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Azimuth-dependent statistics for interpolating geodetic data
Abstract Most authors using statistical interpolation techniques on geodetic data have assumed isotropy for the undulation autocorrelation. Tests of actual data,414 deflections of the vertical, indicate this assumption is not valid. The results of interpolation, however, are not very sensitive to the parameters in the covariance function. A special limiting case for which statistical interpolation degenerates into a completely deterministic process is given in the spherical domain. In this case the covariance function has absolutely no effect on the results, so that the covariance of the output of a prediction need not be that assumed for the interpolation. This provides a self-correcting process whereby the information in the data corrects for a poor choice of covariance function. Estimates of the precision of the interpolation, on the other hand, are very sensitive to the covariance function, particularly to the modeling of azimuth dependence. A simple procedure for generalizing isotropic functions to azimuth dependence is given, which provides sufficiently accurate estimates of precision. The advisability of trend removal is illustrated by some numerical examples.
Azimuth-dependent statistics for interpolating geodetic data
Abstract Most authors using statistical interpolation techniques on geodetic data have assumed isotropy for the undulation autocorrelation. Tests of actual data,414 deflections of the vertical, indicate this assumption is not valid. The results of interpolation, however, are not very sensitive to the parameters in the covariance function. A special limiting case for which statistical interpolation degenerates into a completely deterministic process is given in the spherical domain. In this case the covariance function has absolutely no effect on the results, so that the covariance of the output of a prediction need not be that assumed for the interpolation. This provides a self-correcting process whereby the information in the data corrects for a poor choice of covariance function. Estimates of the precision of the interpolation, on the other hand, are very sensitive to the covariance function, particularly to the modeling of azimuth dependence. A simple procedure for generalizing isotropic functions to azimuth dependence is given, which provides sufficiently accurate estimates of precision. The advisability of trend removal is illustrated by some numerical examples.
Azimuth-dependent statistics for interpolating geodetic data
Morrison, F. (author)
Bulletin géodésique ; 51
1977
Article (Journal)
English
Geodäsie , Geometrie , Geodynamik , Zeitschrift , Mathematik , Mineralogie
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