On optimal estimation of gravity from gravity gradients at aircraft altitude

Details On optimal estimation of gravity from gravity gradients at aircraft altitude On optimal estimation of gravity from gravity gradients at aircraft altitude

Aug 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985rvgeo..23..301j&link_type=abstract

Reviews of Geophysics (ISSN 8755-1209), vol. 23, Aug. 1985, p. 301-311.

Physics

Geophysics

4

Earth Gravitation, Geodesy, Gravity Gradiometers, Collocation, Conjugate Gradient Method, Least Squares Method, Root-Mean-Square Errors

Scientific paper

Some possible techniques to estimate the gravity disturbance vector on the earth's surface on the basis of airborne gradiometry data are analyzed. The least squares collocation method is found to be the best method for estimation, but requires excessive amounts of computations in the more general case. Other methods such as integral formulas may turn out to be adequate in some applications, but probably not for estimations with accuracies near 1 mGal since it would require more gravity information than can be provided by a single-gradient observation in a limited area. The conjugate gradient technique for inverting the covariance matrix of the least squares collocation solution promises considerable reductions in computational time since each iteration involves O(n squared) operations (n is the matrix size) and the number of iterations requires for virtually optimal results seems to be much less than n. An example of a least squares collocation solution for the root mean square error (in milligals) of the residual gravity difference at ground level is presented.

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