airborne data. Airborne data is heavily
  smoother to remove high frequency dynamic errors.
  
• Preliminary results show the combination results
  are promising.

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Future Work

• Using truncated Stokes kernel to let satellite
  model controls the long wavelength
• Refine parameters used in both methods
• Include the geopotential numbers in the
  computations if it helps to improve the
  solution
• Compare the results against independent data
  sets, such GSVS11 GPS/leveling data (1cm relative
  geoid accuracy along 300km line)