Welcome to GFEAT’s documentation!

Contents:

GFEAT

PyPI version License: GPL v3 Documentation

Gravity Field Error Analysis Tool (GFEAT) is a C++ library that employs an analytical method to estimate gravity field error from different orbital configurations and observations.

Features

  • Estimation of gravity field error.

    • Error propagation from observations PSD to the Stokes’ coefficients.

    • Several observation types supported: gravity potential, radial, along-track and cross-track displacements, inter-satellite range…

    • Combination of multiple observation types: 3D GPS position and multi-pair constellations.

  • Processing of gravity field data.

    • Gravity field I/O handling.

    • Error covariance handling from normal equations.

    • Synthesis with different functionals: EWH, gravity anomalies, geoid heights.

    • Covariance synthesis also supported.

    • FFT employed for efficient computation.

Installation

The library is available in the Python Package Index.

pip install gfeatpy

Future Improvements

  • Add and improve unit tests for all components.

  • Extend Constellation class to any observation.

  • Include optimization examples with PyGMO.

  • Extend to eccentric orbits.

C++ development

To use the library natively in C++ is currently not recommended given the limitations for output data as well as the easier to use plotting tools available in Python. However, a good starting point are the C++ unit tests, under the test folder.

Some very descriptive examples can be found in TestConstellation.cpp and TestCollinear.cpp. You can build and run all the tests like this.

mkdir build
cd build
cmake ..
make
ctest

References

Balmino, G., E. Schrama, and N. Sneeuw. 1996. “Compatibility of first-order circular orbit perturbations theories; consequences for cross-track inclination functions.” Journal of Geodesy 70 (9): 554–61. https://doi.org/10.1007/bf00867863.

Jekeli, Christopher. 1981. “Alternative Methods to Smooth the Earth’s Gravity Field.” Report 327. Columbus, Ohio: Department of Geodetic Science; Surveying, The Ohio State University.

Kaula, William M. 1966. Theory of Satellite Geodesy: Applications of Satellites to Geodesy. Blaisdell Publishing Company.

Schrama, E. J. O. 1990. “Gravity field error analysis: Applications of GPS receivers and gradiometers on low orbiting platforms.” NASA.

———. 1991a. “Error Propagation and Correlation Analysis of Covariance Matrices.” Goddard Space Flight Center; Personal communication.

———. 1991b. “Gravity field error analysis: Applications of global positioning system receivers and gradiometers on low orbiting platforms.” Journal of Geophysical Research: Solid Earth 96 (B12): 20041–51. https://doi.org/10.1029/91jb01972.

Sneeuw, Nico. 1994. “Global spherical harmonic analysis by least-squares and numerical quadrature methods in historical perspective.” Geophysical Journal International 118 (3): 707–16. https://doi.org/10.1111/j.1365-246x.1994.tb03995.x.

Sneeuw, Nicolaas. 2000. “A Semi-Analytical Approach to Gravity Field Analysis from Satellite Observations.” PhD thesis, Institut für Astronomische und Physikalische Geodäsie, TU München.

Visser, P. N. A. M., E. J. O. Schrama, N. Sneeuw, and M. Weigelt. 2012. “Dependency of Resolvable Gravitational Spatial Resolution on Space-Borne Observation Techniques.” In Geodesy for Planet Earth, edited by Steve Kenyon, Maria Christina Pacino, and Urs Marti, 373–79. Berlin, Heidelberg: Springer Berlin Heidelberg.

Wahr, John, Mery Molenaar, and Frank Bryan. 1998. “Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE.” Journal of Geophysical Research: Solid Earth 103 (B12): 30205–29. https://doi.org/10.1029/98jb02844.