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Application of variance components estimation to calibrate geoid error models.

Dong-Mei Guo1, Hou-Ze Xu1

  • 1State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, The Chinese Academy of Science, 340 Xudong Street, Wuhan, China.

Springerplus
|August 26, 2015
PubMed
Summary

This study enhances geoid height accuracy by refining stochastic models in combined adjustments. Variance component estimation calibrates errors in heterogeneous height data for improved geoid modeling.

Keywords:
Errors-invariables modelGeoid refiningVariance component estimationWeighted least-squares adjustment

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Area of Science:

  • Geodesy and Geophysics
  • Earth Sciences
  • Geodetic Surveying

Background:

  • Global Positioning System (GPS)-leveling data is crucial for determining orthometric heights.
  • Traditional weighted least squares methods using errors-in-variables models have limitations in achieving optimal accuracy.
  • Inaccurate stochastic models in adjustments hinder the full potential of geodetic data integration.

Purpose of the Study:

  • To address the accuracy limitations in orthometric height determination using GPS-leveling data.
  • To investigate and improve the stochastic modeling of observables in combined adjustments involving heterogeneous height types.
  • To calibrate errors within diverse height data sources for more precise geoid modeling.

Main Methods:

  • Employed variance component estimation (VCE) to calibrate errors in heterogeneous height data (ellipsoidal, orthometric, gravimetric geoid).
  • Utilized iterative algorithms of minimum norm quadratic unbiased estimation (MIVQUE) for estimating variance components.
  • Presented two statistical models: direct use of errors-in-variables and bias-corrected variance component estimators.

Main Results:

  • Demonstrated the capability of VCE in calibrating errors within heterogeneous height data during combined least squares adjustment.
  • Numerical tests validated the effectiveness of the proposed variance component estimation procedure.
  • The study successfully improved the geoid error model through enhanced stochastic modeling.

Conclusions:

  • The developed variance component estimation procedure is effective for calibrating geoid error models.
  • Accurate stochastic modeling is essential for improving the accuracy of orthometric heights derived from combined geodetic data.
  • This research provides a robust framework for integrating heterogeneous height data for enhanced geoid determination.